
>> # evaluating formula 1 with 3 points
# r2_3_2g.txt:6 formula 1   : problem  G, 2_3_2  (d=2 n= 3 o=2 plus 0/4 of order 3) quality E
# evaluating formula 2 with 3 points
# r2_3_2g.txt:15 formula 2   : problem E2, 2_3_2  (d=2 n= 3 o=2 plus 0/4 of order 3) quality E
# evaluating formula 3 with 3 points
# r2_3_2g.txt:24 formula 3   : problem E1, 2_3_2  (d=2 n= 3 o=2 plus 0/4 of order 3) quality E
# evaluating formula 4 with 3 points
# r2_3_2g.txt:31 formula 4   : problem  S, 2_3_2  (d=2 n= 3 o=2 plus 0/4 of order 3) quality EI
# G 2 dimensions, degree 2, asymmetric 3 point rule with points at 1 distinct radius: 3=3
# Stroud, A.H. and Don Secrest, "Approximate Integration Formulas for
# Certain Spherically Symmetric Regions", Math. Comp., vol 17, pp
# 105-135, 1963.
#                x1                 x2             Weight     Radius
  1.000000000000000  1.000000000000000  0.333333333333333    1.41421
 -1.366025403784439  0.366025403784439  0.333333333333333    1.41421
  0.366025403784439 -1.366025403784439  0.333333333333333    1.41421

# E_n^{r^2} 2 dimensions, degree 2, asymmetric 3 point rule with points at 1 distinct radius: 3=3
# Stroud, A.H. and Don Secrest, "Approximate Integration Formulas for
# Certain Spherically Symmetric Regions", Math. Comp., vol 17, pp
# 105-135, 1963.
#                x1                 x2             Weight     Radius
  0.707106781186547  0.707106781186547  1.047197551196598    1.00000
 -0.965925826289068  0.258819045102521  1.047197551196598    1.00000
  0.258819045102521 -0.965925826289068  1.047197551196598    1.00000

# E_n^r 2 dimensions, degree 2, asymmetric 3 point rule with points at 1 distinct radius: 3=3
# Stroud, A.H. and Don Secrest, "Approximate Integration Formulas for
# Certain Spherically Symmetric Regions", Math. Comp., vol 17, pp
# 105-135, 1963.
#                x1                 x2             Weight     Radius
  1.732050807568877  1.732050807568878  2.094395102393197    2.44949
 -2.366025403784441  0.633974596215561  2.094395102393195    2.44949
  0.633974596215562 -2.366025403784440  2.094395102393195    2.44949

S_n 2 dimensions, degree 2, asymmetric 3 point rule with points at 1 distinct radius: 3=3
# "S_n: 2-1", A.H. Stroud. Approximate Calculation of Multiple Integrals. Prentice Hall, Englewood Cliffs, NH, 1971.
#                x1                 x2             Weight     Radius
  0.500000000000000  0.500000000000000  1.047197551196598    0.70711
 -0.683012701892219  0.183012701892219  1.047197551196598    0.70711
  0.183012701892219 -0.683012701892219  1.047197551196598    0.70711

>> # evaluating formula 1 with 4 points
# r2_4_3g.txt:6 formula 1   : problem  G, 2_4_3  (d=2 n= 4 o=3 plus 2/5 of order 4) quality E
# evaluating formula 2 with 4 points
# r2_4_3g.txt:14 formula 2   : problem E2, 2_4_3  (d=2 n= 4 o=3 plus 2/5 of order 4) quality E
# evaluating formula 3 with 4 points
# r2_4_3g.txt:22 formula 3   : problem E1, 2_4_3  (d=2 n= 4 o=3 plus 2/5 of order 4) quality E
# evaluating formula 4 with 4 points
# r2_4_3g.txt:30 formula 4   : problem  S, 2_4_3  (d=2 n= 4 o=3 plus 4/5 of order 4) quality EI
# In these formulas, the points form a square.
# G 2 dimensions, degree 3, symmetric 4 point rule with points at 1 distinct radii: 4=4
# equivalent to:
# "E_n^{r^2}: 3-1", A.H. Stroud. Approximate Calculation of Multiple Integrals. Prentice Hall, Englewood Cliffs, NH, 1971.
#                x1                 x2             Weight     Radius     cos1
  1.414213562373095 -0.000000000000000  0.250000000000000    1.41421  1.00000
 -1.414213562373095 -0.000000000000000  0.250000000000000    1.41421 -1.00000
 -0.000000000000000  1.414213562373095  0.250000000000000    1.41421  0.00000
 -0.000000000000000 -1.414213562373095  0.250000000000000    1.41421  0.00000

# E_n^{r^2} 2 dimensions, degree 3, symmetric 4 point rule with points at 1 distinct radii: 4=4
# "E_n^{r^2}: 3-1", A.H. Stroud. Approximate Calculation of Multiple Integrals. Prentice Hall, Englewood Cliffs, NH, 1971.
#                x1                 x2             Weight     Radius     cos1
  1.000000000000000 -0.000000000000000  0.785398163397448    1.00000  1.00000
 -1.000000000000000 -0.000000000000000  0.785398163397448    1.00000 -1.00000
 -0.000000000000000  1.000000000000000  0.785398163397448    1.00000  0.00000
 -0.000000000000000 -1.000000000000000  0.785398163397448    1.00000  0.00000

# E_n^r 2 dimensions, degree 3, symmetric 4 point rule with points at 1 distinct radii: 4=4
# "E_n^r: 3-1", A.H. Stroud. Approximate Calculation of Multiple Integrals. Prentice Hall, Englewood Cliffs, NH, 1971.
#                x1                 x2             Weight     Radius     cos1
  2.449489742783179 -0.000000000000000  1.570796326794897    2.44949  1.00000
 -2.449489742783179 -0.000000000000000  1.570796326794897    2.44949 -1.00000
 -0.000000000000000  2.449489742783179  1.570796326794897    2.44949  0.00000
 -0.000000000000000 -2.449489742783179  1.570796326794897    2.44949  0.00000

# S_n 2 dimensions, degree 3, symmetric 4 point rule with points at 1 distinct radii: 4=4
# "S_n: 3-1",  A.H. Stroud. Approximate Calculation of Multiple Integrals. Prentice Hall, Englewood Cliffs, NH, 1971.
#                x1                 x2             Weight     Radius     cos1
  0.707106781186547 -0.000000000000000  0.785398163397448    0.70711  1.00000
 -0.707106781186547 -0.000000000000000  0.785398163397448    0.70711 -1.00000
 -0.000000000000000  0.707106781186547  0.785398163397448    0.70711  0.00000
 -0.000000000000000 -0.707106781186547  0.785398163397448    0.70711  0.00000

>> # evaluating formula 1 with 6 points
# r2_6_4g.txt:8 formula 1   : problem  G, 2_6_4  (d=2 n= 6 o=4 plus 3/6 of order 5) quality P
# evaluating formula 2 with 6 points
# r2_6_4g.txt:18 formula 2   : problem E2, 2_6_4  (d=2 n= 6 o=4 plus 3/6 of order 5) quality P
# evaluating formula 3 with 6 points
# r2_6_4g.txt:28 formula 3   : problem E1, 2_6_4  (d=2 n= 6 o=4 plus 3/6 of order 5) quality P
# evaluating formula 4 with 6 points
# r2_6_4g.txt:38 formula 4   : problem  S, 2_6_4  (d=2 n= 6 o=4 plus 3/6 of order 5) quality PI
# These rules have a central point plus five points that are the
# vertices of a regular pentagon.

# G 2 dimensions, degree 4, asymmetric 6 point rule with points at 2 distinct radii: 1+5=6
# scaled version of:
# "E_2^{r^2}: 4-1",  A.H. Stroud. Approximate Calculation of Multiple Integrals. Prentice Hall, Englewood Cliffs, NH, 1971.
#                x1                 x2             Weight     Radius     cos1
 -0.000000000000000 -0.000000000000000  0.500000000000000    0.00000  0.00000
 -2.000000000000000 -0.000000000000000  0.100000000000000    2.00000  1.00000
 -0.618033988749895 -1.902113032590307  0.100000000000000    2.00000  0.30902
 -0.618033988749895  1.902113032590307  0.100000000000000    2.00000  0.30902
  1.618033988749895  1.175570504584946  0.100000000000000    2.00000 -0.80902
  1.618033988749895 -1.175570504584946  0.100000000000000    2.00000 -0.80902

# E_n^{r^2} 2 dimensions, degree 4, asymmetric 6 point rule with points at 2 distinct radii: 1+5=6
# "E_2^{r^2}: 4-1",  A.H. Stroud. Approximate Calculation of Multiple Integrals. Prentice Hall, Englewood Cliffs, NH, 1971.
#                x1                 x2             Weight     Radius     cos1
 -0.000000000000000 -0.000000000000000  1.570796326794897    0.00000  0.00000
 -1.414213562373095 -0.000000000000000  0.314159265358979    1.41421  1.00000
 -0.437016024448821 -1.344997023927915  0.314159265358979    1.41421  0.30902
 -0.437016024448821  1.344997023927915  0.314159265358979    1.41421  0.30902
  1.144122805635369  0.831253875554907  0.314159265358979    1.41421 -0.80902
  1.144122805635369 -0.831253875554907  0.314159265358979    1.41421 -0.80902

# E_n^r 2 dimensions, degree 4, asymmetric 6 point rule with points at 2 distinct radii: 1+5=6
# "E_2^r: 4-1" ,  A.H. Stroud. Approximate Calculation of Multiple Integrals. Prentice Hall, Englewood Cliffs, NH, 1971.
#                x1                 x2             Weight     Radius     cos1
 -0.000000000000000 -0.000000000000000  4.398229715025709    0.00000  0.00000
 -4.472135954999579 -0.000000000000000  0.376991118430775    4.47214  1.00000
 -1.381966011250105 -4.253254041760200  0.376991118430775    4.47214  0.30902
 -1.381966011250105  4.253254041760200  0.376991118430775    4.47214  0.30902
  3.618033988749894  2.628655560595668  0.376991118430775    4.47214 -0.80902
  3.618033988749894 -2.628655560595668  0.376991118430775    4.47214 -0.80902

# S_n 2 dimensions, degree 4, asymmetric 6 point rule with points at 2 distinct radii: 1+5=6
# "S_2: 4-1",  A.H. Stroud. Approximate Calculation of Multiple Integrals. Prentice Hall, Englewood Cliffs, NH, 1971.
#                x1                 x2             Weight     Radius     cos1
 -0.000000000000000 -0.000000000000000  0.785398163397448    0.00000  0.00000
 -0.816496580927726 -0.000000000000000  0.471238898038469    0.81650  1.00000
 -0.252311319355707 -0.776534393824027  0.471238898038469    0.81650  0.30902
 -0.252311319355707  0.776534393824027  0.471238898038469    0.81650  0.30902
  0.660559609819570  0.479924648816545  0.471238898038469    0.81650 -0.80902
  0.660559609819570 -0.479924648816545  0.471238898038469    0.81650 -0.80902

>> # evaluating formula 1 with 7 points
# r2_7_5g.txt:6 formula 1   : problem  G, 2_7_5  (d=2 n= 7 o=5 plus 4/7 of order 6) quality P
# evaluating formula 2 with 7 points
# r2_7_5g.txt:18 formula 2   : problem E2, 2_7_5  (d=2 n= 7 o=5 plus 4/7 of order 6) quality P
# evaluating formula 3 with 7 points
# r2_7_5g.txt:30 formula 3   : problem  S, 2_7_5  (d=2 n= 7 o=5 plus 3/7 of order 6) quality PI

# G 2 dimensions, degree 5, symmetric 7 point rule with points at 2 distinct radii: 1+6=7
# "E_2^{r^2}: 5-1", A.H. Stroud. Approximate Calculation of Multiple Integrals. Prentice Hall, Englewood Cliffs, NH, 1971.

#                x1                 x2             Weight     Radius     cos1
 -0.000000000000000 -0.000000000000000  0.500000000000000    0.00000  0.00000
 -1.732050807568877  1.000000000000000  0.083333333333333    2.00000  1.00000
 -0.000000000000000 -2.000000000000000  0.083333333333333    2.00000 -0.50000
 -0.000000000000000  2.000000000000000  0.083333333333333    2.00000  0.50000
  1.732050807568877 -1.000000000000000  0.083333333333333    2.00000 -1.00000
  1.732050807568877  1.000000000000000  0.083333333333333    2.00000 -0.50000
 -1.732050807568877 -1.000000000000000  0.083333333333333    2.00000  0.50000

# E_n^{r^2} 2 dimensions, degree 5, symmetric 7 point rule with points at 2 distinct radii: 1+6=7
# "E_2^{r^2}: 5-1", A.H. Stroud. Approximate Calculation of Multiple Integrals. Prentice Hall, Englewood Cliffs, NH, 1971.

#                x1                 x2             Weight     Radius     cos1
  0.000000000000000  0.000000000000000  1.570796326794897    0.00000  0.00000
 -1.224744871391589  0.707106781186547  0.261799387799148    1.41421  1.00000
  0.000000000000000 -1.414213562373095  0.261799387799148    1.41421 -0.50000
  0.000000000000000  1.414213562373095  0.261799387799148    1.41421  0.50000
  1.224744871391589 -0.707106781186547  0.261799387799148    1.41421 -1.00000
  1.224744871391589  0.707106781186547  0.261799387799148    1.41421 -0.50000
 -1.224744871391589 -0.707106781186547  0.261799387799148    1.41421  0.50000

# S_n 2 dimensions, degree 5, symmetric 7 point rule with points at 2 distinct radii: 1+6=7

# "S_2: 5-1", A.H. Stroud. Approximate Calculation of Multiple Integrals. Prentice Hall, Englewood Cliffs, NH, 1971.
#                x1                 x2             Weight     Radius     cos1
  0.000000000000000  0.000000000000000  0.785398163397448    0.00000  0.00000
 -0.707106781186548  0.408248290463863  0.392699081698724    0.81650  1.00000
  0.000000000000000 -0.816496580927726  0.392699081698724    0.81650 -0.50000
  0.000000000000000  0.816496580927726  0.392699081698724    0.81650  0.50000
  0.707106781186548 -0.408248290463863  0.392699081698724    0.81650 -1.00000
  0.707106781186548  0.408248290463863  0.392699081698724    0.81650 -0.50000
 -0.707106781186548 -0.408248290463863  0.392699081698724    0.81650  0.50000

>> # evaluating formula 1 with 10 points
# r2_10_6bg.txt:4 formula 1   : problem  G, 2_10_6  (d=2 n=10 o=6 plus 4/8 of order 7) quality P
# evaluating formula 2 with 10 points
# r2_10_6bg.txt:17 formula 2   : problem E2, 2_10_6  (d=2 n=10 o=6 plus 4/8 of order 7) quality P
# evaluating formula 3 with 10 points
# r2_10_6bg.txt:33 formula 3   : problem  S, 2_10_6  (d=2 n=10 o=6 plus 4/8 of order 7) quality PO
# In these formulas, the points have bilateral symmetry
# G 2 dimensions, degree 6, asymmetric 10 point rule with points at 6 distinct radii: 1+2+2+2+1+2=10
#                x1                 x2             Weight     Radius
  4.686722930843326  2.848468363227852  0.000241226029733    5.48445
  1.996403631630725 -0.343045648164391  0.075172676336501    2.02566
  1.008381975331479 -2.025705761173867  0.046499521029835    2.26281
  0.978082566181896  1.241246099452505  0.154507383214213    1.58030
  0.000000000000000 -0.369629844190682  0.441628982762271    0.36963
  0.000000000000000  3.303365668574008  0.005529404017163    3.30337
 -0.978082566181896  1.241246099452505  0.154507383214213    1.58030
 -1.008381975331479 -2.025705761173867  0.046499521029835    2.26281
 -1.996403631630725 -0.343045648164391  0.075172676336501    2.02566
 -4.686722930843326  2.848468363227852  0.000241226029733    5.48445

# E_n^{r^2} 2 dimensions, degree 6, asymmetric 10 point rule with points at 6 distinct radii: 1+2+2+2+1+2=10
#                x1                 x2             Weight     Radius
  3.314013565941806  2.014171295633760  0.000757833922865    3.87809
  1.411670545911536 -0.242569904073576  0.236161927729435    1.43236
  0.713033732783175 -1.432390280414699  0.146082553662775    1.60005
  0.691608815107559  0.877693534044218  0.485399260031153    1.11744
  0.000000000000000 -0.261367769356158  1.387418367858287    0.26137
  0.000000000000000  2.335832264987514  0.017371135039050    2.33583
 -0.691608815107559  0.877693534044218  0.485399260031153    1.11744
 -0.713033732783175 -1.432390280414699  0.146082553662775    1.60005
 -1.411670545911536 -0.242569904073576  0.236161927729435    1.43236
 -3.314013565941806  2.014171295633760  0.000757833922865    3.87809

# S_n 2 dimensions, degree 6, asymmetric 10 point rule with points at 6 distinct radii: 1+2+2+2+1+2=10
# Johannes W. Wissmann and Thomas Becker. Partially symmetric cubature
# formulas for even degrees of exactness. SIAM J. Numer. Anal., 23(3):676-
# 685, June 1986.
#                x1                 x2             Weight     Radius
  0.978839047064284  0.662952453661044  0.030327815305342    1.18221
  0.802017004072344 -0.174207378839556  0.340540094500688    0.82072
  0.373683864304499 -0.770749853148807  0.280075256745352    0.85656
  0.458236515708685  0.464889889783278  0.502358408812314    0.65277
  0.000000000000000 -0.206355543412215  0.642883172453234    0.20636
  0.000000000000000  0.914874261544931  0.192106330409168    0.91487
 -0.458236515708685  0.464889889783278  0.502358408812314    0.65277
 -0.373683864304499 -0.770749853148807  0.280075256745352    0.85656
 -0.802017004072344 -0.174207378839556  0.340540094500688    0.82072
 -0.978839047064284  0.662952453661044  0.030327815305342    1.18221

>> # evaluating formula 1 with 11 points
# r2_11_6E1s.txt:4 formula 1   : problem E1, 2_11_6  (d=2 n=11 o=6 plus 4/8 of order 7) quality P
E1 2 dimensions, degree 6, bilaterally symmetric (axis 2) 11 point rule with points at 7 distinct radii: 1+1+2+2+1+2+2=11

#                 x1                  x2              Weight     Radius
   0.000000000000000   0.000000000000000   3.927702275194840    0.00000
  -3.895765525253948   0.000000000000000   0.474246212300936    3.89577
   3.141828043257887   2.312667676618243   0.472797630406369    3.90122
   3.141828043257888  -2.312667676618244   0.472797630406369    3.90122
  -1.228482827331175  -3.752487980256190   0.460111970539923    3.94846
  -1.228482827331175   3.752487980256190   0.460111970539923    3.94846
  10.299713185154499   0.000000000000000   0.003846684331349   10.29971
  -8.794364006109971  -6.251012172182810   0.002944454683352   10.78962
  -8.794364006109971   6.251012172182811   0.002944454683352   10.78962
   3.397224688449697  10.311630315898372   0.002841012046587   10.85683
   3.397224688449696 -10.311630315898379   0.002841012046587   10.85683

>> # evaluating formula 1 with 12 points
# r2_12_7g.txt:4 formula 1   : problem  G, 2_12_7  (d=2 n=12 o=7 plus 4/9 of order 8) quality P
# evaluating formula 2 with 12 points
# r2_12_7g.txt:21 formula 2   : problem E2, 2_12_7  (d=2 n=12 o=7 plus 4/9 of order 8) quality P
# evaluating formula 3 with 12 points
# r2_12_7g.txt:37 formula 3   : problem  S, 2_12_7  (d=2 n=12 o=7 plus 4/9 of order 8) quality PI
G 2 dimensions, degree 7, symmetric 12 point rule with points at 3 distinct radii: 4+4+4=12
# "E_2^{r^2}: 7-1", A.H. Stroud. Approximate Calculation of Multiple Integrals. Prentice Hall, Englewood Cliffs, NH, 1971.
#                x1                 x2             Weight     Radius     cos1     cos2     cos3
  2.449489742783178 -0.000000000000000  0.027777777777778    2.44949  1.00000  0.70711  0.70711
 -2.449489742783178 -0.000000000000000  0.027777777777778    2.44949 -1.00000 -0.70711 -0.70711
 -0.000000000000000  2.449489742783178  0.027777777777778    2.44949  0.00000  0.70711  0.70711
 -0.000000000000000 -2.449489742783178  0.027777777777778    2.44949  0.00000 -0.70711 -0.70711
  0.756933958067121  0.756933958067121  0.210491910111102    1.07047  0.70711  1.00000  1.00000
 -0.756933958067121  0.756933958067121  0.210491910111102    1.07047 -0.70711  0.00000  0.00000
  0.756933958067121 -0.756933958067121  0.210491910111102    1.07047  0.70711  0.00000  0.00000
 -0.756933958067121 -0.756933958067121  0.210491910111102    1.07047 -0.70711 -1.00000 -1.00000
  1.981678829458710  1.981678829458710  0.011730312111120    2.80252  0.70711  1.00000  1.00000
 -1.981678829458710  1.981678829458710  0.011730312111120    2.80252 -0.70711  0.00000  0.00000
  1.981678829458710 -1.981678829458710  0.011730312111120    2.80252  0.70711  0.00000  0.00000
 -1.981678829458710 -1.981678829458710  0.011730312111120    2.80252 -0.70711 -1.00000 -1.00000

# E_n^r 2 dimensions, degree 7, symmetric 12 point rule with points at 3 distinct radii: 4+4+4=12

# "E_2^r: 7-1", A.H. Stroud. Approximate Calculation of Multiple Integrals. Prentice Hall, Englewood Cliffs, NH, 1971.
#                x1                 x2             Weight     Radius     cos1     cos2     cos3
  1.732050807568877  0.000000000000000  0.087266462599716    1.73205  1.00000  0.70711  0.70711
 -1.732050807568877  0.000000000000000  0.087266462599716    1.73205 -1.00000 -0.70711 -0.70711
  0.000000000000000  1.732050807568877  0.087266462599716    1.73205  0.00000  0.70711  0.70711
  0.000000000000000 -1.732050807568877  0.087266462599716    1.73205  0.00000 -0.70711 -0.70711
  0.535233134659635  0.535233134659635  0.661279838445120    0.75693  0.70711  1.00000  1.00000
 -0.535233134659635  0.535233134659635  0.661279838445120    0.75693 -0.70711  0.00000  0.00000
  0.535233134659635 -0.535233134659635  0.661279838445120    0.75693  0.70711  0.00000  0.00000
 -0.535233134659635 -0.535233134659635  0.661279838445120    0.75693 -0.70711 -1.00000 -1.00000
  1.401258538444074  1.401258538444074  0.036851862352611    1.98168  0.70711  1.00000  1.00000
 -1.401258538444074  1.401258538444074  0.036851862352611    1.98168 -0.70711  0.00000  0.00000
  1.401258538444074 -1.401258538444074  0.036851862352611    1.98168  0.70711  0.00000  0.00000
 -1.401258538444074 -1.401258538444074  0.036851862352611    1.98168 -0.70711 -1.00000 -1.00000

# S_n 2 dimensions, degree 7, symmetric 12 point rule with points at 3 distinct radii: 4+4+4=12
# "S_2: 7-1", A.H. Stroud. Approximate Calculation of Multiple Integrals. Prentice Hall, Englewood Cliffs, NH, 1971.
#                x1                 x2             Weight     Radius     cos1     cos2     cos3
  0.866025403784438  0.000000000000000  0.232710566932577    0.86603  1.00000  0.70711  0.70711
 -0.866025403784438  0.000000000000000  0.232710566932577    0.86603 -1.00000 -0.70711 -0.70711
  0.000000000000000  0.866025403784439  0.232710566932577    0.86603  0.00000  0.70711  0.70711
  0.000000000000000 -0.866025403784439  0.232710566932577    0.86603  0.00000 -0.70711 -0.70711
  0.322914992067413  0.322914992067413  0.387077796006217    0.45667  0.70711  1.00000  1.00000
 -0.322914992067388  0.322914992067389  0.387077796006236    0.45667 -0.70711  0.00000  0.00000
  0.322914992067388 -0.322914992067389  0.387077796006236    0.45667  0.70711 -0.00000 -0.00000
 -0.322914992067413 -0.322914992067414  0.387077796006217    0.45667 -0.70711 -1.00000 -1.00000
  0.644171310389468  0.644171310389468  0.165609800458638    0.91100  0.70711  1.00000  1.00000
 -0.644171310389461  0.644171310389461  0.165609800458651    0.91100 -0.70711  0.00000 -0.00000
  0.644171310389461 -0.644171310389461  0.165609800458651    0.91100  0.70711 -0.00000  0.00000
 -0.644171310389469 -0.644171310389468  0.165609800458637    0.91100 -0.70711 -1.00000 -1.00000

>> # evaluating formula 1 with 17 points
# refir2_17_8bg.txt:4 formula 1   : problem  G, 2_17_8  (d=2 n=17 o=8 plus 5/10 of order 9) quality P
# evaluating formula 2 with 17 points
# refir2_17_8bg.txt:25 formula 2   : problem E2, 2_17_8  (d=2 n=17 o=8 plus 5/10 of order 9) quality P
# evaluating formula 3 with 17 points
# refir2_17_8bg.txt:46 formula 3   : problem E1, 2_17_8  (d=2 n=17 o=8 plus 0/10 of order 9) quality P
# evaluating formula 4 with 17 points
# refir2_17_8bg.txt:67 formula 4   : problem  S, 2_17_8  (d=2 n=17 o=8 plus 5/10 of order 9) quality PO
# G 2 dimensions, 17 point rule of degree 8
#  numerically refined by refir2_17_8bg.mac, error=4.962080516648048E-265 
#                                       x1                                       x2                                   Weight        Radius
         3.8391262027822972310389409038377       -1.2183378843358737245298613003981    0.00043159227997033685895830237558456   4.027807990
         2.4511441938792202147453982554619        0.5612690942293263924301297555102      0.020590840517218513424627120438151   2.514583635
         2.3354488916470305530468954166004        2.6728787063826403520916675928112     0.0015458218436945251304322241899381   3.549450958
         1.8414532401989554617337394366770       -1.4292210288836830766861519768449      0.026194435861367780648733407180406   2.331013253
         1.1434156727564973142955657705465       -0.2614051733785441861481623434083       0.14638946642081257439645810551315   1.172916052
         1.0093731811121829285471657847887       -2.8840168977089162979821509485187     0.0051552780589676535957015560497678   3.055550308
         0.8898956958232595656566202050234        1.4192585077729743388087161635985      0.096007240219231923603516774363163   1.675174338
         0.0000000000000000000000000000000        0.2315259971800454758501028290858       0.25553159872414751676451271043679   0.231525997
         0.0000000000000000000000000000000       -1.4066828472387729091092177763195        0.1442975964412073656229960001229   1.406682847
         0.0000000000000000000000000000000        2.9330735603528040795009260066141     0.0075414544321187243402412342765887   2.933073560
        -0.8898956958232595656566202056465        1.4192585077729743388087161639678      0.096007240219231923603516774284154   1.675174338
        -1.0093731811121829285471657858398       -2.8840168977089162979821509480162      0.005155278058967653595701556052234   3.055550308
        -1.1434156727564973142955657700253       -0.2614051733785441861481623427802       0.14638946642081257439645810552226   1.172916052
        -1.8414532401989554617337394363735       -1.4292210288836830766861519755684      0.026194435861367780648733407237113   2.331013253
        -2.3354488916470305530468954178077        2.6728787063826403520916675938262     0.0015458218436945251304322241843567   3.549450958
        -2.4511441938792202147453982558042        0.5612690942293263924301297552212      0.020590840517218513424627120430976   2.514583635
        -3.8391262027822972310389409053240       -1.2183378843358737245298613025129    0.00043159227997033685895830237377754   4.027807990

# E2 2 dimensions, 17 point rule of degree 8
#  numerically refined by refir2_17_8bg.mac, error=1.860780193743018E-265 
#                                       x1                                       x2                                   Weight        Radius
         2.7146721718183225721283542093175       -0.8614949797903674200087290944423     0.0013558871361008814726106426341518   2.848090343
         1.7332206811580301139802155595083        0.3968771825999881692817009257600      0.064688033300132734676483712525222   1.778079140
         1.6514117483982218504705577231735        1.8900106585722919202951076269582     0.0048563425479093478558783565451669   2.509840842
         1.3021040733826217786078859776049       -1.0106118813380670310999616376050      0.082292247267001996823391605256868   1.648275278
         0.8085169759210978853202336069473       -0.1848413707332137566322650307875       0.45989607227055427459111245285208   0.829376894
         0.7137346211122616951463466351702       -2.0393079054265643418625623767042      0.016195783677265424099045528410456   2.160600343
         0.6292512810653480022054488197494        1.0035673151029706936416535462588       0.30161564056416942973216561090522   1.184527134
         0.0000000000000000000000000000000        0.1637136026269874854063297998384       0.80277619331183730650476310509117   0.163713603
         0.0000000000000000000000000000000       -0.9946749802613366891834759463743        0.4533242689103617222987579278743   0.994674980
         0.0000000000000000000000000000000        2.0739962042444382897182307166250      0.023692177841326352782276467382181   2.073996204
        -0.6292512810653480022054488197448        1.0035673151029706936416535462561       0.30161564056416942973216561090779   1.184527134
        -0.7137346211122616951463466351625       -2.0393079054265643418625623767079      0.016195783677265424099045528410376   2.160600343
        -0.8085169759210978853202336069511       -0.1848413707332137566322650307920       0.45989607227055427459111245285178   0.829376894
        -1.3021040733826217786078859776071       -1.0106118813380670310999616376144      0.082292247267001996823391605255023   1.648275278
        -1.6514117483982218504705577231647        1.8900106585722919202951076269508     0.0048563425479093478558783565453485   2.509840842
        -1.7332206811580301139802155595058        0.3968771825999881692817009257621      0.064688033300132734676483712525456   1.778079140
        -2.7146721718183225721283542093066       -0.8614949797903674200087290944268     0.0013558871361008814726106426342106   2.848090343

# E1 2 dimensions, 17 point rule of degree 8
#  numerically refined by refir2_17_8bg.mac, error=4.064936359238081E-261 
#                                       x1                                       x2                                   Weight        Radius
        13.0875994643931305278381730319280       -3.9632060915114992230511472301883    0.00016822750615647217448901998303274  13.674511409
         6.7954581447615227990753511322880        1.6494911571117981162115742202226      0.030528423993412588968132231541429   6.992787175
         7.8896153887526541021804215598298        9.1708382625327923907336969047913    0.00055632865116654258595671155067581  12.097533030
         5.0743818637169737149498823304073       -3.9707126585030624635713506479851      0.041268009008700848067544800202396   6.443284125
         2.5367733872066584552610587591912       -0.5653132389563985238681835584086       0.83787255044650139576383041745516   2.598999476
         2.8494727466365222966298994011436       -8.4426675948583109524810973464603     0.0057096118233079655056553323648394   8.910562892
         2.1561788827687071403815451471183        3.5362964013192529127126046488548       0.31203998939113780387420213524282   4.141799079
         0.0000000000000000000000000000000        0.4627912705171405801189860751050        3.0109403761032583235997669306729   0.462791271
         0.0000000000000000000000000000000       -2.9463675167607205954654284952656       0.81049315112422432026976440337738   2.946367517
         0.0000000000000000000000000000000        9.0595781674783668568955816871619     0.0054654982497762883516398262425282   9.059578167
        -2.1561788817368973602622676672270        3.5362964007166323160892641173710       0.31203998961305053825702742527987   4.141799078
        -2.8494727440540579957296121056234       -8.4426675952849549161402189802342     0.0057096118251780467220848222005391   8.910562892
        -2.5367733875905127165077292364890       -0.5653132396085828814843491616819       0.83787255033701926885763788340879   2.598999477
        -5.0743818653945915876846773260167       -3.9707126607523127536807383626016      0.041268008931095584550260935244152   6.443284128
        -7.8896153849559836462596752516626        9.1708382586384439548464633027087    0.00055632865310748543752891690695153  12.097533025
        -6.7954581435845337961804064485009        1.6494911574222484121707961235930      0.030528424016267104175233110975382   6.992787174
       -13.0875994648819733217211713168950       -3.9632060863535488122195073450402    0.00016822750622654301359173456472027  13.674511408

# S 2 dimensions, 17 point rule of degree 8
#  numerically refined by refir2_17_8bg.mac, error=7.753250807262575E-267 
#                                       x1                                       x2                                   Weight        Radius
         0.9242041030000109705960367583377       -0.5367022484538678112596369258162      0.026051164407523472717582473460728   1.068738755
         0.8824310011565100361877340657561        0.1526717978040671061821253391291       0.16697838225765837858198765696398   0.895540702
         0.5728471339019064560250981216617        0.6878783516382158312374583013674       0.16737551337879190422589877583099   0.895170635
         0.6455718725466734179783771024241       -0.3700485664194306562039785884883       0.28174421750256649895073089635394   0.744109524
         0.4025496553611541219379634313756        0.2343715263219284354187491311818        0.2748985694855031298807977467871   0.465807082
         0.3076014234692947211200477595720       -0.8379025571768507788544062527865       0.17134465238799275529850092517053   0.892580154
         0.2287452046907862997750371996993        0.1236787055843671014618185687611       0.13989189282911137486421870477679   0.260039979
         0.0000000000000000000000000000000        0.7499530714430287174362199025827       0.28435541836072349209393049288434   0.749953071
         0.0000000000000000000000000000000       -0.4178617098973077124314517924695       0.37866426123695495554723187882847   0.417861710
         0.0000000000000000000000000000000        1.0854292306465321595873719502556      0.022004189493820083406576588198047   1.085429231
        -0.2287452046907862997750371996599        0.1236787055843671014618185687360       0.13989189282911137486421870475007   0.260039979
        -0.3076014234692947211200477595721       -0.8379025571768507788544062527864       0.17134465238799275529850092517054   0.892580154
        -0.4025496553611541219379634313669        0.2343715263219284354187491311762       0.27489856948550312988079774682238   0.465807082
        -0.6455718725466734179783771024256       -0.3700485664194306562039785884891       0.28174421750256649895073089635419   0.744109524
        -0.5728471339019064560250981216617        0.6878783516382158312374583013674       0.16737551337879190422589877583105   0.895170635
        -0.8824310011565100361877340657561        0.1526717978040671061821253391292       0.16697838225765837858198765696399   0.895540702
        -0.9242041030000109705960367583410       -0.5367022484538678112596369258181      0.026051164407523472717582473459691   1.068738755

>> # evaluating formula 1 with 24 points
# r2_24_10r2bg.txt:4 formula 1   : problem  G, 2_24_10  (d=2 n=24 o=10 plus 6/12 of order 11) quality N (2 negative weights, stability factor 16.286675)
# evaluating formula 2 with 24 points
# r2_24_10r2bg.txt:32 formula 2   : problem E2, 2_24_10  (d=2 n=24 o=10 plus 6/12 of order 11) quality N (2 negative weights, stability factor 16.286675)
G 2 dimensions, degree 10, bilaterally symmetric (axis 1) 24 point rule with points at 14 distinct radii: 2+1+2+2+2+1+2+2+1+2+2+2+1+2=24
 (2 negative weights, stability factor 16.286675)
#                 x1                  x2             Weight     Radius
  -3.439210584469660   0.246514058101178   0.001306718777311    3.44803
  -2.904953486926174   2.018286506382382   0.000994248866594    3.53726
  -2.851169450011036  -1.453854362807834   0.002889131377256    3.20045
  -2.248430623387705  -4.049029726826461   0.000055608764494    4.63142
  -1.417522439545697   0.471797601265811   1.179434062375544    1.49398
  -1.412547922641572   0.110946789439441   1.336698618339230    1.41690
  -1.338906449324968   2.561557708600659   0.006444713938021    2.89037
  -1.319767315690048   0.291167338695598  -3.821668721259549    1.35150
  -1.310121675041704  -1.912199843795237   0.026039486099245    2.31796
  -1.106348325704051   0.294965536940569   1.646758880819333    1.14499
   0.000000000000000   3.779508397180773   0.000495156019589    3.77951
   0.000000000000000   1.789473775118046   0.069420902982739    1.78947
   0.000000000000000  -1.161819980156596   0.166142850717483    1.16182
   0.000000000000000  -2.950093516516083   0.006035594085231    2.95009
   1.106348325704134   0.294965536940573   1.646758880820558    1.14499
   1.310121675041704  -1.912199843795237   0.026039486099245    2.31796
   1.319767315690007   0.291167338695620  -3.821668721260377    1.35150
   1.338906449324968   2.561557708600660   0.006444713938021    2.89037
   1.412547922641585   0.110946789439414   1.336698618338729    1.41690
   1.417522439545688   0.471797601265812   1.179434062375646    1.49398
   2.248430623387706  -4.049029726826463   0.000055608764494    4.63142
   2.851169450011037  -1.453854362807836   0.002889131377256    3.20045
   2.904953486926176   2.018286506382384   0.000994248866594    3.53726
   3.439210584469701   0.246514058101177   0.001306718777311    3.44803

E_n^{r^2} 2 dimensions, degree 10, bilaterally symmetric (axis 1) 24 point rule with points at 14 distinct radii: 2+1+2+2+2+1+2+2+1+2+2+2+1+2=24
 (2 negative weights, stability factor 16.286675)
#                 x1                  x2             Weight     Radius
  -2.431889126207065   0.174311762141155   0.004105178111108    2.43813
  -2.054112309637009   1.427144075040288   0.003123524935132    2.50122
  -2.016081252414723  -1.028030278799068   0.009076473910043    2.26306
  -1.589880540824942  -2.863096377064903   0.000174700086009    3.27491
  -1.002339729486857   0.333611283202605   3.705301385752653    1.05640
  -0.998822214850832   0.078451227163490   4.199362559437006    1.00190
  -0.946749829692089   1.811294826152200   0.020246665962175    2.04380
  -0.933216418512775   0.205886399651708 -12.006126379165094    0.95566
  -0.926395920601466  -1.352129476531469   0.081805458232642    1.63904
  -0.782306403459768   0.208572131387009   5.173445602219021    0.80963
   0.000000000000000   2.672516017198021   0.001555578513522    2.67252
   0.000000000000000   1.265349041141461   0.218092198816144    1.26535
   0.000000000000000  -0.821530786486749   0.521953159260511    0.82153
   0.000000000000000  -2.086031130662991   0.018961378038212    2.08603
   0.782306403459723   0.208572131387009   5.173445602216247    0.80963
   0.926395920601466  -1.352129476531468   0.081805458232642    1.63904
   0.933216418512795   0.205886399651703 -12.006126379162982    0.95566
   0.946749829692089   1.811294826152200   0.020246665962175    2.04380
   0.998822214850829   0.078451227163498   4.199362559437631    1.00190
   1.002339729486858   0.333611283202602   3.705301385752704    1.05640
   1.589880540824941  -2.863096377064901   0.000174700086009    3.27491
   2.016081252414723  -1.028030278799068   0.009076473910043    2.26306
   2.054112309637008   1.427144075040288   0.003123524935132    2.50122
   2.431889126207055   0.174311762141156   0.004105178111108    2.43813

>> # evaluating formula 1 with 23 points
# r2_23_10Sb.txt:4 formula 1   : problem  S, 2_23_10  (d=2 n=23 o=10 plus 6/12 of order 11) quality PO
S bilaterally symmetric 2 dimensions, degree 10, asymmetric 23 point rule with points at 14 distinct radii: 1+1+2+2+2+1+2+1+2+2+2+2+1+2=23

#                x1                 x2             Weight     Radius
 -1.110190294609973  0.624928370556688  0.000817005952334    1.27399
 -0.926319041282590 -0.087347845160238  0.091503293779175    0.93043
 -0.784453603304868  0.373120754046603  0.153828660473360    0.86867
 -0.736358619148018 -0.540452910796537  0.106540329509943    0.91341
 -0.569322593727058 -0.120605254270782  0.246380499501348    0.58196
 -0.482187150560379  0.771901023210057  0.117555844337428    0.91013
 -0.402418832400371 -0.878373796134950  0.050516657704085    0.96617
 -0.326313811952538 -0.598982175188628  0.184534048760206    0.68210
 -0.312053164433130  0.373917181682970  0.264180129869485    0.48702
  0.000000000000000 -0.893528145730421  0.104281887159220    0.89353
  0.000000000000000 -0.069519326106997  0.267554552405660    0.06952
  0.000000000000000 -0.429830196257665  0.125136811141142    0.42983
  0.000000000000000  0.763271323065754  0.175834159250053    0.76327
  0.000000000000000  0.994869532006091  0.037072303858987    0.99487
  0.312053164433128  0.373917181682969  0.264180129869486    0.48702
  0.326313811952538 -0.598982175188626  0.184534048760206    0.68210
  0.402418832400370 -0.878373796134949  0.050516657704086    0.96617
  0.482187150560379  0.771901023210057  0.117555844337428    0.91013
  0.569322593727060 -0.120605254270781  0.246380499501348    0.58196
  0.736358619148018 -0.540452910796537  0.106540329509943    0.91341
  0.784453603304868  0.373120754046604  0.153828660473361    0.86867
  0.926319041282591 -0.087347845160238  0.091503293779174    0.93043
  1.110190294609980  0.624928370556689  0.000817005952334    1.27399

>> # evaluating formula 1 with 10 points
# r3_10_4g.txt:4 formula 1   : problem  G, 3_10_4  (d=3 n=10 o=4 plus 15/21 of order 5) quality P
# evaluating formula 2 with 10 points
# r3_10_4g.txt:18 formula 2   : problem E2, 3_10_4  (d=3 n=10 o=4 plus 15/21 of order 5) quality P
G_n 3 dimensions, degree 4, asymmetric 10 point rule with points at 4 distinct radii: 1+4+1+4=10

#                x1                 x2                 x3             Weight     Radius     cos1     cos2
 -2.577935474573518  0.000000000000000 -0.000000000000000  0.040678508996924    2.57794
 -0.517638090205042  1.592450434036252  0.000000000000000  0.155502116982037    1.67447  1.00000
 -0.517638090205042 -0.000000000000000  1.592450434036252  0.155502116982037    1.67447  0.09556
 -0.517638090205042  0.000000000000000 -1.592450434036252  0.155502116982037    1.67447  0.09556
 -0.517638090205042 -1.592450434036252 -0.000000000000000  0.155502116982037    1.67447 -0.80887
  1.163721912200423  0.000000000000000  0.000000000000000  0.292654824336409    1.16372 -0.30914
  1.931851652578137 -2.175327747161075  2.175327747161075  0.011164549684630    3.63265 -0.73389
  1.931851652578137  2.175327747161075  2.175327747161075  0.011164549684630    3.63265  0.40510
  1.931851652578137 -2.175327747161075 -2.175327747161075  0.011164549684630    3.63265 -0.73389
  1.931851652578137  2.175327747161075 -2.175327747161075  0.011164549684630    3.63265  0.40510

E_n^{r^2} 3 dimensions, degree 4, asymmetric 10 point rule with points at 4 distinct radii: 1+4+1+4=10

#                x1                 x2                 x3             Weight     Radius     cos1     cos2
 -1.822875655532295  0.000000000000000 -0.000000000000000  0.226511280516944    1.82288
 -0.366025403784439  1.126032500610494  0.000000000000000  0.865886791557674    1.18403  1.00000
 -0.366025403784439 -0.000000000000000  1.126032500610494  0.865886791557674    1.18403  0.09556
 -0.366025403784439  0.000000000000000 -1.126032500610494  0.865886791557674    1.18403  0.09556
 -0.366025403784439 -1.126032500610494 -0.000000000000000  0.865886791557674    1.18403 -0.80887
  0.822875655532295  0.000000000000000  0.000000000000000  1.629598051760292    0.82288 -0.30914
  1.366025403784439 -1.538189001320851  1.538189001320851  0.062167874580944    2.56867 -0.73389
  1.366025403784439  1.538189001320851  1.538189001320851  0.062167874580944    2.56867  0.40510
  1.366025403784439 -1.538189001320851 -1.538189001320851  0.062167874580944    2.56867 -0.73389
  1.366025403784439  1.538189001320851 -1.538189001320851  0.062167874580944    2.56867  0.40510

>> # evaluating formula 1 with 10 points
# refir3_10_4Saa.txt:27 formula 1   : problem  S, 3_10_4  (d=3 n=10 o=4 plus 15/21 of order 5) quality PO
# a: 0.2808104405162235380272704394827b0; (2*sqrt(3)-1)/sqrt(77)
# b: 0.5634471231473684043478274844548b0; 
# c: 0.6659003624568142435187985134767b0; sqrt(48-8*sqrt(3))/sqrt(77)
# e: 0.5087315934354991971551529649500b0; (2*sqrt(3)+1)/sqrt(77)
# f: 0.6337704450481774509598440747859b0; sqrt(4*sqrt(3)+24)/sqrt(77)
# g: 1.0648736595697753281965450078389b0;
# w1:0.8501187487033758552677327964411b0;
# w2:0.60867233065603545431174931381882b0;
# w3:0.16217221745333508244375783956766b0;
# w4:0.18545247900138473520302650430595b0;
d:3;V:2/d*pi^(d/2)/gamma(d/2);
# sum=V=2/d*pi^(d/2)/gamma(d/2)
#    [  1.064873659569775            0.0                   0.0           0.162172217453335  ]
#    [  0.2808104405162235    0.6659003624568143           0.0           0.6086723306560354 ]
#    [  0.2808104405162235   -0.6659003624568143           0.0           0.6086723306560354 ]
#    [  0.2808104405162235           0.0            0.6659003624568143   0.6086723306560354 ]
#    [  0.2808104405162235           0.0           -0.6659003624568143   0.6086723306560354 ]
#    [                                                                                      ]
#    [ -0.5634471231473685           0.0                   0.0           0.8501187487033759 ]
#    [ -0.5087315934354992    0.6337704450481775    0.6337704450481775   0.1854524790013847 ]
#    [ -0.5087315934354992    0.6337704450481775   -0.6337704450481775   0.1854524790013847 ]
#    [ -0.5087315934354992   -0.6337704450481775    0.6337704450481775   0.1854524790013847 ]
#    [ -0.5087315934354992   -0.6337704450481775   -0.6337704450481775   0.1854524790013847 ]
# S 3 dimensions, 10 point rule of degree 4
#  numerically refined to high precision by refir3_10_4Saa.mac, error=3.3589380537835447E-139 
#                                       x1                                       x2                                       x3                                   Weight        Radius
         1.0648736595697753281965450078389        0.0000000000000000000000000000000        0.0000000000000000000000000000000       0.16217221745333508244375783956766   1.064873660
         0.2808104405162235380272704394827        0.6659003624568142435187985134767        0.0000000000000000000000000000000       0.60867233065603545431174931381882   0.722687897
         0.2808104405162235380272704394827        0.0000000000000000000000000000000        0.6659003624568143207350881301534       0.60867233065603531315123457196943   0.722687897
         0.2808104405162235380272704394827        0.0000000000000000000000000000000       -0.6659003624568143207350881301534       0.60867233065603531315123457196943   0.722687897
         0.2808104405162235380272704394827       -0.6659003624568142435187985134767        0.0000000000000000000000000000000       0.60867233065603545431174931381882   0.722687897
        -0.5634471231473684043478274844548        0.0000000000000000000000000000000        0.0000000000000000000000000000000        0.8501187487033758552677327964411   0.563447123
        -0.5087315934354991971551529649500       -0.6337704450481774509598440747859        0.6337704450481774509598440747859       0.18545247900138473520302650430595   1.030600693
        -0.5087315934354991971551529649500        0.6337704450481774509598440747859        0.6337704450481774509598440747859       0.18545247900138473520302650430595   1.030600693
        -0.5087315934354991971551529649500       -0.6337704450481774509598440747859       -0.6337704450481774509598440747859       0.18545247900138473520302650430595   1.030600693
        -0.5087315934354991971551529649500        0.6337704450481774509598440747859       -0.6337704450481774509598440747859       0.18545247900138473520302650430595   1.030600693

>> # evaluating formula 1 with 11 points
# r3_11_4E1aa.txt:4 formula 1   : problem E1, 3_11_4  (d=3 n=11 o=4 plus 10/21 of order 5) quality P
# evaluating formula 2 with 11 points
# r3_11_4E1aa.txt:19 formula 2   : problem E1, 3_11_4  (d=3 n=11 o=4 plus 10/21 of order 5) quality P
E1 (with x3=0 for two points) 3 dimensions, degree 4, asymmetric 11 point rule with points at 8 distinct radii: 1+1+1+2+2+2+1+1=11

#                x1                 x2                 x3             Weight     Radius
 -5.115868855760483  4.874421253388981  0.000000000000000  0.387212730803631    7.06626
 -4.129697090608138 -1.230915361660310  1.597166011471146  1.756806054186920    4.59570
 -3.555626106046339 -1.230915361660310 -4.705304629322245  0.804433885804813    6.02474
  0.000000000000000 -1.798305222198938  0.072829234625449  8.939482372992044    1.79978
  0.000000000000000 -12.137857491665358 -3.133718182395648  0.044060189060386   12.53586
  0.000000000000000  1.961197846315075 -1.405138946429745  7.028335739335231    2.41262
  0.000000000000000  1.749360920359940  3.443387199943258  3.197835587648453    3.86228
  0.000000000000000 -9.070827785868225 11.860112612624533  0.026121998091497   14.93125
  3.555626106046339 -1.230915361660310 -4.705304629322245  0.804433885804814    6.02474
  4.129697090608138 -1.230915361660310  1.597166011471146  1.756806054186921    4.59570
  5.115868855760482  4.874421253388981  0.000000000000000  0.387212730803631    7.06626

E1 (with x3=0 for three points) 3 dimensions, degree 4, asymmetric 11 point rule with points at 8 distinct radii: 1+1+1+2+2+2+1+1=11

#                x1                 x2                 x3             Weight     Radius
 -5.123512671435817  4.925613098468268  0.000000000000000  0.379658096395598    7.10718
 -4.102816292737210 -1.218122471264712  1.544992698170306  1.815112382679153    4.55016
 -3.636092685910456 -1.218122471264712 -4.843920857271974  0.737101279021608    6.17807
  0.000000000000000 -1.836923221947856  0.000000000000000  8.813498359175593    1.83692
  0.000000000000000 -12.639707409137010 -3.423767380484498  0.036648025337593   13.09520
  0.000000000000000  1.948389609086195 -1.422580596633783  7.054048788227520    2.41246
  0.000000000000000  1.703608086180249  3.398957047139019  3.331366718821742    3.80200
  0.000000000000000 -8.635010968135125 11.051160549266545  0.033435820963179   14.02468
  3.636092685910455 -1.218122471264711 -4.843920857271974  0.737101279021608    6.17807
  4.102816292737210 -1.218122471264712  1.544992698170306  1.815112382679154    4.55016
  5.123512671435816  4.925613098468268  0.000000000000000  0.379658096395598    7.10718

>> # evaluating formula 1 with 22 points
# r3_22_6bg.txt:4 formula 1   : problem  G, 3_22_6  (d=3 n=22 o=6 plus 16/36 of order 7) quality P
# evaluating formula 2 with 22 points
# r3_22_6bg.txt:30 formula 2   : problem E2, 3_22_6  (d=3 n=22 o=6 plus 16/36 of order 7) quality P
G 3 dimensions, degree 6, asymmetric 22 point rule with points at 15 distinct radii: 1+2+2+1+1+2+2+1+1+2+1+1+2+1+2=22

#                x1                 x2                 x3             Weight     Radius
 -3.607308355958064  3.106932564320797  3.025924560760767  0.000196439240058    5.64109
 -3.520886301135160 -2.843529692087316  2.821683560444838  0.000277247745769    5.33331
 -2.681235758875105  0.248527426918185 -0.129332652254012  0.014114079977485    2.69583
 -1.523123525034240  0.010074189512432 -1.876798132827016  0.026026587017926    2.41710
 -1.480438998916786 -1.463985676223738 -0.333102253848578  0.049064907877431    2.10853
 -1.208633146814508  0.014750256199373  1.219678442839075  0.097747172562434    1.71716
 -1.161164134633357  1.604772120461069 -0.358346012197562  0.060696435928771    2.01296
  0.000000000000000  5.479883431850585 -0.736585006341946  0.000181769094781    5.52917
  0.000000000000000  1.622744710418311  1.277132413861106  0.055177243139622    2.06503
  0.000000000000000 -0.040269191088254  3.257519176648435  0.005723339409289    3.25777
  0.000000000000000 -1.636853225936983  1.232414692943794  0.058719603649382    2.04893
  0.000000000000000 -0.083255075422586 -0.379757195177931  0.329554267652854    0.38878
  0.000000000000000 -2.661685785614455 -0.649380636435008  0.011270785938516    2.73976
  0.000000000000000  1.383412835421689 -2.125951870446862  0.021516268178498    2.53643
  0.000000000000000 -1.283280997729724 -2.165334035338032  0.021610982237308    2.51704
  1.161164134633357  1.604772120461069 -0.358346012197562  0.060696435928771    2.01296
  1.208633146814508  0.014750256199373  1.219678442839075  0.097747172562434    1.71716
  1.480438998916786 -1.463985676223738 -0.333102253848578  0.049064907877431    2.10853
  1.523123525034240  0.010074189512432 -1.876798132827016  0.026026587017926    2.41710
  2.681235758875105  0.248527426918185 -0.129332652254012  0.014114079977485    2.69583
  3.520886301135161 -2.843529692087317  2.821683560444839  0.000277247745769    5.33331
  3.607308355958065  3.106932564320798  3.025924560760768  0.000196439240058    5.64109

E_n^{r^2} 3 dimensions, degree 6, asymmetric 22 point rule with points at 15 distinct radii: 1+2+2+1+1+2+2+1+1+2+1+1+2+1+2=22

#                x1                 x2                 x3             Weight     Radius
 -2.550752200328842  2.196933084920541  2.139651776272862  0.001093838120090    3.98885
 -2.489642579319490 -2.010679127780233  1.995231579953144  0.001543806384824    3.77122
 -1.895919987060445  0.175735428884693 -0.091451995437654  0.078591826688153    1.90624
 -1.077010973136468  0.007123527719199 -1.327096686640234  0.144924573153895    1.70915
 -1.046828455267083 -1.035194199217779 -0.235538862524853  0.273209500195868    1.49096
 -0.854632694079375  0.010430006182816  0.862442897798558  0.544288317590543    1.21421
 -0.821067033669856  1.134745248637137 -0.253388895236054  0.337977663490077    1.42338
  0.000000000000000  3.874862734773355 -0.520844252904725  0.001012149939430    3.90971
  0.000000000000000  1.147453788871388  0.903068990314332  0.307244987762345    1.46020
  0.000000000000000 -0.028474618091401  2.303413899653326  0.031869431068114    2.30359
  0.000000000000000 -1.157430015867117  0.871448786614494  0.326970012963716    1.44882
  0.000000000000000 -0.058870228399508 -0.268528887914698  1.835066255046757    0.27491
  0.000000000000000 -1.882096068395825 -0.459181451594431  0.062759432887738    1.93730
  0.000000000000000  0.978220597107186 -1.503274984069201  0.119809638485672    1.79353
  0.000000000000000 -0.907416695662527 -1.531122379921554  0.120337037431033    1.77981
  0.821067033669856  1.134745248637137 -0.253388895236054  0.337977663490078    1.42338
  0.854632694079375  0.010430006182816  0.862442897798558  0.544288317590543    1.21421
  1.046828455267083 -1.035194199217779 -0.235538862524853  0.273209500195869    1.49096
  1.077010973136469  0.007123527719199 -1.327096686640234  0.144924573153895    1.70915
  1.895919987060445  0.175735428884693 -0.091451995437654  0.078591826688153    1.90624
  2.489642579319490 -2.010679127780233  1.995231579953144  0.001543806384824    3.77122
  2.550752200328841  2.196933084920541  2.139651776272861  0.001093838120090    3.98885

>> # evaluating formula 1 with 22 points
# r3_22_6Sa.txt:3 formula 1   : problem  S, 3_22_6  (d=3 n=22 o=6 plus 0/36 of order 7) quality PO
S 3 dimensions, degree 6, asymmetric 22 point rule with points at 22 distinct radii
#                x1                 x2                 x3             Weight     Radius
 -0.220489260548182  0.000000000000000  0.000000000000000  0.501754113316118    0.22049
  0.408620239052371 -0.437512828414961  0.000000000000000  0.371185529608121    0.59866
  0.369257441543691  0.440140251590219 -0.435825951748556  0.349372667609754    0.72112
  0.380164558254441  0.431509498917271  0.444127366581874  0.346106195026951    0.72662
 -0.090047325596575 -0.133343834517538  0.790738776994298  0.246946863097625    0.80694
 -0.108497326059076 -0.117900118494891 -0.792730049858867  0.242631580774764    0.80876
 -0.555776399049701 -0.611679530613198  0.025898030255301  0.180552817993158    0.82687
 -0.114804101032266  0.845826405758901  0.001507964828662  0.195675739296919    0.85358
 -0.780776036238835  0.365777197811381  0.006470648516800  0.185621106649098    0.86223
 -0.350113233804760  0.519202628428064  0.595456588114949  0.183319534853002    0.86413
 -0.367263980671512  0.520161992522308 -0.589016201153148  0.179529967056459    0.86740
 -0.053742849384418 -0.758338041474915 -0.430391572785919  0.185555588250930    0.87361
 -0.030671180987993 -0.766768230977565  0.429556785806875  0.176405291006066    0.87943
  0.575313484308305 -0.247103200337271 -0.630188416775836  0.161294762015168    0.88836
  0.885557607427000  0.100247800578484 -0.015162832579187  0.164641376008885    0.89134
  0.602315107377702 -0.249714714969104  0.614606559986787  0.154380126942821    0.89604
 -0.744204316334607 -0.208905632906853 -0.463994875018859  0.149325692660178    0.90154
 -0.735962826291715 -0.194242058033450  0.487091163485124  0.144308613040571    0.90368
  0.646842869101073  0.910338770030295  0.013507512212417  0.030948420027073    1.11683
  0.720793403318753 -0.874307205436497 -0.022684183757210  0.031063994935076    1.13334
  0.429970272483835  0.659474452473975 -1.230012932926630  0.004745123721105    1.46038
  0.431694449787145  0.655565509393769  1.313679818328000  0.003425100896547    1.53032

>> # evaluating formula 1 with 23 points
# refir3_23_6E1.txt:4 formula 1   : problem E1, 3_23_6  (d=3 n=23 o=6 plus 0/36 of order 7) quality P
# E1 3 dimensions, 23 point rule of degree 6
#  numerically refined to high precision by refir3_23_6E1.mac, error=6.585174202826906E-199 
#                                       x1                                       x2                                       x3                                   Weight        Radius
        -0.0658506495996518675231457493343        0.1525012518380789196264347321290        0.0000000000000000000000000000000        14.274874861525105056197517200813   0.166111227
         1.3293851583803251135900832775800       -4.0940943452808267783586707793658        1.6181398169498896916715574916809        1.3528203979031186266931066800841   4.598613908
         1.2891399546037273462852176955275       -1.9539286932993853808348789567653       -3.9602104512079941148875121124585        1.3691377796592383248425849805231   4.600324551
        -3.9709733074006002720711074962187       -2.3927436783355346378395409686331        1.4820636417493000902082360866428        1.1023742519528811000235353057765   4.867274798
         3.9692339170785933772181558198591        1.0030400052950165644823573489059        2.8968308261336460826300095950279        1.0490552733438593119650270261633   5.015230401
         1.0449708989978793046230166037634        5.0043819476572469384734672703989       -0.5394009298641263501100859630066       0.78657243622095777292153610641667   5.140696083
        -4.1099597069380745259642289782454       -0.8788281122142940336231528318014       -3.4439499764884542613695098520203       0.75785201907941166120930816359861   5.433681909
        -3.9952963464091731522519363359622        3.6245655428383937009228426572627       -0.9105869266059721791962743682069       0.71461595067520050772482331825433   5.470743717
        -0.1905608626856502802282318350294       -1.0887400494877479227926472675802        5.3788357232724098117507838178531       0.73326795750572163265834933250684   5.491224096
         4.4249074052025161197260672276529        2.3015559408882439344391285885694       -2.3696529793824512638554153554599       0.67747093926993026102639303833905   5.521976144
         5.2172128826809425171127072982195       -2.5022003426673282219156946674755       -0.7508435899068808244924121076740       0.51007711815150017825468365201927   5.834730749
        -4.1833310984083023830228359306710        1.9212909796307506006550925532758        3.5926851196253042444533813424137       0.46850629150917266672775908225428   5.839435287
         0.0468643965417615094954175864353        4.4021241880993411963921308774591        3.9608833318886290185793254440655       0.48386922800820223898404592734034   5.921949882
        -0.4344849722850196912206790831658        2.8993791748090885746349555523874       -5.3520807845612037844513134608188       0.47774258191824530484808231788112   6.102454057
        -1.7043274815101821777289147432618       -5.6957797193730665308944042564276       -2.0769414653286444560279556732679       0.37202447154812225275467345643208   6.297644371
        -5.8336494209828410794412213509708      -12.4578804141077625962021754834710        9.4169382627876819511916212353627     0.0014846194291351475095482484437085  16.670602155
        12.7162544883854959586594602607040       -9.0117411635643209100132305313060       13.1197851598677507402837327799600    0.00048405273320584003409511014358892  20.372613226
        16.5484526250738895440071788838180       16.3931079193077939115959378348870        5.4099139347250657126326153954951     0.0001692679278534957264553116579939  23.913436397
        -4.6405237569491167291321205053035       23.0593481908552506990173236021860       -4.8881157292121381659837377610915    0.00011583965737235479351085198908684  24.024189375
       -25.0202932332430097150414307390880        0.0000000000000000000000000000000        0.0000000000000000000000000000000    0.00013215945315254258403920198967763  25.020293233
        12.3257831270667488839764134001500      -21.8363699226160943328109195475260      -10.4985162981082021960510606845730    0.00007795521809682962098567208055532  27.184017833
        20.8749118099338343514484651850890        0.2927140343180182129494210190950      -29.2533948404369667978594491334280    0.00001458033413009477992944213695246  35.938958447
       -13.2136351207529286319365521864110      -17.3228764169665969537622789044100      -50.7447892399334279407949900483430  0.0000011956947352788173971220107102551  55.224232321

>> # evaluating formula 1 with 42 points
# r3_42_8Sdas.txt:3 formula 1   : problem  S, 3_42_8  (d=3 n=42 o=8 plus 0/55 of order 9) quality PO
S 3 dimensions, degree 8, asymmetric 42 point rule with points at 42 distinct radii
#                 x1                  x2                  x3              Weight     Radius
  -0.374845573090805   0.000000000000000   0.000000000000000   0.254231663400823    0.37485
   0.262300288857265  -0.407937921354356   0.000000000000000   0.208586573349486    0.48499
   0.176582233797251   0.197706797145846   0.430807224586915   0.213834701704236    0.50583
   0.088575237301455  -0.040380886181428  -0.522975017929816   0.218918097293675    0.53196
   0.007148741219578   0.515393410848912  -0.161780402159342   0.214043116606247    0.54024
  -0.206498694357174  -0.309193807518972   0.479337096145938   0.143451729917477    0.60664
   0.593906593626326   0.164274773264807  -0.052041708092083   0.183649342972641    0.61840
   0.286896812606772  -0.386776537489022   0.476249580797536   0.079040957175656    0.67729
  -0.322213183013516  -0.579742506106718  -0.282350850482702   0.174028536800211    0.72086
  -0.438759504872941   0.512660312593323   0.413739743786981   0.162841810267071    0.79152
  -0.582433959504295   0.193040794089196  -0.551776052549089   0.140566670115432    0.82520
   0.676406255031481  -0.262879841057027  -0.424851427813177   0.101619007606439    0.84091
   0.220528914799775   0.768353877688658   0.289676388896635   0.090239001924305    0.85024
   0.489224387339737   0.435539341572897  -0.585710302462827   0.113282012667202    0.87869
  -0.697150135951702  -0.502409888177705   0.206478193848557   0.090240505700544    0.88378
  -0.247300478140091  -0.797471081354806   0.292066193028081   0.094560991036117    0.88455
   0.784240607098880  -0.238080606584553   0.333175178130226   0.105853301274340    0.88472
  -0.704573183614675  -0.067632651253838   0.534222387939463   0.098251375488657    0.88679
  -0.245662823761274   0.155892580195646   0.841256681549687   0.091882260156935    0.89015
  -0.529515701423433   0.688882085246905  -0.207288502592972   0.099909582768505    0.89326
  -0.140575975665115   0.496304923981988  -0.735893733713921   0.089671222680352    0.89868
   0.183518479217789  -0.609163519817202  -0.635912431303237   0.100802010749671    0.89952
   0.169007949909132  -0.879316345888724  -0.086108581846103   0.084396498609199    0.89954
  -0.865425968314531   0.244045490124090   0.046544640405495   0.093922389430823    0.90038
  -0.395530397825116  -0.312848843982494  -0.756165546873289   0.083713357360717    0.90890
  -0.828757438898013  -0.267376646991108  -0.266978593177920   0.081341297136783    0.91083
   0.357958810886804  -0.094292296120993   0.833797926879259   0.089404646644362    0.91227
   0.686931074835515   0.351855356078963   0.486889112051339   0.085472883869399    0.91254
   0.603372997173217   0.687736961595301  -0.030431781796355   0.075786226028513    0.91541
   0.355510199648162  -0.701724542222177   0.504522936393337   0.069923265917087    0.93453
   0.684748497918764  -0.627125024943325  -0.106547373600599   0.063797324109836    0.93462
   0.039931207457608   0.004706173817430  -0.935664525082567   0.058992082500466    0.93653
  -0.201777831243885  -0.449586252674862   0.798704148950310   0.063778830663680    0.93849
   0.138339587073807   0.553691986144920   0.746146210782251   0.061900294906784    0.93939
   0.081729649540733   0.881115798384140  -0.341913904865303   0.057441672051782    0.94866
  -0.185393979405131   0.906257616256151   0.226906130805369   0.043622144028166    0.95245
   0.542155263317472  -0.091846873719693  -0.777773340200892   0.041742128698128    0.95252
   0.960220564852809   0.146614066057547  -0.163486061794416   0.044443304207422    0.98501
  -0.465016365633564  -0.899949596298773  -0.366208870815785   0.016763870427464    1.07715
  -0.806247822213394   0.705566503860059   0.701009332025700   0.002420325849146    1.28034
  -0.941034157619778  -0.842789978178230   0.928486637255967   0.000177260258247    1.56778
  -1.171702460222946   0.467330365303113  -1.012066523966266   0.000245930432363    1.61727

>> # evaluating formula 1 with 43 points
# r3_43_8Gasdsg.txt:3 formula 1   : problem  G, 3_43_8  (d=3 n=43 o=8 plus 0/55 of order 9) quality P
# evaluating formula 2 with 43 points
# r3_43_8Gasdsg.txt:49 formula 2   : problem E2, 3_43_8  (d=3 n=43 o=8 plus 0/55 of order 9) quality P
G 3 dimensions, degree 8, asymmetric 43 point rule with points at 43 distinct radii
#                 x1                  x2                  x3              Weight     Radius
  -0.087370814868331   0.000000000000000   0.000000000000000   0.176442361893385    0.08737
  -1.391398100783405   0.296820460580432  -0.543170771307965   0.067652182863320    1.52287
   0.752739471770282  -1.135814003314098  -0.718540864626734   0.077301317323424    1.54045
   0.585903087760184   1.292481758983341  -0.601243163098451   0.068361379161631    1.54120
   0.526342873528038   0.874058486444013   1.163273203059349   0.077755288365959    1.54733
   0.655079815235155  -0.941420786041729   1.062972735855403   0.076307127959459    1.56375
   0.415448540687354   0.216207472733153  -1.546813900714491   0.055768308429052    1.61616
  -1.127500222357075  -0.089252824361831   1.165300168399273   0.069034723625409    1.62393
  -0.895996897958251  -1.502876403148311  -0.144064945870394   0.058959424631348    1.75562
   1.771057146825133   0.203593431828235   0.018862377088355   0.055637612471964    1.78282
  -0.890634509806873   1.689677539522777   0.065273965729954   0.044184691397158    1.91115
  -0.892414893061166  -0.634378827293932  -1.742174815619990   0.032827403862513    2.05767
  -0.698726027940909  -1.843283631289088   1.508166042713593   0.013919210404825    2.48203
  -0.868315129751784   1.363548437839748  -1.895795646450336   0.015433807135720    2.49144
  -0.965231594860726   1.562519037166242   1.827449284895545   0.012119500017214    2.59089
   0.876841429884276  -0.197101206236151   2.548149468623124   0.005474645634016    2.70199
  -2.575259909241258  -0.963057631993841   0.000000000000000   0.008630111755414    2.74944
  -0.367711919728085  -0.216489057245846   2.723991499125101   0.007673587372148    2.75721
   2.217687273313547  -0.132182138207714  -1.654452490272658   0.008648049921900    2.76999
   2.369293606549843  -1.425540424375958   0.434279419685581   0.007888296430326    2.79898
   0.593407142203226   2.696255723927239   0.663377551712832   0.007021230822996    2.83937
   0.669443584507521  -2.787874651791032   0.362696339439632   0.007100729438770    2.88997
   2.266257026122928   0.124547527141227   1.880905049128796   0.005397993753517    2.94775
  -2.670365994405126   0.993734056232846   0.761567082187705   0.006060236421451    2.94930
   2.213355535530417   1.812664165096462   0.863590981048910   0.004661477063280    2.98839
  -0.193777422612163  -2.561049013433803  -1.593322587864175   0.004763404591038    3.02245
   2.115188022189201   1.907330726386931  -1.112837447001235   0.004220607531259    3.05783
   0.653466441175937  -1.097010687431607  -2.836189833028930   0.003819505075560    3.11037
  -2.823069459209458   0.521056475505796  -1.547531116892460   0.002580595768186    3.26130
   0.996479097228497   1.245792574969984  -2.870356512237619   0.002467210044488    3.28389
  -2.451311036560305  -1.211453007739479   1.879362476577914   0.002006804874717    3.31791
   0.142772369642451   3.034551739774608  -1.375945591292500   0.002220589310593    3.33498
   2.162553960493824  -2.227854884718889  -1.425684542614907   0.001713605344345    3.41651
  -2.284834946377248  -1.796258583499905  -1.901199714599231   0.001446519607954    3.47298
  -2.277719332843885   2.625776958494620  -0.863034964236379   0.001076153321337    3.58156
   0.877816450489217   1.957243777579278   2.994233743259221   0.001011104092922    3.68331
   1.720288336806453  -2.158627503722846   2.448818893939278   0.000863186465057    3.68996
  -1.337044508911711   0.162822940915216  -3.794719051268982   0.000424876911504    4.02667
  -1.922739456094862  -3.561364051672144   0.261815374809043   0.000443272970774    4.05571
  -0.232760012066044  -2.557588715084339   3.252252693639963   0.000211363754165    4.14398
  -2.563392853172885   0.617976595813674   3.536558043872956   0.000169352835886    4.41136
  -1.542986111242149   3.955223294155374   1.312502773323477   0.000156308839937    4.44379
   4.595932458891034   0.287168857363584  -0.116575532166659   0.000144840504077    4.60637

# E_n^{r^2} 3 dimensions, degree 8, asymmetric 43 point rule with points at 43 distinct radii
#                 x1                  x2                  x3              Weight     Radius
  -0.061780495671197   0.000000000000000   0.000000000000000   0.982488943558052    0.06178
  -0.983867032394037   0.209883760471339  -0.384079735734192   0.376709543884598    1.07683
   0.532267184955546  -0.803141783910037  -0.508085117937209   0.430439089443993    1.08926
   0.414296046473365   0.913922616337034  -0.425143117768967   0.380658581487738    1.08979
   0.372180615100887   0.618052682918212   0.822558370255861   0.432966949109894    1.09413
   0.463211379571207  -0.665685021760076   0.751635229739772   0.424903116974477    1.10574
   0.293766480354075   0.152881770112819  -1.093762598428833   0.310536233161439    1.14280
  -0.797263053018031  -0.063111277346304   0.823991651192952   0.384407984316901    1.14829
  -0.633565482468391  -1.062694095951420  -0.101869300156225   0.328305414851823    1.24141
   1.252326518388949   0.143962296250787   0.013337714748475   0.309808475204510    1.26064
  -0.629773701443196   1.194782446215154   0.046155663802589   0.246034854138167    1.35139
  -0.631032622515422  -0.448573570620713  -1.231903626137314   0.182793751990930    1.45499
  -0.494073912548558  -1.303398355334681   1.066434435958070   0.077506728990978    1.75506
  -0.613991516454368   0.964174346872811  -1.340529957348966   0.085940500371528    1.76171
  -0.682521806141528   1.104867806913322   1.292201781624149   0.067485351253454    1.83204
   0.620020521096444  -0.139371599509634   1.801813768740322   0.030484622556623    1.91060
  -1.820983745142347  -0.680984582256305   0.000000000000000   0.048055292903459    1.94415
  -0.260011591962870  -0.153080880431219   1.926152860925869   0.042729051400465    1.94964
   1.568141709511108  -0.093466886278410  -1.169874575022767   0.048155178498115    1.95868
   1.675343575813324  -1.008009300931787   0.307081922589432   0.043924621860291    1.97918
   0.419602214256435   1.906540706201991   0.469078765303072   0.039096516163908    2.00773
   0.473368098227098  -1.971325071379523   0.256465041129302   0.039539190531828    2.04352
   1.602485711083172   0.088068401021574   1.330000715006993   0.030057799744435    2.08437
  -1.888233902893823   0.702676089858258   0.538509248143381   0.033745384132987    2.08547
   1.565078708350343   1.281747123153557   0.610651038871227   0.025956633238050    2.11311
  -0.137021329569912  -1.810935124350159  -1.126649206496456   0.026524199144512    2.13719
   1.495663793974547   1.348686490593664  -0.786894905132900   0.023501727079948    2.16221
   0.462070551833343  -0.775703696117004  -2.005489063667097   0.021268257046282    2.19937
  -1.996211558367655   0.368442567211310  -1.094269746851852   0.014369603664498    2.30609
   0.704617126960916   0.880908377713127  -2.029648554226187   0.013738234764790    2.32206
  -1.733338656749220  -0.856626636861426   1.328909951495787   0.011174547768062    2.34612
   0.100955310740247   2.145752113056058  -0.972940458146658   0.012364969627639    2.35819
   1.529156570147010  -1.575331296484303  -1.008111207915844   0.009541916614439    2.41584
  -1.615622284475357  -1.270146625157329  -1.344351210583046   0.008054695630934    2.45577
  -1.610590785893617   1.856704693234939  -0.610257875612628   0.005992374668084    2.53254
   0.620709964778031   1.383980347561482   2.117242984316173   0.005630159228328    2.60450
   1.216427548551972  -1.526380145938211   1.731576445802200   0.004806505359863    2.60919
  -0.945433238999707   0.115133205653882  -2.683271573850066   0.002365854001538    2.84729
  -1.359582107859611  -2.518264671211374   0.185131426946372   0.002468289293402    2.86782
  -0.164586182920951  -1.808488323922335   2.299689933805049   0.001176942709833    2.93024
  -1.812592469323699   0.436975441514430   2.500724174882422   0.000943012137408    3.11930
  -1.091055942535965   2.796765212404239   0.928079611343177   0.000870378889575    3.14223
   3.249815007557205   0.203059046387378  -0.082431349315474   0.000806519433928    3.25720

>> # evaluating formula 1 with 45 points
# r3_45_9g.txt:6 formula 1   : problem  G, 3_45_9  (d=3 n=45 o=9 plus 0/66 of order 10) quality P
# evaluating formula 2 with 45 points
# r3_45_9g.txt:57 formula 2   : problem E2, 3_45_9  (d=3 n=45 o=9 plus 0/66 of order 10) quality P
# G_n 3 dimensions, degree 9, symmetric 45 point rule with points at 4 distinct radii: 1+12+20+12=45
# probably:
# S.I. Konjaev. Ninth-order quadrature formulas invariant with respect to
# the icosahedral group. Soviet Math. Dokl., 18:497–501, 1977.
#                x1                 x2                 x3             Weight     Radius     cos1     cos2     cos3
  0.000000000000000  0.000000000000000  0.000000000000000  0.207407407407410    0.00000  0.00000  0.00000  0.00000
  0.063860838773439 -1.223912127824363 -1.223912127824363  0.057870370370370    1.73205  1.00000 -0.18759 -0.44721
 -1.223912127824363  0.063860838773439 -1.223912127824363  0.057870370370370    1.73205  0.44721 -0.79465 -0.44721
 -1.223912127824363 -1.223912127824363  0.063860838773439  0.057870370370370    1.73205  0.44721 -0.79465 -1.00000
  1.576699427250769 -0.506961002497765 -0.506961002497765  0.057870370370370    1.73205  0.44721  0.79465  0.44721
 -0.506961002497765  1.576699427250769 -0.506961002497765  0.057870370370370    1.73205 -0.44721 -0.18759  0.44721
 -0.506961002497765 -0.506961002497765  1.576699427250769  0.057870370370370    1.73205 -0.44721 -0.18759 -0.44721
  0.506961002497765  0.506961002497765 -1.576699427250769  0.057870370370370    1.73205  0.44721  0.18759  0.44721
  0.506961002497765 -1.576699427250769  0.506961002497765  0.057870370370370    1.73205  0.44721  0.18759 -0.44721
 -1.576699427250769  0.506961002497765  0.506961002497765  0.057870370370370    1.73205 -0.44721 -0.79465 -0.44721
  1.223912127824363  1.223912127824363 -0.063860838773439  0.057870370370370    1.73205 -0.44721  0.79465  1.00000
  1.223912127824363 -0.063860838773439  1.223912127824363  0.057870370370370    1.73205 -0.44721  0.79465  0.44721
 -0.063860838773439  1.223912127824363  1.223912127824363  0.057870370370370    1.73205 -1.00000  0.18759  0.44721
  2.923987610591249  0.474497867808079  0.474497867808079  0.004629629629630    3.00000 -0.18759  1.00000  0.79465
  0.474497867808079  2.923987610591249  0.474497867808079  0.004629629629630    3.00000 -0.79465  0.33333  0.79465
  0.474497867808079  0.474497867808079  2.923987610591249  0.004629629629630    3.00000 -0.79465  0.33333  0.18759
  1.732050807568873  1.732050807568873  1.732050807568873  0.004629629629630    3.00000 -0.79465  0.74536  0.79465
  2.403092127540170  0.889224211405935 -1.560265531377233  0.004629629629630    3.00000  0.18759  0.74536  0.79465
  2.403092127540170 -1.560265531377233  0.889224211405935  0.004629629629630    3.00000  0.18759  0.74536  0.18759
  1.560265531377233 -0.889224211405935 -2.403092127540170  0.004629629629630    3.00000  0.79465  0.33333  0.18759
  1.560265531377233 -2.403092127540170 -0.889224211405935  0.004629629629630    3.00000  0.79465  0.33333 -0.18759
  0.889224211405935  2.403092127540170 -1.560265531377233  0.004629629629630    3.00000 -0.18759  0.33333  0.79465
  0.889224211405935 -1.560265531377233  2.403092127540170  0.004629629629630    3.00000 -0.18759  0.33333 -0.18759
 -0.889224211405935  1.560265531377233 -2.403092127540170  0.004629629629630    3.00000  0.18759 -0.33333  0.18759
 -0.889224211405935 -2.403092127540170  1.560265531377233  0.004629629629630    3.00000  0.18759 -0.33333 -0.79465
 -1.560265531377233  2.403092127540170  0.889224211405935  0.004629629629630    3.00000 -0.79465 -0.33333  0.18759
 -1.560265531377233  0.889224211405935  2.403092127540170  0.004629629629630    3.00000 -0.79465 -0.33333 -0.18759
 -2.403092127540170  1.560265531377233 -0.889224211405935  0.004629629629630    3.00000 -0.18759 -0.74536 -0.18759
 -2.403092127540170 -0.889224211405935  1.560265531377233  0.004629629629630    3.00000 -0.18759 -0.74536 -0.79465
 -1.732050807568873 -1.732050807568873 -1.732050807568873  0.004629629629630    3.00000  0.79465 -0.74536 -0.79465
 -0.474497867808079 -0.474497867808079 -2.923987610591249  0.004629629629630    3.00000  0.79465 -0.33333 -0.18759
 -0.474497867808079 -2.923987610591249 -0.474497867808079  0.004629629629630    3.00000  0.79465 -0.33333 -0.79465
 -2.923987610591249 -0.474497867808079 -0.474497867808079  0.004629629629630    3.00000  0.18759 -1.00000 -0.79465
  2.736750716301690  2.736750716301690 -0.142797176597565  0.000462962962963    3.87298 -0.44721  0.79465  1.00000
  2.736750716301690 -0.142797176597565  2.736750716301690  0.000462962962963    3.87298 -0.44721  0.79465  0.44721
 -0.142797176597565  2.736750716301690  2.736750716301690  0.000462962962963    3.87298 -1.00000  0.18759  0.44721
 -3.525607099417704  1.133599263526443  1.133599263526443  0.000462962962963    3.87298 -0.44721 -0.79465 -0.44721
  1.133599263526443 -3.525607099417704  1.133599263526443  0.000462962962963    3.87298  0.44721  0.18759 -0.44721
  1.133599263526443  1.133599263526443 -3.525607099417704  0.000462962962963    3.87298  0.44721  0.18759  0.44721
 -1.133599263526443 -1.133599263526443  3.525607099417704  0.000462962962963    3.87298 -0.44721 -0.18759 -0.44721
 -1.133599263526443  3.525607099417704 -1.133599263526443  0.000462962962963    3.87298 -0.44721 -0.18759  0.44721
  3.525607099417704 -1.133599263526443 -1.133599263526443  0.000462962962963    3.87298  0.44721  0.79465  0.44721
  0.142797176597565 -2.736750716301690 -2.736750716301690  0.000462962962963    3.87298  1.00000 -0.18759 -0.44721
 -2.736750716301690  0.142797176597565 -2.736750716301690  0.000462962962963    3.87298  0.44721 -0.79465 -0.44721
 -2.736750716301690 -2.736750716301690  0.142797176597565  0.000462962962963    3.87298  0.44721 -0.79465 -1.00000

# E_n^{r^2} 3 dimensions, degree 9, symmetric 45 point rule with points at 4 distinct radii: 1+12+20+12=45
# probably:
# S.I. Konjaev. Ninth-order quadrature formulas invariant with respect to
# the icosahedral group. Soviet Math. Dokl., 18:497–501, 1977.
#                x1                 x2                 x3             Weight     Radius     cos1     cos2     cos3
  0.000000000000000  0.000000000000000  0.000000000000000  1.154912473416940    0.00000  0.00000  0.00000  0.00000
  0.045156432148960 -0.865436565161066 -0.865436565161066  0.322241203520354    1.22474  1.00000 -0.18759 -0.44721
 -0.865436565161066  0.045156432148960 -0.865436565161066  0.322241203520354    1.22474  0.44721 -0.79465 -0.44721
 -0.865436565161066 -0.865436565161066  0.045156432148960  0.322241203520354    1.22474  0.44721 -0.79465 -1.00000
  1.114894856901968 -0.358475562663301 -0.358475562663301  0.322241203520354    1.22474  0.44721  0.79465  0.44721
 -0.358475562663301  1.114894856901968 -0.358475562663301  0.322241203520354    1.22474 -0.44721 -0.18759  0.44721
 -0.358475562663301 -0.358475562663301  1.114894856901968  0.322241203520354    1.22474 -0.44721 -0.18759 -0.44721
  0.358475562663301  0.358475562663301 -1.114894856901968  0.322241203520354    1.22474  0.44721  0.18759  0.44721
  0.358475562663301 -1.114894856901968  0.358475562663301  0.322241203520354    1.22474  0.44721  0.18759 -0.44721
 -1.114894856901968  0.358475562663301  0.358475562663301  0.322241203520354    1.22474 -0.44721 -0.79465 -0.44721
  0.865436565161066  0.865436565161066 -0.045156432148960  0.322241203520354    1.22474 -0.44721  0.79465  1.00000
  0.865436565161066 -0.045156432148960  0.865436565161066  0.322241203520354    1.22474 -0.44721  0.79465  0.44721
 -0.045156432148960  0.865436565161066  0.865436565161066  0.322241203520354    1.22474 -1.00000  0.18759  0.44721
  2.067571467554528  0.335520659985651  0.335520659985651  0.025779296281628    2.12132 -0.18759  1.00000  0.79465
  0.335520659985651  2.067571467554528  0.335520659985651  0.025779296281628    2.12132 -0.79465  0.33333  0.79465
  0.335520659985651  0.335520659985651  2.067571467554528  0.025779296281628    2.12132 -0.79465  0.33333  0.18759
  1.224744871391590  1.224744871391590  1.224744871391590  0.025779296281628    2.12132 -0.79465  0.74536  0.79465
  1.699242739199667  0.628776469880398 -1.103274337688476  0.025779296281628    2.12132  0.18759  0.74536  0.79465
  1.699242739199667 -1.103274337688476  0.628776469880398  0.025779296281628    2.12132  0.18759  0.74536  0.18759
  1.103274337688476 -0.628776469880398 -1.699242739199667  0.025779296281628    2.12132  0.79465  0.33333  0.18759
  1.103274337688476 -1.699242739199667 -0.628776469880398  0.025779296281628    2.12132  0.79465  0.33333 -0.18759
  0.628776469880398  1.699242739199667 -1.103274337688476  0.025779296281628    2.12132 -0.18759  0.33333  0.79465
  0.628776469880398 -1.103274337688476  1.699242739199667  0.025779296281628    2.12132 -0.18759  0.33333 -0.18759
 -0.628776469880398  1.103274337688476 -1.699242739199667  0.025779296281628    2.12132  0.18759 -0.33333  0.18759
 -0.628776469880398 -1.699242739199667  1.103274337688476  0.025779296281628    2.12132  0.18759 -0.33333 -0.79465
 -1.103274337688476  1.699242739199667  0.628776469880398  0.025779296281628    2.12132 -0.79465 -0.33333  0.18759
 -1.103274337688476  0.628776469880398  1.699242739199667  0.025779296281628    2.12132 -0.79465 -0.33333 -0.18759
 -1.699242739199667  1.103274337688476 -0.628776469880398  0.025779296281628    2.12132 -0.18759 -0.74536 -0.18759
 -1.699242739199667 -0.628776469880398  1.103274337688476  0.025779296281628    2.12132 -0.18759 -0.74536 -0.79465
 -1.224744871391590 -1.224744871391590 -1.224744871391590  0.025779296281628    2.12132  0.79465 -0.74536 -0.79465
 -0.335520659985651 -0.335520659985651 -2.067571467554528  0.025779296281628    2.12132  0.79465 -0.33333 -0.18759
 -0.335520659985651 -2.067571467554528 -0.335520659985651  0.025779296281628    2.12132  0.79465 -0.33333 -0.79465
 -2.067571467554528 -0.335520659985651 -0.335520659985651  0.025779296281628    2.12132  0.18759 -1.00000 -0.79465
  1.935174989914068  1.935174989914068 -0.100972851906431  0.002577929628163    2.73861 -0.44721  0.79465  1.00000
  1.935174989914068 -0.100972851906431  1.935174989914068  0.002577929628163    2.73861 -0.44721  0.79465  0.44721
 -0.100972851906431  1.935174989914068  1.935174989914068  0.002577929628163    2.73861 -1.00000  0.18759  0.44721
 -2.492980687797695  0.801575726387625  0.801575726387625  0.002577929628163    2.73861 -0.44721 -0.79465 -0.44721
  0.801575726387625 -2.492980687797695  0.801575726387625  0.002577929628163    2.73861  0.44721  0.18759 -0.44721
  0.801575726387625  0.801575726387625 -2.492980687797695  0.002577929628163    2.73861  0.44721  0.18759  0.44721
 -0.801575726387625 -0.801575726387625  2.492980687797695  0.002577929628163    2.73861 -0.44721 -0.18759 -0.44721
 -0.801575726387625  2.492980687797695 -0.801575726387625  0.002577929628163    2.73861 -0.44721 -0.18759  0.44721
  2.492980687797695 -0.801575726387625 -0.801575726387625  0.002577929628163    2.73861  0.44721  0.79465  0.44721
  0.100972851906431 -1.935174989914068 -1.935174989914068  0.002577929628163    2.73861  1.00000 -0.18759 -0.44721
 -1.935174989914068  0.100972851906431 -1.935174989914068  0.002577929628163    2.73861  0.44721 -0.79465 -0.44721
 -1.935174989914068 -1.935174989914068  0.100972851906431  0.002577929628163    2.73861  0.44721 -0.79465 -1.00000

>> # evaluating formula 1 with 182 points
# r3_182_14Ss.txt:3 formula 1   : problem  S, 3_182_14  (d=3 n=182 o=14 plus 102/136 of order 15) quality NO (26 negative weights, stability factor 6.458595)
S 3 dimensions, degree 14, asymmetric 182 point rule with points at 182 distinct radii (26 negative weights, stability factor 6.458595)
#                 x1                  x2                  x3              Weight     Radius
   0.000000000000000   0.000000000000000   0.000000000000000   0.272368100233781    0.00000
  -0.164540267911257  -0.046075734818074   0.030990629644127  -0.458204507031329    0.17366
  -0.285506016771156  -0.047691232327119   0.055393882320631   0.907995524753825    0.29471
  -0.299115234978351  -0.005712632053173   0.118981467752429  -0.661523857716967    0.32196
   0.124322139079422  -0.303538514567711   0.057810704429575   0.091950557701856    0.33307
   0.314056540432796  -0.143214157011793  -0.073101048317533  -0.441446580361941    0.35283
   0.165588049070956   0.325122936491196   0.014627689450087  -0.466626084909189    0.36516
  -0.210674417040635  -0.031801882910128   0.297053133008576   0.152924329789085    0.36556
  -0.288719809742088   0.170485318717588   0.169735534634660   0.155564880535922    0.37581
   0.182629098546798   0.332560781367277   0.000000000000000   0.482516788958966    0.37941
   0.412841398530056  -0.059822968316913   0.089154699607001   0.122171708418898    0.42657
   0.360913455243658  -0.207238329756702  -0.138944011591518   0.718053590872022    0.43876
  -0.122946819813997   0.432549464317246  -0.152163214633758   0.060538088520227    0.47473
   0.428335139684126   0.006905306162080  -0.212441907571305   0.072833569045693    0.47817
  -0.095792045957477  -0.140040245605817  -0.462370735155728   0.075432402449742    0.49252
  -0.468427686590843  -0.103445753122605  -0.125992317644332  -0.215548920338992    0.49598
   0.220855229842624  -0.421432600867872  -0.183662694469373  -0.252883726367595    0.51001
   0.186728703888111   0.364713739771277   0.326768780644660   0.142444745944393    0.52408
  -0.416528078103650   0.096018073360173  -0.308791648791175   0.074408693209949    0.52732
   0.088991667347627   0.258008559911867  -0.474933822625397   0.053562467624115    0.54777
   0.455040266777787  -0.237385995055115  -0.195091239311875  -0.634043737271088    0.54907
   0.214787750386721  -0.463252279844600  -0.237758433462039   0.242538865264082    0.56326
  -0.005834354013555  -0.556255078239625  -0.169820468664573   0.406313922304471    0.58163
  -0.503844244471415  -0.148571084986640  -0.295945512614762   0.434709108246940    0.60292
  -0.045179105050861   0.574276577165421   0.226761840198113   0.058866499127488    0.61908
   0.514176859949805  -0.257884273778340  -0.230738992244953   0.332913845426213    0.61978
   0.035153454455116  -0.603514069500968  -0.165913396868483  -0.715359128449758    0.62689
   0.359414426673972   0.062566555190308  -0.518680442654572   0.023836996157300    0.63413
  -0.463827236029225  -0.144732484169279  -0.426828067253606  -0.735098594615793    0.64673
  -0.170839552402473  -0.533520441582588   0.328947371947890   0.054695884692795    0.64964
   0.214761016123879  -0.191602519361282   0.589246218055782   0.310948152614808    0.65578
   0.207919721320412   0.490569083438569   0.393800636765182  -0.371660975138176    0.66255
   0.062665255093996  -0.646195934301804  -0.136534445430926   0.374832356742944    0.66343
   0.413249043413050  -0.530260071730806  -0.011030804174540   0.049180150096772    0.67236
   0.243377666660610  -0.506890961811720   0.377117898532281   0.036106300136061    0.67704
  -0.394925657281217  -0.167480849382911  -0.524761294621686   0.835462198957345    0.67778
   0.192667340303756   0.501374588821224   0.441568349319101   0.281294023516638    0.69533
   0.403011765337624  -0.013661511673622   0.570646598371866   0.047917488821417    0.69874
  -0.322135370159981  -0.182200347670127  -0.594661967569829  -0.464591864562289    0.70042
  -0.679254826925254   0.033258717741156   0.181694843357115   0.302258382614019    0.70392
  -0.529753712704513  -0.464570394722796   0.070484929285714   0.054790657442842    0.70812
   0.243287739956155  -0.201150425401250   0.634601466502792  -0.568815944766571    0.70878
   0.296238970841447   0.587081939436569   0.271373833003487   0.084519565530481    0.71138
   0.644398040022887   0.345099345941182   0.008545577428477   0.043608536693251    0.73104
  -0.457783778257088  -0.292984035200834   0.496590244975695   0.044023469012921    0.73621
   0.293079066409021  -0.194118990884123  -0.647135804611559   0.042958592250172    0.73645
  -0.307753217186268   0.417199237444194  -0.524466952375898   0.042253452818083    0.73745
   0.458537536571449   0.457928272650358  -0.362066816180314   0.046783234297729    0.74233
   0.508157857727737   0.357823726529359   0.413127782831278   0.043015762849117    0.74628
   0.262654627596142  -0.219341541770395   0.669171343914021   0.322305103525194    0.75159
  -0.199660579999090   0.015831997744487  -0.725364331929070   0.063365973128123    0.75251
  -0.648753147290589   0.382537490886509  -0.125323605416919   0.193097681881928    0.76349
   0.191233052688337   0.725926013981991  -0.168512207548355   0.043322699876939    0.76937
  -0.626585249594257  -0.002971922227830  -0.447470983924113   0.062612826263836    0.76997
   0.586425897728065  -0.309905784160983   0.403677660331764   0.036379551046981    0.77646
  -0.017913962764963  -0.673900663387594  -0.387946569624636   0.051400488500182    0.77780
  -0.745868847151787   0.076511427888592   0.212082629949174  -0.941848273625960    0.77920
  -0.660216037584849   0.180202628927843   0.374187596197164   0.073020021738379    0.77998
  -0.090477480263922  -0.312163497942297   0.711556937424220   0.040768320294912    0.78227
  -0.689019129927465   0.356991862304261  -0.115773135303088  -0.189827694782070    0.78460
  -0.413066545384192  -0.587490576619939  -0.322914733715334   0.036616217078801    0.78743
  -0.761334332479260   0.137104555755049   0.152219056065123   0.314361585322226    0.78842
  -0.257499682975816   0.724633578024022  -0.188985365294190   0.041200206272784    0.79191
   0.036533210267049   0.595141371278202  -0.525084718406911   0.034532334395971    0.79451
  -0.460022299317180   0.619309509769690   0.207470521164103   0.053710093155887    0.79888
   0.801447314682525   0.000000000000000   0.000000000000000   0.030487412740632    0.80145
  -0.360181961227953   0.040381461510408   0.715590041921150   0.041568798579872    0.80214
   0.086727220971029   0.161167143534847   0.781570860396961   0.236942671610699    0.80271
  -0.767916856856007   0.051685719948067   0.244140977325256   0.444989836837858    0.80745
   0.732493516238883   0.114899007620235  -0.355732857211907   0.032846339345501    0.82237
   0.739307343953205   0.069739245558855   0.356545449846043   0.033019480155143    0.82375
  -0.158684472255136  -0.318354075917809  -0.745465753425439   0.251742312583977    0.82598
   0.739245715246796  -0.375542467713034   0.036966987845198   0.193101525729806    0.82999
  -0.302688749965945   0.393869443466423   0.670667863068708   0.104085753714582    0.83460
   0.173734904643806   0.249881350686461  -0.781100607854575   0.032837833254198    0.83830
  -0.296154265970384  -0.786450145563728   0.012014292198755   0.035016951650227    0.84045
   0.118887268758711   0.195608199480256   0.810302506148946  -0.383292835035506    0.84201
   0.747673111315786  -0.386950448043855   0.030126903107474  -0.172391343319104    0.84241
   0.432386639021121  -0.647587126511667   0.339194728252267   0.022520240093977    0.84934
   0.520095799722592   0.170109332113866  -0.649949992079146   0.025320566988494    0.84963
   0.071800607448114  -0.810433261719756   0.299915267444219   0.031398490586798    0.86713
   0.163420903866058   0.225175564841242   0.824157027241226   0.209773483775741    0.86985
   0.385869506740387  -0.553002214459920  -0.560095781644226   0.029518211494478    0.87659
  -0.796689324035767   0.320487583425490  -0.209629930081929   0.050862960127497    0.88395
  -0.836647842851986  -0.283308171322163   0.041407610002434   0.026883834208534    0.88428
  -0.132607702059107  -0.348188221705423  -0.804436689016469  -0.436313893550403    0.88653
  -0.041778277391530   0.881631566417573   0.147885559927706   0.031556144434963    0.89492
   0.563927136888714   0.697793844062197  -0.020215017548709   0.029052095228926    0.89741
   0.636445397053626  -0.223392243093556  -0.594920173947076   0.022531626059967    0.89939
  -0.004194872323523  -0.458455920804765  -0.782712614036990   0.057630198855968    0.90710
  -0.146377939545383  -0.342508544540592  -0.828141667586530   0.258238704760257    0.90805
   0.042809710663976  -0.538296069419333   0.736474806342441   0.269274048992339    0.91323
   0.329865224267087   0.587089026644216  -0.617910433147153   0.021338404256888    0.91395
  -0.333016224220959  -0.720531249671906   0.457015671896517   0.024836356070481    0.91593
  -0.738850799375523  -0.367296394885808  -0.409262619246825   0.029330821594674    0.92103
  -0.564562246420675   0.373010713295442  -0.625954353697604   0.026003509813910    0.92178
   0.041244949970719  -0.512369034947348   0.766549361490571  -0.449964836994696    0.92294
  -0.163278709323386   0.749157577723956   0.515099204240900   0.027851432263869    0.92370
  -0.259355376512875   0.340261194119429   0.819676180547128   0.344199057024870    0.92461
  -0.311022982449422   0.342160428707655   0.801919604630239  -0.712947449403726    0.92568
   0.150351586017669  -0.120266876355487  -0.905472624323041   0.024539673639857    0.92572
  -0.594301437380347  -0.659801248752300   0.274213469909586   0.017117620067227    0.92937
   0.633426024740229  -0.632939868288002  -0.259200208058258   0.024750197852750    0.93222
  -0.158332878212885   0.413091856684163  -0.821291905970275   0.024890127048502    0.93286
  -0.552653863035196   0.666301420016006  -0.353913273528118   0.021728361153651    0.93522
   0.035555915715795  -0.486960129866230   0.797802070992449   0.213885850717953    0.93535
  -0.721645279541794  -0.420141408836597   0.422699533974556   0.021995459327209    0.93593
  -0.354735526393471   0.334064718727447   0.799453504149252   0.350277237249998    0.93625
  -0.687346514748670   0.624542263951955   0.130318907992583   0.064393095434292    0.93781
   0.793824750250747  -0.498634203639416   0.057564183032635   0.025728124470937    0.93921
   0.573949528943889   0.085408000315802   0.738623518470644   0.021599636958927    0.93930
   0.470908014561793  -0.810964300982874   0.054161870300086   0.022546874758760    0.93934
  -0.605781984053732   0.656413542400972   0.292076183206695   0.175539278119911    0.93977
   0.069918797226812  -0.009591489019279   0.938528799611587   0.023385960359841    0.94118
  -0.591897759097474   0.694771208264368   0.230585458097104  -0.458876985073458    0.94139
   0.806592717894332   0.444357594024391   0.208122798648741   0.020959170136770    0.94412
   0.792195647427582   0.448614769463000  -0.257067241959128   0.021844854921511    0.94600
  -0.402546184696619  -0.465102772445592   0.719600244527098   0.020919019774189    0.94667
   0.289046359884951  -0.840023530197971  -0.327512269104703   0.019019649719442    0.94681
  -0.568340129792412   0.728388270517474   0.209576754582943   0.269724444156032    0.94736
  -0.366400750616309  -0.628519704208647  -0.609354791468026   0.022097581793281    0.94900
  -0.442816220642821   0.061159676164573  -0.838421150299546   0.019540738977193    0.95015
   0.552284211658385   0.468536083036472   0.615685295907066   0.019705172360047    0.95059
  -0.237154413514830   0.735520590064913  -0.554391675109831   0.019139162510153    0.95110
   0.373841903912632  -0.559337343042225   0.673675454869719   0.018864529542860    0.95208
   0.105316870915336   0.879669507014937  -0.351831808770976   0.018999140018069    0.95326
  -0.932750137282253  -0.076643656758154  -0.193217180144644   0.018725201780954    0.95563
   0.715026659925871  -0.266393547432584   0.575789777629954   0.018128504940478    0.95591
  -0.668903668872196  -0.114405538958878   0.674135961780232   0.019318226336061    0.95655
   0.105233966392488  -0.951438807965135  -0.028924841955818   0.015848570944871    0.95768
  -0.207610947111581  -0.892183653331815  -0.283230201523514   0.017935563692705    0.95881
   0.568170631847146   0.694883699370840   0.339871457809528   0.013199978041716    0.95979
   0.175975685432338   0.627040699955995   0.706076947307210   0.017587092372500    0.96057
   0.918501867947152  -0.177334233747009   0.224681752190130   0.016349958066720    0.96207
   0.951506752517039   0.155089831715524  -0.020666400951439   0.015564251778079    0.96428
  -0.302934798686737  -0.129419862218026   0.907347559034427   0.014467682880456    0.96530
  -0.569690919659384  -0.288799329044269  -0.724137131468783   0.014106263127488    0.96557
   0.868253144472824  -0.260161580679010  -0.336723419443698   0.192268003657391    0.96692
   0.254941838424792   0.898151941115087   0.252734600138486   0.228351902988051    0.96724
   0.621554694528078   0.406339874778026  -0.621080729726163   0.014085906901572    0.96808
  -0.227883205475887   0.929735916859421  -0.145051667903194   0.013525295512567    0.96818
   0.655672168524285  -0.603418987654125   0.379969926158649   0.012449231032038    0.96871
   0.256665453126882   0.909737239367622   0.213944054337086  -0.395205985994880    0.96916
   0.527616010571261   0.004646081546400  -0.813688584215714   0.012543476649904    0.96979
   0.261106305115596   0.918951796621254   0.168620775636681   0.195449681632772    0.97009
   0.853815621298188  -0.271268813057928  -0.374903810942026  -0.321179822353760    0.97115
   0.383821323326825  -0.358390785817470  -0.819103770205000   0.010247258421741    0.97298
  -0.792190931787666   0.051926779414435  -0.563701252761620   0.013270661145837    0.97366
   0.834956310779201  -0.288848610420185  -0.409808140603711   0.155507152336577    0.97392
   0.839665149314246   0.170285205299843   0.468806714974856   0.011435214988378    0.97663
  -0.187964219205898  -0.936000835653301   0.205932748592221   0.010322338443965    0.97665
   0.035468217222793  -0.773797509654001  -0.595980262792650   0.010748629622139    0.97735
   0.856383665488033   0.036342881592225  -0.475181176251479   0.012999237790032    0.98006
   0.405698914927069  -0.219034844650953   0.868228212093639   0.009431517794509    0.98305
   0.271696371396247   0.302187611235911  -0.895524413917421   0.009249172240481    0.98341
  -0.088090269864266   0.085195717713929  -0.977192812436460   0.008555310019875    0.98485
   0.275660178292462  -0.861481356879782   0.399114094870425   0.008440180205552    0.98865
   0.128200643649224   0.662530865210733  -0.723126534546899   0.007633420326965    0.98909
  -0.530614405511293  -0.833862833236567   0.045457028246690   0.007283056559867    0.98942
  -0.708419874222951  -0.666539627156092  -0.184994130039496   0.179918796469259    0.99013
  -0.801375592394624   0.256056456376421   0.523569877734334   0.009413870082788    0.99091
  -0.755413217700750  -0.629112362177899  -0.129375789699492   0.147140630230438    0.99155
  -0.732037218449131  -0.651401927031303  -0.160708529880715  -0.300722156695047    0.99299
  -0.079303947064262  -0.792379683233257   0.600936859676218   0.005595079739658    0.99764
   0.582987949988195   0.769865584960881  -0.254908501581816   0.177249385366683    0.99877
  -0.949584106916608  -0.183391967955404   0.275228415503966   0.006142981437443    1.00553
   0.604313156635105   0.771299920380785  -0.230212163125210  -0.287985511205999    1.00653
   0.463927900427082  -0.637271435833379  -0.628581842068032   0.004238538702035    1.00820
  -0.974377803862155   0.253468616662023   0.082818755984192   0.005603777459432    1.01021
   0.624412400407263   0.771765407803407  -0.205597586974559   0.125832347823581    1.01380
  -0.838879198935362   0.451937641100510  -0.363473744437315   0.003482542311575    1.01984
  -0.561114764862006   0.868822726164474  -0.040423712218624   0.267309767112310    1.03505
  -0.561222355407036   0.868954229312493  -0.038588740229227  -0.267233847175003    1.03515
  -0.471837591080187   0.518275877734486  -0.768832654842035   0.001709450545518    1.04036
  -0.099286462068407   1.001054701618312   0.282071734332166   0.002194754246416    1.04476
   0.372037371999577   0.307741083571376   0.985414129203293   0.000569788772729    1.09734
  -0.372500796220553   0.502268516674734   0.902532345979775   0.088835078782528    1.09800
  -0.379471820691115   0.499410074087266   0.928805195104941  -0.128859528842403    1.12075
  -0.384888462623530   0.498956348721603   0.951245544942612   0.049362860822947    1.14104
  -0.638058642166554  -0.734448314757244   0.599338716363741   0.000205677055314    1.14269
  -0.933839356408375  -0.617328732501791  -0.370445705738179   0.000172206680420    1.17914
   0.892478854507492  -1.115953108443451  -0.150333997543177   0.000002754435781    1.43683

>> # evaluating formula 1 with 220 points
# r3_220_14Gsg.txt:3 formula 1   : problem  G, 3_220_13  (d=3 n=220 o=13 plus 119/120 of order 14) quality N (81 negative weights, stability factor 59.098185)
# evaluating formula 2 with 220 points
# r3_220_14Gsg.txt:226 formula 2   : problem E2, 3_220_14  (d=3 n=220 o=14 plus 0/136 of order 15) quality N (81 negative weights, stability factor 59.098185)
G 3 dimensions, degree 13, asymmetric 220 point rule with points at 220 distinct radii (81 negative weights, stability factor 59.098185)
#                 x1                  x2                  x3              Weight     Radius
   0.000000000000000   0.000000000000000   0.000000000000000   0.024506146386244    0.00000
   0.959881737523679  -0.307809998440880   0.434665581546499   0.268593186551859    1.09775
  -0.605763637057306  -0.743804591839435   0.569701265162456  -0.223559326652955    1.11569
  -0.482486701708893   0.742621679978674  -0.768875254546132  -0.209070830272149    1.17280
   0.654871471650803   0.099524554629796  -0.992371498924829   0.414155852948733    1.19313
  -0.711213885917637  -0.962428368861819   0.285048265985502   0.362630167379750    1.23018
  -1.228480895641120   0.125883459433600   0.000000000000000   0.229007388933933    1.23491
  -0.485873204006933   1.107214795951482  -0.338069844197639   0.398632533689203    1.25550
  -0.873740104391505   0.698335940758017  -0.758131531865951   0.366035160835076    1.35124
  -0.648544313520631   0.981903108057728  -0.680799881147175  -0.291004032127102    1.35950
   0.861335547930270  -0.873125077132902   0.590138456451259  -0.643658138395797    1.36107
   0.267587801646181  -1.072316650662180   0.801529667026788   0.751520087976061    1.36525
  -0.842663705181584   1.055845971470732   0.404969808401532  -0.366037396050258    1.41028
   0.883280133623214  -0.021786812206113  -1.194664349452723  -0.699092817872479    1.48589
   1.551458883808437   0.000000000000000   0.000000000000000  -0.238746471490238    1.55146
   0.021139814518423  -0.249858465488304   1.532962786383152   0.083729078206025    1.55334
  -0.263284286134001  -1.397008598520329   0.696778970304722  -0.590704861881962    1.58318
   0.748809140206565   1.317284966832216   0.568296932636805   0.374275600119025    1.61831
   0.142892233178368  -0.980508312030347   1.288886791762645  -0.281104720858891    1.62574
  -0.657336773601075   1.027086780661034   1.083210934348180   0.482444782168802    1.63106
   0.668172349771077   1.234982741488324   0.835085881817311  -0.253341467229562    1.63371
  -1.347481079151250   0.551409897064720  -0.774308180087685  -0.202014831901097    1.64903
  -1.555137460754958  -0.503308121414160  -0.397272265969452  -0.607170070179277    1.68214
   0.827515275439335   1.468173127022384  -0.214679380149544  -0.280087968238322    1.69894
   1.356292116941303  -1.024696601858460   0.173356602725411   0.443243985787064    1.70868
   0.708341010039910  -0.378876482098167  -1.548902966622426   0.356800640573242    1.74482
   1.437377339898038   0.294104737806085  -1.022544667343071   0.497418720161690    1.78834
  -1.605888293985348  -0.419196883945043  -0.822016882872350   0.431780118952736    1.85211
   1.849428628999772   0.174421158805120  -0.205968883763124   0.474154570179259    1.86902
  -1.767499797551942  -0.601319108379940  -0.252368139629791   0.241317946105764    1.88397
  -0.443933466592562   0.610767778515154  -1.734616218658639   0.144310303834521    1.89183
   1.853450489075170  -0.290151748891602  -0.246104325614154  -0.523856468912626    1.89210
  -0.668601322695217  -1.050611893080434   1.456604654961898   0.226356180168376    1.91638
   0.949811948176861   1.566772998105832  -0.683977411389066   0.296917218052899    1.95570
   1.421960755940660   0.821251405803807  -1.089809735450913  -0.307689631445277    1.97081
  -0.452165636361436  -1.686380534593096   0.929774582233373   0.483202186717265    1.97808
  -0.701642131781884   0.888328724173461   1.631800105430532  -0.353929120796932    1.98600
   0.098456994455257  -1.893106224116953  -0.625496946178367   0.038987547717223    1.99619
   1.841983146390435  -0.743952734379801  -0.198344724471878   0.580675316311489    1.99642
   1.314301528037247  -0.716793237485841   1.365588909005244   0.134415859812479    2.02633
   1.816369916968089   0.236108090078166  -0.877518306970935  -0.130701739580945    2.03101
  -0.163446710560751   1.666178309425574   1.174641004193608  -0.387169710414495    2.04515
  -0.023658205702296  -1.092603812261799   1.748976585420770   0.450554112487239    2.06234
  -0.404979902767503  -1.134881227538963   1.673838234570918  -0.399399166579028    2.06245
  -0.445049387219039   0.200591790831428  -2.011886486628900  -0.185390147989633    2.07026
   0.357702565321086  -0.935559307508470   1.827024703467906  -0.174078039339850    2.08356
   1.901989483430220   0.744316767197777  -0.516071519350579  -0.338851771185084    2.10663
  -0.234526693076342   1.788716478413922   1.130168646914678   0.282010303206953    2.12880
   1.776272541453722  -1.191846355051405  -0.071723361934778  -0.962311930704405    2.14028
   1.844545539450339   0.898391544466115  -0.666080554398761   0.290843613143031    2.15711
  -0.139682582053347  -0.478157230228031  -2.129776946208362  -0.277576774667882    2.18726
  -0.462059728316696  -1.739008116073368   1.261115523277344  -0.426999029580815    2.19728
   0.714649978996690   1.508863216662732   1.458914152303722   0.281343267461705    2.21717
  -0.622631177321905   0.863272121349150   1.988627097299424   0.159720673255280    2.25556
   1.825509173755582  -1.331849391767817  -0.073219196340826   0.501796895614439    2.26090
  -0.370922031515816  -0.279307007320872  -2.247149150551646   0.915098779211847    2.29462
   0.845269271069574  -1.020796909120580  -1.880520565751312  -0.821290208621443    2.30062
  -0.726139685071392  -1.772511352924336   1.313410101661145   0.462300689132389    2.32252
  -1.424440795478377   1.839922091532613  -0.171399451046546   0.633333632645245    2.33318
   0.698026319868674  -1.021509849264590  -1.980548722454582   0.426150618714860    2.33523
  -0.406014333354107  -0.256839272947705  -2.289804143629424  -0.610187320481184    2.33966
   0.188226042319506  -1.784623438213617  -1.510659852491619   0.286729657416554    2.34572
   1.026388273373093   1.578813064257737   1.425052465696952  -0.368332726534848    2.36155
  -1.773231668549405   1.034643134261799  -1.176075061855899   0.669377071687624    2.36601
  -1.804341750733083   1.072701919244881  -1.113243268943967  -0.579996510780366    2.37606
   1.056161494511251   1.423850376035342  -1.624426140544273   0.159205514468867    2.40449
  -1.296403331272780   2.015527059164621  -0.289334583308137  -1.191849931028122    2.41386
   1.155805304854291  -1.077921976845189  -1.840010588144260   0.618876689417754    2.42558
   0.221912264286492  -1.957265287944798  -1.464706365441609  -0.595459461249454    2.45469
  -1.242311876199389   2.101884361175276  -0.341264533354510   0.688002234941640    2.46530
  -1.072238121772349  -1.928448472350232   1.150327249457551  -0.531820778547844    2.48835
  -1.995054853457487   1.491424286083698   0.176741906389504   0.715151342995304    2.49716
  -2.032909777069706  -0.253961507850696  -1.432438817478335  -0.488429752856005    2.49982
  -1.703054037192347   0.468943096408110  -1.776270766700341  -0.664800221086267    2.50508
  -1.982638550349453   1.538699355240155   0.169498388691515  -0.791475051104374    2.51539
   0.253632120473984  -2.037885024919528  -1.463451398292745   0.340410515461478    2.52170
   1.041987182827797   2.032667314871754  -1.085962688032168  -0.822689549129162    2.52919
   1.324111180532828   1.470972343980677   1.584488697554251   0.535836563875007    2.53528
  -1.699101890235266   0.310877469389817  -1.856254490423951   0.805452457947457    2.53560
   1.150159107552453   2.118600520886026  -0.878189362243644   1.042288565180151    2.56565
   1.392416481149837  -1.044677512204388  -1.892895073570596  -0.339584546116752    2.57162
   1.381913556674120   1.225405072911300   1.791328271561084  -0.783352993854191    2.57297
   2.408695034943690   0.331248522271848  -0.852315613100279   0.018746306484612    2.57643
   1.272685636485656   2.160515545423834  -0.627476934591934  -0.502895980591853    2.58482
   1.406832858916514   0.909947335379267   1.992856535439962   0.762011568989886    2.60359
   0.751966975767055  -1.555808777117829  -1.985981523467268  -0.024220585414640    2.63251
   1.553989063328829   2.119967092878756   0.227443246078295   0.400665388768351    2.63835
   1.564728178188303   2.102781665571854   0.317287392005999  -0.350145359290875    2.64022
  -1.918672393011775   0.032391763200637   1.817960609775852   0.512865095283806    2.64336
  -1.877619660329970  -0.035819872614356  -1.871115678533020  -0.572850667080495    2.65100
   1.806959465645532  -0.654619548833373   1.832886256072379  -0.124890113555710    2.65577
  -2.033998314375989  -0.216685171324925  -1.724716775671727   0.559220934045563    2.67558
  -2.563231935077984  -0.330837235007362  -0.723594660491026  -0.709028290864949    2.68388
   1.426812897770801   0.514536093882509   2.220822486523322  -0.647329412207723    2.68935
  -2.562401685002761  -0.322678780582695  -0.752722511820798   0.736607555326610    2.69010
  -1.245375591599311  -2.094043076181226   1.141666764150954   0.367121050126908    2.69061
  -2.075708226394521  -0.048226982457374   1.715258825651476  -0.588909855279884    2.69314
  -2.225600241725141   0.138398516204828  -1.528910410389552   0.417288590593705    2.70370
   1.661944351821061  -0.720001413502420   2.055335052040483   0.070980048667698    2.73950
   1.610641538317380  -0.982723946048809  -1.996893054709111   0.075538114033901    2.74727
   0.442891030262153   2.739937188148114   0.514265999860560   0.361330215462342    2.82274
   1.515380647840724   0.181796748328099   2.381548013464967   0.623976734321003    2.82864
   0.432719301290259   2.747731587242427   0.521050636232417  -0.356584290741842    2.82998
  -0.024060339852475   0.520829885927656  -2.791726334200668   0.005583455433118    2.84000
  -2.437097930540232  -0.236299511680900   1.522497515649041   0.178990721197211    2.88328
  -1.320742052392313  -2.271180953021641   1.190527961440467  -0.101452246522363    2.88444
  -2.454977002860169   0.141460639121031  -1.575560282569950  -0.434943983958410    2.92050
   1.595557164812921   0.024848478985068   2.450811621342557  -0.314371317263543    2.92453
  -1.998828176650174   2.003104772434917   0.758156381415914   0.018973478696818    2.92960
   0.624202228151044   2.419008423737723  -1.568696943976229   0.585425008620757    2.94992
  -1.289869684902591   2.264116897207892   1.388592749212603  -0.019416022488276    2.95266
  -1.489687866396330   0.003325209940882   2.584319997499455  -0.381744956764126    2.98293
   0.611840202019800   2.481908438365895  -1.555176488691723  -0.493602266181184    2.99212
   0.527519496361920  -2.529469994424572   1.556068918436854   0.003177733400230    3.01626
   2.403581923995028  -0.820928030275242   1.634403145645196   0.020153388321339    3.02033
   0.575020543694598   1.643505615964503  -2.470065710217568  -0.323663642833164    3.02208
  -2.564661821545819   0.188645389194561  -1.614733155317967   0.170935516492325    3.03652
  -1.476733829166255  -0.073223662701836   2.691365073711744   0.436489119115537    3.07076
  -1.157603024096960  -2.565528958521106  -1.247379364560790   0.005111274795030    3.07863
  -1.862669129212497   1.047367000637963  -2.224287970816587   0.004775698272879    3.08447
   0.797600571278340   1.339259294270040  -2.738988606289608  -0.416196467411658    3.15148
   0.931128536096368   1.193075066501035  -2.773073121682098   0.146731805466270    3.15917
   0.603041512546633   1.545019152785098  -2.691433914131413   0.771121409879786    3.16142
  -1.186601775998338   2.865512716072253   0.802564220063207   0.002596643246090    3.20364
   1.533402165463012   0.509517983247994  -2.779091886008374  -0.001568298443375    3.21470
  -2.447426633245036   2.071008446100542  -0.262093851163407   0.068906864882057    3.21678
  -1.437289469688509  -0.276941987055818   2.864489923413259  -0.180731489745316    3.21680
  -1.395821910633248  -0.412156705543990   2.908020882511080   0.069838650587363    3.25189
  -0.767739020980199   1.825718271332848   2.607736876657256   0.524561935368975    3.27459
  -2.484834543490168   2.126130961138228  -0.273170602835924  -0.052711994346185    3.28169
   3.070838422596639   0.895898060274696   0.752084176000276   0.006521060068694    3.28608
  -0.670384817963583   1.807740959343846   2.690636553495934  -0.486529166438548    3.31012
  -1.443884747735349   2.042942060016922   2.169798070223961  -0.400940041556314    3.31156
   0.323935219450528   1.760773231569447  -2.800408457008861   0.129012896930389    3.32378
   0.454010704608178   1.646315010688203  -2.860537930652447  -0.553347489768006    3.33154
  -1.587062746604172   2.117528234033291   2.049575090516802   0.374518743320385    3.34716
   0.301056378781788   3.221946243220887   0.912341013148382   0.001959121109408    3.36213
   2.436752532886732  -0.128731973724863   2.314305318219707   0.353858716542368    3.36309
   2.363326896966686   0.045730822051502   2.410950037354830  -0.359309750556909    3.37640
  -1.201253325296273  -2.863531780722394   1.376062517982248   0.002663790970840    3.39652
  -3.092779782141216  -0.575923239573128   1.302856961820872  -0.089373995383112    3.40506
  -1.591124413140071   2.005802909163460   2.247222810432985   0.050014608653229    3.40660
   0.467137021685699   1.626133992213026  -2.958388420725692   0.191553932312827    3.40802
   2.567067296493887  -0.313634222163207   2.219655616368539  -0.115714683252889    3.40809
   2.291862863856406   0.177463349393546   2.518160881862219   0.128476289825885    3.40958
   0.617601187754883  -3.397793881725180   0.160837058982612   0.000642229514197    3.45721
  -2.584285843317712  -2.287087492149737  -0.347205585144163   0.129647186471878    3.46841
  -2.595745625365331  -2.279070154852318  -0.337518226611640  -0.133945446058140    3.47073
  -3.150738493046895  -0.621845347743725   1.316164288127542   0.058884036555001    3.47075
  -2.161624004413850  -1.200618542355516  -2.441533632381000   0.008512358966462    3.47494
   3.403218250229154   0.502600743205023   0.545515620393945  -0.064642731417905    3.48311
  -1.944121125352351   2.243239399528772   1.875563665331154  -0.186404783999457    3.51133
   3.473049521938780   0.431100857992493   0.440765219858152   0.384905252744622    3.52735
  -2.839651676800027  -2.093578490507934  -0.185863695608777   0.005458004265539    3.53288
   3.481872056937561   0.421600864517627   0.425265674945953  -0.325597193768411    3.53299
  -2.287186024295264  -0.931895669784096  -2.567005789539800   0.055383301070288    3.56219
  -2.041873150638823   2.279077099998350   1.834424884625398   0.094064635497638    3.56771
   2.883836978344780   0.245213054361106   2.112008025777547   0.003855847614368    3.58291
  -2.365427512432576  -1.020646909498156  -2.530667384343470  -0.244069230335676    3.61127
   2.887017984708595  -2.151168094853941  -0.349580744988770  -0.441195063709864    3.61726
   2.895815024838151  -2.135599880804399  -0.403581163238103   0.289036945674876    3.62069
   2.763496897132804  -2.342862877193617   0.018406226203277  -0.275911180978584    3.62302
   2.799929943103350  -2.294989109917144  -0.174428925386964   0.595765726458042    3.62450
  -2.389448434917844  -1.038185011453449  -2.527769891730566   0.180762047277117    3.63000
   2.722324442928047  -2.405238300488595   0.120030112888809   0.105505348186073    3.63464
   2.743017861724281  -2.389006408149624  -0.235288633255721  -0.445970218852340    3.64511
   2.700083692123814  -2.456808568677442  -0.270879879450140   0.170692610303818    3.66057
   0.454440238170202   3.347496866208454  -1.423170318784065   0.004891747472979    3.66574
   1.132232816201368  -0.736081117946189   3.411303833633657   0.000772004435146    3.66889
  -1.610791151562495  -3.008555421188298  -1.360813620390509  -0.003791117000051    3.67394
   2.071482628453563   2.968977086632880  -0.722172804724575   0.000387899934305    3.69153
   3.408478238897142  -1.402745585156399  -0.242724923377316   0.001250532953603    3.69382
  -0.214473753937805   1.837703696625487   3.217260361758754   0.109665684051653    3.71132
  -1.074173488595399   3.523634716734526  -0.654499254037041  -0.009115034578009    3.74142
  -0.984359584729575   3.581618775474530  -0.627914801202751   0.007259020601336    3.76713
  -3.661597347364181  -0.705623820692391   0.709701258481236   0.008073277458391    3.79590
  -0.153789773108879   1.857369514622489   3.309791559180021  -0.069822785405388    3.79845
  -0.960664653899230  -3.674726392056919  -0.200798436783494   0.000219575794448    3.80353
  -1.651238556138409  -3.116924127441242  -1.433703854107302   0.002217243008705    3.80753
   3.106061620704797  -0.781409708850655   2.188630314481327   0.001455324552964    3.87922
  -3.428819695436679   0.587335796304201   1.852828348052914   0.000177312310471    3.94141
   0.175237399203515   0.016253234153103   3.962294166324690  -0.001273290073816    3.96620
  -0.162239398776153  -1.241275946390049  -3.763868429565999   0.000121484891270    3.96658
  -0.643868252278808   0.417107801066838  -3.914814169420794   0.000112995809835    3.98928
   1.427076568582505   1.270688464500744   3.507174635364843   0.114405305023860    3.99393
   0.024817712748026  -0.025078808274672   3.993875094238679   0.001162532138928    3.99403
   1.419787872733066   1.248048431345897   3.519589813837310  -0.173957774161036    3.99511
   1.400568859661067   1.208509361644696   3.545882848862641   0.059371942229133    3.99942
  -1.828855610433658   3.441696786525238  -0.947225620853426   0.001512048403898    4.01089
   1.491746468989496  -2.515717297804525  -2.748028653732066   0.000138173822554    4.01320
   3.043861498533826   0.214747805847064  -2.608821861611676   0.000103269178560    4.01462
  -4.016453096459856  -0.855402208664648   0.534107246882061  -0.004353801356097    4.14112
  -0.474988841700605  -2.719284630465417  -3.104500075701824   0.000065157072454    4.15428
  -2.285752978691347  -2.558467467783204   2.404254193258082   0.000063935475130    4.18937
   1.075389483597785   3.561047066612390  -1.999051079936048  -0.001074258447266    4.22300
  -2.489013263185506   3.253674571660606  -1.041628581233391  -0.122309898010062    4.22689
  -2.491067902937740   3.252668575658489  -1.040765009453276   0.121801843631546    4.22711
   2.699393452023564   1.925476562255682  -2.675018184708005   0.000044482686314    4.26027
   1.102056013120738   3.569042426692002  -2.067648618604419   0.000891588409450    4.26940
   0.391200125929335   4.084022378425283  -1.197545360702989  -0.000370947867513    4.27392
   4.177767579121491   0.260243150582436  -0.884223267970714   0.000057258380926    4.27824
  -0.228919447978093  -2.622315902802872   3.394448141239828   0.000046154754871    4.29549
   2.120399608836522   3.500538193589565   1.368000525910889   0.000033126292313    4.31524
  -2.317362764171297   3.185525675023014  -1.843232449055162   0.000099475963630    4.34917
  -4.247395824680915  -0.932339664286311   0.406152616861440   0.001133183238833    4.36745
   3.678095855430483   2.184882627600045  -0.970869155593476   0.000028997981157    4.38688
  -2.876526705888030  -3.286686192744841   0.654944356958979   0.000032060811267    4.41652
  -2.135872353264253  -0.644880089193421   3.852768911677678   0.000048470482867    4.45215
   1.831944610262735  -2.948047633068955   2.816368289983684   0.000022717288828    4.46978
   0.085511837526305   2.071359846644104   3.976781440259721   0.000334996694753    4.48471
   1.636893815280484  -0.714743227585456  -4.184116684154334   0.000016965900285    4.54941
   3.562512912573794   2.690588053198667   1.422926779055349   0.000010782328254    4.68567
  -4.426287732450010   1.569783787242206  -0.203837346365611   0.000012632080702    4.70083
   0.445756317323856   3.693315382656729   2.888885693258252   0.000009675099148    4.71009
   0.626786804072964  -4.527183547230152  -1.610080155436264   0.000006996148885    4.84568
   0.751314765735983   4.788951064350488  -0.928303053354816   0.000019749008416    4.93561
  -2.096143296357651   4.308848206085370   2.069672998934101   0.000001525381093    5.21953
   0.584491546625084  -5.304626015221226   1.859261469454745   0.000000660793064    5.65133
  -3.118005474573131   2.251701222443406  -5.409585823469877   0.000000046917416    6.63745
   5.228604886636841  -1.946235258132262  -4.783182893520107   0.000000008756741    7.34881

# E_n^{r^2} 3 dimensions, degree 13, asymmetric 220 point rule with points at 220 distinct radii (81 negative weights, stability factor 59.098185)
#                 x1                  x2                  x3              Weight     Radius
   0.000000000000000   0.000000000000000   0.000000000000000   0.136458261017141    0.00000
   0.678738885740324  -0.217654537214797   0.307354980260003   1.495614960434872    0.77623
  -0.428339575559173  -0.525949270767350   0.402839627846646  -1.244851657554602    0.78891
  -0.341169618610519   0.525112825768879  -0.543676906376280  -1.164174957525280    0.82929
   0.463064058409951   0.070374487473254  -0.701712616345788   2.306155631026203    0.84367
  -0.502904161606260  -0.680539626028689   0.201559561843825   2.019243713516299    0.86987
  -0.868667171865937   0.089013047804424   0.000000000000000   1.275188255282325    0.87322
  -0.343564237350850   0.782919090447574  -0.239051479346961   2.219716697789559    0.88777
  -0.617827552809650   0.493798079256144  -0.536079947213871   2.038203833902736    0.95547
  -0.458590081990789   0.694310346176036  -0.481398212590449  -1.620405899284270    0.96131
   0.609056206818468  -0.617392662864918   0.417290904395652  -3.584099632417868    0.96242
   0.189213149106805  -0.758242375262550   0.566767062876845   4.184710346058576    0.96538
  -0.595853220193953   0.746595846315590   0.286356897696372  -2.038216280313937    0.99722
   0.624573372172330  -0.015405602651305  -0.844755262739806  -3.892778110143237    1.05069
   1.097047097472909   0.000000000000000   0.000000000000000  -1.329418661343892    1.09705
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   1.003941632655979   0.882503509053884   2.488725824359587  -0.968653944127423    2.82497
   0.990351738185075   0.854545164746360   2.507317807723990   0.330602448140757    2.82802
  -1.293196203948658   2.433647136539903  -0.669789659819185   0.008419581459990    2.83613
   1.054824044033360  -1.778880760825784  -1.943149695948765   0.000769397164560    2.83776
   2.152335106606202   0.151849629759425  -1.844715629253380   0.000575036658183    2.83876
  -2.840061220824375  -0.604860702388655   0.377670856151142  -0.024243393983802    2.92821
  -0.335867830954451  -1.922824602178191  -2.195213055722478   0.000362815950739    2.93752
  -1.616271431349788  -1.809109695914780   1.700064443748952   0.000356013696157    2.96234
   0.760415196268556   2.518040528926118  -1.413542574561236  -0.005981823387768    2.98611
  -1.759998156861585   2.300695353395478  -0.736542633267888  -0.681061629379059    2.98886
  -1.761451006563286   2.299984006800534  -0.735931995806124   0.678232615959255    2.98902
   1.908759415016485   1.361517534186435  -1.891523498204330   0.000247694187577    3.01247
   0.779271280125020   2.523694102256541  -1.462048359326316   0.004964656702007    3.01892
   0.276620261845861   2.887839918302098  -0.846792445331609  -0.002065559396038    3.02212
   2.954127785417720   0.184019696534183  -0.625240268865226   0.000318833445561    3.02517
  -0.161870494010709  -1.854257357285083   2.400237299055975   0.000257004813734    3.03737
   1.499348942233919   2.475254294489985   0.967322448538141   0.000184458060919    3.05133
  -1.638622925014932   2.252506806452739  -1.303362164029715   0.000553914793293    3.07533
  -3.003362390015179  -0.659263698985980   0.287193269579278   0.006309935954337    3.08825
   2.600806521228875   1.544945322072512  -0.686508163564969   0.000161470270326    3.10199
  -2.034011539997481  -2.324038094521943   0.463115596105706   0.000178525112981    3.12295
  -1.510289824741763  -0.455999084120906   2.724319023792046   0.000269899546770    3.14815
   1.295380456674814  -2.084584472603716   1.991473116166080   0.000126497315392    3.16061
   0.060466000186489   1.464672593839430   2.812009123704534   0.001865371474238    3.17117
   1.157458716867107  -0.505399783032582  -2.958617280641574   0.000094471697549    3.21692
   2.519077038545980   1.902533057796581   1.006161174602203   0.000060039540289    3.31327
  -3.129858071098294   1.110004760955524  -0.144134769873981   0.000070339568633    3.32399
   0.315197314736484   2.611568352136816   2.042750663775825   0.000053874125461    3.33054
   0.443205199517987  -3.201202185922137  -1.138498596162840   0.000038956851709    3.42641
   0.531259765657394   3.386299772372865  -0.656409384023468   0.000109968956474    3.49001
  -1.482197139193439   3.046815785626598   1.463479812384869   0.000008493822246    3.69077
   0.413297936164632  -3.750937027021362   1.314696393050724   0.000003679512520    3.99609
  -2.204762814847430   1.592193203596032  -3.825154819186149   0.000000261251560    4.69339
   3.697181971486136  -1.376196148809552  -3.382221059663531   0.000000048760407    5.19639

>> # evaluating formula 1 with 213 points
# r3_213_15Sa.txt:3 formula 1   : problem  S, 3_213_15  (d=3 n=213 o=15 plus 125/153 of order 16) quality NO (19 negative weights, stability factor 4.676882)
S 3 dimensions, degree 15, asymmetric 213 point rule with points at 213 distinct radii (19 negative weights, stability factor 4.676882)
#                 x1                  x2                  x3              Weight     Radius
   0.000000000000000   0.000000000000000   0.000000000000000   0.009979201301862    0.00000
  -0.263966076756088  -0.000000000000000  -0.000000000000000   0.044400103853144    0.26397
   0.089998036637181  -0.269962834519047   0.000000000000000   0.050972166632886    0.28457
  -0.058402289795146   0.021517027781820  -0.284886491947345   0.042736414790634    0.29161
   0.249697777404679   0.172169391623375  -0.007408153566851   0.052523052105892    0.30339
  -0.037906506975464  -0.067202363813538   0.327982686852104   0.047978544617830    0.33694
  -0.024132791614672   0.293158938427724   0.171887548920630   0.042675056886493    0.34069
   0.000216816864241   0.438721957514461  -0.118643718371233   0.032074903389705    0.45448
   0.284304282020868   0.218464723973429   0.286667053809328   0.308216552876397    0.45906
   0.278678114658997   0.276395730330226   0.260739381052533  -0.467962179977067    0.47121
   0.452736854673732  -0.126235351477147  -0.035947227680084   0.039154094845668    0.47138
   0.123283094442280  -0.299733263977734  -0.345485441273309   0.044781518644843    0.47371
   0.251193231616136   0.138339103351912  -0.383667529523830   0.037867523748668    0.47900
  -0.366205254008845   0.322784693658062  -0.055168576170477   0.039296825793135    0.49126
   0.289764617599019   0.355737759888442   0.233462860840414   0.235210197317515    0.51480
  -0.304729125557217  -0.423442806268682  -0.038434683923867   0.053542706649453    0.52311
  -0.330972409298236  -0.147156459172855  -0.396034237972047   0.039692609885335    0.53669
  -0.315478078857010   0.273906535284418   0.359131944820656   0.040853432915531    0.55093
  -0.090305745339333   0.391796175528282  -0.378609017382781   0.035353021083146    0.55227
   0.375575851905435  -0.301178308930279   0.271665183795411   0.042716776682094    0.55278
   0.029747512946595  -0.462873273031874   0.338319306704415   0.043851358918564    0.57410
  -0.435708410305345  -0.326714888772199   0.194525378413455   0.169246571972070    0.57829
  -0.413164933282019   0.227286091601330  -0.347374395868244   0.030411254454768    0.58569
   0.111281690233979   0.411128241443771   0.409300362765565   0.048484312997743    0.59071
   0.446222116112200  -0.052969516649534  -0.402878789980578   0.030417314408633    0.60352
  -0.360932262739653  -0.057459337042105   0.482384855814132   0.036097586334786    0.60520
  -0.203635268837755  -0.455873014376995  -0.364841134523646   0.031270963774487    0.61838
  -0.594012142191861  -0.101370120369292  -0.171936215102433   0.038747140312519    0.62665
   0.235751325746884  -0.576376191703150  -0.082889804348262  -0.468029290680635    0.62822
  -0.084686113361951   0.088012093656852  -0.617986094344935   0.035190721922942    0.62994
   0.261226027768166  -0.568187114084042  -0.083016357571864   0.427959040326806    0.63085
   0.113966991157023  -0.621087597401621  -0.061965706803193   0.115250269496968    0.63449
  -0.603453130845264   0.105644310380660   0.166135474841764   0.039908377645797    0.63476
  -0.460303505910412  -0.403215676365498   0.188751437311856  -0.519893859274065    0.64038
  -0.403994599407370  -0.452117350299948   0.231646636085466   0.187608579827490    0.64906
   0.566087916190256   0.302461930748596  -0.125407316378808   0.039798246029795    0.65396
   0.284830419434229   0.507378259975765  -0.314643102544371   0.038574428674391    0.66148
   0.439486227100457  -0.384281124466959  -0.330346889378326   0.025666005222830    0.67078
  -0.515225021182342  -0.409138120128951   0.166425951194545   0.258491266372687    0.67864
  -0.062137099066776   0.160054978603193   0.657855786412817   0.039869578775380    0.67989
   0.659949210635424  -0.083536133644231  -0.163687662090781   0.020867361330146    0.68506
   0.147931851689342  -0.276978907255016   0.608881387575570   0.208806221088163    0.68508
   0.640380310991749   0.119041389612913   0.216886752447777   0.036158886952204    0.68651
  -0.107984623654734   0.678446519112372   0.055045146815505   0.041641000173957    0.68919
  -0.037610248542793  -0.276788969851701  -0.659492399013903   0.029328210817944    0.71621
   0.229692786467207  -0.146035209006988  -0.663174761350030   0.029491763565613    0.71686
   0.149514278033400  -0.334711214396022   0.620224255376888  -0.433872267100355    0.72046
  -0.444849920936084   0.546563657795345   0.168651840346326   0.034177291270270    0.72461
  -0.088305941056265  -0.319694703574033   0.645008541158681   0.043731461060755    0.72529
   0.242266777576381   0.600650268068685   0.355715657638199  -0.504090989333516    0.73892
   0.532699594297578  -0.135889370805104   0.494968568466746   0.030009275014941    0.73975
   0.167293603162622   0.282243901521220  -0.666181890055337   0.028260345440984    0.74259
   0.238754570064761   0.612837748739176   0.353577884033418   0.500190745062037    0.74672
   0.166807104216009  -0.371754460551394   0.626874242532167   0.272739706746965    0.74766
   0.307028361773123   0.687145893501613  -0.020439881287059   0.031424932899759    0.75290
   0.105415040209032  -0.631232870930134  -0.404749748524682   0.033621209201140    0.75722
   0.305417738042634   0.108325617933784   0.693578718929518   0.031270714344153    0.76555
  -0.187415269538685   0.660187374399478  -0.349523342720914   0.022932085412863    0.77015
   0.360912060194118   0.468174646149818   0.498982612121392   0.039965817819282    0.77358
  -0.456529087682565   0.581311044351976  -0.236556606844566   0.030500360871777    0.77608
  -0.157276093015540   0.614762444829750   0.447183444496298   0.033452803761466    0.77630
   0.720794645192514  -0.260956383448136   0.132175125354306   0.034708891259148    0.77789
  -0.718449649940406   0.246470939735362  -0.170094677796060   0.033474212767758    0.77836
  -0.426269939153482   0.298593617957115  -0.599644590960204   0.262567708914696    0.79400
   0.268951094882370  -0.662941039721816   0.346377535955442   0.023824914462618    0.79486
   0.525199571743576   0.279992753103684  -0.528260116942581   0.033216843188070    0.79579
  -0.401717720935980   0.329688892831950  -0.611947180704564  -0.390347609628924    0.80284
  -0.336262722348355  -0.094009229269608  -0.726519406910137   0.026622352585080    0.80607
  -0.609991631838124  -0.480467133517574  -0.232261683332546   0.033684633834547    0.81048
  -0.351802892802763   0.372726106583005  -0.629284272201309   0.176158347031733    0.81160
  -0.432566861645281  -0.412826560577100  -0.559214532453307   0.026109731547582    0.81869
  -0.505934858172084  -0.312578283898399   0.563161135015951   0.028933050148173    0.81904
  -0.660507005140543  -0.108124065497905  -0.480234622402487   0.028574570034881    0.82376
   0.615216982421768   0.512015796506558   0.215981315759578   0.031614721456092    0.82904
   0.463006313376861  -0.681902104102882   0.095965854463433   0.510921017145220    0.82980
  -0.071028746013399  -0.786738367900782   0.264912783865233   0.028836440732506    0.83318
   0.091596984618209   0.567472565954515  -0.606896811128549   0.026205846678086    0.83591
   0.449521677626503  -0.700194154112304   0.080188291340573  -0.742266090155804    0.83593
  -0.758860963420759  -0.158549653677295   0.313862460092767   0.026303495867181    0.83637
  -0.366810540473071  -0.752008334882191   0.008977398105960   0.033937395230495    0.83675
  -0.584782766701014   0.122078167664982   0.586989514428237   0.033773259290671    0.83751
   0.733617984931458  -0.300451157595419  -0.271524987631823   0.025506386251260    0.83797
  -0.337326123551489   0.357007635378161   0.680079946153801   0.026319123506200    0.83890
   0.775815197707093   0.109363369316281  -0.302747471870265   0.025446240477792    0.83994
   0.062572293073801   0.796697561292669  -0.266832360827765   0.026054377058160    0.84252
  -0.264617146767313  -0.727096935915418  -0.333996950349035   0.025570710704006    0.84276
   0.416544575664357  -0.736247652366310   0.058601428999294   0.264291148905738    0.84794
  -0.773691511850862   0.240334018096734   0.258032604464331   0.022216650244993    0.85026
   0.634575711315912   0.197608288317574   0.532771000013772   0.025434036610169    0.85181
  -0.153032020401698  -0.610049814234877   0.579209475294584   0.023141124296128    0.85502
   0.843247163161746   0.161989068772742   0.051133966351149   0.020314643236866    0.86019
  -0.257293469514623  -0.052944123073420   0.821632579443638   0.027736980670804    0.86260
   0.602470581077869  -0.614824492523623  -0.098630372994830   0.029342197331419    0.86643
   0.636021470680597   0.563666020783835  -0.181712301352833   0.022646782538750    0.86906
  -0.696993714589271   0.526026087920616   0.033329124608252   0.022808467214748    0.87385
   0.272851100276630   0.076938234154852  -0.829824250105967   0.021980456607237    0.87691
  -0.578051941518001   0.406155856914406   0.524649388745775   0.142183350336426    0.87998
  -0.114175214644488  -0.540070431572240  -0.689451136115102   0.023112850388892    0.88321
   0.594346479311709  -0.434490398973123   0.490840269568345   0.025221837327940    0.88485
   0.543464082515892  -0.174674780351845  -0.683235098056325   0.198253911867974    0.89032
  -0.586709101467411   0.383910694488531   0.550298808907625  -0.149132622003768    0.89132
   0.074934615776429   0.480526093327880   0.747421466002367   0.032994997062693    0.89172
   0.329811213529448  -0.784028586222463  -0.273849208330691   0.016623994156245    0.89357
  -0.122714280089245   0.147208968161319  -0.877152963033175   0.024313483220626    0.89785
   0.137831266661320  -0.153317695353240   0.875361663162218   0.026388351906954    0.89931
   0.384355358322110  -0.534306389200659  -0.613852580451124   0.331876473125093    0.90002
  -0.587771903365137   0.459565484779236  -0.511048259216646   0.025800204045979    0.90435
  -0.895154924154183  -0.125590980890706  -0.085895093995427   0.092566826756099    0.90799
   0.518587878963479  -0.203771876726039  -0.718547042112625  -0.454612214621291    0.90927
  -0.347279796918157   0.841526677143295  -0.073492376337987   0.021796613175252    0.91333
   0.442732106252727   0.659366448827040  -0.458175597828283   0.023733661198579    0.91690
   0.389004326935605  -0.558133546395907  -0.616803134492470  -0.851221774145527    0.91830
   0.500930940843278  -0.217991696706036  -0.739074633755147   0.292303739105038    0.91907
  -0.471233276283285  -0.662542566655190   0.436243722830755   0.021678024546182    0.92268
   0.039899943969415   0.915079431533476   0.116366432610559   0.023715227865278    0.92331
   0.823285829683202  -0.097445239968772   0.410321672355948   0.019002324919682    0.92502
   0.420844344151136  -0.569556531249381  -0.595208028690071   0.315121228613788    0.92508
  -0.037572084674430  -0.917125968006210  -0.115436146044760   0.024814343503587    0.92513
   0.354585688580221  -0.567519834410398  -0.644236636494131   0.256739059509227    0.92890
   0.017887251841083  -0.223042845610102  -0.901862341547513   0.021998515872906    0.92921
  -0.818211457609294   0.144698183459869  -0.422873543014679   0.017847530427495    0.93232
   0.519775099733201  -0.133177744351375   0.766023488063496   0.020606759766759    0.93525
   0.450518271053726   0.823984511738865  -0.017578856918281   0.017984189469576    0.93927
   0.828345356292516   0.433730885721713  -0.109014327222862   0.012135380192907    0.94136
  -0.314190456388691   0.836985257273703   0.301792139338238   0.025639766334179    0.94358
  -0.930899393960809  -0.101247554191007  -0.128392056635652  -0.622579488703534    0.94515
  -0.636868716166465   0.360145941468699   0.598947843351622   0.035049778563696    0.94554
   0.214918052316913  -0.792417046440818  -0.470127100367442   0.011289893734659    0.94612
   0.941121857539574  -0.109912956668213  -0.000265304849203   0.018152897175673    0.94752
  -0.944954369775166   0.043032347559098  -0.059888864380601   0.045208610938568    0.94783
  -0.516337874629354   0.180026162758521  -0.774326931341422   0.018987518435146    0.94794
  -0.931789466764675  -0.106436024636237  -0.138897957674268   0.535393880475950    0.94808
   0.181362862243504  -0.759476413227976   0.541475845336681   0.015157542859907    0.95021
  -0.252986288345682   0.760346385116959  -0.510714142239930   0.016595706671828    0.95024
   0.063168867350175   0.328224340982443   0.890047799625273   0.208493215386474    0.95074
   0.430650195748216   0.410071026433634  -0.742572904065259   0.016752456941539    0.95133
  -0.373167885082576  -0.399523641475552   0.780232990974571   0.016357536321609    0.95270
   0.380712122241689   0.279590146342833   0.829101939450813   0.019308248920790    0.95421
   0.185208825332028  -0.463568535117712   0.814421582021685  -0.152998907154026    0.95524
   0.080030323836890  -0.456113186814854   0.836297724612737   0.050776630014429    0.95595
   0.878912352457795   0.259491253668804   0.275161505642555   0.015424873370454    0.95684
   0.221354639853944  -0.468575656601333   0.804540773612875   0.126197530786403    0.95700
   0.428413450244591   0.784986782601571   0.342392656201361   0.014436843922791    0.95759
   0.070434535010742   0.365225101579291   0.882763699563855  -0.382145359506580    0.95793
   0.143475207969552   0.756688687704359   0.570861284254370   0.114796047486345    0.95867
   0.191318295728493   0.726223015598799   0.596053846729052  -0.228374597601847    0.95879
   0.227025060949588   0.703094419920697   0.612760805898946   0.136922938092873    0.95987
   0.060361596743109   0.437118196263330  -0.852776296336272   0.014123936678872    0.96018
  -0.366734184372504  -0.241076927581216  -0.854235576123472   0.014317770441723    0.96038
  -0.485489501764585  -0.751157789886409  -0.352924258329743   0.012372522703147    0.96151
   0.813151471432253  -0.486058956582504   0.172124809080137   0.014914594676496    0.96286
  -0.739251371372553  -0.421975333646162  -0.450200286818764   0.013251445943903    0.96293
  -0.754695663270261  -0.575636333202946   0.164238459558715   0.022431946998953    0.96327
  -0.662775499104523  -0.180342096327423  -0.675524155607082   0.010549643860776    0.96339
  -0.745484118444333  -0.345334102217821   0.503573768392948   0.013803841128602    0.96363
   0.642421934396440   0.473562160645082   0.541924238539752   0.013431284012289    0.96470
  -0.279861490487206   0.622039731903871   0.682656149796594   0.013342129685913    0.96503
   0.691376789140567  -0.315263377185072  -0.595539923453071   0.013222389017952    0.96543
   0.070842071292062   0.392969711138779   0.879328372380301   0.187898076258746    0.96574
   0.554093713002567  -0.783523317835411   0.110878073825181   0.011406617360157    0.96603
  -0.369530818479081   0.267410005051244   0.852157121080338   0.012309359316349    0.96656
  -0.438618027259888  -0.568630833692439  -0.650594072988696   0.011024369136248    0.96902
   0.232704507533476   0.897585864914923  -0.282302187074829   0.011115353267723    0.96928
   0.877439405864235  -0.012345482197410  -0.411931474309005   0.012119360114061    0.96940
  -0.100663514934679  -0.825236770879403  -0.499021183284553   0.012201241835993    0.96962
  -0.601877877336814  -0.068182480963399   0.757224484258389   0.012548345057821    0.96969
  -0.864950573165961   0.049550422640047   0.435656252933098   0.012338142874616    0.96974
   0.621131148957068   0.075283030787191  -0.741116347327974   0.012293742349034    0.96991
   0.506012516941316  -0.701793995492068   0.440564119972137   0.010492786609274    0.97091
   0.090816567997424   0.745957785138318  -0.616781512983048   0.010779399515956    0.97217
   0.159672434340088  -0.934189907389874   0.217543113121393   0.011517370061346    0.97238
   0.857170423834043  -0.398241527939409  -0.228904528811811   0.010758181067066    0.97249
  -0.240952349634358  -0.901224896901627   0.275960493958409   0.011231785612805    0.97284
   0.830254555706602   0.337172813408013  -0.379626894754190   0.108576601826758    0.97320
  -0.949613083612739  -0.193760654014755   0.105795654104496   0.012610485086697    0.97494
  -0.304456072138056   0.504829940282606  -0.778515710716606   0.010142860072252    0.97654
   0.859055320779327   0.320851926359919  -0.336828886585485  -0.186545411178261    0.97692
  -0.858721291590135   0.414881108992360   0.213895588050510   0.010787023665363    0.97738
   0.884639949593255  -0.214726228730427   0.359390242288497   0.004059390538999    0.97870
   0.741315727720427   0.617450468801624   0.169561162344674   0.009111679592853    0.97956
   0.882278743442090   0.305944341540991  -0.296737280043181   0.096483208384374    0.97983
  -0.139504542997893   0.945903083438205  -0.218241903736594   0.008576110545242    0.98073
  -0.797435057926652   0.507956367835679  -0.262079280172305   0.020570202953330    0.98113
  -0.747649960360058  -0.633890795081363  -0.046653513224648   0.026438421108173    0.98131
  -0.619313663695591   0.688244513300512  -0.326269116300833   0.017042298581487    0.98167
  -0.133094587621775  -0.748081212848957   0.622495575904869   0.007660201487433    0.98226
  -0.530836115919702   0.735160457289924   0.385603278468518   0.011764526486116    0.98536
  -0.512991127509512   0.818612666258676   0.206678169372894   0.171358393180601    0.98793
   0.649007442989410  -0.702068080519045  -0.250271658985218   0.006637270347507    0.98830
   0.729645572802857   0.103859674943667   0.659052553094080   0.007024464423650    0.98870
  -0.198106613730165  -0.091188620087925   0.965809673952688   0.007196281278945    0.99013
  -0.502691217202457   0.825529886769253   0.216759400864271  -0.175433135594730    0.99055
   0.237167169037643   0.094222144306784  -0.957119285723501   0.006692862552547    0.99056
  -0.690095190906605  -0.712895623209066   0.056392706358802  -0.455147813996390    0.99380
  -0.685618488807131  -0.717462196482067   0.058109653888685   0.440016110585025    0.99408
  -0.083254498694646  -0.559581538411196  -0.818356012167404   0.005240716669737    0.99487
   0.692792999409920  -0.389116889425643   0.607847722715351   0.004853959756091    1.00043
  -0.725488053065591   0.551972307569388  -0.415675996419543  -0.186304839484467    1.00189
  -0.724678553656643   0.548152319239606  -0.424765274424469   0.172959695606898    1.00302
  -0.798437995871409   0.041730217927295  -0.608622078680829   0.002820695501445    1.00482
   0.665488080392241   0.718252626219979  -0.240191710734909   0.003926846438852    1.00819
  -0.212928064818754   0.081250887454649  -0.983194846197880   0.003805891615409    1.00926
   0.282654671456558  -0.953140781317762  -0.193762129181464   0.003781299404578    1.01287
  -0.505997976082287  -0.616854647077674   0.627287826188537   0.002269726646647    1.01491
   0.261882374976903  -0.089892822060940   0.977080667253772   0.003264500013520    1.01555
   0.200800174608802   0.985507417354647   0.144209168589341   0.002407431263059    1.01604
   0.169898120569536  -0.325848948631984  -0.960188235550339   0.001404461559651    1.02811
  -0.412379677986680   0.918699009963609   0.226486558800189   0.006311475387116    1.03216
   0.465853079150056   0.666618358869664  -0.638914160440516   0.001235229618392    1.03422
  -0.362564315153064  -0.963770077048737  -0.097322385805251   0.003181531639154    1.03430
   1.050461885170187   0.044276721544755   0.183885908700571   0.000485477629202    1.06735
  -0.698725256939279  -1.016779965260834   0.027641987549413  -0.329885704276116    1.23403
  -0.698766964913640  -1.016791123111483   0.027653233013472   0.329671925223774    1.23406

>> # evaluating formula 1 with 234 points
# r3_234_15E2sa.txt:3 formula 1   : problem E2, 3_234_15  (d=3 n=234 o=15 plus 0/153 of order 16) quality N (65 negative weights, stability factor 18.310337)
E2 3 dimensions, degree 15, asymmetric 234 point rule with points at 234 distinct radii (65 negative weights, stability factor 18.310337)
#                 x1                  x2                  x3              Weight     Radius
   0.000000000000000   0.000000000000000   0.000000000000000  -0.406919730277092    0.00000
   0.501392673221522  -0.000000000000000   0.000000000000000   0.557381441324378    0.50139
  -0.189056713388595  -0.477276135903188   0.000000000000000   0.693160199467193    0.51336
  -0.505825452990380   0.096727368532303  -0.065877690927480   0.302703169677450    0.51919
  -0.095605031528574   0.411566473840992   0.378029369452848   0.471653657827597    0.56695
  -0.012161902555852   0.441419411117165  -0.571073143298772   0.384191693709328    0.72189
  -0.523828096897358  -0.519504466575707   0.264698444769698  -0.777913046427438    0.78380
  -0.607158677016745  -0.385926799885191   0.379900483410088   0.682117038822647    0.81358
   0.111776517842841  -0.286366500048306  -0.827073981792374   0.228190856149136    0.88236
   0.188614240165255  -0.429742829913517   0.751850696266294   0.244047093395952    0.88630
   0.733543541516541   0.624451316975170   0.466239998618906   0.177894465365158    1.07024
   0.857511154826773  -0.772431100532927  -0.256309318261492   0.209861626686665    1.18223
  -0.803628163426959   0.025469747794033  -0.922684874859180   0.154949897043823    1.22385
  -0.775526662949666  -0.954039399719300  -0.148661549870422   0.623449600311471    1.23844
  -0.692171526119396   1.026090350200342  -0.154157495821932   0.166313741882584    1.24729
  -0.063551018542607  -1.002027612179990   0.799724379206168   0.119602137466406    1.28361
  -0.030797930469710  -1.322606843727177  -0.375236182869469   0.132146075825884    1.37515
  -0.768527608951306  -1.156347535639975  -0.103104152710769  -0.865849234155305    1.39227
  -1.349153054969340   0.282595917512489  -0.255835263929734   0.111732601009668    1.40197
   0.611958365687671   1.160321773396219  -0.527552258311868   0.858359262977034    1.41391
   0.759799569059090   1.137219640229129  -0.574297061960883  -1.421729561888923    1.48337
  -0.710585776440077  -1.278602877669651   0.261906054340625   0.330965145037269    1.48605
   0.249386515294311   0.655852255620287   1.328114378798336   0.110587126713681    1.50207
   0.033464539825501   1.423861326379615   0.498213607993966   0.103477127626979    1.50888
  -0.082984469666334  -0.117883005330205   1.511337538413483   1.216579219037286    1.51820
  -0.077386478901870  -0.157788404864223   1.518703447368633  -1.069761757487971    1.52884
   0.927879178193160   1.096596444567839  -0.552706714470514   0.755576723283341    1.53915
   1.343763524489750  -0.444848748491403   0.649856834153084  -1.283898112634289    1.55753
  -0.504102671858538  -0.836220274477130  -1.234911121418336   0.072956026241367    1.57429
  -1.415329329420756  -0.383521797199300   0.604511898572460   0.119297179183724    1.58609
  -0.869484594716684  -1.331686196171346  -0.110528752669665   0.396359214942347    1.59424
   1.456410942978356  -0.522433610404023   0.403223774192098   1.232835863345392    1.59896
   0.801421388020066  -0.207695933075287  -1.372441345850529   1.105535985081724    1.60281
   0.731428923407134  -0.340571918565457  -1.396790655307050  -1.089824191200436    1.61307
   1.164441524233978   0.367234002939157  -1.055054461615210   0.820304222602479    1.61367
  -1.061340679067605   0.659791893711958   1.053581276808635   0.339190797701234    1.63457
  -0.355118051880804   0.498228031766551   1.516846552275889  -0.746071728652624    1.63559
   1.228875144361830  -0.413868347167134   1.001998382679693   1.308792028114832    1.63873
   0.574114354714830  -0.627120276966778  -1.401075263393287   0.318234465533742    1.63887
  -0.450749024842829   0.551119026666744   1.485606365836740   0.777962140377500    1.64740
  -0.861464902315120  -0.540154867755621   1.328424365405265   0.076940077718541    1.67290
   1.530220836928976   0.501954615860932   0.488271656116565   0.209654268547338    1.68284
   1.095527046747464   0.253160940902160  -1.277798990283212  -1.358382799948010    1.70207
   1.459586773937607  -0.872191632520870   0.143575543165068  -0.727334635363685    1.70638
   1.061968447616491   0.901356992650454  -1.002594069674233   0.903185131235480    1.71622
  -0.056368705099395   0.205278425980725  -1.715306985085285   0.052704344330950    1.72847
  -0.832161321502129   0.959491260613426  -1.191014070584589   0.045232651559210    1.74116
   1.203709188613757  -1.064233343698281   0.698397510550791   1.266617597187477    1.75193
   1.190885962242860   0.878223482588251  -0.945625041611112  -1.299781101877653    1.75604
   1.428884014206542   0.849502841127136   0.597493911168234  -0.496221207174462    1.76646
   1.250949489952440  -0.906411026607471   0.859589140759796  -1.381315307627023    1.76787
   1.395054934160263   0.925993878065935   0.632209786484012   0.398338733561256    1.78979
  -1.013204373956949   0.674847609586158   1.328515051208958  -0.547024853383095    1.80193
   1.671681611448953  -0.442089557804388  -0.545810863190547  -0.414055624535908    1.81325
   0.934081927894429  -1.483818995162359   0.540900309313148   0.936926464546900    1.83488
  -0.960100470245339  -1.531075500343462   0.362218632971446  -1.057277190285504    1.84315
   1.243194671227306  -0.380215854198948   1.315059796441953  -1.275328620094396    1.84918
   0.995825796551347  -1.460886724935025   0.565980663266527  -1.265542496058087    1.85639
  -1.556566908190471  -0.456513566280297   0.906161590127630  -0.758321040480159    1.85807
   1.302031082176366  -0.681767715012146   1.138683708901561   0.680999357715087    1.85922
   1.343697865885852   0.894259770688360  -0.924670083291758   0.364403650161306    1.86017
   1.072435897384468   0.165735146243122  -1.524333383338354   0.953215162167781    1.87114
  -1.575164362867193  -0.462107616252894   0.915216643942460   0.697030564337589    1.87944
  -0.972279837796259  -1.556967864122042   0.420606527714240   0.929396454509268    1.88319
   1.702465076096440  -0.583488869680479  -0.566882766218149   1.197027593866988    1.88685
   1.722737820753975  -0.657053576652835  -0.562026030059112  -0.823495420281618    1.92754
   1.526554057316565  -1.179047506508819  -0.126365185296322   0.701275296692578    1.93300
   1.879328825101650  -0.200821226620731   0.452924233869657  -1.359955371256288    1.94354
   1.907992654852384  -0.188804598808191   0.378987087166799   0.821725860689060    1.95441
   1.872217022011855  -0.217666194117458   0.615383176484906   0.451215425783793    1.98274
  -0.786571849218152   1.084301486744603   1.497602914030492   0.668611973881299    2.00928
   0.170912214983779  -1.623899953559609  -1.176048874977183   0.675400755468602    2.01230
  -0.483852360156408   1.916701926118240  -0.426165221729682   0.015155885869429    2.02225
   0.183407409848545  -1.676124567962870  -1.119492275610358  -0.601152389310295    2.02393
   1.486705756476943  -1.364141457882188  -0.209909085030708  -0.834732616863994    2.02860
   1.162923542392487  -0.194074931656984   1.654349979355866   1.104889994965555    2.03148
   0.134603196006411  -1.308702066809690  -1.550722745971314  -0.913548287255976    2.03361
   0.518906545368489   1.494418512015278  -1.288772593931881   0.090419595602054    2.04046
   1.156861674398076  -1.606948810457800   0.508532864484646   0.111225994844545    2.04431
   0.128939301140345  -1.296769906703915  -1.578399003824080   0.791934256131739    2.04685
  -0.712897534123979   1.137118374722260   1.545594697107467  -0.867028868734884    2.04698
   1.019076336171975  -0.016534635360430  -1.778473080780144  -1.077274340367733    2.04982
  -1.117926838395564   0.349896159043650   1.688160229388307   0.796078795793866    2.05477
   0.312418709445692   1.342659510418637  -1.536690121126447  -0.436190887587332    2.06440
   1.450426216839178  -1.449305575347787  -0.265273182138674   0.429240151337562    2.06751
   0.707192583776119  -1.352547785785839   1.399811229440166   0.594338549936062    2.07098
  -0.670883471321394  -0.366027568926689   1.934705328383352   0.625453639620403    2.08018
  -0.704824039346500  -0.343492390142848   1.926856566933723  -0.698481762934465    2.08027
  -0.148919866769657   0.613467438882762   1.984914000337952   0.019449510490595    2.08288
   0.656325766127312  -1.304962805899411   1.495340737387177  -1.082995887923768    2.09039
  -1.106332297371592   0.269595890271793   1.756314331075600  -0.800268619577411    2.09315
  -0.632760019823517   1.207657161725914   1.592715106320804   0.290913893903470    2.09656
  -1.841334844698175  -1.000865995954405  -0.276263346958991   0.017812784857653    2.11390
  -1.973209065634097   0.735987130563462   0.205849106354862   0.009588280558027    2.11604
   1.097782267321287  -0.132672547105429   1.804377868833639  -1.173333863457633    2.11625
   1.014739837882803  -0.087833479707663  -1.862685491273098   0.701432891927156    2.12297
   0.107055717075728   1.328354583346006  -1.667550614277462   0.838502702862533    2.13465
  -1.013352718895545   0.005437204986280   1.887556493811437   0.227567666006506    2.14238
   0.585548448953634  -1.936752692607198  -0.765049269053934   0.325687826291563    2.16314
   1.050913398399501  -0.111110975095643   1.887724643852673   0.505932675625169    2.16339
   0.620767317066549  -1.940050432575796  -0.748922429219032  -0.288266884115885    2.17026
  -1.689976626103551  -1.014006991721093  -0.935008322785714   0.244834048865315    2.18139
   0.609899792313983  -1.250871991202918   1.690660176287671   1.260821297754585    2.18975
   0.106417815764050   2.083552558866118   0.691741938164307   0.327986694833651    2.19796
   0.162144017687867   2.084092076043976   0.687979521788356  -0.388136052935779    2.20069
  -0.122057382836168   1.364909697005573  -1.752782850373502  -1.071776256185010    2.22489
  -0.333142336442997   1.435745687604476  -1.671836095596490   0.842398141575863    2.22876
   0.609933740872536  -1.250335778925334   1.764569539362145  -0.729981557648889    2.24701
  -0.326542901455509  -2.076987348565181  -0.804452697591604   0.010022664208160    2.25114
  -0.584317904542944   1.587925818835115  -1.516706996112660  -0.749769207040474    2.27230
  -0.606639580067562  -1.872381170886708   1.158646853556571  -0.945394870987860    2.28392
  -1.712681821124838  -1.195973981746621  -0.943006553243415  -0.582762030002896    2.29192
  -1.700706695213239   1.502153544313353   0.391824080431043   0.537350309784801    2.30269
   1.127273595197811   0.745474820849299   1.866948097107300   0.006609577114650    2.30477
  -1.731311096987730   1.481385989671714   0.420660105731190  -0.930493275696005    2.31709
  -0.781234873019475   1.730790846526403  -1.340954036237797   0.926000724494851    2.32468
  -1.764332065211830   1.458483918422415   0.455200874125540   0.404428829994600    2.33393
  -0.542168781993797  -1.850919506152241   1.320579701902711   1.276858052363677    2.33747
  -1.083367321630203  -0.106645508269450  -2.092568929824633   0.125725625265376    2.35879
   2.014884356888531  -1.021941612489103  -0.696511224521089   0.010916241467417    2.36416
  -0.900964021874033   1.813144877150390  -1.223788354986883  -0.857839308980616    2.36577
   2.030029378056082   1.212189143723771   0.215039162793698   0.004300406244590    2.37417
   0.665900853605821   2.246672981183840   0.395133127962174   0.438616003254255    2.37636
   0.690614505685202   2.059737920134254   0.966950352641521   0.248095088677618    2.37791
  -0.513966421913037  -2.093078896086163   1.011777176812616   0.673133644610283    2.38093
  -1.031056669557268  -0.168994250267030  -2.142609762739322  -0.404819270223875    2.38378
  -1.011275069560247  -0.192553569848260  -2.159294926907079   0.289857110820182    2.39213
  -1.715560512353577  -1.368269457772396  -0.962467611808060   0.555208612958963    2.39617
  -0.980495618292158   1.863136583224780  -1.144384529911034   0.331258443951150    2.39630
   0.734883072280867   2.256802477007125   0.373729122571839  -0.738541293682051    2.40268
   0.793985381268717   2.261604101501228   0.316148737470408   0.288732892312712    2.41769
  -0.405926735786783  -1.808720444983849   1.554370540447134  -0.825727210263160    2.41916
  -1.889814098131251   1.344350630384750  -0.732449284436764  -0.429509895336696    2.43211
  -1.934429285114181   1.260561955430042  -0.795787482822558   1.131616688622864    2.44219
   0.794978418428753   2.085272815529595   1.006265265200778  -0.613202880931993    2.44804
  -0.464295390680105  -2.166549686616241   1.042527233598683  -0.793453665426209    2.44875
   0.802958551404919   2.213183375763521   0.700253886441593   0.099483195800889    2.45627
  -1.989450824407092   1.158279723234890  -0.882049525546962  -1.063886874046897    2.46527
   0.830630723309954   2.082580598073404   1.044000125967061   0.353391525156425    2.47326
   1.264349802004175  -0.950421513414504  -1.921210003155201   0.781913564863933    2.48856
   1.263149977426381  -0.945907482288063  -1.927695245894641  -0.796825633288867    2.49124
   1.165234528050489  -0.546090092808541  -2.134046404204033  -0.559044561968166    2.49202
  -1.002102716143030  -1.264907821960896   1.903581426635697   0.002853154411450    2.49556
   1.172528989401326  -0.568569326168224  -2.134552248867894   0.544306899981220    2.50088
  -0.228613259109952   1.388237701567254  -2.070568254082125   0.409926150220719    2.50334
  -2.054963852898315   1.019881185377284  -1.004741238707381   0.415388942225029    2.50450
  -0.069501586957659  -2.470843131019612   0.404558191021709   0.001987603970377    2.50471
  -0.422623974380077  -2.226639435333968   1.068022498577696   0.281994628104369    2.50544
  -1.707052903201384  -1.570219740078705  -0.969547241373539  -0.307193733124621    2.51389
   2.399393779121459   0.082659270061035  -0.785511546438716   0.001426089203817    2.52605
  -0.160997303845723  -1.722598842439121   1.852507783009250   0.749232218320694    2.53477
  -2.543105537266528   0.091160323914470   0.067500199156103  -0.762808712482042    2.54563
  -2.542477092762353   0.158431114909115   0.016248326550749   0.339703953546135    2.54746
  -2.545440662345314  -0.030726270262334   0.150230353070312   0.742614372904123    2.55006
  -0.247902078077589   1.345751594186263  -2.165231988825410  -0.795071740678746    2.56139
  -2.554898070018341  -0.179349125629797   0.238265079433139  -0.544748133383183    2.57224
  -0.250887590627853   1.322858015040723  -2.194418295152137   0.503096643477775    2.57456
  -1.696997958128023  -1.684642679876029  -0.956711483485774   0.108093993813311    2.57548
  -2.563617074843795  -0.256201186947670   0.279354915202766   0.228679164188282    2.59149
  -0.012304173244684  -1.667642504241307   2.004751862406674  -0.906114588983671    2.60772
  -2.333990186825956  -0.735816687131729  -0.956472735674024   0.001377163170192    2.62750
   0.061110249954693  -1.641772970424265   2.075369325971863   0.455143048976693    2.64694
   2.270428653670678  -0.395714973251001   1.341192679183307  -0.021296197918971    2.66650
  -2.208584555851363   0.903515530678476  -1.200718285605660   0.689415024308005    2.67131
  -2.212622121605860   0.877924093659326  -1.218292596320473  -0.922871474031834    2.67408
  -2.237064564900940   0.809346703008865  -1.278106000132846   0.188059218056600    2.70057
   2.293725361105264  -0.389437276295020   1.387325890382218   0.017000571484099    2.70878
  -1.092466431245908   1.110223951869285  -2.263271076239773  -0.599383394432098    2.74745
  -1.093202791234452   1.110852880778705  -2.263092731580369   0.598644088115620    2.74785
  -1.354221552297752  -1.645312763593735  -1.743527356077438   0.001494531235707    2.75334
  -2.450646113578325   0.199568401975240   1.373081000077574   0.000503042506486    2.81618
   1.998570554692860  -0.142306520802899  -1.980236713608687   0.000463750559637    2.81707
   2.562918225813535  -0.884073232194603   0.771465029849011   0.000615947868562    2.81874
   2.221098237178180   1.069961483746763   1.373270355006608   0.000547546653893    2.82205
  -1.595840454641792  -2.210470614462993   0.881589084611467  -0.088296782961509    2.86532
  -1.559960328853266  -2.241557184086202   0.868105751700635   0.045136441436493    2.86560
  -1.634158578159197  -2.180109209191729   0.894337002987518   0.043426195416765    2.86761
  -1.562885786127427  -0.653727287787331  -2.347346014551879  -0.013474950088817    2.89482
  -1.594702204263047  -0.716875685056248  -2.319099610081835   0.014290437955191    2.90434
   1.263791305554812   1.598845912202339  -2.074170030043208   0.000382058820854    2.90786
  -1.848986179363411   0.151258071356224   2.299352292272652   0.000293151539374    2.95443
   0.975609138983378  -1.689592550920703  -2.276161160191522   0.000276285905862    2.99791
  -1.332917185771166   2.377428824098198   1.291594055097306   0.000206330454194    3.01613
   2.021557612846643   2.080025106183752  -0.839535620309426   0.000214666588758    3.01961
  -1.875073625598100  -1.290719369810909  -2.026332361132973  -0.101454292111146    3.04760
  -1.877526153202032  -1.293604573157614  -2.024961092720732   0.099735584958799    3.04942
   1.320985189173392  -2.492986063228140  -1.165094324558769   0.000172491952577    3.05245
   0.227682949167537  -0.388415560763463  -3.020130725366204   0.000198467537715    3.05351
  -1.338028419715137  -0.016847414600295  -2.746863782158377   0.000392506235554    3.05546
   2.877146674217332   0.924377449065906  -0.524745810479909   0.000146194955165    3.06721
   2.161549304627691  -1.642275343238378   1.455061445084215   0.000134429166509    3.08003
  -2.245940368937591   2.149757716237097  -0.020568948377873   0.000177728468154    3.10904
   0.852718481142572  -3.000056200861621  -0.132320605694751   0.000129530953936    3.12169
   1.730645229850673   0.371858848824131   2.574656042738829   0.000123944918770    3.12446
  -0.930218607361900   1.735734445269953   2.429941246722660   0.000106606413194    3.12773
  -2.088921158440216  -1.172258749981787   2.027471613406392   0.000091784427230    3.13822
   2.326353690655319  -2.107716318284499  -0.030231695724453   0.000130582205686    3.13932
   1.312126420009776   0.375343067481715  -2.830071535439845   0.000135067772697    3.14195
   0.527272876718992   1.537740061289569   2.722396706752058   0.000104423295281    3.17082
   0.089112622832496   3.040701486514933  -0.963605837011650   0.022971942197124    3.19098
   0.090832619324442   3.042003084723740  -0.963315825624821  -0.022780080513307    3.19218
   0.732985114389413   3.135493823486556   0.060702334065479   0.000106361595332    3.22060
  -0.908060472801799   3.105282904095459   0.225766936847268   0.000066630070536    3.24320
   3.136045410251220   0.438854908511777   0.707221907538830   0.000060904086633    3.24462
   2.855635276054901  -0.201992995464625  -1.534801283754428   0.000034054143366    3.24824
  -0.103311507905897  -2.788579942567520  -1.742424847847775   0.000056205005965    3.28982
   2.484314343943334   1.119221458474579  -1.862885837721726   0.000044449261304    3.30073
   0.942634516603272   2.856994668319414  -1.438682154539097   0.000044598900040    3.33478
   0.092647720942681   2.845841159935135   1.757048386671691   0.000041816826070    3.34584
  -3.249479581696045   0.767336719704939   0.467974986209761   0.000034767034878    3.37149
   0.663049345436763  -1.528478820176016   2.965977830208394   0.431828579084768    3.40190
  -1.029156994171248  -0.052748796496668   3.245960503878320   0.487703074752036    3.40561
  -1.028327422352546  -0.055706174698241   3.249361307607225  -0.526394511323494    3.40865
   0.656473193141203  -1.529845509252409   2.974869177658126  -0.902376900268017    3.40899
   0.650919839403532  -1.530857233567982   2.982643897879058   0.470719505633055    3.41517
  -0.544188131434601  -1.693277111252632  -2.917493760071562   0.000026042753355    3.41688
  -0.750000458250258  -3.326231979300292  -0.326692604334677   0.000026321635030    3.42535
  -1.018667067296589  -0.089011783971460   3.287863427754416   0.039052056118399    3.44320
  -0.067550279248851   0.151381323126039   3.444601792868026   0.000035302814114    3.44859
   1.407176299693229  -2.884683010825984   1.295073523617433   0.000021754009643    3.46103
   3.392691722557140  -0.739112252969404  -0.368957104477203   0.000016735547724    3.49182
  -2.448031712430424   1.601569111479146   1.909109526451757   0.000018268427036    3.49322
  -2.824007657427889  -2.069928080955155  -0.284658599374110   0.000015583059287    3.51293
  -3.476217342540809  -0.369783861406359  -0.693288954101062   0.000010036905511    3.56391
   2.747270097241626   2.314338005941327   0.507134412346525   0.000008835803467    3.62779
   2.548083239577941  -1.732052536200570  -2.024112251151514   0.000007112209296    3.68643
  -3.315073193718689  -0.954197780736501   1.756161265713609   0.000001595996551    3.87096
  -1.657305483772988   2.986763251656919  -1.850720441301690   0.000002555649766    3.88492
  -0.374454281461091  -2.574397177878989   2.982160887402668   0.000100298475878    3.95740
   2.295072520464817   2.059688607186275   2.488343410541167   0.000001478282225    3.96252
  -0.744667132608065  -0.567575233668233   3.916206653792170  -0.000020256408854    4.02658
  -0.331535970687268   2.181296790972140  -3.445646977607893   0.000002647369633    4.09151
  -0.244550055243171  -2.627736949400728   3.181503721953696  -0.000088853343636    4.13361
  -0.045233509936243  -2.680968318902021   3.449130827030317   0.000018041074383    4.36877

>> # evaluating formula 1 with 16 points
# r4_16_4ag.txt:4 formula 1   : problem  G, 4_16_4  (d=4 n=16 o=4 plus 0/56 of order 5) quality P
# evaluating formula 2 with 16 points
# r4_16_4ag.txt:24 formula 2   : problem E2, 4_16_4  (d=4 n=16 o=4 plus 0/56 of order 5) quality P
# evaluating formula 3 with 16 points
# r4_16_4ag.txt:44 formula 3   : problem E1, 4_16_4  (d=4 n=16 o=4 plus 0/56 of order 5) quality P
# evaluating formula 4 with 16 points
# r4_16_4ag.txt:64 formula 4   : problem  S, 4_16_4  (d=4 n=16 o=4 plus 0/56 of order 5) quality NO (1 negative weight, stability factor 1.444444)
G 4 dimensions, degree 4, asymmetric 16 point rule with points at 3 distinct radii: 1+10+5=16

#                x1                 x2                 x3                 x4             Weight     Radius     cos1     cos2
 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.083333333333333    0.00000  0.00000  0.00000
  1.321119219639140  1.321119219639140 -0.504622638711413 -0.504622638711413  0.090000000000000    2.00000  1.00000  0.40825
  1.321119219639140 -0.504622638711413  1.321119219639140 -0.504622638711413  0.090000000000000    2.00000  0.16667  0.40825
  1.321119219639140 -0.504622638711413 -0.504622638711413  1.321119219639140  0.090000000000000    2.00000  0.16667  0.40825
 -0.504622638711413  1.321119219639140  1.321119219639140 -0.504622638711413  0.090000000000000    2.00000  0.16667  0.40825
 -0.504622638711413  1.321119219639140 -0.504622638711413  1.321119219639140  0.090000000000000    2.00000  0.16667  0.40825
 -0.504622638711413 -0.504622638711413  1.321119219639140  1.321119219639140  0.090000000000000    2.00000 -0.66667  0.40825
 -1.981678829458710 -0.155936971108157 -0.155936971108157 -0.155936971108157  0.090000000000000    2.00000 -0.66667 -0.61237
 -0.155936971108157 -1.981678829458710 -0.155936971108157 -0.155936971108157  0.090000000000000    2.00000 -0.66667 -0.61237
 -0.155936971108157 -0.155936971108157 -1.981678829458710 -0.155936971108157  0.090000000000000    2.00000  0.16667 -0.61237
 -0.155936971108157 -0.155936971108157 -0.155936971108157 -1.981678829458710  0.090000000000000    2.00000  0.16667 -0.61237
  2.449489742783180  2.449489742783180  2.449489742783180  2.449489742783180  0.003333333333333    4.89898  0.40825  1.00000
  3.495546745592950 -1.981678829458710 -1.981678829458710 -1.981678829458710  0.003333333333333    4.89898  0.40825 -0.25000
 -1.981678829458710  3.495546745592950 -1.981678829458710 -1.981678829458710  0.003333333333333    4.89898  0.40825 -0.25000
 -1.981678829458710 -1.981678829458710  3.495546745592950 -1.981678829458710  0.003333333333333    4.89898 -0.61237 -0.25000
 -1.981678829458710 -1.981678829458710 -1.981678829458710  3.495546745592950  0.003333333333333    4.89898 -0.61237 -0.25000

E_n^{r^2} 4 dimensions, degree 4, asymmetric 16 point rule with points at 3 distinct radii: 1+10+5=16

#                x1                 x2                 x3                 x4             Weight     Radius     cos1     cos2
  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.822467033424114    0.00000  0.00000  0.00000
  0.934172358962716  0.934172358962716 -0.356822089773090 -0.356822089773090  0.888264396098042    1.41421  1.00000  0.40825
  0.934172358962716 -0.356822089773090  0.934172358962716 -0.356822089773090  0.888264396098042    1.41421  0.16667  0.40825
  0.934172358962716 -0.356822089773090 -0.356822089773090  0.934172358962716  0.888264396098042    1.41421  0.16667  0.40825
 -0.356822089773090  0.934172358962716  0.934172358962716 -0.356822089773090  0.888264396098042    1.41421  0.16667  0.40825
 -0.356822089773090  0.934172358962716 -0.356822089773090  0.934172358962716  0.888264396098042    1.41421  0.16667  0.40825
 -0.356822089773090 -0.356822089773090  0.934172358962716  0.934172358962716  0.888264396098042    1.41421 -0.66667  0.40825
 -1.401258538444074 -0.110264089708268 -0.110264089708268 -0.110264089708268  0.888264396098042    1.41421 -0.66667 -0.61237
 -0.110264089708268 -1.401258538444074 -0.110264089708268 -0.110264089708268  0.888264396098042    1.41421 -0.66667 -0.61237
 -0.110264089708268 -0.110264089708268 -1.401258538444074 -0.110264089708268  0.888264396098042    1.41421  0.16667 -0.61237
 -0.110264089708268 -0.110264089708268 -0.110264089708268 -1.401258538444073  0.888264396098042    1.41421  0.16667 -0.61237
  1.732050807568877  1.732050807568877  1.732050807568877  1.732050807568878  0.032898681336965    3.46410  0.40825  1.00000
  2.471724807763345 -1.401258538444075 -1.401258538444075 -1.401258538444075  0.032898681336964    3.46410  0.40825 -0.25000
 -1.401258538444075  2.471724807763344 -1.401258538444074 -1.401258538444074  0.032898681336964    3.46410  0.40825 -0.25000
 -1.401258538444075 -1.401258538444075  2.471724807763345 -1.401258538444075  0.032898681336964    3.46410 -0.61237 -0.25000
 -1.401258538444075 -1.401258538444074 -1.401258538444075  2.471724807763345  0.032898681336964    3.46410 -0.61237 -0.25000

E_n^r 4 dimensions, degree 4, asymmetric 16 point rule with points at 3 distinct radii: 1+10+5=16

#                x1                 x2                 x3                 x4             Weight     Radius     cos1     cos2
  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 40.888361090227292    0.00000  0.00000  0.00000
  3.495352908115876  3.495352904785498 -1.335106010502894 -1.335106010567142  7.613694823697507    5.29150  1.00000  0.40825
  3.495352907994936 -1.335106010728173  3.495352904776393 -1.335106010682325  7.613694823697505    5.29150  0.16667  0.40825
  3.495352908065736 -1.335106010658474 -1.335106010552395  3.495352904781845  7.613694823697510    5.29150  0.16667  0.40825
 -1.335106003680044  3.495352908389807  3.495352908494145 -1.335106006963473  7.613694823697503    5.29150  0.16667  0.40825
 -1.335106003609243  3.495352908459505 -1.335106006834645  3.495352908500696  7.613694823697508    5.29150  0.16667  0.40825
 -1.335106003730183 -1.335106007054165  3.495352908444643  3.495352908385514  7.613694823697506    5.29150 -0.66667  0.40825
 -5.243029362088274 -0.412570441699426 -0.412570441860552 -0.412570441766189  7.613694823697507    5.29150 -0.66667 -0.61237
 -0.412570450413295 -5.243029360817405 -0.412570445578303 -0.412570445485041  7.613694823697504    5.29150 -0.66667 -0.61237
 -0.412570450292355 -0.412570445303734 -5.243029360857591 -0.412570445369859  7.613694823697505    5.29150  0.16667 -0.61237
 -0.412570450363155 -0.412570445373433 -0.412570445528801 -5.243029360834027  7.613694823697511    5.29150  0.16667 -0.61237
  6.480740713157078  6.480740693193997  6.480740693825246  6.480740693455115  0.281988697173982   12.96148  0.40825  1.00000
  9.248347373107745 -5.243029368095719 -5.243029368243591 -5.243029368156550  0.281988697173982   12.96148  0.40825 -0.25000
 -5.243029361917197  9.248347389258218 -5.243029357090339 -5.243029356999995  0.281988697173981   12.96148  0.40825 -0.25000
 -5.243029362280017 -5.243029357282798  9.248347388747529 -5.243029357345542  0.281988697173981   12.96148 -0.61237 -0.25000
 -5.243029362067613 -5.243029357073696 -5.243029357238842  9.248347389046964  0.281988697173982   12.96148 -0.61237 -0.25000

S_n 4 dimensions, degree 4, asymmetric 16 point rule with points at 3 distinct radii: 1+10+5=16
 (1 negative weight, stability factor 1.444444)
#                x1                 x2                 x3                 x4             Weight     Radius     cos1     cos2
  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 -1.096622711232152    0.00000  0.00000  0.00000
  0.467086179481367  0.467086179481347 -0.178411044886541 -0.178411044886553  0.592176264065362    0.70711  1.00000  0.40825
  0.467086179481349 -0.178411044886548  0.467086179481369 -0.178411044886535  0.592176264065361    0.70711  0.16667  0.40825
  0.467086179481356 -0.178411044886540 -0.178411044886537  0.467086179481365  0.592176264065361    0.70711  0.16667  0.40825
 -0.178411044886548  0.467086179481361  0.467086179481350 -0.178411044886555  0.592176264065361    0.70711  0.16667  0.40825
 -0.178411044886541  0.467086179481369 -0.178411044886556  0.467086179481344  0.592176264065362    0.70711  0.16667  0.40825
 -0.178411044886559 -0.178411044886527  0.467086179481354  0.467086179481363  0.592176264065362    0.70711 -0.66667  0.40825
 -0.700629269222036 -0.055132044854129 -0.055132044854146 -0.055132044854139  0.592176264065361    0.70711 -0.66667 -0.61237
 -0.055132044854139 -0.700629269222038 -0.055132044854127 -0.055132044854118  0.592176264065362    0.70711 -0.66667 -0.61237
 -0.055132044854121 -0.055132044854143 -0.700629269222037 -0.055132044854136  0.592176264065362    0.70711  0.16667 -0.61237
 -0.055132044854128 -0.055132044854151 -0.055132044854131 -0.700629269222036  0.592176264065362    0.70711  0.16667 -0.61237
  0.866025403784424  0.866025403784461  0.866025403784441  0.866025403784429  0.021932454224643    1.73205  0.40825  1.00000
  1.235862403881684 -0.700629269222073 -0.700629269222003 -0.700629269222014  0.021932454224643    1.73205  0.40825 -0.25000
 -0.700629269222006  1.235862403881653 -0.700629269222060 -0.700629269222075  0.021932454224643    1.73205  0.40825 -0.25000
 -0.700629269222060 -0.700629269222033  1.235862403881670 -0.700629269222020  0.021932454224643    1.73205 -0.61237 -0.25000
 -0.700629269222041 -0.700629269222008 -0.700629269222047  1.235862403881679  0.021932454224643    1.73205 -0.61237 -0.25000

>> # evaluating formula 1 with 16 points
# r4_16_4g.txt:4 formula 1   : problem  G, 4_16_4  (d=4 n=16 o=4 plus 48/56 of order 5) quality P
# evaluating formula 2 with 16 points
# r4_16_4g.txt:24 formula 2   : problem  S, 4_16_4  (d=4 n=16 o=4 plus 48/56 of order 5) (15 non-zero weight) quality PB
# evaluating formula 3 with 16 points
# r4_16_4g.txt:44 formula 3   : problem E1, 4_16_4  (d=4 n=16 o=4 plus 48/56 of order 5) quality P
# evaluating formula 4 with 16 points
# r4_16_4g.txt:64 formula 4   : problem E2, 4_16_4  (d=4 n=16 o=4 plus 48/56 of order 5) quality P
# G_n 4 dimensions, degree 4, asymmetric 16 point rule with points at 3 distinct radii: 1+6+9=16
#
#                x1                 x2                 x3                 x4             Weight     Radius     cos1     cos2
 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.250000000000000    0.00000
 -0.000000000000000 -0.000000000000000 -0.000000000000000 -2.000000000000000  0.083333333333333    2.00000  1.00000
 -0.000000000000000  2.000000000000000 -0.000000000000000 -0.000000000000000  0.083333333333333    2.00000  0.00000
 -1.732050807568877 -1.000000000000000 -0.000000000000000 -0.000000000000000  0.083333333333333    2.00000  0.00000
  1.732050807568877 -1.000000000000000 -0.000000000000000 -0.000000000000000  0.083333333333333    2.00000  0.00000
 -0.000000000000000 -0.000000000000000  1.732050807568877  1.000000000000000  0.083333333333333    2.00000 -0.50000
 -0.000000000000000 -0.000000000000000 -1.732050807568877  1.000000000000000  0.083333333333333    2.00000 -0.50000
  1.732050807568877  1.000000000000000  1.732050807568877 -1.000000000000000  0.027777777777778    2.82843  0.35355  1.00000
 -1.732050807568877  1.000000000000000  1.732050807568877 -1.000000000000000  0.027777777777778    2.82843  0.35355  0.25000
 -0.000000000000000 -2.000000000000000  1.732050807568877 -1.000000000000000  0.027777777777778    2.82843  0.35355  0.25000
  1.732050807568877  1.000000000000000 -1.732050807568877 -1.000000000000000  0.027777777777778    2.82843  0.35355  0.25000
 -0.000000000000000 -2.000000000000000 -1.732050807568877 -1.000000000000000  0.027777777777778    2.82843  0.35355 -0.50000
 -1.732050807568877  1.000000000000000 -1.732050807568877 -1.000000000000000  0.027777777777778    2.82843  0.35355 -0.50000
 -1.732050807568877  1.000000000000000 -0.000000000000000  2.000000000000000  0.027777777777778    2.82843 -0.70711 -0.50000
  1.732050807568877  1.000000000000000 -0.000000000000000  2.000000000000000  0.027777777777778    2.82843 -0.70711  0.25000
 -0.000000000000000 -2.000000000000000 -0.000000000000000  2.000000000000000  0.027777777777778    2.82843 -0.70711 -0.50000

# S_n 4 dimensions, degree 4, asymmetric 16 point rule with points at 3 distinct radii: 1+6+9=16
# Same structure as the other rules, but zero weight on the central point so it actually has 15 points.
#                x1                 x2                 x3                 x4             Weight     Radius     cos1     cos2
 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.000000000000000    0.00000
 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.707106781186547  0.548311355616076    0.70711  1.00000
 -0.000000000000000  0.707106781186547 -0.000000000000000 -0.000000000000000  0.548311355616076    0.70711  0.00000
 -0.612372435695794 -0.353553390593274 -0.000000000000000 -0.000000000000000  0.548311355616076    0.70711  0.00000
  0.612372435695794 -0.353553390593274 -0.000000000000000 -0.000000000000000  0.548311355616076    0.70711  0.00000
 -0.000000000000000 -0.000000000000000  0.612372435695794  0.353553390593274  0.548311355616076    0.70711 -0.50000
 -0.000000000000000 -0.000000000000000 -0.612372435695794  0.353553390593274  0.548311355616076    0.70711 -0.50000
  0.612372435695794  0.353553390593274  0.612372435695794 -0.353553390593274  0.182770451872025    1.00000  0.35355  1.00000
 -0.612372435695794  0.353553390593274  0.612372435695794 -0.353553390593274  0.182770451872025    1.00000  0.35355  0.25000
 -0.000000000000000 -0.707106781186547  0.612372435695794 -0.353553390593274  0.182770451872025    1.00000  0.35355  0.25000
  0.612372435695794  0.353553390593274 -0.612372435695794 -0.353553390593274  0.182770451872025    1.00000  0.35355  0.25000
 -0.000000000000000 -0.707106781186547 -0.612372435695794 -0.353553390593274  0.182770451872025    1.00000  0.35355 -0.50000
 -0.612372435695794  0.353553390593274 -0.612372435695794 -0.353553390593274  0.182770451872025    1.00000  0.35355 -0.50000
 -0.612372435695794  0.353553390593274 -0.000000000000000  0.707106781186547  0.182770451872025    1.00000 -0.70711 -0.50000
  0.612372435695794  0.353553390593274 -0.000000000000000  0.707106781186547  0.182770451872025    1.00000 -0.70711  0.25000
 -0.000000000000000 -0.707106781186547 -0.000000000000000  0.707106781186547  0.182770451872025    1.00000 -0.70711 -0.50000

# E_n^r 4 dimensions, degree 4, asymmetric 16 point rule with points at 3 distinct radii: 1+6+9=16
#
#                x1                 x2                 x3                 x4             Weight     Radius     cos1     cos2
 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 54.987795948926397    0.00000
 -0.000000000000000 -0.000000000000000 -0.000000000000000 -5.291502622129182  7.049717429349553    5.29150  1.00000
 -0.000000000000000  5.291502622129182 -0.000000000000000 -0.000000000000000  7.049717429349553    5.29150  0.00000
 -4.582575694955840 -2.645751311064591 -0.000000000000000 -0.000000000000000  7.049717429349553    5.29150  0.00000
  4.582575694955840 -2.645751311064591 -0.000000000000000 -0.000000000000000  7.049717429349553    5.29150  0.00000
 -0.000000000000000 -0.000000000000000  4.582575694955840  2.645751311064591  7.049717429349553    5.29150 -0.50000
 -0.000000000000000 -0.000000000000000 -4.582575694955840  2.645751311064591  7.049717429349553    5.29150 -0.50000
  4.582575694955840  2.645751311064591  4.582575694955840 -2.645751311064591  2.349905809783180    7.48331  0.35355  1.00000
 -4.582575694955840  2.645751311064591  4.582575694955840 -2.645751311064591  2.349905809783180    7.48331  0.35355  0.25000
 -0.000000000000000 -5.291502622129182  4.582575694955840 -2.645751311064591  2.349905809783180    7.48331  0.35355  0.25000
  4.582575694955840  2.645751311064591 -4.582575694955840 -2.645751311064591  2.349905809783180    7.48331  0.35355  0.25000
 -0.000000000000000 -5.291502622129182 -4.582575694955840 -2.645751311064591  2.349905809783180    7.48331  0.35355 -0.50000
 -4.582575694955840  2.645751311064591 -4.582575694955840 -2.645751311064591  2.349905809783180    7.48331  0.35355 -0.50000
 -4.582575694955840  2.645751311064591 -0.000000000000000  5.291502622129182  2.349905809783180    7.48331 -0.70711 -0.50000
  4.582575694955840  2.645751311064591 -0.000000000000000  5.291502622129182  2.349905809783180    7.48331 -0.70711  0.25000
 -0.000000000000000 -5.291502622129182 -0.000000000000000  5.291502622129182  2.349905809783180    7.48331 -0.70711 -0.50000

# E_n^{r^2} 4 dimensions, degree 4, asymmetric 16 point rule with points at 3 distinct radii: 1+6+9=16
#
#                x1                 x2                 x3                 x4             Weight     Radius     cos1     cos2
 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  2.467401100272339    0.00000
 -0.000000000000000 -0.000000000000000 -0.000000000000000 -1.414213562373095  0.822467033424114    1.41421  1.00000
 -0.000000000000000  1.414213562373095 -0.000000000000000 -0.000000000000000  0.822467033424114    1.41421  0.00000
 -1.224744871391589 -0.707106781186548 -0.000000000000000 -0.000000000000000  0.822467033424114    1.41421  0.00000
  1.224744871391589 -0.707106781186548 -0.000000000000000 -0.000000000000000  0.822467033424114    1.41421  0.00000
 -0.000000000000000 -0.000000000000000  1.224744871391589  0.707106781186548  0.822467033424114    1.41421 -0.50000
 -0.000000000000000 -0.000000000000000 -1.224744871391589  0.707106781186548  0.822467033424114    1.41421 -0.50000
  1.224744871391589  0.707106781186548  1.224744871391589 -0.707106781186548  0.274155677808038    2.00000  0.35355  1.00000
 -1.224744871391589  0.707106781186548  1.224744871391589 -0.707106781186548  0.274155677808038    2.00000  0.35355  0.25000
 -0.000000000000000 -1.414213562373095  1.224744871391589 -0.707106781186548  0.274155677808038    2.00000  0.35355  0.25000
  1.224744871391589  0.707106781186548 -1.224744871391589 -0.707106781186548  0.274155677808038    2.00000  0.35355  0.25000
 -0.000000000000000 -1.414213562373095 -1.224744871391589 -0.707106781186548  0.274155677808038    2.00000  0.35355 -0.50000
 -1.224744871391589  0.707106781186548 -1.224744871391589 -0.707106781186548  0.274155677808038    2.00000  0.35355 -0.50000
 -1.224744871391589  0.707106781186548 -0.000000000000000  1.414213562373095  0.274155677808038    2.00000 -0.70711 -0.50000
  1.224744871391589  0.707106781186548 -0.000000000000000  1.414213562373095  0.274155677808038    2.00000 -0.70711  0.25000
 -0.000000000000000 -1.414213562373095 -0.000000000000000  1.414213562373095  0.274155677808038    2.00000 -0.70711 -0.50000

>> # evaluating formula 1 with 16 points
# r4_16_4ms.txt:4 formula 1   : problem  S, 4_16_4  (d=4 n=16 o=4 plus 46/56 of order 5) quality PB
 16 point rule by Mysovskikh: J. MYSOVSKIH , Interpolatorische kubaturformeln, Apr. 1992. Übertragung aus dem Russischen von Irina Dietrich und Hermann Engels. 4 dimensions, degree 4, bilaterally symmetric (axis 2,3,4) 16 point rule with points at 3 distinct radii: 1+8+7=16

#                 x1                  x2                  x3                  x4              Weight     Radius     cos1     cos2
   1.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.182770451872025    1.00000 -0.50000  0.31623
  -0.500000000000000   0.866025403784439   0.000000000000000   0.000000000000000   0.182770451872025    1.00000  1.00000  0.31623
  -0.500000000000000  -0.866025403784439   0.000000000000000   0.000000000000000   0.182770451872025    1.00000 -0.50000 -0.63246
  -0.500000000000000   0.000000000000000   0.866025403784439   0.000000000000000   0.182770451872025    1.00000  0.25000  0.31623
  -0.500000000000000   0.000000000000000  -0.866025403784439   0.000000000000000   0.182770451872025    1.00000  0.25000 -0.63246
  -0.500000000000000   0.000000000000000   0.000000000000000   0.866025403784439   0.182770451872025    1.00000  0.25000 -0.63246
  -0.500000000000000   0.000000000000000   0.000000000000000  -0.866025403784439   0.182770451872025    1.00000  0.25000  0.31623
  -0.500000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.731081807488101    0.50000  0.50000 -0.31623
   0.250000000000000   0.433012701892219   0.433012701892219   0.433012701892219   0.365540903744050    0.79057  0.31623  0.40000
   0.250000000000000   0.433012701892219   0.433012701892219  -0.433012701892219   0.365540903744050    0.79057  0.31623  1.00000
   0.250000000000000   0.433012701892219  -0.433012701892219   0.433012701892219   0.365540903744050    0.79057  0.31623 -0.20000
   0.250000000000000   0.433012701892219  -0.433012701892219  -0.433012701892219   0.365540903744050    0.79057  0.31623  0.40000
   0.250000000000000  -0.433012701892219   0.433012701892219   0.433012701892219   0.365540903744050    0.79057 -0.63246 -0.20000
   0.250000000000000  -0.433012701892219   0.433012701892219  -0.433012701892219   0.365540903744050    0.79057 -0.63246  0.40000
   0.250000000000000  -0.433012701892219  -0.433012701892219   0.433012701892219   0.365540903744050    0.79057 -0.63246 -0.80000
   0.250000000000000  -0.433012701892219  -0.433012701892219  -0.433012701892219   0.365540903744050    0.79057 -0.63246 -0.20000

>> # evaluating formula 1 with 22 points
# r4_22_5S.txt:5 formula 1   : problem  S, 4_22_5  (d=4 n=22 o=5 plus 0/84 of order 6) quality PO
# S_n: 5-1  S: 4 dimensions, degree 5, 22 point rule with points at 3 distinct radii: 2+8+12=22
# A.H. Stroud, Approximate Calculation of Multiple Integrals, Prentice Hall, Englewood Cliffs, NH, 1971.
# \cite[$S_n$:5-1]{stroud71approximate}
                 x1                 x2                 x3                 x4             Weight     Radius
  1.183012701892220  1.183012701892220  1.183012701892220  1.183012701892220  0.002460436508531    2.36603
 -1.183012701892220 -1.183012701892220 -1.183012701892220 -1.183012701892220  0.002460436508531    2.36603
 -0.296418983404190 -0.296418983404190 -0.296418983404190  0.889256950212571  0.104038597432280    1.02683
 -0.296418983404190 -0.296418983404190  0.889256950212571 -0.296418983404190  0.104038597432280    1.02683
 -0.296418983404190  0.889256950212571 -0.296418983404190 -0.296418983404190  0.104038597432280    1.02683
  0.889256950212571 -0.296418983404190 -0.296418983404190 -0.296418983404190  0.104038597432280    1.02683
 -0.889256950212571  0.296418983404190  0.296418983404190  0.296418983404190  0.104038597432280    1.02683
  0.296418983404190 -0.889256950212571  0.296418983404190  0.296418983404190  0.104038597432280    1.02683
  0.296418983404190  0.296418983404190 -0.889256950212571  0.296418983404190  0.104038597432280    1.02683
  0.296418983404190  0.296418983404190  0.296418983404190 -0.889256950212571  0.104038597432280    1.02683
 -0.531672220881311 -0.531672220881311  0.091220531629185  0.091220531629185  0.341464379005782    0.76288
 -0.531672220881311  0.091220531629185 -0.531672220881311  0.091220531629185  0.341464379005782    0.76288
 -0.531672220881311  0.091220531629185  0.091220531629185 -0.531672220881311  0.341464379005782    0.76288
  0.091220531629185 -0.531672220881311 -0.531672220881311  0.091220531629185  0.341464379005782    0.76288
  0.091220531629185 -0.531672220881311  0.091220531629185 -0.531672220881311  0.341464379005782    0.76288
  0.091220531629185  0.091220531629185 -0.531672220881311 -0.531672220881311  0.341464379005782    0.76288
 -0.091220531629185 -0.091220531629185  0.531672220881311  0.531672220881311  0.341464379005782    0.76288
 -0.091220531629185  0.531672220881311 -0.091220531629185  0.531672220881311  0.341464379005782    0.76288
 -0.091220531629185  0.531672220881311  0.531672220881311 -0.091220531629185  0.341464379005782    0.76288
  0.531672220881311 -0.091220531629185 -0.091220531629185  0.531672220881311  0.341464379005782    0.76288
  0.531672220881311 -0.091220531629185  0.531672220881311 -0.091220531629185  0.341464379005782    0.76288
  0.531672220881311  0.531672220881311 -0.091220531629185 -0.091220531629185  0.341464379005782    0.76288
>> # evaluating formula 1 with 23 points
# r4_23_5g.txt:4 formula 1   : problem  G, 4_23_5  (d=4 n=23 o=5 plus 3/84 of order 6) quality P
# evaluating formula 2 with 23 points
# r4_23_5g.txt:31 formula 2   : problem  S, 4_23_5  (d=4 n=23 o=5 plus 3/84 of order 6) quality PI
# evaluating formula 3 with 23 points
# r4_23_5g.txt:58 formula 3   : problem E1, 4_23_5  (d=4 n=23 o=5 plus 3/84 of order 6) quality P
# evaluating formula 4 with 23 points
# r4_23_5g.txt:85 formula 4   : problem E2, 4_23_5  (d=4 n=23 o=5 plus 3/84 of order 6) quality P
G_n 4 dimensions, degree 5, symmetric 23 point rule with points at 2 distinct radii: 1+22=23

#                x1                 x2                 x3                 x4             Weight     Radius     cos1
  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.333333333333333    0.00000
 -2.449489742783179 -0.000000000000000 -0.000000000000000  0.000000000000000  0.031250000000000    2.44949  1.00000
 -1.154700538379251  2.160246899469286 -0.000000000000000 -0.000000000000000  0.031250000000000    2.44949  0.47140
 -1.154700538379251  0.308606699924183  2.138089935299394  0.000000000000000  0.031250000000000    2.44949  0.47140
 -1.154700538379251  0.308606699924183  0.267261241912424  2.121320343559643  0.031250000000000    2.44949  0.47140
 -1.154700538379251  0.308606699924183 -1.603567451474547 -1.414213562373096  0.031250000000000    2.44949  0.47140
 -1.154700538379251 -1.543033499620919  0.534522483824846 -1.414213562373096  0.031250000000000    2.44949  0.47140
 -1.154700538379251 -1.543033499620919 -1.336306209562124  0.707106781186547  0.031250000000000    2.44949  0.47140
 -0.816496580927726 -1.745743121887941  1.133893419027680  1.000000000000000  0.031250000000000    2.44949  0.33333
 -0.816496580927726  0.872871560943970 -1.889822365046136  1.000000000000000  0.031250000000000    2.44949  0.33333
 -0.816496580927726  0.872871560943970  0.755928946018456 -1.999999999999999  0.031250000000000    2.44949  0.33333
  0.816496580927726 -0.872871560943970 -0.755928946018456  1.999999999999999  0.031250000000000    2.44949 -0.33333
  0.816496580927726 -0.872871560943970  1.889822365046136 -1.000000000000000  0.031250000000000    2.44949 -0.33333
  0.816496580927726  1.745743121887941 -1.133893419027680 -1.000000000000000  0.031250000000000    2.44949 -0.33333
  1.154700538379251  1.543033499620919  1.336306209562124 -0.707106781186547  0.031250000000000    2.44949 -0.47140
  1.154700538379251  1.543033499620919 -0.534522483824846  1.414213562373096  0.031250000000000    2.44949 -0.47140
  1.154700538379251 -0.308606699924183  1.603567451474547  1.414213562373096  0.031250000000000    2.44949 -0.47140
  1.154700538379251 -0.308606699924183 -0.267261241912424 -2.121320343559643  0.031250000000000    2.44949 -0.47140
  1.154700538379251 -0.308606699924183 -2.138089935299394 -0.000000000000000  0.031250000000000    2.44949 -0.47140
  1.154700538379251 -2.160246899469286  0.000000000000000  0.000000000000000  0.031250000000000    2.44949 -0.47140
  2.449489742783179  0.000000000000000  0.000000000000000 -0.000000000000000  0.031250000000000    2.44949 -1.00000
  0.000000000000000 -1.603567451474547 -1.388730149658828 -1.224744871391586  0.020833333333333    2.44949 -0.00000
 -0.000000000000000  1.603567451474547  1.388730149658828  1.224744871391586  0.020833333333333    2.44949  0.00000

S_n 4 dimensions, degree 5, symmetric 23 point rule with points at 2 distinct radii: 1+22=23

#                x1                 x2                 x3                 x4             Weight     Radius     cos1
  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.548311355616075    0.00000
 -0.866025403784439 -0.000000000000000 -0.000000000000000  0.000000000000000  0.205616758356028    0.86603  1.00000
 -0.408248290463863  0.763762615825973 -0.000000000000000 -0.000000000000000  0.205616758356028    0.86603  0.47140
 -0.408248290463863  0.109108945117996  0.755928946018454  0.000000000000000  0.205616758356028    0.86603  0.47140
 -0.408248290463863  0.109108945117996  0.094491118252307  0.750000000000000  0.205616758356028    0.86603  0.47140
 -0.408248290463863  0.109108945117996 -0.566946709513841 -0.500000000000000  0.205616758356028    0.86603  0.47140
 -0.408248290463863 -0.545544725589981  0.188982236504613 -0.500000000000000  0.205616758356028    0.86603  0.47140
 -0.408248290463863 -0.545544725589981 -0.472455591261535  0.250000000000000  0.205616758356028    0.86603  0.47140
 -0.288675134594813 -0.617213399848368  0.400891862868636  0.353553390593274  0.205616758356028    0.86603  0.33333
 -0.288675134594813  0.308606699924184 -0.668153104781061  0.353553390593274  0.205616758356028    0.86603  0.33333
 -0.288675134594813  0.308606699924184  0.267261241912425 -0.707106781186547  0.205616758356028    0.86603  0.33333
  0.288675134594813 -0.308606699924184 -0.267261241912425  0.707106781186547  0.205616758356028    0.86603 -0.33333
  0.288675134594813 -0.308606699924184  0.668153104781061 -0.353553390593274  0.205616758356028    0.86603 -0.33333
  0.288675134594813  0.617213399848368 -0.400891862868636 -0.353553390593274  0.205616758356028    0.86603 -0.33333
  0.408248290463863  0.545544725589981  0.472455591261535 -0.250000000000000  0.205616758356028    0.86603 -0.47140
  0.408248290463863  0.545544725589981 -0.188982236504613  0.500000000000000  0.205616758356028    0.86603 -0.47140
  0.408248290463863 -0.109108945117996  0.566946709513841  0.500000000000000  0.205616758356028    0.86603 -0.47140
  0.408248290463863 -0.109108945117996 -0.094491118252307 -0.750000000000000  0.205616758356028    0.86603 -0.47140
  0.408248290463863 -0.109108945117996 -0.755928946018454 -0.000000000000000  0.205616758356028    0.86603 -0.47140
  0.408248290463863 -0.763762615825973  0.000000000000000  0.000000000000000  0.205616758356028    0.86603 -0.47140
  0.866025403784439  0.000000000000000  0.000000000000000 -0.000000000000000  0.205616758356028    0.86603 -1.00000
  0.000000000000000 -0.566946709513841 -0.490990253030983 -0.433012701892219  0.137077838904019    0.86603 -0.00000
 -0.000000000000000  0.566946709513841  0.490990253030983  0.433012701892219  0.137077838904019    0.86603  0.00000

E_n^r 4 dimensions, degree 5, symmetric 23 point rule with points at 2 distinct radii: 1+22=23

#                x1                 x2                 x3                 x4             Weight     Radius     cos1
  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 62.037513378276003    0.00000
 -6.480740698407860 -0.000000000000000 -0.000000000000000  0.000000000000000  2.643644036006079    6.48074  1.00000
 -3.055050463303893  5.715476066494078 -0.000000000000000 -0.000000000000000  2.643644036006079    6.48074  0.47140
 -3.055050463303893  0.816496580927723  5.656854249492377  0.000000000000000  2.643644036006079    6.48074  0.47140
 -3.055050463303893  0.816496580927723  0.707106781186547  5.612486080160913  2.643644036006079    6.48074  0.47140
 -3.055050463303893  0.816496580927723 -4.242640687119287 -3.741657386773944  2.643644036006079    6.48074  0.47140
 -3.055050463303893 -4.082482904638630  1.414213562373089 -3.741657386773944  2.643644036006079    6.48074  0.47140
 -3.055050463303893 -4.082482904638630 -3.535533905932742  1.870828693386970  2.643644036006079    6.48074  0.47140
 -2.160246899469286 -4.618802153517010  2.999999999999994  2.645751311064591  2.643644036006079    6.48074  0.33333
 -2.160246899469286  2.309401076758504 -4.999999999999999  2.645751311064591  2.643644036006079    6.48074  0.33333
 -2.160246899469286  2.309401076758504  2.000000000000003 -5.291502622129179  2.643644036006079    6.48074  0.33333
  2.160246899469286 -2.309401076758504 -2.000000000000003  5.291502622129179  2.643644036006079    6.48074 -0.33333
  2.160246899469286 -2.309401076758504  4.999999999999999 -2.645751311064591  2.643644036006079    6.48074 -0.33333
  2.160246899469286  4.618802153517010 -2.999999999999994 -2.645751311064591  2.643644036006079    6.48074 -0.33333
  3.055050463303893  4.082482904638630  3.535533905932742 -1.870828693386970  2.643644036006079    6.48074 -0.47140
  3.055050463303893  4.082482904638630 -1.414213562373089  3.741657386773944  2.643644036006079    6.48074 -0.47140
  3.055050463303893 -0.816496580927723  4.242640687119287  3.741657386773944  2.643644036006079    6.48074 -0.47140
  3.055050463303893 -0.816496580927723 -0.707106781186547 -5.612486080160913  2.643644036006079    6.48074 -0.47140
  3.055050463303893 -0.816496580927723 -5.656854249492377 -0.000000000000000  2.643644036006079    6.48074 -0.47140
  3.055050463303893 -5.715476066494078  0.000000000000000  0.000000000000000  2.643644036006079    6.48074 -0.47140
  6.480740698407860  0.000000000000000  0.000000000000000 -0.000000000000000  2.643644036006079    6.48074 -1.00000
  0.000000000000000 -4.242640687119287 -3.674234614174771 -3.240370349203926  1.762429357337385    6.48074 -0.00000
 -0.000000000000000  4.242640687119287  3.674234614174771  3.240370349203926  1.762429357337385    6.48074  0.00000

E_n^{r^2} 4 dimensions, degree 5, symmetric 23 point rule with points at 2 distinct radii: 1+22=23

#                x1                 x2                 x3                 x4             Weight     Radius     cos1
  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  3.289868133696452    0.00000
 -1.732050807568877 -0.000000000000000 -0.000000000000000  0.000000000000000  0.308425137534043    1.73205  1.00000
 -0.816496580927726  1.527525231651945 -0.000000000000000 -0.000000000000000  0.308425137534043    1.73205  0.47140
 -0.816496580927726  0.218217890235992  1.511857892036908  0.000000000000000  0.308425137534043    1.73205  0.47140
 -0.816496580927726  0.218217890235992  0.188982236504613  1.500000000000000  0.308425137534043    1.73205  0.47140
 -0.816496580927726  0.218217890235992 -1.133893419027682 -1.000000000000000  0.308425137534043    1.73205  0.47140
 -0.816496580927726 -1.091089451179962  0.377964473009225 -1.000000000000000  0.308425137534043    1.73205  0.47140
 -0.816496580927726 -1.091089451179962 -0.944911182523069  0.500000000000000  0.308425137534043    1.73205  0.47140
 -0.577350269189626 -1.234426799696736  0.801783725737272  0.707106781186547  0.308425137534043    1.73205  0.33333
 -0.577350269189626  0.617213399848368 -1.336306209562121  0.707106781186547  0.308425137534043    1.73205  0.33333
 -0.577350269189626  0.617213399848368  0.534522483824849 -1.414213562373094  0.308425137534043    1.73205  0.33333
  0.577350269189626 -0.617213399848368 -0.534522483824849  1.414213562373094  0.308425137534043    1.73205 -0.33333
  0.577350269189626 -0.617213399848368  1.336306209562121 -0.707106781186547  0.308425137534043    1.73205 -0.33333
  0.577350269189626  1.234426799696736 -0.801783725737272 -0.707106781186547  0.308425137534043    1.73205 -0.33333
  0.816496580927726  1.091089451179962  0.944911182523069 -0.500000000000000  0.308425137534043    1.73205 -0.47140
  0.816496580927726  1.091089451179962 -0.377964473009225  1.000000000000000  0.308425137534043    1.73205 -0.47140
  0.816496580927726 -0.218217890235992  1.133893419027682  1.000000000000000  0.308425137534043    1.73205 -0.47140
  0.816496580927726 -0.218217890235992 -0.188982236504613 -1.500000000000000  0.308425137534043    1.73205 -0.47140
  0.816496580927726 -0.218217890235992 -1.511857892036908 -0.000000000000000  0.308425137534043    1.73205 -0.47140
  0.816496580927726 -1.527525231651945  0.000000000000000  0.000000000000000  0.308425137534043    1.73205 -0.47140
  1.732050807568877  0.000000000000000  0.000000000000000 -0.000000000000000  0.308425137534043    1.73205 -1.00000
  0.000000000000000 -1.133893419027682 -0.981980506061967 -0.866025403784438  0.205616758356028    1.73205 -0.00000
 -0.000000000000000  1.133893419027682  0.981980506061967  0.866025403784438  0.205616758356028    1.73205  0.00000

>> # evaluating formula 1 with 31 points
# ml4_31_5S.txt:7 formula 1   : problem  S, 4_31_5  (d=4 n=31 o=5 plus 41/84 of order 6) quality PI
Meng-Luo (2013) S 4 dimensions, degree 5, centrally and bilaterally symmetric (axis 4) 31 point rule with points at 2 distinct radii: 1+30=31
Zhaoliang Mang and Zhongxuan Luo, "Constructing cubature formulae of
degree 5 with few points", J. Computational and Applied Mathematics,
237 (2013) 354-362. \cite{meng-luo13few}

#                 x1                  x2                  x3                  x4              Weight     Radius     cos1
   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.548311355616075    0.00000  0.00000
   0.866025403784439   0.000000000000000   0.000000000000000   0.000000000000000   0.175459633797144    0.86603  1.00000
  -0.216506350946110   0.838525491562421   0.000000000000000   0.000000000000000   0.175459633797144    0.86603 -0.25000
  -0.216506350946110  -0.279508497187474   0.790569415042095   0.000000000000000   0.175459633797144    0.86603 -0.25000
  -0.216506350946110  -0.279508497187474  -0.395284707521047   0.684653196881458   0.175459633797144    0.86603 -0.25000
  -0.216506350946110  -0.279508497187474  -0.395284707521047  -0.684653196881458   0.175459633797144    0.86603 -0.25000
  -0.866025403784439  -0.000000000000000  -0.000000000000000  -0.000000000000000   0.175459633797144    0.86603 -1.00000
   0.216506350946110  -0.838525491562421  -0.000000000000000  -0.000000000000000   0.175459633797144    0.86603  0.25000
   0.216506350946110   0.279508497187474  -0.790569415042095  -0.000000000000000   0.175459633797144    0.86603  0.25000
   0.216506350946110   0.279508497187474   0.395284707521047  -0.684653196881458   0.175459633797144    0.86603  0.25000
   0.216506350946110   0.279508497187474   0.395284707521047   0.684653196881458   0.175459633797144    0.86603  0.25000
   0.530330085889911   0.684653196881458   0.000000000000000   0.000000000000000   0.131594725347858    0.86603  0.61237
   0.530330085889911  -0.228217732293819   0.645497224367903   0.000000000000000   0.131594725347858    0.86603  0.61237
  -0.353553390593274   0.456435464587638   0.645497224367903   0.000000000000000   0.131594725347858    0.86603 -0.40825
   0.530330085889911  -0.228217732293819  -0.322748612183951   0.559016994374947   0.131594725347858    0.86603  0.61237
  -0.353553390593274   0.456435464587638  -0.322748612183951   0.559016994374947   0.131594725347858    0.86603 -0.40825
  -0.353553390593274  -0.456435464587638   0.322748612183951   0.559016994374947   0.131594725347858    0.86603 -0.40825
   0.530330085889911  -0.228217732293819  -0.322748612183951  -0.559016994374947   0.131594725347858    0.86603  0.61237
  -0.353553390593274   0.456435464587638  -0.322748612183951  -0.559016994374947   0.131594725347858    0.86603 -0.40825
  -0.353553390593274  -0.456435464587638   0.322748612183951  -0.559016994374947   0.131594725347858    0.86603 -0.40825
  -0.353553390593274  -0.456435464587638  -0.645497224367903   0.000000000000000   0.131594725347858    0.86603 -0.40825
  -0.530330085889911  -0.684653196881458  -0.000000000000000  -0.000000000000000   0.131594725347858    0.86603 -0.61237
  -0.530330085889911   0.228217732293819  -0.645497224367903  -0.000000000000000   0.131594725347858    0.86603 -0.61237
   0.353553390593274  -0.456435464587638  -0.645497224367903  -0.000000000000000   0.131594725347858    0.86603  0.40825
  -0.530330085889911   0.228217732293819   0.322748612183951  -0.559016994374947   0.131594725347858    0.86603 -0.61237
   0.353553390593274  -0.456435464587638   0.322748612183951  -0.559016994374947   0.131594725347858    0.86603  0.40825
   0.353553390593274   0.456435464587638  -0.322748612183951  -0.559016994374947   0.131594725347858    0.86603  0.40825
  -0.530330085889911   0.228217732293819   0.322748612183951   0.559016994374947   0.131594725347858    0.86603 -0.61237
   0.353553390593274  -0.456435464587638   0.322748612183951   0.559016994374947   0.131594725347858    0.86603  0.40825
   0.353553390593274   0.456435464587638  -0.322748612183951   0.559016994374947   0.131594725347858    0.86603  0.40825
   0.353553390593274   0.456435464587638   0.645497224367903  -0.000000000000000   0.131594725347858    0.86603  0.40825
>> # evaluating formula 1 with 43 points
# r4_43_6bg.txt:4 formula 1   : problem  G, 4_43_6  (d=4 n=43 o=6 plus 50/120 of order 7) quality P
# evaluating formula 2 with 43 points
# r4_43_6bg.txt:51 formula 2   : problem E2, 4_43_6  (d=4 n=43 o=6 plus 50/120 of order 7) quality P
G 4 dimensions, degree 6, asymmetric 43 point rule with points at 31 distinct radii: 1+1+1+2+1+1+1+2+1+1+2+2+2+2+2+1+1+1+1+1+1+1+2+1+1+2+2+2+2+1+1=43

#                x1                 x2                 x3                 x4             Weight     Radius
 -4.005498341690290 -0.734623144971638  0.530389301299374 -0.390121310259784  0.000979985235819    4.12519
 -2.259110522164485 -2.250678087672609 -2.330755804195401 -0.588605842047131  0.001385073582390    3.99350
 -2.201824119830292  2.574184312136103 -1.697934389128880 -0.631536988941968  0.001752947555763    3.84139
 -1.826718539389831 -0.924939607715428 -0.135816152201344  1.795967244650576  0.012798998918690    2.72697
 -1.806056816291788  0.108089945824682 -1.421907382158588 -2.714314331771669  0.002832032940712    3.55849
 -1.773089416219244  0.280328246376847 -2.442051294079424  1.323088146235946  0.004185000774394    3.30705
 -1.744093114886252  1.379747201372397  0.248655936296692  1.318941035517735  0.017438979106455    2.59750
 -1.682563507519514  1.372746801623248  0.957002998821395 -1.006132573135921  0.017568473205710    2.57752
 -1.541437771936959 -0.210648133384139  1.866168449131238  0.552759948463113  0.021190481925126    2.49169
 -1.537231915114044  0.048913174322688 -0.659664803213914 -0.259733138876819  0.077437605451596    1.69354
 -1.431567923160785 -0.881242783198389  0.975364500390827 -1.783966027779672  0.014179380621390    2.63815
 -1.053927154387063 -1.920821508423947  0.292868777199585 -0.045862979677204  0.034591536526672    2.21093
  0.000000000000000  0.308346213267512 -0.597919074270802  3.046014838388997  0.006453812200695    3.11942
  0.000000000000000  0.909689869851248  1.714613908530340  2.073173072631419  0.010366478872022    2.83998
  0.000000000000000 -1.602822962275993  1.437122235956583  1.911756845767055  0.010208746425307    2.87909
  0.000000000000000 -2.176419963963196 -1.275776833680554  1.509521366518481  0.008227634181943    2.93991
  0.000000000000000  1.672909243176292 -1.198250825228100  1.085506682944407  0.027768381515810    2.32653
  0.000000000000000 -0.083795123852135  0.122014245170761  0.887900693182013  0.151856390444488    0.90015
  0.000000000000000 -0.489067988239011 -1.591667088045968  0.790458950388538  0.044396078981781    1.84321
  0.000000000000000  2.137858838938466  0.825854782251165  0.244440323893373  0.027803772792399    2.30483
  0.000000000000000  1.326891057820803  3.130478062886694 -0.211684377900050  0.003359725127755    3.40666
  0.000000000000000  0.074149686937881  0.997943077970066 -0.457934393587688  0.124170467816352    1.10050
  0.000000000000000 -1.761333522701865  2.515834090527005 -0.542253679881469  0.006218904649601    3.11861
  0.000000000000000  1.261821528685590 -0.773698307208464 -0.813113438852565  0.067631055041226    1.68877
  0.000000000000000 -1.307302119143762 -1.339505458006013 -0.838476445000374  0.034081528993129    2.05094
  0.000000000000000  0.440193889723158 -2.716234522830002 -0.877346876498629  0.009972575128059    2.88815
  0.000000000000000 -0.694619983558608 -0.290271789188303 -1.732093708650069  0.041955060013643    1.88862
  0.000000000000000  8.116098587968162 -0.367053633880515 -2.128146837242609  0.000011151586284    8.39850
  0.000000000000000  1.352398840943804  0.179660275265531 -2.406533885984697  0.010376335817287    2.76635
  0.000000000000000  0.465136323788613  2.447891314091191 -2.468606854596966  0.002395528172207    3.50750
  0.000000000000000 -5.282009301408198 -0.090529342739201 -3.985448382029300  0.000065380550579    6.61752
  1.053927154387063 -1.920821508423947  0.292868777199585 -0.045862979677204  0.034591536526672    2.21093
  1.431567923160935 -0.881242783198389  0.975364500390827 -1.783966027779554  0.014179380621390    2.63815
  1.537231915114044  0.048913174322688 -0.659664803213914 -0.259733138876691  0.077437605451596    1.69354
  1.541437771936959 -0.210648133384139  1.866168449131238  0.552759948463241  0.021190481925126    2.49169
  1.682563507519514  1.372746801623248  0.957002998821395 -1.006132573135782  0.017568473205710    2.57752
  1.744093114886144  1.379747201372397  0.248655936296692  1.318941035517879  0.017438979106455    2.59750
  1.773089416219128  0.280328246376847 -2.442051294079424  1.323088146236092  0.004185000774394    3.30705
  1.806056816292011  0.108089945824682 -1.421907382158588 -2.714314331771519  0.002832032940712    3.55849
  1.826718539389683 -0.924939607715428 -0.135816152201344  1.795967244650727  0.012798998918690    2.72697
  2.201824119830292  2.574184312136103 -1.697934389128880 -0.631536988941786  0.001752947555763    3.84139
  2.259110522164485 -2.250678087672609 -2.330755804195401 -0.588605842046944  0.001385073582390    3.99350
  4.005498341690290 -0.734623144971638  0.530389301299374 -0.390121310259452  0.000979985235819    4.12519

E_n^{r^2} 4 dimensions, degree 6, asymmetric 43 point rule with points at 31 distinct radii: 1+1+1+2+1+1+1+2+1+1+2+2+2+2+2+1+1+1+1+1+1+1+2+1+1+2+2+2+2+1+1=43

#                x1                 x2                 x3                 x4             Weight     Radius
 -2.832315039440677 -0.519457007426036  0.375041871617583 -0.275857423969957  0.009672066596443    2.91695
 -1.597432369672388 -1.591469738061275 -1.648093234436474 -0.416207182357479  0.013670128324588    2.82383
 -1.556924766112097  1.820223183135464 -1.200620920562867 -0.446564087450934  0.017300898911238    2.71627
 -1.291685066521683 -0.654031068803605 -0.096036522216235  1.269940617481395  0.126321056057437    1.92826
 -1.277075022008188  0.076431133670720 -1.005440352143549 -1.919310070267526  0.027951044775683    2.51623
 -1.253763549858682  0.198222003971201 -1.726791030048943  0.935564600311027  0.041304302061519    2.33844
 -1.233260068556799  0.975628602413583  0.175826298737681  0.932632150199849  0.172115824939573    1.83671
 -1.189752065944072  0.970678572279942  0.676703310082470 -0.711443165237030  0.173393880471496    1.82258
 -1.089961101313707 -0.148950723560214  1.319580365217081  0.390860307926639  0.209141673669432    1.76189
 -1.086987111433525  0.034586837252932 -0.466453455662648 -0.183659063798621  0.764278531574887    1.19752
 -1.012271386196187 -0.623132747871287  0.689686852354983 -1.261454475649393  0.139944877385588    1.86546
 -0.745239037743734 -1.358225914055547  0.207089498355638 -0.032430023935172  0.341404781144087    1.56336
  0.000000000000000  0.218033698354650 -0.422792632017667  2.153857747819708  0.063696573299787    2.20576
  0.000000000000000  0.643247875748525  1.212415121838573  1.465954738231026  0.102313045499108    2.00817
  0.000000000000000 -1.133366985666864  1.016198878438873  1.351816229621688  0.100756288648818    2.03583
  0.000000000000000 -1.538961315228155 -0.902110450376223  1.067392794611200  0.081203494532653    2.07883
  0.000000000000000  1.182925470159611 -0.847291284081165  0.767569136533307  0.274062940419562    1.64511
  0.000000000000000 -0.059252100306211  0.086277100161601  0.627840601169239  1.498762499464462    0.63650
  0.000000000000000 -0.345823290945066 -1.125478591348749  0.558938884069335  0.438171736509692    1.30335
  0.000000000000000  1.511694482232989  0.583967516805138  0.172845410620439  0.274412238318751    1.62976
  0.000000000000000  0.938253664880879  2.213582266622907 -0.149683459084381  0.033159157907339    2.40887
  0.000000000000000  0.052431746456634  0.705652317670807 -0.323808515044402  1.225513395645594    0.77817
  0.000000000000000 -1.245450877833679  1.778963345751935 -0.383431254167546  0.061378128699660    2.20519
  0.000000000000000  0.892242559580754 -0.547087319619658 -0.574958026486560  0.667491758485204    1.19414
  0.000000000000000 -0.924402193506095 -0.947173392792442 -0.592892380124954  0.336371208546443    1.45023
  0.000000000000000  0.311264084460129 -1.920667850386101 -0.620377925825017  0.098425371374081    2.04223
  0.000000000000000 -0.491170500721979 -0.205253150522199 -1.224775207037021  0.414079844958622    1.33546
  0.000000000000000  5.738948348330854 -0.259546113576080 -1.504827059974959  0.000110061745069    5.93864
  0.000000000000000  0.956290391300193  0.127038998950097 -1.701676429934990  0.102410329649481    1.95610
  0.000000000000000  0.328901048727110  1.730920547801524 -1.745568646969104  0.023642915391349    2.48018
  0.000000000000000 -3.734944595316151 -0.064013912147252 -2.818137577001868  0.000645280169744    4.67930
  0.745239037743734 -1.358225914055547  0.207089498355638 -0.032430023935172  0.341404781144087    1.56336
  1.012271386196187 -0.623132747871287  0.689686852354983 -1.261454475649393  0.139944877385588    1.86546
  1.086987111433525  0.034586837252932 -0.466453455662648 -0.183659063798621  0.764278531574887    1.19752
  1.089961101313707 -0.148950723560214  1.319580365217081  0.390860307926639  0.209141673669432    1.76189
  1.189752065944072  0.970678572279942  0.676703310082470 -0.711443165237030  0.173393880471496    1.82258
  1.233260068556799  0.975628602413583  0.175826298737681  0.932632150199849  0.172115824939573    1.83671
  1.253763549858682  0.198222003971201 -1.726791030048943  0.935564600311027  0.041304302061519    2.33844
  1.277075022008188  0.076431133670720 -1.005440352143549 -1.919310070267526  0.027951044775683    2.51623
  1.291685066521683 -0.654031068803605 -0.096036522216235  1.269940617481395  0.126321056057437    1.92826
  1.556924766112097  1.820223183135464 -1.200620920562867 -0.446564087450934  0.017300898911238    2.71627
  1.597432369672388 -1.591469738061275 -1.648093234436474 -0.416207182357479  0.013670128324588    2.82383
  2.832315039440677 -0.519457007426036  0.375041871617583 -0.275857423969957  0.009672066596443    2.91695

>> # evaluating formula 1 with 43 points
# r4_43_6Sba.txt:4 formula 1   : problem  S, 4_43_6  (d=4 n=43 o=6 plus 50/120 of order 7) quality NO (2 negative weights, stability factor 1.000595)
S bilaterally symmetric 4 dimensions, degree 6, asymmetric 43 point rule with points at 31 distinct radii: 1+1+1+1+2+2+2+1+2+1+1+2+2+2+2+1+1+2+1+1+1+2+1+2+1+1+1+1+2+1+1=43
 (2 negative weights, stability factor 1.000595)
#                x1                 x2                 x3                 x4             Weight     Radius
 -1.167281512418500 -1.006498780447378  1.082711463927769 -0.077967497907586  0.000777450616032    1.88519
 -0.870201978349951  0.085528724264383 -0.083451682837955  0.157004751835775  0.111544103132102    0.89229
 -0.665828426091953  0.618277410602523  0.293144025526936 -0.344399652396703  0.049786463718494    1.01496
 -0.647901815239106 -0.259213759776813 -0.618307930846157 -0.335490356915604  0.059056862864842    0.99087
 -0.582897011676605 -0.156160809921786  0.151957301455155 -0.621783800577997  0.126021915355264    0.87969
 -0.526870174277677 -0.227341186917065  0.232978886692078  0.689877161592786  0.090387861504756    0.92708
 -0.526171053552720 -0.590317397703037  0.000000000000000 -0.000000000000000  0.198151168112751    0.79078
 -0.513678551079992  0.002931911698409  0.576894949574179  0.000000000000000  0.213812268025947    0.77245
 -0.448098842039986  0.386185933998481 -0.352710673471913 -0.322133504715338  0.205403478703402    0.76033
 -0.404743745889165  0.592962607537870  0.245001410340373  0.466651679293803  0.118818261533311    0.89062
 -0.397542169650095 -0.241132188658009 -0.578385835123785  0.468153501097876  0.127915010426319    0.87743
 -0.355057183750208  0.460987028499151 -0.462699298397311  0.362543784046788  0.148611934826167    0.82711
  0.000000000000000  0.583100875503531 -0.711197970820345  1.818486114523060  0.000637894725578    2.03782
  0.000000000000000 -0.732891074049596 -0.077969051490395  0.544831145346821  0.094230030176619    0.91654
  0.000000000000000 -0.805557725293435 -0.513688749579881 -0.120423414473578  0.069457946611192    0.96296
  0.000000000000000  0.064161516748775 -0.025910332464285  0.710104318893556  0.235742237598890    0.71347
  0.000000000000000 -0.180916945101167 -0.629052683303985 -0.103806806103201  0.218059861754219    0.66273
  0.000000000000000  0.316194387769280 -1.121407627682214 -0.125815553362861  0.030255248537292    1.17191
  0.000000000000000 -0.555497244031555  0.572258205857253  0.213029512878887  0.167773977740544    0.82549
  0.000000000000000  0.096120288116151  0.773362976203932  0.536815259882271  0.080851203429697    0.94631
  0.000000000000000  0.728617902515721 -2.079621090824714 -0.624815331449214 -0.000227950371588    2.29044
  0.000000000000000 -0.068327109265359  0.045258956709694 -0.088264679342198  0.307352441403765    0.12045
  0.000000000000000 -0.752272323566850  0.231354937908897 -0.483393472178632  0.095406990755454    0.92364
  0.000000000000000 -0.281086928765509 -0.312086153804118 -0.725354050241737  0.149613931785352    0.83818
  0.000000000000000  0.927039535016180 -0.164281311801578 -0.091192568145440  0.084168425279192    0.94589
  0.000000000000000  0.544854785538305  0.389645227951718 -0.111582780530918  0.208173159294021    0.67907
  0.000000000000000  0.437807678560770 -0.577532528098455 -0.829847872873873  0.026975634298501    1.10176
  0.000000000000000 -0.253147398101131  0.774700910684558 -0.583555215043472  0.086807266772730    1.00239
  0.000000000000000  0.348290785547371  0.216494325265701 -0.737481951000971  0.149657425823797    0.84383
  0.000000000000000  0.502438997114945  0.929621840054363 -0.158230623082574  0.030533814333471    1.06849
  0.000000000000000 -0.698575803227988  1.227734234957057 -1.187480247633557 -0.001240897042823    1.84539
  0.355057183750208  0.460987028499151 -0.462699298397311  0.362543784046788  0.148611934826167    0.82711
  0.397542169650095 -0.241132188658009 -0.578385835123785  0.468153501097876  0.127915010426320    0.87743
  0.404743745889165  0.592962607537870  0.245001410340373  0.466651679293803  0.118818261533311    0.89062
  0.448098842039986  0.386185933998480 -0.352710673471913 -0.322133504715338  0.205403478703402    0.76033
  0.513678551079992  0.002931911698409  0.576894949574179  0.000000000000000  0.213812268025948    0.77245
  0.526171053552719 -0.590317397703037  0.000000000000000 -0.000000000000000  0.198151168112751    0.79078
  0.526870174277677 -0.227341186917065  0.232978886692078  0.689877161592786  0.090387861504756    0.92708
  0.582897011676605 -0.156160809921786  0.151957301455155 -0.621783800577997  0.126021915355264    0.87969
  0.647901815239106 -0.259213759776812 -0.618307930846158 -0.335490356915604  0.059056862864841    0.99087
  0.665828426091953  0.618277410602524  0.293144025526936 -0.344399652396703  0.049786463718494    1.01496
  0.870201978349951  0.085528724264383 -0.083451682837955  0.157004751835775  0.111544103132102    0.89229
  1.167281512418497 -1.006498780447375  1.082711463927766 -0.077967497907585  0.000777450616032    1.88519

>> # evaluating formula 1 with 45 points
# r4_45_6E1a.txt:4 formula 1   : problem E1, 4_45_6  (d=4 n=45 o=6 plus 0/120 of order 7) quality P
E1 4 dimensions, degree 6, asymmetric 45 point rule with points at 45 distinct radii: 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=45

#                x1                 x2                 x3                 x4             Weight     Radius
 -1.580014367811964 -0.000000000000000 -0.000000000000000  0.000000000000000 33.131676190125951    1.58001
  1.143989699581585  2.231133412001415 -0.000000000000000 -0.000000000000000 17.915350200474386    2.50732
  2.622546567675287 -1.635723161551501  1.516814439029659 -0.000000000000000 12.994053176370793    3.44297
  0.584625234169210 -3.209856593615266 -2.031726781458286  2.249139437461329  7.128905513749065    4.45326
  0.152317097848113  1.941817668108900 -4.228102992823627  1.745082269693918  4.858917352839078    4.97152
  0.839014500584366 -2.343112403879817 -2.093985533261506 -3.169494697761218  6.646442009781919    4.54143
 -0.045984211332136 -1.124611245294550  3.321917443110395  4.345888111121615  3.640960386025457    5.58469
  0.183152708012812  0.955310878841526  1.630388620501219 -4.887195252886261  4.570746429972354    5.24300
 -2.247363249017907 -1.776127287697294  4.928537362683238 -0.644105025951847  3.452390066974404    5.73678
  3.179574605222971  1.156144323809069 -0.581280635833043  4.762917620431319  2.698833034892786    5.87108
  4.854783112019280  0.922185235887916 -2.549069471026253 -2.342541598934321  2.597650531100785    6.03362
 -3.194478508470068 -5.227270471624005 -0.175854503471945 -1.552036296294930  2.175478534995899    6.32209
 -4.471563801579701  2.891488585665542  1.876643264823342  3.687950859318142  1.577034566336214    6.74376
 -4.065764903025386  0.683839382208537 -3.219892738978984 -4.326848912933883  1.533016054812401    6.78877
 -2.955968762303473 -1.097587268382764 -2.178526838149088  5.677889355534723  1.407758750817020    6.85032
  3.163333365734309  1.233679555379470  5.933954739206274 -1.702799171780787  1.275001606623190    7.04557
  0.328919028481288  4.187556167775485  4.477427200298155  2.136954945122813  1.773050568508936    6.50060
 -3.941557997387075  5.390247796815489  0.440046298079007 -2.695281840294106  1.107135068855621    7.21449
  0.505480114415028  4.462384989499864 -4.500062693700899 -4.088477754700813  0.980491859492944    7.55874
 -0.130256613475099 -1.547058037784525 -7.285817321661964 -1.262070100105589  0.918922788254944    7.55555
 -3.306430910708157  3.915989282668998  5.770397750006603 -2.537174881956323  0.566180638247142    8.12417
 -6.077462293901728 -2.221764297782452 -4.805683000785705  0.888553118184294  0.660231563150079    8.10900
  0.269771706909130  8.667277576603100 -0.558690539568566  1.465397825850931  0.400184733887869    8.81215
  5.791884147246031 -1.734881380589748 -4.847645427135749  2.483809816427842  0.616970911342190    8.13786
  1.416847675925724 -5.295357539436946  3.699018367827697 -5.021309261117506  0.606494524234911    8.30329
 -5.246548141577474  4.777571469604249 -4.407783522815121  1.770240371719506  0.501800916684640    8.53896
 -8.993647931982002  0.032815779453116  1.710487230228053 -0.469552400910224  0.348647510297023    9.16695
  1.020268490499507 -7.634992340213018  2.775023361199239  2.052106458952347  0.522008956695467    8.44073
 -0.329014460620258  4.872978139864806 -0.978471877244910  7.500438038439133  0.311127877591877    9.00379
  7.522561265391727  4.556661964515432  1.583371903730805  1.463973058564884  0.372285976110160    9.05552
 -5.960790979550677 -5.247286847141343  2.382204862455764  4.604584686846112  0.285640871530872    9.48378
  3.666558987073945  6.910624877298243  1.967055381494316 -5.093609067285237  0.268854375500831    9.54015
 -5.888571700289162 -1.977416182494094  2.581502975418556 -7.194161640520134  0.219304066974086    9.84914
  9.248347563796134 -3.972822992920441  2.395061191190509  2.957444346073589  0.128106820583716   10.76095
  6.110480816089536  1.075182397273967  7.997639556055825  6.697564281312418  0.045995797682997   12.13728
  9.477407113621402 -1.305316472666914  2.751991541682789 -6.759154596502923  0.073031779899831   12.03265
  6.350934773042782 -8.961867582460213 -3.181159619663354 -2.758116871464581  0.088680661643863   11.76335
  8.337576196676356 10.296788984545204 -9.555038875317145  3.153010967729304  0.011021651843622   16.63668
 -2.072628266761579 -12.825797830105722 -9.261575997513853  2.979560435036615  0.010806401983256   16.23119
  5.419197744456431 -9.337276451499079 -0.709482005261682 15.641681192515867  0.004938849899962   19.01889
  5.581221169504939 -8.602853390520268 17.997714331288421  2.372914081563659  0.002442648791554   20.84964
 -6.431123358451874 -14.450701205277692 -9.593535374399911 -15.032114640882991  0.000971136950623   23.83658
  3.801257196914396 -0.766173683409561 -5.106427383638199 -17.339859866821115  0.005554938892954   18.48737
 -19.103554061969859  3.411053599164827 34.211316057694930 16.092915159637272  0.000035725001851   42.49679
  0.314709798462680 -1.199369493653011 -27.073912084892328 22.854272076607927  0.000118786646754   35.45211

>> # evaluating formula 1 with 49 points
# r4_49_7S.txt:6 formula 1   : problem  S, 4_49_7  (d=4 n=49 o=7 plus 130/165 of order 8) quality PO

# S_n:7-1  S: 4 dimensions, degree 7, 49 point rule with points at 3 distinct radii: 1+24+24=49
# A. H. Stroud, Some seventh degree integration formulas for
# symmetric regions, SIAM J. Numer. Anal., v. 4, 1967, pp. 37-44. \cite{stroud67seventh}
                 x1                 x2                 x3                 x4             Weight     Radius
 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.308425137534045    0.00000
  0.797389191721246 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.159980273738844    0.79739
 -0.000000000000000  0.797389191721246 -0.000000000000000 -0.000000000000000  0.159980273738844    0.79739
 -0.000000000000000 -0.000000000000000  0.797389191721246 -0.000000000000000  0.159980273738844    0.79739
 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.797389191721246  0.159980273738844    0.79739
 -0.797389191721246 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.159980273738844    0.79739
 -0.000000000000000 -0.797389191721246 -0.000000000000000 -0.000000000000000  0.159980273738844    0.79739
 -0.000000000000000 -0.000000000000000 -0.797389191721246 -0.000000000000000  0.159980273738844    0.79739
 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.797389191721246  0.159980273738844    0.79739
 -0.398694595860623 -0.398694595860623 -0.398694595860623 -0.398694595860623  0.159980273738844    0.79739
 -0.398694595860623 -0.398694595860623 -0.398694595860623  0.398694595860623  0.159980273738844    0.79739
 -0.398694595860623 -0.398694595860623  0.398694595860623 -0.398694595860623  0.159980273738844    0.79739
 -0.398694595860623 -0.398694595860623  0.398694595860623  0.398694595860623  0.159980273738844    0.79739
 -0.398694595860623  0.398694595860623 -0.398694595860623 -0.398694595860623  0.159980273738844    0.79739
 -0.398694595860623  0.398694595860623 -0.398694595860623  0.398694595860623  0.159980273738844    0.79739
 -0.398694595860623  0.398694595860623  0.398694595860623 -0.398694595860623  0.159980273738844    0.79739
 -0.398694595860623  0.398694595860623  0.398694595860623  0.398694595860623  0.159980273738844    0.79739
  0.398694595860623 -0.398694595860623 -0.398694595860623 -0.398694595860623  0.159980273738844    0.79739
  0.398694595860623 -0.398694595860623 -0.398694595860623  0.398694595860623  0.159980273738844    0.79739
  0.398694595860623 -0.398694595860623  0.398694595860623 -0.398694595860623  0.159980273738844    0.79739
  0.398694595860623 -0.398694595860623  0.398694595860623  0.398694595860623  0.159980273738844    0.79739
  0.398694595860623  0.398694595860623 -0.398694595860623 -0.398694595860623  0.159980273738844    0.79739
  0.398694595860623  0.398694595860623 -0.398694595860623  0.398694595860623  0.159980273738844    0.79739
  0.398694595860623  0.398694595860623  0.398694595860623 -0.398694595860623  0.159980273738844    0.79739
  0.398694595860623  0.398694595860623  0.398694595860623  0.398694595860623  0.159980273738844    0.79739
 -0.000000000000000 -0.000000000000000  0.734321520592939  0.734321520592939  0.032785437219933    1.03849
 -0.000000000000000  0.734321520592939 -0.000000000000000  0.734321520592939  0.032785437219933    1.03849
 -0.000000000000000  0.734321520592939  0.734321520592939 -0.000000000000000  0.032785437219933    1.03849
  0.734321520592939 -0.000000000000000 -0.000000000000000  0.734321520592939  0.032785437219933    1.03849
  0.734321520592939 -0.000000000000000  0.734321520592939 -0.000000000000000  0.032785437219933    1.03849
  0.734321520592939  0.734321520592939 -0.000000000000000 -0.000000000000000  0.032785437219933    1.03849
 -0.734321520592939 -0.000000000000000 -0.000000000000000  0.734321520592939  0.032785437219933    1.03849
 -0.000000000000000 -0.734321520592939 -0.000000000000000  0.734321520592939  0.032785437219933    1.03849
 -0.000000000000000 -0.000000000000000 -0.734321520592939  0.734321520592939  0.032785437219933    1.03849
 -0.000000000000000 -0.000000000000000  0.734321520592939 -0.734321520592939  0.032785437219933    1.03849
 -0.734321520592939 -0.000000000000000  0.734321520592939 -0.000000000000000  0.032785437219933    1.03849
 -0.000000000000000 -0.734321520592939  0.734321520592939 -0.000000000000000  0.032785437219933    1.03849
 -0.000000000000000  0.734321520592939 -0.734321520592939 -0.000000000000000  0.032785437219933    1.03849
 -0.000000000000000  0.734321520592939 -0.000000000000000 -0.734321520592939  0.032785437219933    1.03849
 -0.734321520592939  0.734321520592939 -0.000000000000000 -0.000000000000000  0.032785437219933    1.03849
  0.734321520592939 -0.734321520592939 -0.000000000000000 -0.000000000000000  0.032785437219933    1.03849
  0.734321520592939 -0.000000000000000 -0.734321520592939 -0.000000000000000  0.032785437219933    1.03849
  0.734321520592939 -0.000000000000000 -0.000000000000000 -0.734321520592939  0.032785437219933    1.03849
 -0.734321520592939 -0.734321520592939 -0.000000000000000 -0.000000000000000  0.032785437219933    1.03849
 -0.734321520592939 -0.000000000000000 -0.734321520592939 -0.000000000000000  0.032785437219933    1.03849
 -0.734321520592939 -0.000000000000000 -0.000000000000000 -0.734321520592939  0.032785437219933    1.03849
 -0.000000000000000 -0.734321520592939 -0.734321520592939 -0.000000000000000  0.032785437219933    1.03849
 -0.000000000000000 -0.734321520592939 -0.000000000000000 -0.734321520592939  0.032785437219933    1.03849
 -0.000000000000000 -0.000000000000000 -0.734321520592939 -0.734321520592939  0.032785437219933    1.03849
>> # evaluating formula 1 with 105 points
# r4_105_8ag.txt:3 formula 1   : problem  G, 4_105_8  (d=4 n=105 o=8 plus 0/220 of order 9) quality N (14 negative weights, stability factor 12.248673)
# evaluating formula 2 with 105 points
# r4_105_8ag.txt:111 formula 2   : problem E2, 4_105_8  (d=4 n=105 o=8 plus 0/220 of order 9) quality N (14 negative weights, stability factor 12.248673)
G 4 dimensions, degree 8, asymmetric 105 point rule with points at 105 distinct radii (14 negative weights, stability factor 12.248673)
#                x1                 x2                 x3                 x4             Weight     Radius
  0.617793893884375  0.000000000000000 -0.000000000000000  0.000000000000000  0.495757980445975    0.61779
  0.279675260331183  0.821381299324199 -0.000000000000000  0.000000000000000 -0.900396377920598    0.86769
  0.355801270334567  0.927704325253957 -0.236411839047600 -0.000000000000000  0.587605396782432    1.02133
  0.609252566236994  0.465386291296651  0.202374163738787 -0.837328945806972  0.190344626147593    1.15319
 -0.519979478033700  1.120846922073790  0.461958488761044  0.038684468229179  0.214436086980330    1.31969
 -0.928933393366117 -0.277422861841375 -0.490136513315713  0.751796159608114  0.597415857342602    1.32110
 -0.784742863583918 -0.489875703110287 -0.462010642567525  0.886942373637280 -1.158031536747173    1.36232
  1.284394723396816 -0.155627435563501 -0.155360924028302 -0.480575477730377 -0.876225995551127    1.38888
 -0.706124814284347 -0.682128749529107 -0.424630499749669  0.982152790220661  0.639610087064177    1.45219
  1.004625101445660  0.864738439535922  0.534783402165526  0.267385921621954  0.096478928631151    1.45414
 -0.287745417843086 -0.269159028825295 -0.874082601412348 -1.441434048584744  0.040445008166046    1.73118
  1.601819933914318 -0.294647253183121 -0.282133242898721 -0.622281646584956  0.866423590535266    1.76620
 -0.064500977177702  0.376465887583954 -0.195177241349894  1.713324780586776  0.050444008128409    1.76620
  0.085054337189132 -1.627955509691070 -0.570062347307119 -0.470560208707290  0.038679764342630    1.78994
 -1.424270020067888 -0.886342511892619  0.481728834762665 -0.448991051321244  0.030121316072049    1.80217
 -0.757352118068434 -0.182547963866763  1.468085669996558  0.802396682528215  0.039274678005547    1.84554
  0.165534366944248 -0.358775849373376 -1.698019375898238  0.672982663237182  0.039872552860994    1.86877
  0.542436090696750  0.624952726096409  1.493536576963007  1.174793520700187  0.012155648857569    2.07258
  1.874481377601598 -0.406912628340991 -0.346315632925142 -0.789726166247441 -0.274287037722871    2.10306
 -1.533472669664316  0.209791610467941  0.482716412380605 -1.479368177821715  0.019462566145640    2.19479
  1.025974946334524 -1.017177370903382  1.443225602442489 -0.806465598835885  0.072474320116723    2.19558
  0.487313476256946 -1.026440835036074  1.183870571434872 -1.669608060485017  0.038868755468563    2.34098
 -1.720409493175682  1.307431274593527  0.888713635482028  0.332700581956997 -0.074047820686762    2.36002
 -0.654638310486346 -1.917120982832276  1.301514330393487 -0.417949804621957  0.009949917274374    2.44388
 -0.724801173681815 -0.158440373317608  2.106213134886493 -1.019405345641025  0.011888057683162    2.45474
  0.555148772009980 -1.807893323886091  1.121695773755337  1.114570316971115  0.011017744869811    2.46518
 -1.351695453539790 -0.943747938356001 -1.764369053691902 -0.590542636681822  0.013150253298674    2.48586
  1.016311907583300  0.468451733137686  1.904122823987524 -1.164079432467592  0.011083601581841    2.49662
 -1.979236297273163  1.645593198132122  0.424156595633145  0.440954145408311 -0.416185402966228    2.64570
 -2.005689215147100  1.683362655163862  0.308067167344335  0.299534699167949  0.217986150826023    2.65351
  0.975099337383981 -1.068282672488343  1.758845317391804 -1.394628697212803 -0.829419812899736    2.67031
 -2.009717095599482  1.539895206033676  0.650300545933812  0.556038954699410  0.256459501791636    2.67251
  1.824876477250913 -1.210333830553888  0.297571395792055  1.512347271932252  0.008608697491101    2.67784
  0.979426754518148 -1.073374111906191  1.780157057765492 -1.405504340095135  0.764430245746722    2.69366
 -1.417872566688207  1.965730717575601 -0.477191395226128  1.084145550574631  0.013103723962485    2.69769
 -1.124634959024498  0.559580703206098 -1.982481223911954 -1.332091333584976  0.042797742189081    2.69864
  2.068206689961673 -0.631958823604614  0.575441239677673 -1.703891805100606  0.009900856912032    2.81269
  0.424454487764782  2.335190597707394  0.235978841792798  1.498541893750933  0.005688998457361    2.81684
 -0.832890653485202  0.148708745157917 -1.854769194271225  1.993732679168469  0.005982010592315    2.85148
 -0.760864435813659  0.207541752239264 -2.324098622744917 -1.475428934246835  0.232514693797120    2.86362
 -0.855190575737518  0.202612104228064 -2.301256984831041 -1.510334994912438 -0.304839246230929    2.88952
  2.805677641302256  0.013139108638160  0.832249695380173  0.298387105502322  0.004975866761858    2.94171
  1.839943763051263 -0.064733569587569 -1.295181400301324 -1.907748226178272  0.005360509584070    2.95069
  1.871977640130523 -2.236268130267910 -0.085656784642075 -0.626425269510193  0.004005440367786    2.98411
  1.102055617155910  2.559663159932451  0.780247379108650 -0.787539053837331  0.004510115365664    2.99923
 -0.463081261814400  1.765830815947156 -2.307572521730339  0.663387518706107  0.003844021781293    3.01622
 -2.430259095088177  1.045297969889386  1.450907350081550  0.190376613503705  0.026184797512635    3.02327
  1.216982373612689 -1.365197235965445 -2.379762095378044 -0.410225619360199  0.004173108682945    3.02925
 -1.043374165018133  0.065769704306279 -2.318795620905335 -1.719025633744829  0.047063202427355    3.06999
  0.138743259645780  1.687282658605464  2.542215970631841  0.404734725950121  0.003538794518588    3.08105
  0.025866949224230 -0.938339706975079  1.468622491216184  2.558341293834112  0.003077796489316    3.09566
  1.698922717517749  0.980012275908635 -2.402919564380695  0.123213654623821  0.004719359291847    3.10419
 -2.684482373356237  0.997375305199952  1.104023469885931  0.519433684986964 -0.157229125525742    3.11286
  0.211078657183958 -3.052336429080476  0.491139602096888  0.378595697165501  0.001629277302478    3.12184
 -2.734342030352458  0.928920133092160  1.069836770817713  0.543515621228931  0.125599275978706    3.12722
 -1.639983145714150 -0.221636181066794  0.381073609534113  2.637445524123260  0.003009610493668    3.13688
 -0.702525212182419  1.886795449445571  1.889367335774865 -1.504758500778453  0.002957158269017    3.14445
 -2.038675293703069 -1.666498999491537  1.351652822848854  1.063516654225019  0.002886276095247    3.14507
 -1.341310986177180 -1.758476451448536 -0.121813562472652 -2.259451646544815  0.003246372804137    3.16407
  1.747689597083349  0.415056674569292  0.491587040919919  2.570283089934976  0.002935739674312    3.17407
  1.086428180797889 -2.592617145969724 -1.044005047593123  1.098657671744391  0.002671340043255    3.19358
  0.934105209601402 -1.721395101226184 -0.928775179070247 -2.355381232148098  0.002510139696325    3.20097
 -1.365126245656364 -2.880832724134089 -0.328788364805309 -0.157468259486881  0.002168622707543    3.20869
  2.613430746039040  1.323676123157145 -0.084794912650440 -1.328748247303248  0.002826714976572    3.21790
 -0.791199730486801  1.949374917383770 -0.110544854730144 -2.446915823626321  0.003519170272383    3.22888
 -0.273982883890267  0.020822622648911  3.240111760729841 -0.020383658742270  0.001442323430202    3.25181
 -2.855878709713080 -1.571068962908708 -0.504659081351979 -0.112230996472496  0.001852550223178    3.30024
 -0.157313383757044  1.328330716148546  1.729248089582779  2.506853029140287  0.001858745750342    3.32623
  1.675613224540945 -0.784043664195391  2.540141799254227  1.117140243665023  0.005851864341426    3.33508
  1.943732226628639  1.587035925877283 -1.651352543172399  1.488919858204338  0.118816551057189    3.35270
 -2.332091475567359 -1.155313654636651 -1.118690663626241  1.795425640895108  0.001522425089341    3.35387
  2.119350272812420  1.570461014816704 -1.562222033309282  1.371647197172725  0.185455610205222    3.35856
  2.054246041554074  1.583788914957333 -1.602958563437006  1.414353465418119 -0.299229197925992    3.36128
 -0.823557456050141 -2.138014765322590 -2.212117886437338  1.097038623410491  0.001738640675830    3.36843
 -0.392717467755995  2.946011497515914 -1.221050940801576 -1.021943388061862  0.002337813613055    3.37173
 -2.811222658843170  0.561898449812601 -1.820652679984471  0.574148583090233  0.001347755674678    3.44429
 -1.285845957464238  0.066764199161101 -3.299252005865966 -0.248626214065879  0.001209094424009    3.55031
 -0.884332457432438  3.309825917447867  0.882449099482749  0.316646376497735  0.001206447329622    3.55190
 -3.160036813253191 -0.000729875437609 -0.434376183819928 -1.581003061774128  0.001033825537688    3.56007
 -0.089455907394275  0.331887539017707 -0.316852970070344 -3.548760517851145  0.001484080739392    3.57942
  1.772006773408704  2.773783337471595 -1.461219475694223  0.745847946289343  0.001406210054405    3.67768
  1.994961138686940 -1.376765465498475  2.578132780356269  1.030238099603262 -0.003350949139308    3.68558
  0.250087176250989  2.386528729727130 -1.769858714775813 -2.170620774986459  0.018125376339000    3.68810
 -0.250203726364695 -1.988551664219675  3.063841912645765  0.576662350967272  0.000780785423936    3.70629
  3.350699257334631 -1.018152292310849 -0.964078487972567 -0.897029266124772  0.001520715942613    3.74138
  0.075710610789448  2.532553888473210 -1.916054289775685 -2.303786584991581 -0.021597478568512    3.92406
  2.424670508408991  2.247774238872383  1.636593857287256  1.361376272633358  0.000512430963787    3.93234
  0.954390478358890 -1.459796758412569 -1.054406155782167  3.506679257404954  0.000767433451076    4.05591
 -0.234324866373218 -3.166147265833649 -2.146308112285785 -1.345386771479063  0.000340056935829    4.06154
  2.573227308791177  1.348142461080302  2.754521172678922 -0.858557771197825  0.000291787187915    4.09432
 -0.993575543167501 -3.202975929031410  0.326459014296876  2.368323017899319  0.000327305210323    4.11847
  0.502532479523109 -3.542155029744108  1.145018777800305 -1.690813923527126  0.000317531743960    4.11938
 -0.083106878053005  2.664912162616476 -2.111538933770020 -2.463448911669353  0.006375277219168    4.19950
 -0.036596306794282  1.280914589468380  1.159219131182017 -3.831049748013183  0.010075702327690    4.20271
 -0.380424517211447  1.127144354133320  1.218559636118373 -3.865495207746306  0.024375179162303    4.22399
 -0.289832253895789  1.180143815656111  1.195788348442242 -3.873084715589106 -0.033294328700746    4.23172
  2.598977630366290 -2.164528089123201  2.615581635829928  0.889145288357174  0.000569896082588    4.36712
 -2.739756401521599 -1.807574069354339  2.522627642590098 -1.771498580068083  0.000207267196657    4.50283
  2.801364431134999 -1.570305609780924 -1.500758441744506  2.935976939548957  0.211364688129967    4.60280
 -0.498890327036938  1.833328176989160 -0.712348025251614  4.138556936394724  0.000134138313827    4.60924
 -3.076904328251031  1.668465344137535 -1.302017140083989  2.708431935013023  0.000054128957687    4.61324
 -2.143627469581572  0.282544081963836  3.490979951371663  2.121720178366409  0.000136073066664    4.62208
  2.839110402085008 -1.597010306303383 -1.505603577950687  2.978323960236288 -0.276202306630946    4.66350
  2.928864284608228 -1.658645903347112 -1.518030893066071  3.075148602718483  0.067644491625233    4.80524
  0.974998393808913 -0.937823021091100 -5.988685706915742  2.591387084240561  0.000006334126432    6.66407

E_n^{r^2} 4 dimensions, degree 8, asymmetric 105 point rule with points at 105 distinct radii (14 negative weights, stability factor 12.248673)
#                x1                 x2                 x3                 x4             Weight     Radius
  0.436846251741587  0.000000000000000  0.000000000000000  0.000000000000000  4.892935145684865    0.43685
  0.197760273110790  0.580804286691677  0.000000000000000  0.000000000000000 -8.886556054247402    0.61355
  0.251589491008672  0.655986019323056 -0.167168414543146  0.000000000000000  5.799432810188472    0.72219
  0.430806621041381  0.329077802447156  0.143100143517041 -0.592080975664040  1.878626159948114    0.81543
 -0.367681014996409  0.792558459270513  0.326653980030179  0.027354049811662  2.116399347808917    0.93316
 -0.656855101719619 -0.196167586863999 -0.346578852273193  0.531600162528839  5.896258174909019    0.93416
 -0.554897000327758 -0.346394431607616 -0.326690858340420  0.627162966920571 -11.429313151680084    0.96331
  0.908204218634707 -0.110045215026027 -0.109856762911726 -0.339818179175250 -8.648003942038976    0.98208
 -0.499305644544390 -0.482337864434127 -0.300259105872228  0.694486898126299  6.312698530269932    1.02685
  0.710377221782542  0.611462414548539  0.378148970137516  0.189070398372650  0.952208858629809    1.02823
 -0.203466736211771 -0.190324174500042 -0.618069734775545 -1.019247790387433  0.399176230597784    1.22413
  1.132657737511056 -0.208347070784084 -0.199498329251638 -0.440019572108237  8.551258082355364    1.24890
 -0.045609078355200  0.266201581996114 -0.138011150892028  1.211503570727977  0.497862404632578    1.24889
  0.060142498595762 -1.151138380372434 -0.403094951480162 -0.332736314533276  0.381753972389210    1.26568
 -1.007110989430780 -0.626738800613132  0.340633725753351 -0.317484617080893  0.297285473671390    1.27432
 -0.535528818432432 -0.129080903142028  1.038093332616861  0.567380135417439  0.387625534895160    1.30499
  0.117050473386097 -0.253692836017495 -1.200681015284001  0.475870604795866  0.393526323199482    1.32142
  0.383560238092231  0.441908310543372  1.056089841520177  0.830704464980789  0.119971445462911    1.46554
  1.325458493310554 -0.287730678850730 -0.244882132472108 -0.558420727434103 -2.707104554669916    1.48709
 -1.084328923484033  0.148345070397790  0.341332048584203 -1.046071270409283  0.192087828487548    1.55195
  0.725473841880284 -0.719253016635800  1.020514610269082 -0.570257293730164  0.715292868789588    1.55251
  0.344582663624599 -0.725803274941193  0.837122909109090 -1.180591181492526  0.383619240037417    1.65532
 -1.216513219042416  0.924493520200051  0.628415438182308  0.235254837606750 -0.730822696943046    1.66879
 -0.462899188569983 -1.355609247315968  0.920309608832033 -0.295535141043580  0.098201747321643    1.72808
 -0.512511824922873 -0.112034262386972  1.489317590302337 -0.720828432680331  0.117330426430144    1.73577
  0.392549461255244 -1.278373628981926  0.793158688050112  0.788120229239741  0.108740783257205    1.74315
 -0.955793021296659 -0.667330566941793 -1.247597322381675 -0.417576702977676  0.129787797832049    1.75777
  0.718641041652527  0.331245397159976  1.346418161054272 -0.823128460537326  0.109390762952019    1.76538
 -1.399531407372441  1.163610109473605  0.299924005057033  0.311801666410614 -4.107585284784603    1.87079
 -1.418236444983248  1.190317148662523  0.217836383089952  0.211803016982431  2.151437073569473    1.87632
  0.689499353794309 -0.755389921941258  1.243691450986164 -0.986151409036317 -8.186045435745724    1.88820
 -1.421084586565074  1.088870342502838  0.459831925839047  0.393178915471970  2.531153827584652    1.88975
  1.290382531891946 -0.855835259084263  0.210414751851456  1.069391011492240  0.084964438645801    1.89352
  0.692559299794899 -0.758990113279623  1.258761127123283 -0.993841649868161  7.544624117747890    1.90471
 -1.002587306763190  1.389981520384597 -0.337425271488422  0.766606670604633  0.129328571690768    1.90756
 -0.795237005885078  0.395683309858508 -1.401825917003235 -0.941930815138118  0.422396784666550    1.90822
  1.462442975367084 -0.446862369601916  0.406898402751199 -1.204833449794931  0.097717540953477    1.98887
  0.300134646603738  1.651229107001968  0.166862239248672  1.059629134963418  0.056148164212546    1.99181
 -0.588942629065807  0.105152962123474 -1.311519874805581  1.409781897313121  0.059040078069258    2.01630
 -0.538012402126990  0.146754180388332 -1.643385896289159 -1.043285804564985  2.294828045218385    2.02488
 -0.604711055310284  0.143268392850781 -1.627234419226865 -1.067968116766094 -3.008642766225094    2.04320
  1.983913685988062  0.009290752816440  0.588489403244437  0.210991545719281  0.049109836492074    2.08011
  1.301036711855885 -0.045773546025822 -0.915831551019184 -1.348981707527647  0.052906108982972    2.08645
  1.323688083565594 -1.581280359463756 -0.060568493275107 -0.442949555977405  0.039532111882227    2.11009
  0.779271000135492  1.809955177941459  0.551718212771672 -0.556874205417691  0.044513054462368    2.12078
 -0.327447900468680  1.248630944384945 -1.631700178195122  0.469085813031294  0.037938974290527    2.13279
 -1.718452686176868  0.739137282869222  1.025946426115788  0.134616594387857  0.258433592771899    2.13778
  0.860536488966479 -0.965340223207779 -1.682745915252468 -0.290073317266408  0.041186931823423    2.14200
 -0.737776947398800  0.046506203912056 -1.639636107727866 -1.215534682654857  0.464495189805096    2.17081
  0.098106299738853  1.193089009677912  1.797618152074778  0.286190669301237  0.034926501955215    2.17863
  0.018290695204887 -0.663506369859014  1.038472922541508  1.809020477459833  0.030376633776613    2.18896
  1.201319774269441  0.692973325941530 -1.699120718618878  0.087125210718966  0.046578209237118    2.19499
 -1.898215690176148  0.705250841694979  0.780662482144621  0.367295081031527 -1.551789269268159    2.20112
  0.149255149858178 -2.158327787466177  0.347288143151401  0.267707584794115  0.016080322435109    2.20747
 -1.933471791745805  0.656845725290264  0.756488835407145  0.384323581452270  1.239615166973246    2.21128
 -1.159643203366051 -0.156720446588574  0.269459733432081  1.864955615117876  0.029703664973862    2.21811
 -0.496760341489138  1.334165857014509  1.335984455279057 -1.064024939948536  0.029185982266606    2.22346
 -1.441561124815254 -1.178392743381192  0.955762876845426  0.752019838107756  0.028486403252410    2.22390
 -0.948450094006058 -1.243430623375983 -0.086135196065310 -1.597673581034793  0.032040415315295    2.23733
  1.235803165506991  0.293489389164522  0.347604530178140  1.817464602462169  0.028974589210034    2.24440
  0.768220733914655 -1.833257164935576 -0.738223048746672  0.776868289893069  0.026365069447703    2.25821
  0.660512128050821 -1.217210149178316 -0.656743227318146 -1.665506041531584  0.024774085794189    2.26343
 -0.965290025479468 -2.037056354699122 -0.232488482330094 -0.111346874104832  0.021403448218664    2.26888
  1.847974602685697  0.935980362779057 -0.059959057744113 -0.939566896158105  0.027898558573396    2.27540
 -0.559462694700240  1.378416223157012 -0.078167016404646 -1.730230771878636  0.034732818408500    2.28316
 -0.193735155128709  0.014723817676478  2.291104997814301 -0.014413423321740  0.014235161674517    2.29937
 -2.019411201884205 -1.110913517384206 -0.356847858612247 -0.079359298664922  0.018283937835926    2.33362
 -0.111237360426168  0.939271657046597  1.222763050497815  1.772612776343074  0.018345085238102    2.35200
  1.184837473717152 -0.554402591698580  1.796151491428016  0.789937441832287  0.057755586058666    2.35825
  1.374426238260636  1.122203865174818 -1.167682581406348  1.052825328379237  1.172672355237224    2.37072
 -1.649037696720701 -0.816930119590321 -0.791033754301248  1.269557645792887  0.015025733362105    2.37154
  1.498606949615842  1.110483633166271 -1.104657793471479  0.969901034516032  1.830373506687974    2.37486
  1.452571306209133  1.119907881734705 -1.133462870166831  1.000098926391526 -2.953273808785549    2.37678
 -0.582343061869435 -1.511804738835960 -1.564203558284760  0.775723449836808  0.017159695666085    2.38184
 -0.277693184540203  2.083144707346646 -0.863413400414287 -0.722623099687300  0.023073295524378    2.38417
 -1.987834605492863  0.397322204201392 -1.287395856203320  0.405984356511534  0.013301815338386    2.43548
 -0.909230396083496  0.047209417968304 -2.332923466191296 -0.175805281947446  0.011933283648540    2.51045
 -0.625317477473926  2.340400350774212  0.623985742296467  0.223902800059765  0.011907157874124    2.51157
 -2.234483459450503 -0.000516099871212 -0.307150345165630 -1.117937986056956  0.010203449076719    2.51735
 -0.063254878735740  0.234679929430617 -0.224048883775460 -2.509352626979615  0.014647289797071    2.53103
  1.252998005786410  1.961361007468982 -1.033238200064384  0.527394140554742  0.013878736941801    2.60051
  1.410650549366797 -0.973520196756884  1.823015171789076  0.728488346466661 -0.033072542372974    2.60610
  0.176838338215995  1.687530648285549 -1.251479098958437 -1.534860669376508  0.178890294085655    2.60788
 -0.176920751591322 -1.406118366509859  2.166463392914322  0.407761858824238  0.007706043256398    2.62074
  2.369302166578394 -0.719942390173795 -0.681706436440670 -0.634295477000294  0.015008864760031    2.64556
  0.053535486297653  1.790786028259125 -1.354854981420539 -1.629023116653500 -0.213158569529637    2.77473
  1.714500958638914  1.589416406882766  1.157246614537087  0.962638394125504  0.005057490895447    2.78058
  0.674855979147990 -1.032232187027819 -0.745577742879202  2.479596682357764  0.007574264566269    2.86796
 -0.165692702012779 -2.238804201905537 -1.517669020713291 -0.951332109431625  0.003356227430485    2.87194
  1.819546479580571  0.953280676234923  1.947740600124479 -0.607092022054083  0.002879824114024    2.89512
 -0.702564004195208 -2.264845999394769  0.230841382787192  1.674657265996472  0.003230372944309    2.91220
  0.355344124036658 -2.504681841545984  0.809650542368048 -1.195585991050305  0.003133912697680    2.91284
 -0.058765437035067  1.884377461453050 -1.493083498808528 -1.741921430548705  0.062921464099060    2.96950
 -0.025877496701979  0.905743392333237  0.819691708541165 -2.708961255883853  0.099443196038806    2.97177
 -0.269000755849797  0.797011416183693  0.861651781980468 -2.733317874041978  0.240573375537188    2.98681
 -0.204942352135837  0.834487694825874  0.845550050048283 -2.738684466503442 -0.328601853077154    2.99228
  1.837754706585324 -1.530552489891754  1.849495511442192  0.628720662857250  0.005624648884779    3.08802
 -1.937300330315934 -1.278147881937709  1.783767112483192 -1.252638658827816  0.002045645236325    3.18398
  1.980863785831429 -1.110373745211680 -1.061196471081160  2.076049203363051  2.086085856202406    3.25467
 -0.352768733315717  1.296358786089828 -0.503706119220472  2.926401674051528  0.001323892092500    3.25922
 -2.175699915568056  1.179783159014651 -0.920665148974502  1.915150587629320  0.000534231399018    3.26205
 -1.515773520079104  0.199788836339979  2.468495596599916  1.500282725903288  0.001342987337622    3.26830
  2.007554217852632 -1.129256817212230 -1.064622499748332  2.105993068854086 -2.726007501115806    3.29759
  2.071019796822598 -1.172839765844323 -1.073409938538381  2.174458430139179  0.667624372253787    3.39782
  0.689427975909576 -0.663141017765359 -4.234640273757052  1.832387379945337  0.000062515322112    4.71221

>> # evaluating formula 1 with 103 points
# r4_103_8E1da.txt:4 formula 1   : problem E1, 4_103_7  (d=4 n=103 o=7 plus 161/165 of order 8) quality N (3 negative weights, stability factor 1.204165)
E1 4 dimensions, degree 6, asymmetric 103 point rule with points at 103 distinct radii (3 negative weights, stability factor 1.204165)
This double precision rule was refined to meet the degree 8 constraints - see refir4_103_8E1da.txt
#                x1                 x2                 x3                 x4             Weight     Radius
  1.623116860557871  0.000000000000000  0.000000000000000  0.000000000000000 22.122041859601346    1.62312
 -0.895894051472418  1.878836183843965 -0.000000000000000 -0.000000000000000 18.946156688548378    2.08150
 -1.364042554338949 -2.243744490260241  1.650407268179663  0.000000000000000 11.493498081643976    3.10143
 -3.153180168985258 -0.742489812667928 -2.016184876303474  1.622875239160143  6.610787941880262    4.14639
  0.648962338189704 -3.443652535080874 -1.797473124730501 -1.656399333713096  4.957635254479064    4.27252
  0.755563112141901 -0.788909745545194 -3.883531592682618  1.423034682566925  5.045916275014252    4.27786
  0.648796652484824 -0.046448788315100  1.659711720336455 -4.072054497943573  5.262255404949394    4.44515
  0.078821868682119  1.261915419085991 -3.381932595868446 -2.845326640806754  4.288957225791144    4.59695
 -0.711388135346329 -0.285339853730906  0.832220508913328  4.465363111399967  4.530904732128214    4.60647
 -3.065155426152947 -1.877782652012254 -1.407207659710711 -2.964050620689259  3.168230523817789    4.86694
  3.134956768376220 -2.408940785109974  2.802410310537608  2.277663265261078  2.459184605133174    5.35464
 -3.514393404125753  0.518903840220526  3.468739392887263 -2.410644955590564  1.965667804287281    5.51938
  0.547698233742111 -4.715117922929466 -0.438323125362760  2.826217285609601  2.096838352123636    5.54184
  3.072731040074449 -0.280048564468902 -1.867929012316377  4.399651215966339  1.644942545531503    5.68913
 -3.721584285536383  2.351686381404980 -0.731316026628274 -3.623621021154505  1.566395172900407    5.74857
  4.977223893068051  3.175365388601434 -0.222397967871428 -0.309883383550898  1.465468673687637    5.91618
  0.810368707697674 -0.646605474454419  5.828440284891794 -0.595705135514391  1.821213086337371    5.94982
 -1.580307257857329  2.063204631236483  4.875527037333649  2.646151229980269  3.772788135787436    6.12593
  3.049165537752688  3.726930465863351 -0.656909530537824  3.881219820093658  1.197446447581700    6.21955
  0.993887170631962  4.389122462590914  3.822092375952588 -2.053908097546435  1.366468713515149    6.25133
  1.098898603726711  2.738182500585284  5.003577231843050  2.776941498163838  5.775216635235475    6.43835
 -1.636144350135066  4.167482198575762 -3.035459783639440  3.852812542438165  1.534693808449635    6.64101
  5.550721538519119 -0.448009282696285  3.058363570339955 -2.267352967503524  1.016926384869253    6.74579
  4.652097414108080 -0.848104238210603 -2.414170581805411 -4.470509148934196  0.918415589914102    6.94082
 -6.718333058576110  1.645330123250782  0.881640670939111  0.670729118094997  0.859042627657506    7.00502
  2.145218669171672  5.173728822081476 -0.754829018936472 -4.151706162525425  0.879472405465683    7.01255
  4.462841674668817  2.894768178427820 -4.849628074540151  0.015786404280629  0.700204224974018    7.19832
  0.174034562313039  2.630511425914618  6.010736462502829  3.144638866952262 -7.388942188913624    7.27788
  3.042588693859408 -5.471019751314911  2.265980261918274 -3.029258327056930  0.758519100829839    7.31440
  6.054685627619590 -3.568599680663747 -2.265621486488760  0.526161940747926  0.744787118089260    7.40297
 -2.434083485198016 -0.375965882469999 -7.320335419826010 -1.543518618454453  0.390787255025646    7.87629
 -0.499121095099277  6.141700488664952 -5.257181004775686  0.471241548411775  0.526415914025332    8.11355
 -5.787073336300380  3.260440148619909 -2.651548322686361  4.052112038850953 -2.354375153208198    8.22016
 -5.934130818919559 -3.257681148421718  3.390830261810831  3.359120036789236  0.370567897049864    8.28298
 -5.982880668263680  3.268442237385091 -1.970741636776981  4.518390796883459  1.794334982370751    8.41292
  0.112076773268155  2.660074100993530  7.120482259694745  3.679239110725980  1.934060477961850    8.44551
 -2.961762924393001 -5.795364325026943  3.693644345941628 -4.230095917898532  0.220208612408823    8.59622
 -0.384200996110425 -3.191391828638847 -1.606136807802146 -7.811186549441311  0.231746014426518    8.59808
  1.355946276848884  8.467001060740662 -0.399368159319720  1.222821156111187  0.300720885286773    8.67084
 -5.918991479103775  4.246647071975421 -4.487354997052982  1.717801984111865  0.514061310022737    8.72672
 -4.860585200930540 -6.950938802885220 -3.089574452811298 -0.000702940822793  0.225222880842751    9.02698
 -0.466548731520786 -5.841361918599923 -5.301716505420235  4.393021395312574  0.154272748534098    9.04135
 -3.816709263800715  6.731662885444527  2.089970144706889 -4.481557940522365  0.172744519071296    9.18340
 -0.491656358725313 -3.352125577687914  6.792788457962519  5.194599145626223  0.167934024202856    9.19806
 -3.647459447935271  6.649356596970324  5.168166306079161  0.973407621246652  0.159786202743934    9.22905
 -3.247302697843488  7.918334745915328 -2.824337574260407  2.167185817231593  2.432480371971547    9.26923
  8.563938844916819  0.301425439225208  2.010336578927880  3.620450533171667  0.151622079501219    9.51741
 -3.110827870549817  8.120868345714907 -3.231948403226352  2.372806393283748 -2.346867638079379    9.57609
 -5.743402196904550  1.744877182026132 -5.267817900911161  5.493718371860032  0.183117330082568    9.69341
  0.428629938652907 -6.053732883782975 -7.185669450803923 -2.617169068271779  0.119905557819316    9.76293
 -8.224217616288907 -0.777189851541513 -4.933826912954934 -2.222783990083653  0.090004486006750    9.87548
 -3.200523003811279 -9.197765801873979  2.704360782202579  1.340167136652676  0.081518438243816   10.19568
 -8.753096640273709 -4.450942117184684  1.757436509252201 -2.585436266825588  0.089618652003752   10.30537
 -5.513793183451724 -5.416391960476590 -1.444550337582733  6.707392232524413  0.075925286924449   10.33514
  1.217269537040841 -7.882034512070984  6.597663491755810  0.375536222200854  0.068798310068266   10.35753
 -1.137192021452203  6.483655393778497  3.525129035957219  7.319569170004740  0.083437396505863   10.45627
 -0.629750622407401 -1.919787781498450 -4.064253203329152  9.469983272465235  0.071732354719821   10.50147
 -1.530264004627217 -3.185739548859672  6.787619069961687 -7.230517250291205  0.060063476626452   10.52819
  5.203264431407155 -1.462728438595045 -9.148577453600769 -1.682606875203422  0.061745880809445   10.75831
 -0.136953776229322  3.434476172748812 -0.492350887491652 -10.366390235337489  0.058716697288844   10.93247
  7.850928547829859  6.639254794713808  3.393383368157430 -1.861304193630770  0.041587413804523   10.98619
  4.192474558621838  0.096092038543897  3.978810684857129  9.374281344787091  0.055602370694223   11.01336
  1.401296304117003  1.170031055352503 -9.533488796368452  5.402624276931303  0.051669686021057   11.10893
 -4.783587038460594  4.053412910064482 -6.146126247139209 -7.326241081375054  0.038343787597084   11.43510
  4.413969608491213  3.302869414248042  6.657748861206780 -7.591403986803283  0.035881087833499   11.50422
 -6.583786494381473 -1.387206857066455  1.080574465453114 -9.374742837354368  0.035833833255311   11.58982
  2.603329772693516 -11.312826637450877 -1.999630042851459  0.489002951499725  0.031759600202178   11.78961
  1.269599477009834 -1.273473680187433 -7.572129101716358 -8.994142162387012  0.026138364188076   11.89392
 -8.735537171552108  1.181663258907821  7.674655130756587 -2.709371474285986  0.022713385981842   11.99779
 -1.053438884410784  3.812443315492080 11.192249763824259 -2.084980045596476  0.025646526343042   12.05230
 -3.326102344962764  3.514234142126775  6.799793515702369 -8.743877253536613  0.021879368808881   12.08741
 -0.167535902139111 -7.966717664044105  3.153855722890674  8.562269232824104  0.022603148150671   12.11429
 -4.969950499287193 -4.476998171671930 10.103528721138872 -0.302952671508979  0.025841298024680   12.12093
 -2.056437745118743 -10.073784194786525 -0.784351748524694 -6.519488887605213  0.023178816439048   12.19955
  7.613664254021238 -8.537086396549805  3.005433677028951  3.009784516483346  0.020429681810528   12.20415
  5.885657843467600 -5.803008880255763 -1.119267456923764  8.948621679611451  0.021902877541199   12.23301
  8.335734469871028  2.821793573979126 -0.155034606942384 -8.559977166190393  0.020432455200565   12.27779
  8.859951857276318  0.558590699945171 -5.692371504451321  6.577573518531139  0.018533753809209   12.42893
 -4.935026353052047 -4.403751126864082 -10.267681168796356  3.024107951419396  0.017025708784308   12.58245
 -2.819713713957395 10.586334561588622 -4.632267183200265 -4.140983928330332  0.016597684317843   12.59472
  8.333302205587163  3.128732214111970  9.250386470301677  0.153110966112981  0.012905041414134   12.83846
  5.425249799853296 -6.866293286678987 -8.430360620712596  4.149933552099951  0.013644259552359   12.84026
 -4.431788582452764 -0.158235044888703  3.298115733976923 11.595377742715538  0.015958868392698   12.84508
 -3.328190778371885 10.717018822873692 -5.091515277657476  4.272602840985575  0.053861152252517   13.04262
  4.641434212581768 -4.038703212100565 10.767247898364722 -4.793979993364307  0.010719295966151   13.29548
 12.728651131705835  1.471915794936181 -3.624905348078940 -1.358811552259236  0.011182979887057   13.38549
  4.743682906287391 -4.282592541076016  3.156399587252256 -11.521999546836607  0.010326039649199   13.54852
  2.217821880446353  4.949997652235183 -2.810809264321740 12.173335593450432  0.009433758238772   13.62028
  4.959525603698967  6.278952685773116 -8.472059138138153 -7.410049409540633  0.008865382219795   13.80966
 -6.756245957125272 -5.249549715299494 -7.652910384097667 -7.831425164935897  0.007719429579077   13.89615
  7.300530366018253 -8.748154761479356 -4.351217286759722 -7.097449467262861  0.007529943097232   14.11151
 -13.196882543752766 -2.928549448705459 -3.517821811061461  3.718646989355436  0.005664748339383   14.45467
  9.577919621390642  8.927349010854847  2.522998153144250  7.134524918205901  0.004028063238609   15.12287
  8.420808845644547 -4.196892906868859 11.252375367778246  4.269774320628891  0.003593985529810   15.27648
  7.386293722106116  9.356890280202439 -8.014046173374835  5.993284392827103  0.002700129311381   15.56448
 -13.556228942157070  4.747401933211039 -0.562924713920911 -6.234744880374238  0.002941728809588   15.66838
  2.708309305982893 12.620808205485893  8.703523595107230  1.820991423644536  0.002752941094991   15.67441
 13.715955393168828 -5.653500192897686  3.727663284851919 -4.264348399674556  0.002717027460384   15.87985
 -1.088375686524726  4.222026401488878 -15.327334313918367 -2.107711327561518  0.002333762101736   16.07419
 -12.814510942297701  2.383918251976580  9.642760291465152  8.075539307700307  0.000948841116623   18.11331
 -15.272974833680459 12.439451131236718  6.004653199115309 -0.171765700623628  0.000245854240429   20.59342
 13.935848634347872 16.925121602789076 -6.180856633392469 -3.806154744226289  0.000120540357354   23.09453
  4.042287184764585 24.627057881732675  7.668077347731298 -14.254341645569568  0.000017709847217   29.74589

>> # evaluating formula 1 with 105 points
# r4_105_8Sa.txt:3 formula 1   : problem  S, 4_105_8  (d=4 n=105 o=8 plus 0/220 of order 9) quality NO (12 negative weights, stability factor 1.392987)
S 4 dimensions, degree 8, asymmetric 105 point rule with points at 105 distinct radii (12 negative weights, stability factor 1.392987)
#                x1                 x2                 x3                 x4             Weight     Radius
 -0.338641126057335  0.000000000000000  0.000000000000000 -0.000000000000000  0.150093752235220    0.33864
  0.110087974101078  0.383929664181764 -0.000000000000000 -0.000000000000000  0.188404215685415    0.39940
  0.088537089442230 -0.361711492274167  0.158674868147026  0.000000000000000  0.146318110466651    0.40479
  0.316174734083790 -0.129260208509697 -0.426382284311794 -0.099357673738737  0.168591174435278    0.55529
 -0.165803498599298  0.182368714029046 -0.527632988135409  0.455606658645308  0.106045726640039    0.73941
  0.216709584478486 -0.197713013291016  0.124712837058524 -0.691861295208790  0.136432575079455    0.76176
 -0.019250405019692 -0.206819446545268 -0.137537107281649  0.720143994990035  0.113895143139563    0.76202
  0.049745400015336 -0.138861766984052  0.746618104155162 -0.114733980011500  0.115912582791325    0.76965
 -0.211223098852320 -0.113129638852469  0.459366650553797  0.570069131001734  0.134732679641259    0.77033
 -0.682133599261324  0.325870315759300 -0.109988159467278 -0.110055400824623  0.094922764609103    0.77182
 -0.318237764117344  0.102688533001497 -0.302407010521243 -0.630068309621642  0.096942892372740    0.77476
  0.057137631191617  0.374118237209410  0.678964894253883  0.031360089752498  0.107615337527179    0.77795
 -0.409944707767069  0.076071009211196  0.420632148247779 -0.510909016292143  0.122708468100409    0.78218
  0.462026218387999  0.169066769364253  0.347937132320606  0.510043127519254  0.115931417035209    0.78947
 -0.534423090785282 -0.527709252722069  0.041455391548463  0.247900975696935  0.108065617540445    0.79200
  0.635417670841233 -0.035608327665375  0.454276630169112 -0.179406076812798  0.115716791456056    0.80223
  0.488849424924421 -0.376139929123908  0.233488933654679  0.471101686582231  0.100852102304860    0.81050
  0.453367656669990  0.112145809141205 -0.395113047656684  0.534383353066741  0.097840241154950    0.81228
  0.265501245926818  0.333300846583794  0.351545172749579 -0.599287347145121  0.091410126667735    0.81505
 -0.095326438437711 -0.689843367454943 -0.418050312210351  0.076126117914008  0.098901753659806    0.81580
 -0.382567297036186  0.468768287708263  0.338053027777458  0.445136607717250  0.081606633048625    0.82373
 -0.194198378908837 -0.220481918628889 -0.700600011738681 -0.320617251088408  0.093378139076167    0.82460
 -0.534332067579472 -0.446953148695396  0.166394651448575 -0.429069460283211  0.078465385869081    0.83490
  0.130996802984732  0.348040920879564 -0.658541822001285 -0.356128282706586  0.088973486874813    0.83594
 -0.022880078321293  0.413471550879573 -0.009418086266569  0.730917693399850  0.081622273056051    0.84013
 -0.249645618800100 -0.549202943748746 -0.287963338943426 -0.522999855876745  0.075054861870293    0.84876
  0.713238771218170  0.205190424273715 -0.216927589638872 -0.353875477921208  0.085183822630489    0.85035
  0.713201907542406 -0.397846546783667 -0.159041770221362 -0.188240266613399  0.077204792401839    0.85303
 -0.768089115314034 -0.231074203772375 -0.289396365631519 -0.084918596930786  0.080048842417759    0.85692
 -0.298093993410027  0.664716129547345 -0.399748888190393 -0.232589617402229  0.070243201087574    0.86290
 -0.774926885508008  0.122977786232220  0.204370712859574  0.303189031884337  0.052715293880831    0.86564
 -0.386278197002438 -0.285935726244585 -0.620314672854846  0.365711689850282  0.079063051346884    0.86574
  0.049279281397467  0.805086046020135  0.176906230215798 -0.270903662792019  0.062694971227103    0.86907
  0.542188609139773  0.562722252274960 -0.365458530171453  0.115696494604073  0.067241844981707    0.87039
 -0.031908310747143 -0.650320864395191  0.576155725894062  0.066466639301455  0.060212159511675    0.87196
 -0.523295152856294  0.500066542541041  0.471039650836242 -0.195223734890006  0.053123689063944    0.88538
  0.251965320181962  0.371491852345455 -0.196834602408928 -0.744020979954024  0.056355082685675    0.89096
  0.221603382539850 -0.486409137394387 -0.459483908169651  0.553233292738978  0.051244147786424    0.89604
 -0.041630871646124  0.815018546397945 -0.224123495625653  0.295097056743318  0.057524957829289    0.89627
  0.255422693715208 -0.737009267854224 -0.085147002056154 -0.442044220750917  0.053839510163773    0.90060
  0.474043923021628 -0.598242466363215  0.450544260487774 -0.194999351474620  0.052935034270928    0.90754
 -0.517138258148860  0.217612082589868 -0.712081440810548 -0.047287770691853  0.059550535309934    0.90779
  0.348427900126902 -0.822345847348710 -0.013098670446424  0.189213750797110  0.047875836927569    0.91303
  0.462997379682117  0.680587302483883  0.214054745956584  0.333425420960896  0.045295944733108    0.91354
  0.640336550383826  0.558335311481659  0.290904770405994 -0.176049944609900  0.047254358149431    0.91509
  0.686328610239317 -0.406803796569076 -0.299581345877446  0.340179950276592  0.039180930729174    0.91761
  0.879785313184531  0.105398297901176 -0.027169206488096  0.238347646025413  0.055354844001243    0.91798
  0.066555062346732  0.485918179847784 -0.739761646920062  0.259869075144925  0.044833389453867    0.92484
 -0.342098766136431  0.528223896993488  0.044575805669846 -0.684863469701450  0.050000181850675    0.93117
 -0.079325759177962 -0.544936694725947  0.460086725197481 -0.597901095321751  0.044721864437867    0.93403
 -0.571804430907270  0.477344161888007 -0.318291192497744  0.478646313263909  0.043629997513743    0.94087
 -0.256258424973796 -0.895519498808209  0.125031362031061 -0.090890565908342  0.038962859087327    0.94420
 -0.025685322059824 -0.678092992877431  0.302490147401649  0.594643015723747  0.038702735496552    0.95161
 -0.569211377052587  0.759172023919731  0.072200814571265  0.009865165005453  0.029386597651130    0.95166
 -0.050598294518617  0.827563332139395  0.404785348044419  0.237536615375701  0.028634215986737    0.95273
 -0.671786045004979 -0.055680401331159 -0.108183382154347  0.677721459765948  0.046460374864584    0.96198
 -0.577807661409819 -0.341341210154430  0.692660924530087 -0.028322083741345  0.053028792190028    0.96486
  0.327415191624075  0.816704515628043 -0.279766163320363 -0.339768811016028  0.024955636696655    0.98383
  0.362923605058295 -0.229969099264163 -0.496410541670510 -0.737681076632796  0.039639051110475    0.98752
  0.355739284056715 -0.608241187394515 -0.701214091230715 -0.164644417620320  0.024254383357864    1.00763
 -0.012991208877608  0.588003222734525  0.721961486597785 -0.411000443683723  0.016424015451832    1.01787
  0.040064421607060  0.384309784576808  0.686990983719212  0.647643782782599  0.018418208700334    1.02015
  0.247368566209204 -0.131411760732528 -0.965278603881616  0.192121487115521  0.038870229928605    1.02330
 -0.526263785568866  0.091167039832996  0.862763893839117  0.143317691431540  0.031709056333654    1.02478
 -0.878082285034088 -0.091600389559344  0.554087012104893 -0.077485087385207  0.032504799319495    1.04520
  0.311007131613660 -0.242340733955046  0.864107221842163  0.443427252792986  0.024153420364652    1.04822
  0.432817864122301  0.547788741560932 -0.216655504538443  0.765785259203977  0.010417759257938    1.05866
  0.581690505234332  0.341405774448466  0.833462230132493  0.082413980503422  0.011782200619949    1.07535
 -0.472308440004212  0.058512010372855 -0.264235393570751 -1.019978148540369  0.214753396694764    1.15615
 -0.329986032979886 -0.849595431877462 -0.054912801386195  0.715329430770358  0.028994100010864    1.15992
 -0.691131229534799 -0.495023905149026  0.590534608925715  0.541775258171265  0.005550240689374    1.16832
  0.095077138391101 -0.039340173646096  0.869381891925658 -0.776868546080622  0.014328830890499    1.17044
  0.865581291171632 -0.243014633298392  0.242160153378095 -0.720010807822628  0.007348058860143    1.17701
 -0.488760550118804  0.100552882394730 -0.326787341118712 -1.034314471947134 -0.416965833685498    1.19398
  0.544179755209678 -0.014308053872503 -1.063724572661648 -0.041027991201708  0.213167987931603    1.19563
 -0.051722838930199 -0.007099459611123  0.186878183479415  1.194751495853207  0.005342603318444    1.21040
 -0.492850211519859  0.124854917576282 -0.370289116110274 -1.036695611363204  0.226461493978578    1.21258
 -0.811109633283540 -0.170298439372686  0.882271397272420 -0.073365382904585 -0.021994653592488    1.21272
 -0.337700801524470 -0.901446008540447  0.002029051219539  0.742125327805702 -0.017208320657464    1.21548
  0.503609332042064 -0.020489254357955 -1.107725194467557 -0.052554330751956 -0.350054621734804    1.21814
  0.462575864480213 -0.020394016910754 -1.142774609162894 -0.074143701142663  0.150838088752380    1.23524
  0.855381649842473  0.469299367575960  0.262604087788881 -0.822572807819851  0.000895407033036    1.30288
 -0.819483221844637 -0.184591666742102  1.123620076752821 -0.271813217195829  0.003024330930098    1.42900
 -0.065657970016407  0.117213133659822 -0.730728688686480  1.222443100246535  0.001646722338418    1.43052
  0.518922923764468 -0.098618853049034  0.008127467716267  1.340491098149921  0.002689278805558    1.44083
  1.150157820797765 -0.430739340000933  0.805796620940840 -0.107631203730823  0.033579703159827    1.47285
  1.155380951782259 -0.431085951016214  0.820921206571939 -0.129688856048442 -0.031531436098722    1.48710
 -1.376677759973709 -0.055729048826771 -0.382345486467314 -0.658041500998676  0.018039311656246    1.57402
 -1.382796684019203 -0.808869810105980 -0.156035567820564 -0.233183837934752  0.000359756675782    1.62638
  0.860541471883480 -0.351372501293885  1.189401702472507 -0.607074868618041  0.000727044387400    1.62703
 -1.470686949331898 -0.107169707949997 -0.441427340917014 -0.670634052348378 -0.012557093493794    1.67899
 -0.195825855075193  0.116471675589739  0.256769138164309 -1.670712963708117  0.000288710416246    1.70562
  0.219375728625357 -0.135801084967823  1.269575235202683 -1.174875407365534 -0.000492446061292    1.74892
 -1.595834628190904  0.364618900500196 -0.153417359965780  0.989708065091749  0.052000829045957    1.91903
 -1.435738237622479 -0.794197812046068 -0.889022804785796 -0.459705797387801  0.017665102437163    1.92192
 -1.593375030340223  0.374866415881084 -0.134076944312944  1.013298961166806 -0.100287158763123    1.92980
 -1.591176698140178  0.385382885537413 -0.114716116735195  1.035838544210136  0.048391791636414    1.94074
  0.385070820930509  0.005417650184955 -0.138469753716289  1.902439752980890 -0.000253491192219    1.94596
 -1.489336052919614 -0.785976663615442 -0.898574962001765 -0.485050855401727 -0.018154901508944    1.96941
 -0.514342772045079  1.451644049567610 -1.319211347270460 -0.279274564346926  0.000014577434078    2.04698
 -1.713735008384975 -0.689620115687730 -0.907464008111660 -0.612472052460274  0.002136567217642    2.14734
  0.525821226952442 -0.922929517087970 -0.628918727010175 -1.799097641903820  0.000144292215232    2.18187
  0.647238634213903 -0.880627125074230 -0.703136095150276 -1.813041193910243 -0.000131464332321    2.23068
  0.973602586919131 -0.355819915007437  1.695866617778817  1.015901447207431 -0.000025587836771    2.23216
  0.229013906389563 -2.137087488269457 -0.271600865129123  0.674645046247558  0.000004109838334    2.26903

>> # evaluating formula 1 with 124 points
# r4_124_9pcacg.txt:4 formula 1   : problem  G, 4_124_9  (d=4 n=124 o=9 plus 4/286 of order 10) quality N (6 negative weights, stability factor 15.378967)
# evaluating formula 2 with 124 points
# r4_124_9pcacg.txt:132 formula 2   : problem E2, 4_124_9  (d=4 n=124 o=9 plus 4/286 of order 10) quality N (6 negative weights, stability factor 15.378967)
G 4 dimensions, degree 9, symmetric 124 point rule with points at 62 distinct radii: 2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2=124
 (6 negative weights, stability factor 15.378967)
#                x1                 x2                 x3                 x4             Weight     Radius
 -1.003171385581765  0.000000000000000  0.000000000000000  0.000000000000000  0.089258193216936    1.00317
  1.003171385581765  0.000000000000000  0.000000000000000  0.000000000000000  0.089258193216936    1.00317
 -0.368489903210367  1.593564323950286  0.000000000000000  0.000000000000000  1.315589333970517    1.63561
  0.368489903210367 -1.593564323950286  0.000000000000000  0.000000000000000  1.315589333970517    1.63561
  0.474905134791107 -1.608926921223814  0.041482650760168  0.000000000000000 -1.900897408326932    1.67806
 -0.474905134791107  1.608926921223814 -0.041482650760168  0.000000000000000 -1.900897408326932    1.67806
 -0.599060904739653  1.319007128457579 -0.463452481324583 -0.773250112223656  0.058684571308040    1.70627
  0.599060904739653 -1.319007128457579  0.463452481324583  0.773250112223656  0.058684571308040    1.70627
  0.329385872350136 -0.533178828999469  1.873555475665041 -0.258498189685281 -1.692291607289385    1.99244
 -0.329385872350136  0.533178828999469 -1.873555475665041  0.258498189685281 -1.692291607288887    1.99244
  0.653811724144578 -1.652367928554599  0.097320111001739 -0.047623285429909  0.612532302444208    1.78032
 -0.653811724144578  1.652367928554599 -0.097320111001739  0.047623285429909  0.612532302444208    1.78032
 -0.151362935118168  0.196126817257689  1.555373432490109  0.748459494400577  0.039595772817669    1.74378
  0.151362935118168 -0.196126817257689 -1.555373432490109 -0.748459494400577  0.039595772817669    1.74378
 -0.005771283655567 -0.405426912643060 -0.126897985312159 -1.606135612207448  0.042239933768101    1.66138
  0.005771283655567  0.405426912643060  0.126897985312159  1.606135612207448  0.042239933768101    1.66138
  0.284646222178194 -0.540035849113396  1.758463680452738 -0.305291381374908  0.875255553406926    1.88628
 -0.284646222178194  0.540035849113396 -1.758463680452738  0.305291381374908  0.875255553406737    1.88628
 -0.841685168376396  0.945546931499350  0.881991786644233 -0.870571470721751  0.034700115812166    1.77152
  0.841685168376396 -0.945546931499350 -0.881991786644233  0.870571470721751  0.034700115812166    1.77152
 -1.761337395918505  0.572213034157575  0.289840549735276  1.268542062545995  0.013112936574830    2.26339
  1.761337395918505 -0.572213034157575 -0.289840549735276 -1.268542062545995  0.013112936574830    2.26339
  0.635097482999637  0.269848493411912  1.968589068690007 -0.501977868660329  0.031817503272878    2.14557
 -0.635097482999637 -0.269848493411912 -1.968589068690007  0.501977868660329  0.031817503272878    2.14557
  0.367966478759102 -0.550602280498941  1.953248288184231 -0.219350317597210  0.847759573220562    2.07409
 -0.367966478759102  0.550602280498941 -1.953248288184231  0.219350317597210  0.847759573220254    2.07409
  1.130016041508878  0.932870279404981  0.490994175837837 -1.566882691237867  0.017117780069906    2.20077
 -1.130016041508878 -0.932870279404981 -0.490994175837837  1.566882691237867  0.017117780069906    2.20077
  1.564424187475478  0.786898589417963  1.216169511903867  0.961711161091520  0.012622553142006    2.33893
 -1.564424187475478 -0.786898589417963 -1.216169511903867 -0.961711161091520  0.012622553142006    2.33893
  1.382105254479588  1.300805629774458 -1.249395587463160 -0.924912897312779  0.013001589486706    2.45332
 -1.382105254479588 -1.300805629774458  1.249395587463160  0.924912897312779  0.013001589486706    2.45332
 -1.005252099344836  1.844673471072762  1.829613817651442  0.490590320071158  0.004258115241204    2.82870
  1.005252099344836 -1.844673471072762 -1.829613817651442 -0.490590320071158  0.004258115241204    2.82870
  2.131537850237212  1.217166484115125 -0.319866651001613  0.393968059491377  0.007391001672592    2.50649
 -2.131537850237212 -1.217166484115125  0.319866651001613 -0.393968059491377  0.007391001672592    2.50649
 -1.391188363962224 -1.057042799170948  1.093933254169020 -1.532785563346768  0.007862863524909    2.56883
  1.391188363962224  1.057042799170948 -1.093933254169020  1.532785563346768  0.007862863524909    2.56883
 -0.987064132505403 -0.289094640304148  2.414018224153061 -0.420045072631628  0.008708801273160    2.65740
  0.987064132505403  0.289094640304148 -2.414018224153061  0.420045072631628  0.008708801273160    2.65740
 -1.776623420060432  0.211146864891873 -0.163768807181658 -2.162769031871039  0.005421201673462    2.81165
  1.776623420060432 -0.211146864891873  0.163768807181658  2.162769031871039  0.005421201673462    2.81165
  0.014866558086627 -0.136719336921899  1.630816997617840 -2.342127969044730  0.004617845596675    2.85728
 -0.014866558086627  0.136719336921899 -1.630816997617840  2.342127969044730  0.004617845596675    2.85728
 -2.302358354859969  0.678443308441652  1.555359184780202  0.260893728814662  0.003950234901141    2.87199
  2.302358354859969 -0.678443308441652 -1.555359184780202 -0.260893728814662  0.003950234901141    2.87199
 -2.672515440085048  0.439898054817325 -1.084560031839180 -0.129959912155263  0.003916045412310    2.92045
  2.672515440085048 -0.439898054817325  1.084560031839180  0.129959912155263  0.003916045412310    2.92045
  0.232740885541704  0.909562450216709 -1.283570346710776 -2.465048669021328  0.004420566463324    2.93351
 -0.232740885541704 -0.909562450216709  1.283570346710776  2.465048669021328  0.004420566463324    2.93351
  2.202400015604034  1.501764984695092  1.254987803812897 -0.596111776969196  0.002978607811643    3.00603
 -2.202400015604034 -1.501764984695092 -1.254987803812897  0.596111776969196  0.002978607811643    3.00603
 -0.176595533114029  2.761376952613131 -0.662848807063256 -0.994505589352590  0.003194806833057    3.01410
  0.176595533114029 -2.761376952613131  0.662848807063256  0.994505589352590  0.003194806833057    3.01410
  2.012927867391067 -0.717989804921034  1.605514710959735 -1.458388177859602  0.003053388530457    3.04499
 -2.012927867391067  0.717989804921034 -1.605514710959735  1.458388177859602  0.003053388530457    3.04499
  0.514853493087923  2.516702167134769 -1.606038035849456  0.667745976280477  0.002754191060084    3.10227
 -0.514853493087923 -2.516702167134769  1.606038035849456 -0.667745976280477  0.002754191060084    3.10227
  1.006098063178377  2.117897761235724  0.357988625272452  1.896121140162817  0.003120078736560    3.03664
 -1.006098063178377 -2.117897761235724 -0.357988625272452 -1.896121140162817  0.003120078736560    3.03664
 -0.853368478231815  1.651607958154165  1.311448579049113  2.232063409156895  0.002215445826020    3.18717
  0.853368478231815 -1.651607958154165 -1.311448579049113 -2.232063409156895  0.002215445826020    3.18717
 -0.733378610120093  1.991263877521042 -0.919377603837381  2.174792004491012  0.002397036769544    3.17458
  0.733378610120093 -1.991263877521042  0.919377603837381 -2.174792004491012  0.002397036769544    3.17458
  0.565141487756058  2.645835072884623  1.232030389743641 -1.184188929842737  0.001912629145274    3.20000
 -0.565141487756058 -2.645835072884623 -1.232030389743641  1.184188929842737  0.001912629145274    3.20000
 -2.884588631253524 -0.090368597972500  0.845089466737416 -0.754455676624675  0.001853644064459    3.10039
  2.884588631253524  0.090368597972500 -0.845089466737416  0.754455676624675  0.001853644064459    3.10039
  0.850342816844730  2.275875160792616  2.106805862375714  0.671522842480479  0.001706165485654    3.28516
 -0.850342816844730 -2.275875160792616 -2.106805862375714 -0.671522842480479  0.001706165485654    3.28516
 -1.669730299914548  0.885490857494445 -2.075564351206090 -1.464453257204635  0.002061428838536    3.16618
  1.669730299914548 -0.885490857494445  2.075564351206090  1.464453257204635  0.002061428838536    3.16618
 -2.825102240392934  1.586629424549324  0.014158045737753 -0.921293768312748  0.001118983074093    3.36862
  2.825102240392934 -1.586629424549324 -0.014158045737753  0.921293768312748  0.001118983074093    3.36862
 -0.304436342538283  1.566690683089989  0.678143235613070 -2.719540176278652  0.001974517711964    3.22536
  0.304436342538283 -1.566690683089989 -0.678143235613070  2.719540176278652  0.001974517711964    3.22536
 -0.175818637555203  1.506140750108340  2.812861443133926 -1.256238811774602  0.001077177304179    3.43361
  0.175818637555203 -1.506140750108340 -2.812861443133926  1.256238811774602  0.001077177304179    3.43361
 -1.520676298167696  2.662677388182751  1.044167202494776 -0.995622581064745  0.001170211825719    3.38878
  1.520676298167696 -2.662677388182751 -1.044167202494776  0.995622581064745  0.001170211825719    3.38878
 -1.828712150078592 -0.308634900634798  2.193206309982631  2.044134324919008  0.001126315397349    3.52535
  1.828712150078592  0.308634900634798 -2.193206309982631 -2.044134324919008  0.001126315397349    3.52535
 -0.156137103454183  0.586332445802596  3.490207480888186  1.127106968544137  0.000522454553060    3.71754
  0.156137103454183 -0.586332445802596 -3.490207480888186 -1.127106968544137  0.000522454553060    3.71754
  1.873827694496361  2.949672346514661 -0.043659759043380  0.093253194097010  0.000974928575487    3.49605
 -1.873827694496361 -2.949672346514661  0.043659759043380 -0.093253194097010  0.000974928575487    3.49605
  0.232542008102945 -1.198390061671204  3.311651673396159 -1.572021893175423  0.000384873091505    3.86374
 -0.232542008102945  1.198390061671204 -3.311651673396159  1.572021893175423  0.000384873091505    3.86374
  0.886974718578745  0.717496414003429  2.140839813308244  2.586689729083613  0.000815674683419    3.54622
 -0.886974718578745 -0.717496414003429 -2.140839813308244 -2.586689729083613  0.000815674683419    3.54622
  1.672601680282656 -0.148920117320421  0.074661112549413 -3.168571313758540  0.000794747921550    3.58681
 -1.672601680282656  0.148920117320421 -0.074661112549413  3.168571313758540  0.000794747921550    3.58681
  3.444140477374587  0.651542894458644 -0.137193024439136 -1.331922749291780  0.000559134376097    3.75226
 -3.444140477374587 -0.651542894458644  0.137193024439136  1.331922749291780  0.000559134376097    3.75226
 -3.305929904071852  2.506663310043678  0.320994868281707  1.559397923592992  0.000129573521813    4.44379
  3.305929904071852 -2.506663310043678 -0.320994868281707 -1.559397923592992  0.000129573521813    4.44379
 -2.103942999895554  0.796485496050983  2.057686019955306 -2.208973107295402  0.000524872993558    3.76492
  2.103942999895554 -0.796485496050983 -2.057686019955306  2.208973107295402  0.000524872993558    3.76492
 -0.499786576104967  3.947934387509878  0.492075315319781  0.984737394820741  0.000233802948929    4.12890
  0.499786576104967 -3.947934387509878 -0.492075315319781 -0.984737394820741  0.000233802948929    4.12890
 -0.578338661303021 -0.629605397353512 -0.024543177121715 -3.758155985464380  0.000396577997632    3.85425
  0.578338661303021  0.629605397353512  0.024543177121715  3.758155985464380  0.000396577997632    3.85425
 -1.935605356897258  2.513960350712880 -1.008434005930953 -2.851781310718311  0.000110987884716    4.38362
  1.935605356897258 -2.513960350712880  1.008434005930953  2.851781310718311  0.000110987884716    4.38362
 -1.994639465467040  2.848435657643772 -2.170536221308767  0.120193952322765  0.000269498164487    4.10096
  1.994639465467040 -2.848435657643772  2.170536221308767 -0.120193952322765  0.000269498164487    4.10096
  0.617831848067343  1.882295802287879 -2.645921147955000 -1.553198971389861  0.001130390998483    3.65213
 -0.617831848067343 -1.882295802287879  2.645921147955000  1.553198971389861  0.001130390998483    3.65213
  2.184211936845214  1.432950017591872  2.721650511346093 -3.138012969555080  0.000044425763049    4.90700
 -2.184211936845214 -1.432950017591872 -2.721650511346093  3.138012969555080  0.000044425763049    4.90700
  1.845359382865253  2.600457081157037 -0.843626635150063 -2.532464345395754  0.000242176801955    4.15846
 -1.845359382865253 -2.600457081157037  0.843626635150063  2.532464345395754  0.000242176801955    4.15846
  1.165805263043866  1.571156224317206 -2.103256795089229 -1.845045760759430 -0.001552848289753    3.41402
 -1.165805263043866 -1.571156224317206  2.103256795089229  1.845045760759430 -0.001552848289753    3.41402
 -2.594042787310671 -2.771070186278672  2.745864046989544 -4.302404074151996  0.000003377904693    6.36069
  2.594042787310671  2.771070186278672 -2.745864046989544  4.302404074151996  0.000003377904693    6.36069
  3.263700451196720  0.874011514077258  4.497698912662958  0.189151997365458  0.000014427347411    5.62856
 -3.263700451196720 -0.874011514077258 -4.497698912662958 -0.189151997365458  0.000014427347411    5.62856
 -3.428675721894808 -2.158740897158547  3.074111468160210 -0.181242546660453  0.000034736259751    5.08910
  3.428675721894808  2.158740897158547 -3.074111468160210  0.181242546660453  0.000034736259751    5.08910
 -4.015584681714537  2.927585955357756  5.995867926288754  0.270974126197024  0.000000546932949    7.79227
  4.015584681714537 -2.927585955357756 -5.995867926288754 -0.270974126197024  0.000000546932949    7.79227
  5.157671015960664  2.030864515229603  1.228613648293242  2.807615858847580  0.000005638500706    6.33389
 -5.157671015960664 -2.030864515229603 -1.228613648293242 -2.807615858847580  0.000005638500706    6.33389

E_n^{r^2} 4 dimensions, degree 9, symmetric 124 point rule with points at 62 distinct radii: 2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2=124
 (6 negative weights, stability factor 15.378967)
#                x1                 x2                 x3                 x4             Weight     Radius
 -0.709349289437159  0.000000000000000  0.000000000000000  0.000000000000000  0.880943056607167    0.70935
  0.709349289437159  0.000000000000000  0.000000000000000  0.000000000000000  0.880943056607167    0.70935
 -0.260561709358811  1.126820139722181  0.000000000000000  0.000000000000000 12.984346280581612    1.15655
  0.260561709358811 -1.126820139722181  0.000000000000000  0.000000000000000 12.984346280581612    1.15655
  0.335808641231090 -1.137683136430929  0.029332663654108  0.000000000000000 -18.761105427242939    1.18657
 -0.335808641231090  1.137683136430929 -0.029332663654108  0.000000000000000 -18.761105427242793    1.18657
 -0.423600028085139  0.932678884965733 -0.327710392302349 -0.546770397906598  0.579193503257907    1.20652
  0.423600028085139 -0.932678884965733  0.327710392302349  0.546770397906598  0.579193503257907    1.20652
  0.232910983965800 -0.377014365570642  1.324803781771965 -0.182785822850923 -16.702248695229237    1.40887
 -0.232910983965800  0.377014365570642 -1.324803781771965  0.182785822850923 -16.702248695225627    1.40887
  0.462314703761890 -1.168400567296098  0.068815710435158 -0.033674748069873  6.045451508012783    1.25887
 -0.462314703761890  1.168400567296098 -0.068815710435158  0.033674748069873  6.045451508012783    1.25887
 -0.107029757842373  0.138682602455448  1.099815101391154  0.529240783934106  0.390794613665792    1.23304
  0.107029757842373 -0.138682602455448 -1.099815101391154 -0.529240783934106  0.390794613665792    1.23304
 -0.004080913809007 -0.286680119205445 -0.089730425933145 -1.135709382897097  0.416891436219368    1.17477
  0.004080913809007  0.286680119205445  0.089730425933145  1.135709382897097  0.416891436219368    1.17477
  0.201275273941308 -0.381863010991931  1.243421592918415 -0.215873606008020  8.638426061984786    1.33380
 -0.201275273941308  0.381863010991931 -1.243421592918415  0.215873606008020  8.638426061979157    1.33380
 -0.595161290183084  0.668602647193325  0.623662373286977 -0.615586990454902  0.342476415738062    1.25266
  0.595161290183084 -0.668602647193325 -0.623662373286977  0.615586990454902  0.342476415738062    1.25266
 -1.245453616611431  0.404615716736108  0.204948218180634  0.896994694646649  0.129419496530145    1.60046
  1.245453616611431 -0.404615716736108 -0.204948218180634 -0.896994694646649  0.129419496530145    1.60046
  0.449081736943549  0.190811699584556  1.392002679840440 -0.354951954935303  0.314026170333636    1.51715
 -0.449081736943549 -0.190811699584556 -1.392002679840440  0.354951954935303  0.314026170333636    1.51715
  0.260191592379868 -0.389334606277592  1.381155109916111 -0.155104097028424  8.367051614920774    1.46660
 -0.260191592379868  0.389334606277592 -1.381155109916111  0.155104097028424  8.367051614922790    1.46660
  0.799042005800504  0.659638900534653  0.347185311258037 -1.107953376298129  0.168945717514818    1.55618
 -0.799042005800504 -0.659638900534653 -0.347185311258037  1.107953376298129  0.168945717514818    1.55618
  1.106214951616166  0.556421328683581  0.859961708939594  0.680032483550612  0.124579606043321    1.65387
 -1.106214951616166 -0.556421328683581 -0.859961708939594 -0.680032483550612  0.124579606043321    1.65387
  0.977295997756097  0.919808481819180 -0.883456092279764 -0.654012181696757  0.128320544819145    1.73476
 -0.977295997756097 -0.919808481819180  0.883456092279764  0.654012181696757  0.128320544819145    1.73476
 -0.710820576248721  1.304381120470494  1.293732337413941  0.346899742106760  0.042025912924929    2.00019
  0.710820576248721 -1.304381120470494 -1.293732337413941 -0.346899742106760  0.042025912924929    2.00019
  1.507224868258553  0.860666674750777 -0.226179877998609  0.278577486437242  0.072946262636276    1.77235
 -1.507224868258553 -0.860666674750777  0.226179877998609 -0.278577486437242  0.072946262636276    1.77235
 -0.983718726065551 -0.747442131298218  0.773527622188337 -1.083843065947344  0.077603352450610    1.81643
  0.983718726065551  0.747442131298218 -0.773527622188337  1.083843065947344  0.077603352450610    1.81643
 -0.697959741560595 -0.204420780563752  1.706968656206527 -0.297016719261839  0.085952423373790    1.87907
  0.697959741560595  0.204420780563752 -1.706968656206527  0.297016719261839  0.085952423373790    1.87907
 -1.256262467939568  0.149303379991323 -0.115802034105006 -1.529308648576261  0.053505115895597    1.98814
  1.256262467939568 -0.149303379991323  0.115802034105006  1.529308648576261  0.053505115895597    1.98814
  0.010512244035939 -0.096675170256814  1.153161757889841 -1.656134569318201  0.045576309224499    2.02040
 -0.010512244035939  0.096675170256814 -1.153161757889841  1.656134569318201  0.045576309224499    2.02040
 -1.628013205442950  0.479731864049761  1.099805026738871  0.184479724813935  0.038987255765640    2.03081
  1.628013205442950 -0.479731864049761 -1.099805026738871 -0.184479724813935  0.038987255765640    2.03081
 -1.889753790509858  0.311054897592066 -0.766899753117428 -0.091895535167374  0.038649819036204    2.06507
  1.889753790509858 -0.311054897592066  0.766899753117428  0.091895535167374  0.038649819036204    2.06507
  0.164572658425913  0.643157776460884 -0.907621296289156 -1.743052629819844  0.043629242221732    2.07431
 -0.164572658425913 -0.643157776460884  0.907621296289156  1.743052629819844  0.043629242221732    2.07431
  1.557331985918947  1.061908204426443  0.887410386382540 -0.421514679840114  0.029397680766910    2.12558
 -1.557331985918947 -1.061908204426443 -0.887410386382540  0.421514679840114  0.029397680766910    2.12558
 -0.124871898992197  1.952588368604986 -0.468704886375843 -0.703221646159130  0.031531479580171    2.13129
  0.124871898992197 -1.952588368604986  0.468704886375843  0.703221646159130  0.031531479580171    2.13129
  1.423354945071583 -0.507695459882471  1.135270339414403 -1.031236170166830  0.030135736878430    2.15313
 -1.423354945071583  0.507695459882471 -1.135270339414403  1.031236170166830  0.030135736878430    2.15313
  0.364056396280052  1.779577168607883 -1.135640385992660  0.472167707937978  0.027182776208041    2.19364
 -0.364056396280052 -1.779577168607883  1.135640385992660 -0.472167707937978  0.027182776208041    2.19364
  0.711418763012061  1.497579868829607  0.253136184517842  1.340760116160312  0.030793942830096    2.14723
 -0.711418763012061 -1.497579868829607 -0.253136184517842 -1.340760116160312  0.030793942830096    2.14723
 -0.603422637808597  1.167863187072458  0.927334183423119  1.578307172653187  0.021865573874861    2.25367
  0.603422637808597 -1.167863187072458 -0.927334183423119 -1.578307172653187  0.021865573874861    2.25367
 -0.518576988393085  1.408036190926948 -0.650098138144430  1.537810174045886  0.023657804650262    2.24477
  0.518576988393085 -1.408036190926948  0.650098138144430 -1.537810174045886  0.023657804650262    2.24477
  0.399615378322110  1.870887921937936  0.871177043215630 -0.837348022497851  0.018876893029851    2.26275
 -0.399615378322110 -1.870887921937936 -0.871177043215630  0.837348022497851  0.018876893029851    2.26275
 -2.039712182092964 -0.063900248432599  0.597568492639388 -0.533480725045924  0.018294733616638    2.19230
  2.039712182092964  0.063900248432599 -0.597568492639388  0.533480725045924  0.018294733616638    2.19230
  0.601283172124172  1.609286759330483  1.489736711929457  0.474838355639602  0.016839178386199    2.32296
 -0.601283172124172 -1.609286759330483 -1.489736711929457 -0.474838355639602  0.016839178386199    2.32296
 -1.180677617822196  0.626136590013027 -1.467645627526912 -1.035524828900115  0.020345487137347    2.23883
  1.180677617822196 -0.626136590013027  1.467645627526912  1.035524828900115  0.020345487137347    2.23883
 -1.997648951727168  1.121916425328888  0.010011250149425 -0.651453071038835  0.011043920272818    2.38197
  1.997648951727168 -1.121916425328888 -0.010011250149425  0.651453071038835  0.011043920272818    2.38197
 -0.215269002248454  1.107817606034708  0.479519680517775 -1.923005300355903  0.019487708700029    2.28068
  0.215269002248454 -1.107817606034708 -0.479519680517775  1.923005300355903  0.019487708700029    2.28068
 -0.124322550874294  1.065002337823010  1.988993400978194 -0.888294982595592  0.010631313862080    2.42793
  0.124322550874294 -1.065002337823010 -1.988993400978194  0.888294982595592  0.010631313862080    2.42793
 -1.075280522424120  1.882797237296080  0.738337709576605 -0.704011478573351  0.011549527785324    2.39623
  1.075280522424120 -1.882797237296080 -0.738337709576605  0.704011478573351  0.011549527785324    2.39623
 -1.293094762158839 -0.218237831149757  1.550831054329850  1.445421242806407  0.011116287402688    2.49280
  1.293094762158839  0.218237831149757 -1.550831054329850 -1.445421242806407  0.011116287402688    2.49280
 -0.110405604647317  0.414599648456716  2.467949377484062  0.796984980580161  0.005156419756254    2.62870
  0.110405604647317 -0.414599648456716 -2.467949377484062 -0.796984980580161  0.005156419756254    2.62870
  1.324996269553510  2.085733318498963 -0.030872111684526  0.065939965913320  0.009622159359377    2.47208
 -1.324996269553510 -2.085733318498963  0.030872111684526 -0.065939965913320  0.009622159359377    2.47208
  0.164432030840313 -0.847389739114271  2.341691355186185 -1.111587340838059  0.003798545157776    2.73208
 -0.164432030840313  0.847389739114271 -2.341691355186185  1.111587340838059  0.003798545157776    2.73208
  0.627185838248046  0.507346579818841  1.513802349424428  1.829065848260622  0.008050386445329    2.50756
 -0.627185838248046 -0.507346579818841 -1.513802349424428 -1.829065848260622  0.008050386445329    2.50756
  1.182707990351877 -0.105302424812372  0.052793378974615 -2.240518262631848  0.007843847584282    2.53626
 -1.182707990351877  0.105302424812372 -0.052793378974615  2.240518262631848  0.007843847584282    2.53626
  2.435375086910677  0.460710398905619 -0.097010117912375 -0.941811608040859  0.005518435099128    2.65325
 -2.435375086910677 -0.460710398905619  0.097010117912375  0.941811608040859  0.005518435099128    2.65325
 -2.337645453296513  1.772478624683311  0.226977648088049  1.102660846340767  0.001278839401149    3.14224
  2.337645453296513 -1.772478624683311 -0.226977648088049 -1.102660846340767  0.001278839401149    3.14224
 -1.487712362456130  0.563200295374364  1.455003738263114 -1.561979863627316  0.005180288807230    2.66220
  1.487712362456130 -0.563200295374364 -1.455003738263114  1.561979863627316  0.005180288807230    2.66220
 -0.353402477109876  2.791611177087749  0.347949792317131  0.696314489565697  0.002307542613735    2.91957
  0.353402477109876 -2.791611177087749 -0.347949792317131 -0.696314489565697  0.002307542613735    2.91957
 -0.408947189229726 -0.445198245940316 -0.017354646974659 -2.657417582078685  0.003914067950807    2.72536
  0.408947189229726  0.445198245940316  0.017354646974659  2.657417582078685  0.003914067950807    2.72536
 -1.368679673563014  1.777638411623156 -0.713070523972902 -2.016513903269959  0.001095406515462    3.09969
  1.368679673563014 -1.777638411623156  0.713070523972902  2.016513903269959  0.001095406515462    3.09969
 -1.410423092054024  2.014148169293446 -1.534800880898419  0.084989958745050  0.002659840270309    2.89981
  1.410423092054024 -2.014148169293446  1.534800880898419 -0.084989958745050  0.002659840270309    2.89981
  0.436873089401503  1.330984125996759 -1.870948786203858 -1.098277525201736  0.011156511973582    2.58245
 -0.436873089401503 -1.330984125996759  1.870948786203858  1.098277525201736  0.011156511973582    2.58245
  1.544471072091817  1.013248674540582  1.924497532592646 -2.218910250223778  0.000438464706510    3.46977
 -1.544471072091817 -1.013248674540582 -1.924497532592646  2.218910250223778  0.000438464706510    3.46977
  1.304866133350235  1.838800836270712 -0.596534114504214 -1.790722711742457  0.002390189230414    2.94048
 -1.304866133350235 -1.838800836270712  0.596534114504214  1.790722711742457  0.002390189230414    2.94048
  0.824348807041350  1.110975220518211 -1.487227142384289 -1.304644369032442 -0.015325998314772    2.41408
 -0.824348807041350 -1.110975220518211  1.487227142384289  1.304644369032442 -0.015325998314772    2.41408
 -1.834265245595314 -1.959442519861471  1.941619087842617 -3.042259096237514  0.000033338583021    4.49768
  1.834265245595314  1.959442519861471 -1.941619087842617  3.042259096237514  0.000033338583021    4.49768
  2.307784720802946  0.618019468439198  3.180353400879596  0.133750660012100  0.000142392211508    3.97999
 -2.307784720802946 -0.618019468439198 -3.180353400879596 -0.133750660012100  0.000142392211508    3.97999
 -2.424439853441547 -1.526460327205561  2.173725065259393 -0.128157833783164  0.000342833142112    3.59854
  2.424439853441547  1.526460327205561 -2.173725065259393  0.128157833783164  0.000342833142112    3.59854
 -2.839447158869286  2.070115881539999  4.239718869777685  0.191607642159948  0.000005398011845    5.50997
  2.839447158869286 -2.070115881539999 -4.239718869777685 -0.191607642159948  0.000005398011845    5.50997
  3.647024150515224  1.436038070389997  0.868761042166480  1.985284212758073  0.000055649771384    4.47874
 -3.647024150515224 -1.436038070389997 -0.868761042166480 -1.985284212758073  0.000055649771384    4.47874

>> # evaluating formula 1 with 125 points
# r4_125_9pag.txt:4 formula 1   : problem  G, 4_125_9  (d=4 n=125 o=9 plus 0/286 of order 10) quality N (6 negative weights, stability factor 8.129637)
# evaluating formula 2 with 125 points
# r4_125_9pag.txt:133 formula 2   : problem E2, 4_125_9  (d=4 n=125 o=9 plus 0/286 of order 10) quality N (6 negative weights, stability factor 8.129637)
G 4 dimensions, degree 9, symmetric 125 point rule with points at 63 distinct radii: 1+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2=125
 (6 negative weights, stability factor 8.129637)
#                x1                 x2                 x3                 x4             Weight     Radius
  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  2.345852044940189    0.00000
 -0.965391448744043  0.000000000000000  0.000000000000000  0.000000000000000  0.373664254839702    0.96539
  0.965391448744043  0.000000000000000  0.000000000000000  0.000000000000000  0.373664254839702    0.96539
 -0.530479365930047  0.202838468163442  0.000000000000000  0.000000000000000 -0.974456507268880    0.56794
  0.530479365930047 -0.202838468163442  0.000000000000000  0.000000000000000 -0.974456507268880    0.56794
 -0.247006920387260 -0.464049599686819 -0.096897576504454  0.000000000000000 -0.807513812045449    0.53455
  0.247006920387260  0.464049599686819  0.096897576504454  0.000000000000000 -0.807513812045449    0.53455
  1.899158490588502  2.622491404437450 -1.766441135109591  0.518307044232044 -0.000438936644717    3.72468
 -1.899158490588502 -2.622491404437450  1.766441135109591 -0.518307044232044 -0.000438936644717    3.72468
 -2.434005743559009 -0.229514346279869 -0.095604148600669  4.331514139865181  0.000039480833187    4.97476
  2.434005743559009  0.229514346279869  0.095604148600669 -4.331514139865181  0.000039480833187    4.97476
 -2.151331833110249  1.221499536263716  2.680648569459676 -2.741503197947244  0.000070187326125    4.56311
  2.151331833110249 -1.221499536263716 -2.680648569459676  2.741503197947244  0.000070187326125    4.56311
 -0.429484167381471  1.549971198774424 -1.192094926931759 -3.776685797352187  0.000152634207774    4.27450
  0.429484167381471 -1.549971198774424  1.192094926931759  3.776685797352187  0.000152634207774    4.27450
 -1.932098276395424  1.376212145186511 -2.103587882336348  2.572606254632480  0.000190557040490    4.08293
  1.932098276395424 -1.376212145186511  2.103587882336348 -2.572606254632480  0.000190557040490    4.08293
 -0.392031633252707 -1.144356076351040 -3.972969991002533 -0.287144442203480  0.000198974215894    4.16295
  0.392031633252707  1.144356076351040  3.972969991002533  0.287144442203480  0.000198974215894    4.16295
 -1.937383776063437 -0.590310453410463  3.548532598723929  0.266912932736219  0.000221023078895    4.09454
  1.937383776063437  0.590310453410463 -3.548532598723929 -0.266912932736219  0.000221023078895    4.09454
  1.936173412039275  2.108044111266928 -1.926305462753212 -2.233422525730645  0.000222512866271    4.10992
 -1.936173412039275 -2.108044111266928  1.926305462753212  2.233422525730645  0.000222512866271    4.10992
 -1.132749093816517 -1.020709868631702 -2.878493557418394  2.236346140375923  0.000323805415087    3.95119
  1.132749093816517  1.020709868631702  2.878493557418394 -2.236346140375923  0.000323805415087    3.95119
 -1.625217913025804 -0.817071534190244 -2.364625017922354 -2.486767600227440  0.000404965259265    3.88386
  1.625217913025804  0.817071534190244  2.364625017922354  2.486767600227440  0.000404965259265    3.88386
  1.507771079049621  2.998071479197522 -2.181143870608117  0.628925424007774  0.000427405783421    4.05151
 -1.507771079049621 -2.998071479197522  2.181143870608117 -0.628925424007774  0.000427405783421    4.05151
 -1.925192139019103  1.849878869122148  2.402097830127550  0.359618616543812  0.000678320102802    3.60941
  1.925192139019103 -1.849878869122148 -2.402097830127550 -0.359618616543812  0.000678320102802    3.60941
  0.700712534612808  1.286293878203533 -1.792466464660076  2.766463315204233  0.000772533931876    3.60719
 -0.700712534612808 -1.286293878203533  1.792466464660076 -2.766463315204233  0.000772533931876    3.60719
  0.038637143062511  1.124357269073478  0.465111896510396  3.262293903428673  0.000958343688699    3.48203
 -0.038637143062511 -1.124357269073478 -0.465111896510396 -3.262293903428673  0.000958343688699    3.48203
  1.262602843726237  2.471334196905907  0.791881250645839 -1.911086000909252  0.001026504620348    3.46136
 -1.262602843726237 -2.471334196905907 -0.791881250645839  1.911086000909252  0.001026504620348    3.46136
 -0.498128134453569  1.385770280239892 -2.920000404799974 -1.220109172644867  0.001080619012091    3.49050
  0.498128134453569 -1.385770280239892  2.920000404799974  1.220109172644867  0.001080619012091    3.49050
 -1.822555235232774 -2.227636773948829 -0.168581838336388 -1.934111121812837  0.001160178622417    3.47178
  1.822555235232774  2.227636773948829  0.168581838336388  1.934111121812837  0.001160178622417    3.47178
 -2.279845177262208  1.749638010984843 -1.185000430988054 -1.493774570632343  0.001184470618940    3.44884
  2.279845177262208 -1.749638010984843  1.185000430988054  1.493774570632343  0.001184470618940    3.44884
 -1.093650067093611  2.357080415971299  0.629142357879696 -2.088983133545666  0.001227348568422    3.39287
  1.093650067093611 -2.357080415971299 -0.629142357879696  2.088983133545666  0.001227348568422    3.39287
 -0.561808180987473  2.651450547987891 -0.418985645013561  1.918788319522043  0.001386466834410    3.34711
  0.561808180987473 -2.651450547987891  0.418985645013561 -1.918788319522043  0.001386466834410    3.34711
 -0.935777735673252  0.330213175874362  2.344503530829467  2.224657870143476  0.001408646865609    3.38091
  0.935777735673252 -0.330213175874362 -2.344503530829467 -2.224657870143476  0.001408646865609    3.38091
  0.576990119859487  3.267267532946469  0.376758051730479  0.109007577619953  0.001478922084005    3.34093
 -0.576990119859487 -3.267267532946469 -0.376758051730479 -0.109007577619953  0.001478922084005    3.34093
 -1.273947712722774  2.462321628321035 -1.788787981686126  0.414058458050549  0.001503078421609    3.32523
  1.273947712722774 -2.462321628321035  1.788787981686126 -0.414058458050549  0.001503078421609    3.32523
 -2.977824296766877 -0.166009012612421  1.192268005565574  0.945964859657316  0.001509996658503    3.34834
  2.977824296766877  0.166009012612421 -1.192268005565574 -0.945964859657316  0.001509996658503    3.34834
 -2.143714453975012  0.307369780499436 -2.508201882399688  0.200434954977581  0.001617291308147    3.31983
  2.143714453975012 -0.307369780499436  2.508201882399688 -0.200434954977581  0.001617291308147    3.31983
 -3.129015395488968 -0.517098444382282 -0.587109986973500 -0.775472963166291  0.001700097596591    3.31726
  3.129015395488968  0.517098444382282  0.587109986973500  0.775472963166291  0.001700097596591    3.31726
 -1.996614295853691  1.577675197831559  0.758319535569123  1.912516543061107  0.001723917449907    3.27235
  1.996614295853691 -1.577675197831559 -0.758319535569123 -1.912516543061107  0.001723917449907    3.27235
 -1.888168853692505 -1.953103115173920 -1.854592996760440 -0.139172028774778  0.001847933394826    3.29221
  1.888168853692505  1.953103115173920  1.854592996760440  0.139172028774778  0.001847933394826    3.29221
 -0.850068999315873  0.340223323365150  2.631944142620251 -1.211440699056210  0.001863086632016    3.03860
  0.850068999315873 -0.340223323365150 -2.631944142620251  1.211440699056210  0.001863086632016    3.03860
 -1.562750001469960  2.787325100581026  0.363378398964156  0.031089259101454  0.002123630169316    3.21627
  1.562750001469960 -2.787325100581026 -0.363378398964156 -0.031089259101454  0.002123630169316    3.21627
 -2.764738662092335  1.270343551614264 -0.633615154944442  0.664586625379398  0.002252657475120    3.17816
  2.764738662092335 -1.270343551614264  0.633615154944442 -0.664586625379398  0.002252657475120    3.17816
 -2.695032380980700  1.128868172990068  0.887555274239203 -0.817800229310562  0.002312262749386    3.16134
  2.695032380980700 -1.128868172990068 -0.887555274239203  0.817800229310562  0.002312262749386    3.16134
 -2.596772327338789 -0.742995525877250 -0.882583200421153  1.393954050349245  0.002372446641235    3.16502
  2.596772327338789  0.742995525877250  0.882583200421153 -1.393954050349245  0.002372446641235    3.16502
 -0.047880363901640  2.255163127936240  1.684972858901451  1.451322029182037  0.002462481536283    3.16757
  0.047880363901640 -2.255163127936240 -1.684972858901451 -1.451322029182037  0.002462481536283    3.16757
 -2.352346847156016 -0.960452519930075  1.539428419134490 -1.078287072837412  0.002514953416930    3.16047
  2.352346847156016  0.960452519930075 -1.539428419134490  1.078287072837412  0.002514953416930    3.16047
 -1.907622406989459  0.067354207527987  0.095741715405336 -2.514019730010328  0.002571085476573    3.15801
  1.907622406989459 -0.067354207527987 -0.095741715405336  2.514019730010328  0.002571085476573    3.15801
 -0.104694219460063  2.664611930236040 -1.007776512364007 -1.152218587823503  0.002944157779163    3.07479
  0.104694219460063 -2.664611930236040  1.007776512364007  1.152218587823503  0.002944157779163    3.07479
 -2.236318729592973 -2.094911750582846  0.449141588480579  0.253531724526091  0.003001692828009    3.10738
  2.236318729592973  2.094911750582846 -0.449141588480579 -0.253531724526091  0.003001692828009    3.10738
 -0.193701700521369  2.223580083686140  1.913380428862488 -0.750014050760679  0.003166871170775    3.03404
  0.193701700521369 -2.223580083686140 -1.913380428862488  0.750014050760679  0.003166871170775    3.03404
 -1.820215408214355  0.122432208250116 -1.625201088657582 -1.177507762780770  0.003358454696577    2.71219
  1.820215408214355 -0.122432208250116  1.625201088657582  1.177507762780770  0.003358454696577    2.71219
 -0.166274415382151  0.997291423714646 -2.655414061555736  0.944799189359758  0.003429952053471    2.99435
  0.166274415382151 -0.997291423714646  2.655414061555736 -0.944799189359758  0.003429952053471    2.99435
  0.017446569886343  0.634712144093815  0.980041016310001 -2.681804557143184  0.004033813953410    2.92502
 -0.017446569886343 -0.634712144093815 -0.980041016310001  2.681804557143184  0.004033813953410    2.92502
  0.773161743065001  1.380623151718200 -0.132724396474192 -1.872902912942420  0.005954348856065    2.45546
 -0.773161743065001 -1.380623151718200  0.132724396474192  1.872902912942420  0.005954348856065    2.45546
 -1.324029573381599  0.443820057461102  1.690791597431170  0.357754006951525  0.010675946419886    2.22189
  1.324029573381599 -0.443820057461102 -1.690791597431170 -0.357754006951525  0.010675946419886    2.22189
 -1.341318456357394 -0.317361965796320  0.563281677622297  1.814393718598517  0.010792201011401    2.34716
  1.341318456357394  0.317361965796320 -0.563281677622297 -1.814393718598517  0.010792201011401    2.34716
 -0.367775803687714  0.701275433252565 -1.165539535176313 -1.878768646702115  0.010848590928183    2.34847
  0.367775803687714 -0.701275433252565  1.165539535176313  1.878768646702115  0.010848590928183    2.34847
 -0.906281344264840  0.578159681051637  1.491208318936785 -1.083258847420189  0.010970855400674    2.13372
  0.906281344264840 -0.578159681051637 -1.491208318936785  1.083258847420189  0.010970855400674    2.13372
 -0.033405601684316 -0.645020069573732 -0.493529104894053 -1.940339617041708  0.011713026637644    2.10372
  0.033405601684316  0.645020069573732  0.493529104894053  1.940339617041708  0.011713026637644    2.10372
  0.422779345020868  1.863581810898995 -0.823514775180716  0.829337333942783  0.011713320998552    2.24001
 -0.422779345020868 -1.863581810898995  0.823514775180716 -0.829337333942783  0.011713320998552    2.24001
 -1.054526302959777  0.667567782107481 -0.869592644686496  1.754576998991987  0.012381862885237    2.32216
  1.054526302959777 -0.667567782107481  0.869592644686496 -1.754576998991987  0.012381862885237    2.32216
 -0.203315268796336 -0.436859629142980 -2.071819213207851 -0.552447511788080  0.015856276440127    2.19768
  0.203315268796336  0.436859629142980  2.071819213207851  0.552447511788080  0.015856276440127    2.19768
  0.910460329621002  1.135207054314259 -1.610004373210594 -0.462132486145458  0.016634924660084    2.21885
 -0.910460329621002 -1.135207054314259  1.610004373210594  0.462132486145458  0.016634924660084    2.21885
 -0.810643292940162 -0.569122544068402 -1.469415314324695  0.863873501552766  0.021504184549113    1.97142
  0.810643292940162  0.569122544068402  1.469415314324695 -0.863873501552766  0.021504184549113    1.97142
 -0.669289609306480 -0.622033763861960  0.788690308861257 -1.184483292961037  0.028291798684311    1.69113
  0.669289609306480  0.622033763861960 -0.788690308861257  1.184483292961037  0.028291798684311    1.69113
 -0.962706563756564 -0.862158859235432 -0.679770385462454 -0.938170131817165  0.031231121693707    1.73562
  0.962706563756564  0.862158859235432  0.679770385462454  0.938170131817165  0.031231121693707    1.73562
 -0.825097877059778  0.899346939433475  0.142857665293156 -0.953833269944523  0.045783136747703    1.55558
  0.825097877059778 -0.899346939433475 -0.142857665293156  0.953833269944523  0.045783136747703    1.55558
 -0.765052255329425  0.816453144753215 -0.826331200653570 -0.042011441516369  0.074940097057106    1.39158
  0.765052255329425 -0.816453144753215  0.826331200653570  0.042011441516369  0.074940097057106    1.39158
 -0.597766715036525  0.900408898524816  0.344562607115380  0.376140358732355  0.131599594801784    1.19510
  0.597766715036525 -0.900408898524816 -0.344562607115380 -0.376140358732355  0.131599594801784    1.19510
  0.385911560631940  0.963469258676783  0.191997783225182 -0.175530971739889  0.222003928493795    1.06999
 -0.385911560631940 -0.963469258676783 -0.191997783225182  0.175530971739889  0.222003928493795    1.06999

E_n^{r^2} 4 dimensions, degree 9, symmetric 125 point rule with points at 63 distinct radii: 1+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2=125
 (6 negative weights, stability factor 8.129637)
#                x1                 x2                 x3                 x4             Weight     Radius
  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 23.152631667046112    0.00000
 -0.682634839906419  0.000000000000000  0.000000000000000  0.000000000000000  3.687918374095695    0.68263
  0.682634839906419  0.000000000000000  0.000000000000000  0.000000000000000  3.687918374095695    0.68263
 -0.375105556928680  0.143428456323865  0.000000000000000  0.000000000000000 -9.617500232811041    0.40159
  0.375105556928680 -0.143428456323865  0.000000000000000  0.000000000000000 -9.617500232811041    0.40159
 -0.174660268405833 -0.328132618745447 -0.068516933426840  0.000000000000000 -7.969841873304166    0.37798
  0.174660268405833  0.328132618745447  0.068516933426840  0.000000000000000 -7.969841873304166    0.37798
  1.342907847243143  1.854381455681106 -1.249062505202838  0.366498425713241 -0.004332131040502    2.63374
 -1.342907847243143 -1.854381455681106  1.249062505202838 -0.366498425713241 -0.004332131040502    2.63374
 -1.721101966717614 -0.162291150634128 -0.067602341785108  3.062843021104192  0.000389660204985    3.51769
  1.721101966717614  0.162291150634128  0.067602341785108 -3.062843021104192  0.000389660204985    3.51769
 -1.521221327774723  0.863730605308293  1.895504781442960 -1.938535501913068  0.000692721142822    3.22661
  1.521221327774723 -0.863730605308293 -1.895504781442960  1.938535501913068  0.000692721142822    3.22661
 -0.303691167167715  1.095995145297237 -0.842938406651524 -2.670520137718595  0.001506439248806    3.02252
  0.303691167167715 -1.095995145297237  0.842938406651524  2.670520137718595  0.001506439248806    3.02252
 -1.366199793158056  0.973128940212648 -1.487461256421893  1.819107327973553  0.001880722605484    2.88707
  1.366199793158056 -0.973128940212648  1.487461256421893 -1.819107327973553  0.001880722605484    2.88707
 -0.277208226312631 -0.809181941679863 -2.809314022088555 -0.203041782262121  0.001963796796886    2.94365
  0.277208226312631  0.809181941679863  2.809314022088555  0.203041782262121  0.001963796796886    2.94365
 -1.369937205815238 -0.417412524611835  2.509191463819193  0.188735944724177  0.002181410352203    2.89528
  1.369937205815238  0.417412524611835 -2.509191463819193 -0.188735944724177  0.002181410352203    2.89528
  1.369081349206056  1.490612286117232 -1.362103655349495 -1.579268213198927  0.002196113964245    2.90615
 -1.369081349206056 -1.490612286117232  1.362103655349495  1.579268213198927  0.002196113964245    2.90615
 -0.800974565620568 -0.721750869733524 -2.035402314052329  1.581335520940160  0.003195831349839    2.79392
  0.800974565620568  0.721750869733524  2.035402314052329 -1.581335520940160  0.003195831349839    2.79392
 -1.149202607206409 -0.577756822540422 -1.672042385136264 -1.758410233355842  0.003996846905127    2.74631
  1.149202607206409  0.577756822540422  1.672042385136264  1.758410233355842  0.003996846905127    2.74631
  1.066155154472927  2.119956673422551 -1.542301621650499  0.444717432176534  0.004218326001107    2.86485
 -1.066155154472927 -2.119956673422551  1.542301621650499 -0.444717432176534  0.004218326001107    2.86485
 -1.361316416587439  1.308061892729963  1.698539664756676  0.254288762399078  0.006694751071965    2.55224
  1.361316416587439 -1.308061892729963 -1.698539664756676 -0.254288762399078  0.006694751071965    2.55224
  0.495478584887127  0.909547123876443 -1.267465192210633  1.956184970084743  0.007624604294039    2.55067
 -0.495478584887127 -0.909547123876443  1.267465192210633 -1.956184970084743  0.007624604294039    2.55067
  0.027320585865185  0.795040649438224  0.328883776033027  2.306790141337959  0.009458473087737    2.46217
 -0.027320585865185 -0.795040649438224 -0.328883776033027 -2.306790141337959  0.009458473087737    2.46217
  0.892795032744224  1.747497169210390  0.559944602226146 -1.351341870673602  0.010131194518726    2.44755
 -0.892795032744224 -1.747497169210390 -0.559944602226146  1.351341870673602  0.010131194518726    2.44755
 -0.352229781771934  0.979887562324408 -2.064752087301524 -0.862747469765086  0.010665282157637    2.46815
  0.352229781771934 -0.979887562324408  2.064752087301524  0.862747469765086  0.010665282157637    2.46815
 -1.288741165920143 -1.575177068879738 -0.119205361072541 -1.367623089802193  0.011450504037857    2.45492
  1.288741165920143  1.575177068879738  0.119205361072541  1.367623089802193  0.011450504037857    2.45492
 -1.612093984897561  1.237180902189121 -0.837921840460633 -1.056258128458131  0.011690256433648    2.43870
  1.612093984897561 -1.237180902189121  0.837921840460633  1.056258128458131  0.011690256433648    2.43870
 -0.773327378687029  1.666707545935313  0.444870827588426 -1.477134139514440  0.012113444832564    2.39912
  0.773327378687029 -1.666707545935313 -0.444870827588426  1.477134139514440  0.012113444832564    2.39912
 -0.397258374502321  1.874858662463005 -0.296267590808918  1.356788232395592  0.013683879170853    2.36676
  0.397258374502321 -1.874858662463005  0.296267590808918 -1.356788232395592  0.013683879170853    2.36676
 -0.661694782577939  0.233495975897895  1.657814345165317  1.573070665798481  0.013902787304391    2.39066
  0.661694782577939 -0.233495975897895 -1.657814345165317 -1.573070665798481  0.013902787304391    2.39066
  0.407993626430272  2.310307028497085  0.266408173245245  0.077079997335808  0.014596375909161    2.36239
 -0.407993626430272 -2.310307028497085 -0.266408173245245 -0.077079997335808  0.014596375909161    2.36239
 -0.900817066543370  1.741124320848090 -1.264864111955257  0.292783543495204  0.014834789405097    2.35130
  0.900817066543370 -1.741124320848090  1.264864111955257 -0.292783543495204  0.014834789405097    2.35130
 -2.105639753425916 -0.117386098556336  0.843060791727184  0.668898167027875  0.014903069666394    2.36763
  2.105639753425916  0.117386098556336 -0.843060791727184 -0.668898167027875  0.014903069666394    2.36763
 -1.515835027333354  0.217343256122960 -1.773566559629672  0.141728915851464  0.015962025412728    2.34747
  1.515835027333354 -0.217343256122960  1.773566559629672 -0.141728915851464  0.015962025412728    2.34747
 -2.212548004587356 -0.365643816563729 -0.415149453091300 -0.548342190881705  0.016779290721596    2.34565
  2.212548004587356  0.365643816563729  0.415149453091300  0.548342190881705  0.016779290721596    2.34565
 -1.411819508012142  1.115584830896509  0.536212885907157  1.352353416729983  0.017014383250713    2.31390
  1.411819508012142 -1.115584830896509 -0.536212885907157 -1.352353416729983  0.017014383250713    2.31390
 -1.335137000471201 -1.381052457096062 -1.311395284350380 -0.098409485298144  0.018238371566497    2.32795
  1.335137000471201  1.381052457096062  1.311395284350380  0.098409485298144  0.018238371566497    2.32795
 -0.601089553892725  0.240574219069344  1.861065550950962 -0.856617933307995  0.018387928022962    2.14861
  0.601089553892725 -0.240574219069344 -1.861065550950962  0.856617933307995  0.018387928022962    2.14861
 -1.105031123338704  1.970936479992316  0.256947330044262  0.021983425932727  0.020959389665367    2.27424
  1.105031123338704 -1.970936479992316 -0.256947330044262 -0.021983425932727  0.020959389665367    2.27424
 -1.954965456174115  0.898268539783038 -0.448033572723773  0.469933709491670  0.022232838130594    2.24730
  1.954965456174115 -0.898268539783038  0.448033572723773 -0.469933709491670  0.022232838130594    2.24730
 -1.905675672108781  0.798230340186944  0.627596353092435 -0.578272087801402  0.022821118607810    2.23541
  1.905675672108781 -0.798230340186944 -0.627596353092435  0.578272087801402  0.022821118607810    2.23541
 -1.836195321858826 -0.525377174739086 -0.624080565979117  0.985674361664409  0.023415109811681    2.23800
  1.836195321858826  0.525377174739086  0.624080565979117 -0.985674361664409  0.023415109811681    2.23800
 -0.033856530000528  1.594641140445576  1.191455734644490  1.026239648520054  0.024303718608101    2.23981
  0.033856530000528 -1.594641140445576 -1.191455734644490 -1.026239648520054  0.024303718608101    2.23981
 -1.663360407326808 -0.679142489850264  1.088540274321294 -0.762464101269121  0.024821595312269    2.23479
  1.663360407326808  0.679142489850264 -1.088540274321294  0.762464101269121  0.024821595312269    2.23479
 -1.348892739925657  0.047626616884498  0.067699616205556 -1.777680399127071  0.025375596535165    2.23305
  1.348892739925657 -0.047626616884498 -0.067699616205556  1.777680399127071  0.025375596535165    2.23305
 -0.074029992531257  1.884165165100484 -0.712605605813120 -0.814741576859172  0.029057672574730    2.17421
  0.074029992531257 -1.884165165100484  0.712605605813120  0.814741576859172  0.029057672574730    2.17421
 -1.581316138589670 -1.481326304824517  0.317591062927525  0.179274001658312  0.029625520746039    2.19725
  1.581316138589670  1.481326304824517 -0.317591062927525 -0.179274001658312  0.029625520746039    2.19725
 -0.136967785966032  1.572308555685833  1.352964276238288 -0.530340021278051  0.031255765644761    2.14539
  0.136967785966032 -1.572308555685833 -1.352964276238288  0.530340021278051  0.031255765644761    2.14539
 -1.287086658368602  0.086572644689282 -1.149190710581529 -0.832623723962103  0.033146619254200    1.91781
  1.287086658368602 -0.086572644689282  1.149190710581529  0.832623723962103  0.033146619254200    1.91781
 -0.117573766654550  0.705191528527796 -1.877661289784179  0.668073913655840  0.033852269882466    2.11732
  0.117573766654550 -0.705191528527796  1.877661289784179 -0.668073913655840  0.033852269882466    2.11732
  0.012336587875073  0.448809261190211  0.692993648473759 -1.896322188172926  0.039812147947755    2.06830
 -0.012336587875073 -0.448809261190211 -0.692993648473759  1.896322188172926  0.039812147947755    2.06830
  0.546707911475266  0.976247992843080 -0.093850320775811 -1.324342350245621  0.058767067675444    1.73627
 -0.546707911475266 -0.976247992843080  0.093850320775811  1.324342350245621  0.058767067675444    1.73627
 -0.936230289829649  0.313828172257344  1.195570204116803  0.252970284312096  0.105367367771502    1.57111
  0.936230289829649 -0.313828172257344 -1.195570204116803 -0.252970284312096  0.105367367771502    1.57111
 -0.948455376220988 -0.224408798105279  0.398300293964859  1.282970102163299  0.106514754599562    1.65969
  0.948455376220988  0.224408798105279 -0.398300293964859 -1.282970102163299  0.106514754599562    1.65969
 -0.260056764743923  0.495876614332423 -0.824160909064189 -1.328490050363723  0.107071300770415    1.66062
  0.260056764743923 -0.495876614332423  0.824160909064189  1.328490050363723  0.107071300770415    1.66062
 -0.640837684192523  0.408820631080271  1.054443514481978 -0.765979676791128  0.108278002746219    1.50877
  0.640837684192523 -0.408820631080271 -1.054443514481978  0.765979676791128  0.108278002746219    1.50877
 -0.023621327480604 -0.456098065196992 -0.348977776783511 -1.372027301015116  0.115602939252963    1.48756
  0.023621327480604  0.456098065196992  0.348977776783511  1.372027301015116  0.115602939252963    1.48756
  0.298950141809870  1.317751335782583 -0.582312881937610  0.586430052722120  0.115605844478684    1.58393
 -0.298950141809870 -1.317751335782583  0.582312881937610 -0.586430052722120  0.115605844478684    1.58393
 -0.745662699762439  0.472041705629846 -0.614894855927771  1.240673294101190  0.122204088425817    1.64201
  0.745662699762439 -0.472041705629846  0.614894855927771 -1.240673294101190  0.122204088425817    1.64201
 -0.143765605284663 -0.308906406193650 -1.464997415051848 -0.390639381834991  0.156495175738364    1.55400
  0.143765605284663  0.308906406193650  1.464997415051848  0.390639381834991  0.156495175738364    1.55400
  0.643792673076343  0.802712606156421 -1.138445010037207 -0.326777014760053  0.164180125636959    1.56897
 -0.643792673076343 -0.802712606156421  1.138445010037207  0.326777014760053  0.164180125636959    1.56897
 -0.573211369561383 -0.402430410236920 -1.039033533138352  0.610850811035323  0.212237794467760    1.39401
  0.573211369561383  0.402430410236920  1.039033533138352 -0.610850811035323  0.212237794467760    1.39401
 -0.473259221318306 -0.439844292553778  0.557688265651918 -0.837556168654936  0.279228860809403    1.19581
  0.473259221318306  0.439844292553778 -0.557688265651918  0.837556168654936  0.279228860809403    1.19581
 -0.680736339525071 -0.609638375825444 -0.480670249210291 -0.663386462114603  0.308238816119162    1.22727
  0.680736339525071  0.609638375825444  0.480670249210291  0.663386462114603  0.308238816119162    1.22727
 -0.583432304011589  0.635934319512772  0.101015623873253 -0.674461973299087  0.451861447940833    1.09996
  0.583432304011589 -0.635934319512772 -0.101015623873253  0.674461973299087  0.451861447940833    1.09996
 -0.540973637705500  0.577319555176070 -0.584304395488162 -0.029706575183635  0.739629111732884    0.98399
  0.540973637705500 -0.577319555176070  0.584304395488162  0.029706575183635  0.739629111732884    0.98399
 -0.422684897769933  0.636685237987604  0.243642556034594  0.265971398337593  1.298835940037285    0.84506
  0.422684897769933 -0.636685237987604 -0.243642556034594 -0.265971398337593  1.298835940037285    0.84506
  0.272880681461127  0.681275646275136  0.135762934491312 -0.124119140425542  2.191090949721370    0.75660
 -0.272880681461127 -0.681275646275136 -0.135762934491312  0.124119140425542  2.191090949721370    0.75660

>> # evaluating formula 1 with 147 points
# r4_147_9Sd.txt:3 formula 1   : problem  S, 4_147_9  (d=4 n=147 o=9 plus 1/286 of order 10) quality NO (12 negative weights, stability factor 2.362126)
S 4 dimensions, degree 9, asymmetric 147 point rule with points at 147 distinct radii (12 negative weights, stability factor 2.362126)
#                x1                 x2                 x3                 x4             Weight     Radius
  0.153844964266078  0.000000000000000  0.000000000000000  0.000000000000000 -0.239877110129594    0.15384
  0.036321024520412  0.382130253793144  0.000000000000000  0.000000000000000  0.159825953515276    0.38385
  0.083331463586263 -0.396280817046666 -0.028525350965991  0.000000000000000  0.162423794501907    0.40595
  0.229077515200429  0.052640988423616  0.321069675063800 -0.111173718354354  0.133473743201898    0.41315
 -0.383653668128355 -0.116277913929351 -0.151602541768765  0.031307091671295  0.134502965787791    0.42974
  0.120780813094342  0.087238936695054  0.032159886958892  0.409401138264866  0.128108195230993    0.43685
  0.252507743506869  0.055318558898154 -0.325235025528618 -0.225806437761101  0.213138603254729    0.47285
  0.473912541592585 -0.029130795365131 -0.042106821995529 -0.009878714716112  0.152670579369081    0.47677
 -0.115360998982217 -0.184996706777667  0.422672256024764  0.190372621286744  0.101953057196442    0.51227
  0.366600979122015 -0.027354834078239 -0.372077848882599 -0.004325573054750 -0.756975499705463    0.52307
  0.359527103370915 -0.034217155609702 -0.381540504304845  0.035211029900619  0.703454694481608    0.52654
 -0.177922136666925  0.008343233858636  0.092578032459224 -0.527469504080476  0.112778592495622    0.56438
 -0.126992206317808 -0.012631975356912 -0.572143091554090  0.329158785870001  0.073847748419817    0.67229
 -0.361540685716754 -0.011672602599950  0.204617920352720  0.588400251115997  0.036716092133621    0.72037
 -0.420960522583029  0.408438916512742  0.361969795445120 -0.277692372840499  0.082094521965359    0.74308
 -0.261419816441013  0.384324215608789 -0.594423628222877 -0.036549993821796  0.065487986034711    0.75546
 -0.662076363723336  0.238287723399319  0.096377724474775  0.288978799017410  0.068495458600666    0.76676
 -0.085497465704751 -0.364049060001412 -0.665896909406507 -0.135437501111885  0.037857220476123    0.77563
  0.137294200144398 -0.153677802089138  0.675290933260510 -0.325401873450501  0.059606446522032    0.77741
  0.421436678933710 -0.470053950617177 -0.257105137321182  0.409028410706051  0.047399957727478    0.79496
  0.222140661542441 -0.313957269656642  0.273259107150570  0.648444689598234  0.045023733404948    0.80191
  0.413720750085465 -0.329659721477844  0.133900002099293 -0.593068724661146  0.058813391643215    0.80592
 -0.221507899492924  0.204210537755435 -0.282375502692852  0.698673227782634  0.053832269512673    0.81157
 -0.364481693879280  0.346311408479417 -0.351883633514495 -0.537792958730760  0.064866701538323    0.81598
 -0.328737685518181 -0.630288541758401  0.407167745074499 -0.058058353403051  0.061119869423719    0.82127
 -0.703167479858058 -0.044950009371277  0.434771169242825 -0.073711112854915  0.059748041763075    0.83122
 -0.120049650599240 -0.602317037572155 -0.119477970025542  0.559694444036702  0.062214903851190    0.83948
 -0.151368390897895  0.295964874558654  0.769171283899828  0.080340701273043  0.059955746142201    0.84178
 -0.187337548564995 -0.370440625610518 -0.254947349500720 -0.689170047930528  0.732399542419744    0.84396
  0.175754515735958  0.590755007297718  0.106355167077304 -0.567357870529701  0.059511696892049    0.84445
  0.159726448991220 -0.694439260896174  0.298685068703926 -0.344476332319101  0.058313765397183    0.84595
  0.414161554159528  0.614777863878303 -0.409579592669323 -0.006643221837572  0.041636897424365    0.84692
  0.306849207027577  0.366990871994144  0.569740915794876  0.409918045589045  0.054276999534487    0.84940
  0.431473221813857 -0.448119266493892  0.494885857308058  0.309364383446291  0.049072730377759    0.85299
 -0.353293643240356  0.582769834023706  0.385869295973993  0.338710350507975  0.058548901821811    0.85326
 -0.269860752768957  0.663038061679999 -0.236714553386967  0.403626192015690  0.055784841266623    0.85521
 -0.180160524895460  0.756864461324878 -0.197472139486475 -0.297260025892649  0.031489197909241    0.85596
  0.320240809328700 -0.600195886485782 -0.387351366545467 -0.349786350917031  0.053598992781492    0.85743
  0.703855755053877 -0.211479852400744 -0.205977840152099 -0.396275161560363  0.041082116130305    0.86000
 -0.140499138299264 -0.389444118214958 -0.261873805598771 -0.707789305500578 -1.365047290053310    0.86078
  0.596700865524048  0.531180157292110  0.325622369946942 -0.065266350400071  0.053629226987953    0.86516
  0.577445027557173  0.348318531629260  0.058693458762508  0.539205483148773  0.046374267572450    0.86542
  0.251497266079193 -0.276624864419771 -0.785958219721107 -0.063192569420056  0.044980396947597    0.87264
 -0.526636413490912 -0.409474030621172  0.263339869642405  0.497428691321737  0.048704680208479    0.87281
 -0.090358848765414 -0.398096692228643 -0.275011951602239 -0.720901623805923  0.683104069063866    0.87291
 -0.640088778725950  0.580886060561844 -0.110389121831512 -0.070749713507091  0.050211222045631    0.87426
 -0.428544672856285 -0.120539322848405  0.663960975118190 -0.357596925229453  0.030766210667181    0.87573
  0.688964237970794  0.060163883495886 -0.541172338019561  0.024901215941656  0.051632431978877    0.87851
 -0.690015129446370 -0.055236596890307 -0.495548983869093 -0.226066869658713  0.051629779077763    0.88082
  0.357541832950115  0.199396053938824 -0.581291835188649  0.520854128280943  0.035302379776109    0.88135
  0.219745827710238  0.575694919267402 -0.471080237584935  0.420678968150292  0.039821011131695    0.88238
 -0.691829947863932 -0.418207855048176  0.063200247712341 -0.352024208776456  0.054869062049651    0.88399
  0.768679541380247 -0.180527141281809  0.384140818387048 -0.129574858414112 -0.485734528810640    0.88759
  0.731367077367093  0.001759997978094  0.468382218161634  0.184054412089817  0.057292864967164    0.88778
  0.760133615245140 -0.194270176802131  0.394337273559259 -0.145582293702798  0.494403947404150    0.89008
  0.309832001493251  0.133226713271940 -0.136119227690847 -0.813159903029335  0.040266856716193    0.89079
 -0.612575221162183 -0.537050911134730 -0.357652720084263  0.088551728637425  0.042717527476977    0.89411
  0.646073135676969 -0.607185894631578  0.117481637177651  0.014509488022957  0.043174993564991    0.89448
  0.742213709581986 -0.215528254123299  0.048423119910496  0.454458485001711  0.035480356240525    0.89789
  0.544228561703977  0.228690904710960  0.353446840147513 -0.579029895662916  0.045797379925993    0.89927
 -0.580926477134665 -0.246700602778506 -0.315593831857165  0.559369283716330  0.046912358650978    0.90046
  0.221285883996462  0.795707344997892  0.084006793913505  0.350023676650712  0.043933451859895    0.90094
  0.303632041780669 -0.139862455961749 -0.225025353580079  0.806646052758656  0.038930139328331    0.90170
 -0.265525707644361 -0.450244990826806  0.499807167494561 -0.541204915809546  0.035295057174882    0.90329
 -0.319317167254929 -0.490127341428033 -0.537503587907321 -0.430857826799092  0.039384210065006    0.90373
 -0.159866663606231  0.027803064634256  0.590555694257387  0.668387222402227  0.035922029905736    0.90655
 -0.201904952798696 -0.811979100431508 -0.124185617145312 -0.327288101229934  0.041700499536078    0.90698
 -0.029559087300459  0.000119292068366 -0.555602856286255 -0.716863724901680  0.028154071051480    0.90745
 -0.781796200638559  0.198627398296536 -0.017977872525737 -0.415515910945658  0.039260843318131    0.90754
  0.103322733951879  0.670786126515800  0.563476744601992 -0.215025969771786  0.039257508645976    0.90795
  0.740327861742123  0.460502589345022 -0.157894863545314  0.198377620054204  0.034512694070292    0.90798
 -0.080100441700173  0.430387171691339  0.281952998272781  0.744243329262710  0.034933054482289    0.90832
  0.655816369282530  0.392140004506429 -0.242381898986714 -0.427889506847719  0.042350308421180    0.90868
 -0.118117592148333 -0.674740590885595 -0.572420247827579  0.174055249055560  0.038437873232656    0.90950
  0.257745798785498  0.374462028575198 -0.779042450709705 -0.117837515413214  0.038533052882952    0.90964
 -0.022351483171994  0.297916496726919  0.586672712522344 -0.628458247740600  0.040897609612447    0.91016
 -0.395420239886523 -0.800334854318814  0.025267506277504  0.179491923835286  0.034303051503648    0.91091
  0.187912176936565  0.669872025003291  0.530449920358935  0.263927637038073  0.016702463588006    0.91382
  0.079943535937712 -0.137661424605676  0.324884529140894 -0.841849111799652  0.027798039861561    0.91630
  0.892613176762831  0.073724965773649  0.143185764905703 -0.150595094218342  0.038977197197250    0.91944
 -0.184192118108795 -0.476753742090955 -0.052726441313531 -0.765002154016176  0.052779902489222    0.92154
 -0.189349763387359  0.050431589575629 -0.839116205258104 -0.330722461134025  0.034638253744785    0.92298
 -0.692295187179927  0.259754102073668 -0.483289473654475  0.267941219454306  0.042452453569744    0.92310
 -0.032717124919591 -0.341128239497490 -0.578384685739219  0.632709390429090  0.032103652433734    0.92319
 -0.215241812997649  0.877331162856496  0.205248146985056 -0.048926882825311  0.031636928299403    0.92766
  0.213754092255670 -0.872968498701683 -0.220865794940567  0.072053237824706  0.030517124143600    0.92830
 -0.546645461211885  0.075956745545449  0.666239371313300  0.336907670482084  0.028451025835414    0.92842
  0.449828047415116 -0.051252076004431 -0.646038637499107 -0.500771890026502  0.031321883940988    0.93440
 -0.306601139866859 -0.393525458654236  0.776813665783982  0.150862084832423  0.029852165178909    0.93545
  0.356648896339885  0.844267747123787 -0.037986043879658 -0.185752189310782  0.026450206243581    0.93591
  0.703077127062727 -0.472009398528139 -0.398871857280535 -0.057736467899146  0.021496411017918    0.93784
  0.203953840623383 -0.111317247402537  0.849286431333789  0.331624811935007  0.031467110289461    0.94088
  0.121635616435552  0.542427272621217 -0.494067242386625 -0.577990743937599  0.031228993041143    0.94191
 -0.170965553807148 -0.167753117905211  0.050979878374746  0.915885476100539  0.028377282576864    0.94806
  0.419440151142889  0.206458772812181  0.807805072648094 -0.167005857424289  0.029838932197311    0.94815
  0.192639889067188  0.420007786257930 -0.114750136804686  0.820023201679667  0.023521569166983    0.94822
 -0.076941449165227  0.840817433376443 -0.434742939913475 -0.038726430534547  0.022280789307899    0.95047
 -0.534323327635779  0.028776953945985  0.341583354366463 -0.709869184340403  0.025259897899119    0.95233
  0.934522229566612 -0.176628197673389 -0.040552078639516  0.095844598084282  0.015280288427571    0.95674
  0.226787091311779 -0.529915783997572  0.760317583017580 -0.079876327663725  0.025435851408050    0.95745
  0.407635956328736  0.011457137510673  0.375934607868373  0.781358732289730  0.023834414343475    0.95820
  0.463878300542480 -0.481314769171600 -0.591840934999973  0.351797641173048  0.020964958710398    0.95963
 -0.420476770412445 -0.178428464775428 -0.830852004130524  0.186463872763713  0.024893090138743    0.96629
 -0.590026994046205  0.316638948452786 -0.016937803198153  0.703372855514454  0.017053762583334    0.97129
 -0.143582379547361  0.246690481941770  0.005261087734646 -0.934903688945766  0.018593173856775    0.97752
  0.722766582166785  0.017341151012654 -0.384495833830692  0.548942289735520  0.013466482400947    0.98583
  0.174127544535972 -0.875848524265663  0.322107281669156  0.279859506415856  0.030987147767860    0.98970
 -0.057462719849783 -0.585829125350478  0.530443769650702  0.593052323176162  0.020451505615706    0.98974
 -0.195192672170651 -0.001362642693722  0.936862004029372 -0.256196112947348  0.013550753460770    0.99068
 -0.312450588954822  0.419198854286714 -0.809203840706856  0.278739822226268  0.026949685989046    1.00293
 -0.987080644197703 -0.152928636842173  0.072533264377697  0.075416117913466  0.046213546061978    1.00432
 -0.365082851715092  0.674277163175611  0.115566789935262 -0.663958395194364  0.015535480627204    1.02085
 -0.477067809873436  0.404910107177140 -0.781737171573158  0.211761976115816 -0.014562408050166    1.02348
  0.320545245795946 -0.310614587652286  0.656484760022955 -0.661533827904769  0.009345160927233    1.03336
 -0.737943519871080  0.035321800431977  0.295187015482506  0.669206353631273  0.006613109825883    1.03961
 -0.560187675727569  0.516537304472041  0.671117691166137 -0.276531258020144  0.008517873556077    1.05237
 -0.970639736305680 -0.312120504722256  0.268465600861822  0.049921633711038  0.181721145188608    1.05552
 -0.989743718510422 -0.287511238171548  0.260971083794856  0.037233133931632 -0.202176588075836    1.06384
 -0.193819107334271  0.199723858247307 -0.664400643887747  0.783510702433836  0.007711487246484    1.06432
 -0.577189556485188  0.546765295426162 -0.698360164915953 -0.220461809758755  0.007288520515917    1.08093
  0.106163804923641  0.082728564175773 -0.989867648664051  0.419814461068829  0.065268943578379    1.08360
  0.489070215200760 -0.816684382579742  0.087991315638847 -0.521790202940862  0.005098281314795    1.08911
  0.361064383732395 -0.836649897459756  0.204097798055293  0.577870142119021  0.164578334934221    1.09815
  0.090140181162961  0.095922049498735 -1.001173311821671  0.438641358449426 -0.052391843445534    1.10095
  0.356332076027230 -0.845994836578983  0.217953463176642  0.571315409841853 -0.159548634700770    1.10299
  0.722631152285562 -0.234895947672113 -0.094986753297294 -0.805440600758572  0.003737234354483    1.11136
 -0.669780080598068  0.841747708234200 -0.149052758518470  0.372301392704204  0.001491294597572    1.14803
 -1.079753585770908 -0.217139215322783  0.363148942023821 -0.074506967147588  0.010783036784739    1.16209
 -0.314725027115518  0.940239541236379 -0.008268305014548  0.664839341031826  0.000857008709587    1.19381
 -0.980494896141261  0.556200913914822  0.469734639660517  0.094996795836978  0.003816512171468    1.22491
  0.114613406830672 -0.758495507027840 -1.010341558884515 -0.450226515719393  0.000524231375695    1.34609
  0.323988721075215 -0.728784207380794  0.984397429185579  0.486379824400194 -0.000505668570129    1.35709
 -0.458512615168909 -1.053107539672618  0.605965748111530 -0.395146905287314  0.000463527877405    1.35743
  0.913297839123925  0.689667120510935  0.545451754934424  0.506768017195007  0.000419973218693    1.36532
 -0.136682821623910  0.755049305355786  1.052195877498698  0.509466479070336  0.000356494947629    1.39838
  0.844142927362233  0.906362219387239  0.380602086604703 -0.541788670264192  0.000170512280522    1.40444
 -0.785234702767017  0.183408228883085 -0.428846594829682 -1.106923895735315  0.061466057109224    1.43507
 -0.796008736062968  0.194837824537326 -0.434888985361613 -1.119385443280130 -0.057459966131324    1.45387
  1.161711894916136  0.597817947720126 -0.843651842316691 -0.073829360636275  0.000062089523761    1.55697
 -1.127446132963190 -0.829400448814748 -0.559331147353362 -0.515124472766213  0.000070344410378    1.59287
 -1.265833141042572  0.703057806629526  0.678444176517087  0.084564065825314 -0.000201344890983    1.60127
  0.695044047319852  1.287668583939732 -0.801607359633952  0.587130126706084  0.000025123853888    1.76875
 -0.978592692694631  0.403393652674694 -0.559233125308159 -1.329861440613157  0.000516137111737    1.78931
  0.915317958912021 -1.105318027336959  1.087568883341463  0.898083479938925  0.000022002200267    2.01219
  0.044450727668988  1.714336404005738  0.352290328953731 -2.014154495097745 -0.026430205808653    2.66868
  0.044487802344899  1.714397184450941  0.352307481184015 -2.014212470568947  0.026422938119151    2.66877
 -0.725805757657070 -1.884728955879559 -0.451508920756711  1.775088252672390  0.000001062073775    2.72650
>> # evaluating formula 1 with 154 points
# r4_154_9E1a.txt:3 formula 1   : problem E1, 4_154_9  (d=4 n=154 o=9 plus 0/286 of order 10) quality N (24 negative weights, stability factor 2.629341)
E1 4 dimensions, degree 7, asymmetric 154 point rule with points at 154 distinct radii (24 negative weights, stability factor 2.629341)
#                x1                 x2                 x3                 x4             Weight     Radius
 -0.173151900509060  0.000000000000000  0.000000000000000  0.000000000000000 17.111103492542835    0.17315
 -0.105166972058350 -0.862897418097841 -0.000000000000000  0.000000000000000 11.286561754241632    0.86928
 -1.610783220214646 -0.985990472764453 -1.348473049451019  0.000000000000000 13.725376084941271    2.32060
  1.002385938028301  1.930814785092456  1.223314508113800 -0.072704119265955  9.019536246134281    2.49692
 -2.374746476787996 -1.109144877439739 -0.864937295947308 -0.938634923948853 -11.300568938265359    2.91527
 -1.075948435282678 -1.350072210054480  0.087272679097386 -3.338952663462888  6.230560343047743    3.75986
 -0.063105498767526  1.291015591793257  0.019098479950729  3.575478891877344  5.253806379924774    3.80199
  2.834377451515453 -2.556288802419045 -0.218030671131888  1.604632541191306  5.359307259263939    4.14617
  2.304981400804501  1.196581459872274  0.057052078519202 -3.389148890687467  3.625581673629061    4.27017
  0.778846812834911 -0.819586200510621 -4.237792864234789  0.190960073156134  3.756997985118824    4.39018
 -3.034891313902794  2.583181290283043  1.406257153108863 -1.726295646377128  3.601827082823136    4.56520
 -0.643045876203530  1.431867838638458  4.293500528349360 -0.234794936137805  3.125812497387752    4.57745
 -4.544944204185032 -0.935513091330516 -0.565321327998898 -1.377373880909448  4.308347181402365    4.87324
 -2.310951641530878 -3.145289237226315  2.574679552017455 -1.508795572072984  2.777011712011226    4.91312
 -2.950326828775596  3.334145438654782 -2.154592780113489  0.725807154084419  3.423943839377946    4.99900
 -0.209783888221394  3.671926512602028 -3.108659704722750  1.951049771230860  6.468217822392187    5.19590
  2.635523274105718  2.159286795224022 -3.362760567027000 -2.138911098814892  2.035771883550491    5.24324
 -0.738395884124310  3.674374953026679 -1.594620966425152 -3.364064098105990  2.297114848203160    5.28261
  0.203868508172191 -1.644488835097379  4.997697992009642  0.589876463024116  1.883278650448386    5.29819
 -2.786960542791685 -4.017042509132883  0.260626549507466  2.165777553042285  1.098989778406907    5.35372
 -1.101389747984295  3.408467129900544 -3.677751045051828  1.789791403597171 -6.090127860547368    5.43690
  4.190262148652036 -0.108028347021658  3.284323210763890 -1.146094787293840  2.531187311459997    5.44704
  3.032656109330776 -2.792494128719805 -1.504304269379044 -3.516273654421533  1.761928707241740    5.62336
 -3.933329869829688 -0.876282268445122 -3.583746163366261  1.598080408863563  1.312497190030182    5.62459
  1.892714403816548 -4.050192750256154  2.653307550051660 -2.455687955621349  1.648799161092593    5.74951
 -4.666172886051767 -0.318685882123621  3.208005116938298  1.074811291628080  1.317097155894251    5.77246
  4.209048906384231 -2.075287098957957 -3.532270637765208 -0.142523050961769  0.952648490426907    5.87539
 -1.273423226263734  2.673115621983746 -5.141216226231659  0.755421750449937  1.892083664200812    5.98080
  1.524607011147825 -4.635749744917621  2.279725161599095  2.770613836133268  1.167332740806085    6.05707
 -2.427486213490742 -1.585421566577237  2.441315310438934  4.967738537363427  4.239679035189608    6.24858
 -2.216480020190535 -0.839220659286396 -4.033106542379546 -4.260306344451974  1.745111601883757    6.32718
 -4.897179450939724  0.063326263241283 -0.016786461661379  4.205249051381623  0.979352900577393    6.45529
  5.417973154526161  2.630720948421111 -1.457055159132587  2.374429329738010  5.168857683741429    6.63597
  3.306160052460313  0.844074424154514  3.561776754737833  4.933928969492992  2.019260831818777    6.97661
 -2.870884893310413  2.945779082852139 -4.539606045865363  4.402425195421722  0.461304336525688    7.54380
 -3.450909548320375 -1.476851975455080  2.827181353367397  6.271013109805539 -3.480525691793738    7.83635
 -3.271460034455065  5.004013270751774  3.357139931550054  4.006761073743236  1.064554493425383    7.94148
 -2.129287323477863 -7.308641271829090 -2.674898203380506 -0.004133989457777  3.410695101227506    8.06878
  6.531884490991430  3.622246778858382 -1.585162818992084  2.758474143851990 -6.292981984982318    8.11838
  3.212826073068523  1.148809409676198  4.289942701525587  6.113509572878904 -1.096570401514215    8.21101
  7.697711852795637  2.127575082825258  0.126426966277887 -2.507501072589285  1.177143526534019    8.37167
  1.558084334655345  2.385427883410183  5.432913306264780  5.946182985907960  0.415304881938052    8.54351
  6.902506366329396  4.063292149704342 -1.601587736805926  2.803923667299777  3.512214250019298    8.63609
 -6.575632547584886  0.060760228732043 -3.007436855479300 -5.020460255551487 -1.518998802540848    8.80297
 -3.999102561849332 -1.453067773486500  3.251306543634918  7.020803409569551  1.350163393888734    8.82989
 -0.772820299937012  7.672742597826295  3.564051805784327  2.651112724681181  0.239498406838922    8.89939
 -5.817212334547078  0.037522252825759 -3.365610166406449 -5.972604715170303  4.541618750866101    8.99115
  0.884600016541023 -2.285283877929225 -4.789596090566842  7.241063126130998  3.541245952555967    9.02099
 -2.842511022116272 -3.875350870959993 -1.116733509592829  7.633367099513942  0.127066010488573    9.08920
  3.075812870774322  8.130368097811097  2.612572250704177 -0.506124605927452  3.978584865155038    9.09094
 -5.069147029412514  0.006565588297822 -3.526819473286950 -6.831985993352783 -5.043335898267276    9.20928
 -2.190051274485194  2.312252041070167  6.053290212535925 -6.184040361048725  2.018353356176203    9.22104
  8.074861470480023  3.327948287399598  0.412405397701308 -3.219556109692411 -2.084563598771962    9.31742
 -4.479648627615975  0.175958460386879 -3.436623406794172 -7.579851196882627  1.975228405141562    9.45319
  5.189840346491916  7.109008839578877  1.557513633384256  3.345895245490318  2.201485806017790    9.54428
 -3.291167967238559 -4.821372751233636 -2.032742812949290 -7.284657826867188  0.086783345011149    9.55383
  7.319799713034972 -0.777000060895825  5.958851312201781  1.345837673380978  3.048746352020765    9.56569
  4.982212341025272  7.547177033216567  1.831377527720452  2.589262466013692 -5.643245759174260    9.58335
 -6.227795642051955  1.994490441389856  5.867853204137349 -3.858957155374528  0.125010947992520    9.59618
  3.508151047921165  8.357726190426018  3.205578185888095 -0.236644176996685 -9.455089712136346    9.61720
  4.645866063604847  7.932564617175290  2.222150088514206  1.789547288605723  4.909944730846294    9.62549
 -2.564949916722069 -8.675744443670418 -3.359993242246059  0.073830978525354 -9.861884791090985    9.65104
  8.096914078611027  3.855334031283081  0.510713368454412 -3.554714952352263  1.322230877735527    9.66025
  3.526998548667908  8.218165679659720  3.650786997243893 -0.396951834935682  4.819436971285787    9.66767
  2.176057948472485 -7.948515223285301 -4.349763147954468 -2.576014112014377  0.437624416024699    9.66801
  7.450477831754638 -0.722187270375263  6.075182675285939  0.922803838609648 -4.485801580181497    9.68455
 -2.184566826267912 -8.467302135697956 -4.089768369157995  1.076190014774363  1.129461313410310    9.71349
 -3.077412685334405  3.026891984367059  6.779020196346468 -5.542190642470974 -2.710650650097277    9.76235
 -2.955694569024395 -8.579655424135064 -3.700156983995425 -0.264837049934081  3.279218366456109    9.80346
  4.116006622008221  1.088458961440498 -5.428339696184191  7.047264695987979  0.078271112286004    9.86190
 -2.496351259885920 -9.145597489821247 -3.043452769928907  0.155632947624142  3.515689756458881    9.95794
  7.597743311978155 -0.545623982728119  6.431506899420049  0.283080469620928  1.446705345459757    9.97336
  1.008980197817275 -2.569128964963643 -5.318103329503648  8.095998237939551 -4.799270130707648   10.07203
 -3.331674029714748  3.410284619006529  7.241441697900314 -5.167245929691543  1.350915290705675   10.09302
  2.554678983177933 -0.624864035103220  3.218295635167185  9.340417015811207  0.113092568154564   10.22339
  4.638478621471595 -8.344217871051979 -3.149955745289795  1.902580415619360 -1.324920779166767   10.23149
  0.761403317190051  2.044191265825176  4.736325016204939 -8.853408156973888  0.961295996914728   10.27492
  4.704497707717800 -8.343981686217731 -3.092918135073581  2.068022945443547  1.315335154804154   10.27605
  2.974477282913956 -5.010495239648832 -6.787436058850425 -5.229658627185106  0.133406470061369   10.36201
  7.469604715747558 -6.105022156644956  3.082280242413437  2.232132688390191  1.720772279828904   10.37059
  2.455708661696136  4.969154068101036  0.345024404211812  8.762237012493120  0.048893970694477   10.37395
  7.215113429754965 -6.278014131545508  2.996149131392860  3.001694715793089 -2.949699170687920   10.46224
 -3.438614928744760  6.614904513915970  5.124085189472643  5.558365994302328 -2.504454373162657   10.61757
  7.064211217773638 -6.346514253647172  2.881742477845845  3.786733490229898  1.290555272508822   10.62192
  1.146515038965410 -2.818270885138888 -5.494131691518030  8.596475564646985  2.086545695143187   10.64622
  0.192845966025996 -1.065266209467899  4.867921421606715 -9.447883647265318  0.152522732915958   10.68322
 -4.653201311923771  7.372163647623406  3.382030932243424 -5.206849284311636  0.058660122155013   10.70283
 -3.506618795160922  6.475468795704218  5.441953896247732  5.545632253593881  1.747617737668500   10.70500
  0.048581575928969 -1.989738103991651 -7.626325159755862  7.251677077823648  0.133804581360899   10.71023
 -5.656908191034079 -6.190497256955826  5.896083560921283  3.554939778432384  0.037195309558050   10.85008
  7.911114497939229  0.548480511269046 -0.958486775642665  7.382077918865518  0.045105778011717   10.87660
  6.657955972848531  3.171677904820731 -7.555457157730787  2.675410598794229  0.051444242589194   10.89177
 -3.273398542716651  1.445039722811678 -1.539870477095704 10.311723796736896  0.038118150975113   11.02298
 -3.373447760720685  7.117178157978101  4.280245852166728  6.432088963316856  0.387960991530513   11.03298
 -6.447198373366961 -4.336198668277548  0.641508498104200 -7.835265980664488  0.033917912551126   11.05314
  4.883462514028851  1.490892070496327 -4.291493094450463 -8.821765075623979  0.045427501526652   11.05945
 -0.876542156163806  9.326017442470038 -5.719393288571049 -1.533466533579753  0.037608610755225   11.08178
  4.001221443462735  1.074385438099909  6.575955035929929 -7.953805441302057  3.681103112436003   11.12071
 -5.648270390736390 -3.272709878620527  8.055667005741125 -4.315605503786386  0.032978130223707   11.23084
  0.209244545961497  1.888497037501256  5.901188476399875 -9.371670851569821 -3.122484768885606   11.23666
 10.571505817273325  1.657633439140152  3.378006300768038  0.710949373504912  0.051000795951494   11.24370
 -10.416542926667871  3.900782133454972 -1.546678396400292 -0.641063285290482  0.054368974867143   11.24827
  4.294130139132995  1.153778908292075  6.620640885804129 -7.957638128648894 -4.377077757515630   11.26622
 -6.394269510831553  4.859395524819085 -7.560911360084728 -2.293971641768637  0.029536428213338   11.26633
  2.936261433107541 -7.353863791022706 -2.153955996910382 -7.879971208306312  0.046822384735740   11.37692
 -8.235079356987459 -1.660099078189027 -7.632506576124463  0.892015961266045  0.030905408905640   11.38522
 -4.916393362478307 10.303607662462017 -1.145193415862262 -0.310842113391741  0.027531047711471   11.47795
 -1.892613113047436 -9.212232587324868  6.515796916026797  1.056316009624613  0.027796690903344   11.48994
  9.995101683166677 -2.351994006030627 -3.759658307761373  3.563165893913490  0.028439864308978   11.50066
  0.043253717102558  2.002678748634922  6.142581372778722 -9.646487649902550  1.891640653413702   11.61028
 -2.854269236617278  8.526054678607913  5.988325258350978  4.298228676650329  0.061369730324276   11.62649
 -2.007819068113701 -2.456141247616457 -11.168102237350306 -0.621163157183852  0.032565894691922   11.62654
  6.705962323354849 -7.659805510356229  5.577594169369362 -0.675209425359584  1.561989053907661   11.62790
  6.454852919545793 -8.388087189128660  4.782934932140003 -0.599728438184391  0.739321691149006   11.63019
  4.871883710849262  1.404908648964148  6.765091852287150 -7.995532180937508  0.933405827900606   11.63632
 -0.914943689933201  3.462979643390150 -9.100991370109504 -6.348723864520444  0.029317964117563   11.66035
  4.748773164058935 -4.924716985550290 -9.044903788567039  2.723586155092980  0.028251005116165   11.66327
  6.878505430696361 -7.283575997554949 -4.673366229548723 -3.757343302314307  0.055057970350073   11.67571
  5.759818776352733  6.972757280221917 -7.120740484657811 -2.258835336972422  0.039460746637653   11.73039
 -8.930649894582613 -6.297923631828159 -0.548487497278869  4.285366711941512  0.030946880783908   11.75098
  3.551708381586914 -8.235782568806604 -5.800941308240283 -4.905056982770942 -2.372230214346643   11.75386
  6.717045311259156 -7.913814279557970  5.395963148143191 -1.148778820707498 -4.968213131163292   11.75514
  8.853204326549678 -1.781785819752429  2.259530481004027 -7.192533155196698  0.031698829454864   11.76401
  5.807808685070754  3.231355633313389 -9.549652607763935 -1.821282485139859  0.855288511900214   11.77647
  5.829233117332318  3.337587805562376 -9.512047274141901 -1.778779506096616 -0.851982548946999   11.77975
 -5.317567974511555 -0.607705484795665 10.166266246568940  2.610122149257444  0.025647394887391   11.78183
 -9.085490529868817  1.669890219723789  2.861485246836798 -6.759245318816459  0.022421240368999   11.79874
  6.751205737582366 -7.936563113385164  5.447862162086415 -1.487513275823715  2.743456514982344   11.85157
  3.558816461571825 -8.307374279993718 -5.865630648247163 -4.956409958231722  2.109911954412576   11.85956
  0.359805441457014 -4.369245929053168 10.782812252174338 -2.464846541840391  0.023014821223370   11.89808
  1.173516461014603 -3.587897415129913  9.343089870424730  6.351293356724276  0.025750676951816   11.91144
  2.024959265274798  2.886210443505011 11.412951030400745  0.548411979089462  0.024495840533057   11.95771
  3.737097083818098 10.796705922981085  3.461483180934237 -0.704347719895559  0.136794029723423   11.95879
 -2.087515391173546 -9.196737375293377  4.294864570046037 -6.228860148352885  0.022152566767812   12.09059
 -4.849890204509425  8.482616833698602 -4.428305457173398  5.664096113469776  0.016553238693785   12.13129
  0.968478583661774  5.065968158129145 -10.908724072759693  2.406175152458738  0.016997131281438   12.30414
  2.630202789656755  9.721636692457203 -4.261220811740726  5.804388282279026  0.017232828539664   12.38051
  0.500935408390429  2.224922246836061 -6.076082143919403 10.549084196599873  0.015528575467375   12.38560
 -10.291131588986021 -6.462277510257234  2.794606284781406 -1.457871882115724  0.025857817221287   12.55403
 -11.953489875745872 -3.549800634216380 -1.647032804729339 -1.444419122215880  0.021866540096119   12.66041
  3.079602250661571 -1.695621393244159 -1.093670380128537 -12.117974674416041  0.005884896602276   12.66493
  1.837178634254860  8.643392908166806 -2.206980625400172 -8.815432335747017  0.015161438095268   12.67541
 11.374045547808056  1.044415850215649 -4.556523530966446 -3.316462708335075  0.013940643479303   12.73658
 -6.047809958360989 -3.496771700079830 -6.937809790707504  8.256419502545512  0.011039804302239   12.84932
 -9.322874786259520  7.388672172483259  4.197680009217977  3.144087788860039  0.012875656706437   13.00055
 -6.110429728983997  7.995790020488487 -3.087645043096789 -7.631706521406585  0.008329349937771   13.00179
 -1.136729891045423 -9.463053063510491  2.535632238551141  8.986933309741232  0.009248890950158   13.34301
 -6.262022512126602 -2.750829750649440 -7.622602120557964 -8.853877227632912  0.012595653116549   13.53792
 -12.498812164465489 -5.597046301076934  1.312419181313270 -0.151560524141750 -0.012458543457397   13.75837
 -13.138217337188671 -0.559843473672408  4.064449403333636  2.564008935075896  0.008078502314502   14.00072
 -7.196850979083158  5.184733864567695 -10.924316884623906  4.273477125624685  0.002206200121394   14.70644
 -14.027130583013800  3.641246252056399 -1.285751511680350  5.439758979124409  0.141787498405911   15.53265
 -14.089338450910835  3.658850272382934 -1.244178421622717  5.379226184536320 -0.138580135670992   15.56858
  7.561093181954019  3.654887016714865  8.525805908883875 10.072955608140344  0.002578301548594   15.64232

>> # evaluating formula 1 with 208 points
# r4_208_10Sabds.txt:4 formula 1   : problem  S, 4_208_10  (d=4 n=208 o=10 plus 178/364 of order 11) quality NO (15 negative weights, stability factor 4.452036)
S 4 dimensions, degree 10, bilaterally symmetric (axis 1) 208 point rule with points at 130 distinct radii: 1+1+1+1+2+2+2+1+1+2+2+1+1+1+2+2+2+2+1+2+1+1+1+1+2+1+2+1+1+1+2+2+2+2+1+1+2+2+2+2+2+2+2+1+2+2+2+1+2+2+1+2+2+1+2+2+2+2+2+2+1+1+1+2+1+2+2+1+1+2+2+2+2+2+2+1+2+1+2+2+1+1+2+1+1+2+2+2+1+2+2+2+2+1+1+2+2+2+2+2+1+2+2+1+2+2+2+1+2+1+2+2+2+2+2+1+1+2+2+1+1+1+2+1+2+2+1+1+2+1=208
 (15 negative weights, stability factor 4.452036)
#                 x1                  x2                  x3                  x4              Weight     Radius
   0.000000000000000   0.021426534462400   0.124298963218088  -0.148316324301847   0.062759806816260    0.19470
   0.000000000000000   0.162843629716473  -0.089586540956095   0.391408449856699   0.067723456114483    0.43329
   0.000000000000000   0.319538012572733  -0.171838351365940  -0.257904790136691   0.058886857885546    0.44514
   0.000000000000000  -0.026492072417603  -0.470107264691615  -0.029228204669697   0.046302536849288    0.47176
   0.404241551144358  -0.232962741603379  -0.013954000053693   0.171973408335793   0.268258695754265    0.49745
  -0.404241551144426  -0.232962741603321  -0.013954000053683   0.171973408335753   0.268258695754841    0.49745
  -0.483073859114380  -0.144792195703812  -0.008300744064912   0.113523510156013  -0.471366035056733    0.51699
   0.483073859114511  -0.144792195703612  -0.008300744064920   0.113523510155890  -0.471366035057354    0.51699
   0.518390130891407  -0.064671170365306  -0.017106863638335   0.065638218132220   0.315330760915012    0.52679
  -0.518390130891432  -0.064671170365185  -0.017106863638354   0.065638218132144   0.315330760913814    0.52679
   0.000000000000000  -0.470648436904794  -0.283117395198955   0.066655892878365  -0.800656697748603    0.55327
   0.000000000000000  -0.470845444132477  -0.292875687882593   0.055094437098485   0.839885299063718    0.55723
   0.316748429691694  -0.354604959624756   0.112055465914353  -0.288287584510588   0.055026094401931    0.56722
  -0.316748429691704  -0.354604959624758   0.112055465914345  -0.288287584510579   0.055026094401931    0.56722
   0.281902905375564   0.293740821316439   0.370103042945401   0.186151936089002   0.054467319580163    0.58085
  -0.281902905375562   0.293740821316446   0.370103042945401   0.186151936089001   0.054467319580162    0.58085
   0.000000000000000  -0.218653772012272   0.514969875698312   0.258472448365556   0.052582663599514    0.61629
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   0.480867276703385   0.074909712020670   0.685669177111624  -0.457454322241133   0.017898506178804    0.95721
  -0.480867276703386   0.074909712020672   0.685669177111624  -0.457454322241135   0.017898506178804    0.95721
   0.233595681893497  -0.792976212206410  -0.382224610974236   0.294961268080649   0.014782640382598    0.95733
  -0.233595681893496  -0.792976212206406  -0.382224610974249   0.294961268080647   0.014782640382597    0.95733
   0.000000000000000   0.907549910675906   0.321400076475851  -0.017346443923845   0.014493532212726    0.96294
  -0.481738906836826   0.807621825119957   0.073713430666191  -0.198440566539597   0.012429732984714    0.96392
   0.481738906836820   0.807621825119963   0.073713430666194  -0.198440566539594   0.012429732984713    0.96392
  -0.943985969531349  -0.063830631377421  -0.021594994405948  -0.185132732245145   0.014054060765645    0.96433
   0.943985969531350  -0.063830631377420  -0.021594994405953  -0.185132732245152   0.014054060765645    0.96433
   0.235802153078888  -0.140885937413638   0.125859527237203   0.926552007240181   0.009599867951435    0.97457
  -0.235802153078896  -0.140885937413649   0.125859527237205   0.926552007240178   0.009599867951434    0.97457
   0.000000000000000  -0.684803069130023   0.129818712434256   0.682209480134949   0.014933854752456    0.97530
  -0.381565420562124  -0.567462615673423  -0.071860375599079  -0.692022322512925   0.012705339092912    0.97553
   0.381565420562127  -0.567462615673421  -0.071860375599081  -0.692022322512926   0.012705339092912    0.97553
   0.000000000000000  -0.293804153686270   0.646554560582404   0.670389164279306   0.014827734249383    0.97661
  -0.461961741005053   0.497975182095862  -0.617289240513522   0.336131203894353   0.010571015908388    0.97745
   0.461961741005055   0.497975182095856  -0.617289240513529   0.336131203894344   0.010571015908388    0.97745
   0.406929301590522  -0.360659041074467  -0.789653993546055   0.195532857987693   0.012128014106837    0.97850
  -0.406929301590525  -0.360659041074456  -0.789653993546063   0.195532857987686   0.012128014106837    0.97850
   0.351355339155519   0.020316684013187   0.219620240023603  -0.886493677275294   0.013262552225947    0.97876
  -0.351355339155520   0.020316684013186   0.219620240023603  -0.886493677275294   0.013262552225947    0.97876
   0.238145492014564  -0.791020624536507  -0.381233804240797  -0.361954203392919   0.008948446804499    0.97917
  -0.238145492014578  -0.791020624536498  -0.381233804240812  -0.361954203392924   0.008948446804498    0.97917
  -0.708665716281007  -0.311147890376705   0.308694979264269  -0.518409600674712   0.012212709230028    0.98136
   0.708665716281008  -0.311147890376705   0.308694979264270  -0.518409600674711   0.012212709230028    0.98136
   0.000000000000000   0.046550994959077   0.955321465124374  -0.220169370967425   0.013527682861158    0.98147
   0.000000000000000  -0.658482886535123   0.730823559451367  -0.062761472832879   0.009949695729382    0.98572
   0.540981126716867  -0.326174991971216   0.761427786218208   0.068534355271969   0.009193457019043    0.99173
  -0.540981126716864  -0.326174991971210   0.761427786218213   0.068534355271980   0.009193457019043    0.99173
  -0.663208364146950   0.690194672450952  -0.084826611944063   0.251225003029338   0.008327670452290    0.99324
   0.663208364146931   0.690194672450973  -0.084826611944062   0.251225003029341   0.008327670452290    0.99324
   0.000000000000000  -0.986531703860535   0.179049373147476   0.093588863670909   0.009988161074302    1.00701
   0.000000000000000  -0.377708229013672   0.640495733780391  -0.679157422618255   0.009319845312036    1.00705
   0.000000000000000   0.664653619006446   0.438865852965961  -0.621312849743634   0.005291323055229    1.01015
  -0.429021955542420   0.611207172412409  -0.312921722121952  -0.639867421746248   0.005640649020923    1.03198
   0.429021955542420   0.611207172412414  -0.312921722121961  -0.639867421746248   0.005640649020922    1.03198
   0.000000000000000   0.407129749338967  -0.371324585851299   0.877315516256177   0.005033035899661    1.03601
   0.500570361669096   0.519257891404861   0.744101699145367   0.197529792496063   0.003153941172069    1.05494
  -0.500570361669090   0.519257891404857   0.744101699145384   0.197529792496068   0.003153941172068    1.05494
  -0.887714432764133  -0.343012989471083   0.331075675874492   0.355604308490358   0.003285943402809    1.06853
   0.887714432764136  -0.343012989471081   0.331075675874498   0.355604308490348   0.003285943402809    1.06853
   0.000000000000000   0.729178527996575   0.322306808466343   0.726410455439911   0.002906408854209    1.07854
   0.000000000000000   0.646498881635445  -0.785978525508107  -0.435090517426866   0.001405116664244    1.10681
  -0.857218501734307  -0.639037680482373  -0.318414823911464  -0.045148683818735   0.002154317636240    1.11652
   0.857218501734304  -0.639037680482379  -0.318414823911462  -0.045148683818738   0.002154317636240    1.11652
   0.000000000000000  -0.232852232317941  -1.178079550077854  -0.427391895860321   0.000286950729349    1.27466

>> # evaluating formula 1 with 213 points
# r4_213_10adg.txt:3 formula 1   : problem  G, 4_213_10  (d=4 n=213 o=10 plus 0/364 of order 11) quality N (31 negative weights, stability factor 42.062703)
# evaluating formula 2 with 213 points
# r4_213_10adg.txt:219 formula 2   : problem E2, 4_213_10  (d=4 n=213 o=10 plus 0/364 of order 11) quality N (31 negative weights, stability factor 42.062703)
G 4 dimensions, degree 10, asymmetric 213 point rule with points at 213 distinct radii (31 negative weights, stability factor 42.062703)
#                 x1                  x2                  x3                  x4              Weight     Radius
   0.461051871593653   0.000000000000000   0.000000000000000   0.000000000000000   1.895729299678172    0.46105
   0.471551785143081  -0.077345850563348   0.000000000000000   0.000000000000000  -1.825084596313527    0.47785
   0.275854802642380   0.086061090331119   0.777716170129630   0.000000000000000  -0.190768664844048    0.82967
  -0.164193695498883  -0.980313053965144   0.337296765113589   0.244662931850694   0.843936524839877    1.07778
  -0.025909211916942  -0.351841846191697   1.003977903757577   0.627393923608252   0.129648232667608    1.23534
  -0.348720918461532  -1.128575424080605   0.411323987855228   0.393233281801070  -2.181414953226406    1.31115
  -0.384989419348557   0.686238596602180   0.867676627746885  -0.753091677514324   0.068279652699908    1.39253
  -0.353516089294705  -1.228647160023409   0.507362221205314   0.386787283142150   1.084082261612697    1.42883
   1.158322909201003   0.260740502122822   0.774005213641635  -0.278906102252104  -1.836190432193766    1.44450
  -0.642033182551740  -1.118481783936293   0.001803834505977   0.695973964345620   0.877334761823771    1.46547
   1.357522496944770   0.385471838415189   0.417477836217052  -0.164295384235697   0.359745781130359    1.48079
   1.073853274526659  -0.083314005982935   1.022695450789495  -0.235169141147780   2.040186371694570    1.50377
   0.749894695612951  -0.750785133866602  -1.092972549397033   0.307074287965522   0.053479278687582    1.55400
   1.044535078529642   0.416155978447783   0.921409655053983  -0.572211764482453   0.910805625817711    1.56226
  -0.701419308263216  -1.152955874484061  -0.181879950287322   0.781101968830392  -0.482662995665466    1.56987
   0.654215348097552  -0.407617284536944   0.045262534383626  -1.422906868802592   0.072521815171277    1.61891
   0.572854912556244   0.438797838633018   0.394373131284951   1.408254381180293  -1.050309550148932    1.63077
   0.551012001930875   0.457289626188484   0.388360503974540   1.427773199536949   1.004537814951067    1.64380
   0.913787730304927  -0.115315551617952   0.237421762600862   1.348326948748421   0.061811112531959    1.65005
   0.847906332298622   0.164916873187305   1.172660190569778  -0.800647658405156  -1.237269755078075    1.66202
  -0.640558599288845  -1.247309026483847  -0.553116703237474  -0.715930966379348   0.014944637465302    1.66871
   0.792843761531182   0.032337292680914   1.275431978344159  -0.827993912205384   0.798142975872801    1.71521
   1.064112689298131  -0.258741658017698   1.333172756414675  -0.050352229971705  -1.325635915574287    1.72603
  -1.480307053085105  -0.389126100154138   0.663529906602505  -0.583660369060010   0.078198205677485    1.76739
   1.057059837078187   0.711151284520327   1.206301816607241   0.447214406524785   0.177910568057429    1.81060
  -0.805527143732845   1.021635345106219  -0.697134585642733   1.074221614621206   0.023462838399670    1.82553
  -1.240462069461999   0.990184541694543   0.728503306385563   0.675258426628315   0.024691058925306    1.87241
   1.095098660919219  -0.413299226116369   1.507889202305273   0.022040972721886   0.509621252942104    1.90900
  -1.640392267235776  -0.258069778233358  -0.877246036854523  -0.506289390721266   0.912722290541973    1.94509
  -1.097614770640353  -0.402764180282196   1.554427402749731  -0.235638115163381   0.027781144621158    1.95927
   1.097355609133716  -0.916517764411068   1.214075183184129  -0.618703227556821  -1.129289114766270    1.97509
  -1.695826364076407  -0.251881602582653  -0.846413427219861  -0.499455438104818  -1.039676893790785    1.97614
  -1.823955912649193   0.190136580583911  -0.612976890128561  -0.587373763065323   0.078390506273814    2.02082
   1.107583278292185  -1.004941814024098   1.236488149129305  -0.635306309815642   0.912766840834616    2.04185
   0.501966908041353  -0.736205724970959  -1.067241397201370  -1.563778746986414  -0.313401261760082    2.09246
   0.490144220473234  -0.569641472974514  -1.361968855150106  -1.444586508368654   0.744071029877967    2.12286
  -1.938719370589943  -0.304798602054796  -0.848241147972996  -0.097605170673706   0.067994605665601    2.14023
   0.727004744571850   1.289424224186712   1.494182242185510   0.415297482133570   0.410568306538831    2.14388
  -0.722133949135268  -0.232667974621987  -1.242091032330279   1.576674124792394   0.018803028548248    2.14576
  -0.056219206780017   1.351473917589273  -0.477204441705641  -1.600246106440515   0.013275625451090    2.14899
   0.510794266709435  -0.526205895802966  -1.482865030347078  -1.376024363938359  -0.517115364225926    2.15177
   0.693533288098207  -0.263997111814574  -1.945596680653165  -0.569782832795373   0.060054137166394    2.15886
   1.681630566666042  -1.197252043961005  -0.321053022122100  -0.649778057066390   0.015310017701663    2.18783
   0.478683076054295  -0.023715981179855  -2.057856395984953   0.588711576370153  -0.553854328967421    2.19341
   0.672987148208095  -1.096015018903518  -0.788698246586253  -1.631312545038984   0.065874454198025    2.22202
   0.798764704068105   1.238119680918194   1.613777434037418   0.403631802065444  -0.887649620189770    2.22220
  -1.642403439857501  -0.081584361852197   1.171129401540510  -0.960512224995596  -0.408551997915539    2.23568
   0.328315998656393   0.005217456175299  -2.093218127109668   0.719806547465673   1.054646283056675    2.23774
  -1.664759800879489  -0.056149519712191   1.197201420556824  -0.996812003112943   0.361664628336850    2.28068
   0.800458398784522   1.194316639897977   1.733681529479946   0.373810761119456   0.431582920164309    2.28309
  -0.681849541733859  -1.705723790351050  -1.020426605083823   0.942149779279336   0.019714495788953    2.30290
  -0.843865061914697   2.126810218181957  -0.304545928754247  -0.048854634654314   0.009645273018905    2.30880
   0.126020692755189  -0.006133878444729  -2.151286088356355   0.850330275120562  -0.808435017643562    2.31668
  -0.649305053209472   1.702196378514452  -1.453315752524259  -0.368851517343592   0.037296882003208    2.35950
  -0.029495919325457  -0.047395796149629  -2.198477137248108   0.900349274494778   0.288574285006055    2.37635
  -2.040513937679396  -0.562037802812016  -0.756277589810303  -0.789918093677824   0.037686801244748    2.38233
   0.626965671185469   0.708738141197863   1.267191782457828  -1.815066567255541   0.014823851279502    2.40741
  -0.858470121205551  -0.854294665090561   0.963043124514904  -1.868105903867565   0.008854749444177    2.42571
   0.826985935117944   2.055983002907118  -0.820110460633702   0.646814572184149   0.007905343271742    2.44988
  -0.884417271380250   0.311921801375335  -0.150716285765826  -2.269172542583890   0.007515196639524    2.45995
   1.747244829902636  -0.375822417854083   1.045839908317691  -1.373122275619667   0.011461455081700    2.48462
   1.223911631004090   1.195888604571118  -1.675685907206278  -0.676424495118318   0.007533372565078    2.48869
   0.692203790393130   2.003025358086048   0.874818015836123   1.146648709287310   0.509799210413672    2.56347
   0.706147531880931   1.993615402550708   0.894460568035946   1.139362721863615  -0.533320531611237    2.56347
  -0.886805868003203  -1.437739083448403  -1.371284828079406  -1.392704430283464   0.310103001964538    2.58332
   0.988704952528127   1.826258245378704   1.346260845576465   0.786418551733685   0.041197205647367    2.59685
  -0.935345356488300  -1.459857295573158  -1.456608021536138  -1.345467094281187  -0.546133510861264    2.63402
  -0.970905966424535  -1.490860475865134  -1.545226155165094  -1.285488917724285   0.244698912297637    2.68431
   0.500374664721119  -1.462619026712687  -0.460426636707341   2.158405356945076   0.005964969065845    2.69450
   1.540632623025455  -1.384418218761813  -0.123402682410400  -1.792110943450482  -0.006643762230957    2.74172
   0.685666623595049   1.399440295241756   1.580597941290050   1.625593642959132   0.004767628489617    2.75126
   1.585183648293574  -1.649321202415290  -0.236998805558803   1.534205988825007   0.283979419121961    2.76460
  -0.620379627564951  -0.494847833985372   0.361996412879782   2.638134315412242   0.003270370675412    2.77859
  -1.034947293946412   2.019074722136098  -1.558715117330826  -0.426891670558620  -0.173937552269895    2.78561
   1.632838126183864  -1.596371583487957  -0.288716573490257   1.589148825066872  -0.565132769878089    2.79702
   2.582642588775985  -0.441930525141508   0.917770227892478   0.458562667156980   0.003087328022050    2.81388
  -1.068113647595530   2.040668641623626  -1.566060569880711  -0.439999316660994   0.152451624524971    2.81981
   1.677054721688993  -1.545096336404189  -0.331304340965167   1.628779827641010   0.288953169981111    2.82179
   1.117113798195030   0.890447937353420  -0.493345096881253   2.408657632929752   0.294991313157780    2.84356
   1.055061834145022   0.878261227520575  -0.544117897630960   2.439165492748515  -0.668104643480841    2.85133
   1.007428738289390   0.870264482754815  -0.585724478490854   2.453450971921357   0.380021566684826    2.85215
   1.652085237380420  -0.255681124831457  -2.165644766910586   0.918285152397832   0.009377604052584    2.88583
  -2.262527276356315   0.248070458652159  -0.016359708485159   1.784864060255436   0.003448961857133    2.89250
  -1.251546507373168  -2.129442428213007   1.249707291231202  -0.854037873480884   0.002917376479180    2.89690
  -1.536018105522239  -0.315169659438317   1.679363802603492   1.780321741177178   0.003264099732360    2.90663
   1.023803248793641   2.588168583832341  -0.265316000486854  -0.816590452131680   0.002733136871495    2.91273
  -1.112613674378092   0.346353440381668  -2.281846152106204  -1.397745606253894   0.002742394140053    2.91863
   0.901224064370796  -2.252606627091169  -1.583626933394867  -0.425187571882116   0.003331307533823    2.92833
   1.854128385340161   0.279225611588778  -1.839240251661493   1.305423841796677   0.234578012481748    2.93304
   1.526194984027860   1.481233798066539  -0.664092323957873  -1.966480938773771   0.002088732770100    2.97177
  -1.673140887082426  -1.936885627016250  -0.157319315659541   1.518871621771034   0.271648255235570    2.98038
   0.753069441530984  -0.600807273643534  -1.917967482107408   2.079620447444362   0.002263345443992    2.98856
  -1.650381657376073  -1.985960781024982  -0.106407452995221   1.505577837699323  -0.527998036144491    2.99097
   2.539664088574830   0.222486856294933  -0.978966355950664  -1.229046570787026   0.002380748983237    2.99472
   0.350190169961394  -1.702382044819493   1.544211782445917   1.896166080162047   0.002347147741823    3.00013
  -1.625845726635612  -2.032195226844563  -0.055253639315164   1.505871360828471   0.253624791815182    3.00731
   1.881118396193382   0.267464953978364  -1.874789740182144   1.389355594179270  -0.415014916220559    3.00920
  -1.539831611068156   1.247325987976870  -2.219974934998822   0.455051735919376   0.002602028882222    3.01036
   0.058810893082980  -3.004515397596419  -0.160074669187126  -0.215255726298320   0.002651427909969    3.01704
  -0.218789235760410   1.851849570623606  -1.926528412856141   1.409302705272786   0.001823915909317    3.02900
  -2.770602304861929   0.337175456482759   1.194782204795813   0.164194627547654   0.002446890024155    3.04046
  -1.918255700926428  -2.240871296631137  -0.286330500794661   0.791023057552459   0.005008002417651    3.06739
   1.911170985601377   0.267746977618992  -1.900645697398945   1.469351954963929   0.184803393541310    3.08151
  -0.518585695292128   2.841184333213777   0.636674458341271  -0.875371792825091   0.002582812706737    3.08430
  -1.336589571080383   1.056833281939342   2.592618938595006   0.094943730694736   0.001933842254313    3.10388
   1.717522096693139  -1.872462787119184  -1.794814677830704  -0.452966609153787  -0.002724578306406    3.14365
   1.703008114142663  -0.753269780404403  -1.601889891861187  -1.963700869278555   0.001685981034545    3.14481
  -1.022549786888753   1.025046807425379   0.632601633331354   2.731815928592298   0.001555086629884    3.15584
   2.192882910120803   1.257699675205446   1.920258462210974  -0.016349686426254   0.001575898649769    3.17462
   1.856719743286198  -0.578718515724749   1.567085417119402   1.973606824375065   0.001304770852699    3.18327
  -0.894859037653414   1.406817312868732   2.116518705295846   1.731269839779624   0.001283603744287    3.20263
   0.595085871858105  -0.045360886225175   1.475659354587422   2.817717881141663   0.001187027611529    3.23625
   0.114045726754662  -0.924468141709986  -0.395823102363122  -3.089882022204168   0.001583814633740    3.25141
  -1.791652707933131   2.358826406892726   1.059718447943765  -0.902242639289671   0.005609404969388    3.27279
  -2.549630937329122  -1.500728357936219   0.991705626474533   1.018461264791763   0.001373236663042    3.28231
  -2.332044295347264   1.012672831941187  -1.743966463422616  -1.154754561935474   0.188033802883478    3.29224
  -2.337085196152267   1.002363527158475  -1.751106719472376  -1.144727014552777  -0.196786346586437    3.29294
   3.099457581650577   0.990075904045457   0.478188698285853  -0.202637037367936   0.000842601912697    3.29494
  -1.510294237455446  -1.230693058693261  -1.614298786785208  -2.117903484533019   0.001985276315812    3.29956
   0.289055548132747  -0.962483182966226  -2.664630279158200  -1.676546699858974   0.001509407298992    3.30469
   0.075373969115697   1.123336858847967  -2.493780884835868  -1.863954865775501   0.001023511233576    3.31072
   0.334392363046975  -1.571154941542107  -2.857709551708562   0.604061570221184   0.001182308293026    3.33343
   0.840671326882390   0.540371632726035  -1.365268921151719  -2.881183561656063   0.000807819960623    3.34124
   0.829684239610855   2.101289570311166   2.280625048633391  -0.997001743190835   0.000916880074920    3.36141
  -2.481346286495748   0.798726570209489  -1.899740345527967  -0.979381132135439   0.008817213981649    3.37094
  -1.500785599304150   2.434013837573191   1.068478299278492  -1.439271607899108   0.232798253976579    3.37490
  -1.565665592797455  -2.624482106349966  -0.555933084086675  -1.320563648784406   0.001048763032290    3.37523
  -1.485393309754324   2.448054864373215   1.115445631350748  -1.415845685291163  -0.459956346150935    3.38352
   0.822325929028543  -2.293896400600429   2.256568242284439  -0.666911008081311   0.368651794018241    3.38748
   0.827591166965188  -2.299158066081741   2.254091209264918  -0.663755003966508  -0.372721020066680    3.39006
  -1.465811577472328   2.459041601211446   1.163204432810599  -1.400972969669524   0.224963134083334    3.39282
   0.248586442153284  -2.656038198550627   0.831140361175266  -1.926547614118532   0.001127731881388    3.39392
  -1.311607796656974   2.661625949922938   0.390585601517082   1.620260415136838   0.000835587054422    3.40329
  -2.745307753167295   1.791405433217646  -0.666128436147189   0.641008958208984   0.001045541195180    3.40595
  -0.197367530500874   0.510855353448193  -2.770177515460482   1.911578361810995   0.001288376127716    3.40998
  -0.084617685556328  -0.140431878378998   2.878197096309253   1.828319531746513   0.000866416501829    3.41374
  -0.183413157734589  -0.434964538800584   3.386490855571253   0.054884196443238   0.000906937374332    3.41967
   1.942276191386645  -1.690024305877358  -0.027152119859261  -2.253965299574123   0.001475721823012    3.42195
   2.936189151575770  -1.452507703200667  -1.014823464054837   0.196354936654924   0.000732389827107    3.43503
  -0.449932955448177   0.759964405715499   2.968982883191758  -1.594102391376523   0.000762325840800    3.48368
   1.522904033906316  -2.494127912083717  -1.292723089424775   1.442018665106212   0.000919942865438    3.50578
   2.624172088015652   2.146852527500899  -0.893019404648089  -0.035934424796373   0.000642265654129    3.50628
   1.990164256619723  -1.898329962835377  -2.107145451563264  -0.599534072758653   0.001362473207677    3.51624
   3.316608164495551   0.202239611384979  -0.582330561646116   1.007503369747868   0.000596358819998    3.52065
  -0.972025678094716  -2.009144616615486   2.561509509563474   1.010058507088761   0.000664918292414    3.54444
   1.173580407789108   0.561330072092624  -0.269850601611972   3.288047686304310   0.001211621633403    3.54633
   1.115235787879181   2.123090062436847   1.320523200566788   2.255389379965223   0.000526336023167    3.54709
   2.364067355434901   2.287581989372552   0.157636308792334   1.330870619167662   0.000552777717215    3.55217
   1.919030255467921   0.188537631257538   0.165541285638293  -3.021481657987849   0.000504567071903    3.58817
  -2.221779010357995  -1.174658530118705   2.629412985127726  -0.384357251447755   0.000376784826339    3.65755
  -0.909468311089956   3.179871153999920  -1.285183600038890   0.933561246059556   0.000406027729902    3.66905
  -1.648209721125651   1.658696502972183  -1.180649611148237   2.594242107525945   0.000405250172187    3.68672
  -1.423004535191054   1.171390793234185  -1.174867182535814  -2.996830888442638   0.000271758658542    3.70923
   1.991901987218489  -3.072860201784787  -0.172527265629969  -0.740754180441686   0.000378894988770    3.74014
  -0.640198826316416   3.032705046993508   1.970942114953814   0.821874901238473   0.000279390152333    3.76394
   0.285816092283922   2.230504266464203  -0.335369532879438   3.027090748427140   0.000302664456731    3.78584
   1.992708329729264  -1.992185403235669   0.316139457488218   2.510712123069629   0.000354946393560    3.78726
  -1.020945001652647  -1.134478145456659   2.852684731384565  -1.984667568642250   0.000311971005772    3.79553
  -3.139312038968066  -1.520713979052214   0.947385565013860  -1.175365786858210   0.000334756000984    3.80090
   1.689006763106917   1.986853269623532  -2.761497331454956   0.511449047390389   0.000224778962255    3.83246
  -0.254360721965532   1.953741036410852  -3.306525607029552  -0.172272316421598   0.000241423902097    3.85287
   0.219221621912841   3.291916871048730  -1.922596508763249  -0.564242147015007   0.000259511764611    3.85999
  -1.048972441773083  -0.112070285902754  -3.723799619326062  -0.342372812580276   0.000213950066442    3.88546
   0.860373042972769   2.479001579317624   0.863890982950498  -2.768658495470484   0.000216560724799    3.91120
   3.003696571615134   1.574688355408267   0.531972170007643  -1.875557399795510   0.000199242002966    3.91185
  -0.342432054191804  -3.386039279988712  -0.400162443611336   1.895046254584153   0.000167785135849    3.91585
   0.649268871281487  -1.048516662900701   1.859936773716972  -3.252538093659412   0.000241300583684    3.94453
   2.006232303895243   3.097968836882913   1.037475758500918  -0.932895282683270   0.000172085047589    3.94576
   3.619060509972410  -0.915300661602570   0.274931097729202  -1.262940872033156   0.000189731035275    3.95044
  -0.221845647578552   2.785088791582568  -1.269030659840809  -2.491240404760097   0.000189996675525    3.95255
   1.161208854746649   0.290658879919784  -3.755550849722884   0.328963489148723   0.000180159167386    3.95541
  -0.496347545163934   1.074318903853422   0.984118688993585  -3.766237481442817   0.105825059274589    4.06861
  -1.188833383127906  -0.355197107115377  -1.126457309081667   3.709163285496093   0.000158789855753    4.07017
  -2.830578181597779   0.139529362778071   0.111753867601251  -2.920364055158187   0.000153421486278    4.07095
  -0.515029277898241   1.067313852507211   1.010098325878832  -3.762622927736877  -0.211191024336539    4.07211
  -0.533490348468223   1.059869412971806   1.035785085048784  -3.758442902310748   0.105745812973351    4.07513
   3.153475303814738  -2.236591238888294   1.121718240619161   0.727666154733366   0.000138376715691    4.09078
   1.048106202106897  -3.108341428564347   2.422942274091444  -0.328813937508001   0.002998298031369    4.09134
  -2.282960694979598  -1.495234894610971  -2.965938067130925   0.813798735993978   0.000163802479393    4.11178
  -2.898906615034322   0.126132088283426  -2.200719860031831   1.965646995282199   0.000147526071542    4.13842
  -3.021849664921263   1.873687969803297   1.486432567931383   1.608420854905996   0.000116447840936    4.17598
   1.782050751713426   0.442723602423948  -3.268513048801746  -1.939096659458081   0.000082063388999    4.22078
   3.366895600537883   0.627839262809735   1.188322557532591   2.213498173563048   0.000095561688760    4.24757
  -1.889484892089035  -1.928886044983483   0.668434087830019  -3.256176579068437   0.000090118088096    4.28255
  -4.197321164502241  -0.484627965296941  -0.366486576267444   0.683015420828486   0.000081732332577    4.29572
   0.586763990137183  -3.821478788677463   1.466105690428964   1.176272271987692   0.000091349667456    4.29896
  -3.986019351134517   1.160049123605327   0.062071640470546  -1.213759367582826   0.000073425534497    4.32564
  -2.595741903457729   0.052356034949265   3.318614031956252   1.093313492248976   0.000053042492697    4.35306
   3.450787307922082  -0.285246628373501   2.609371332500529  -0.587409760320075   0.000066576039358    4.37529
  -1.035839108274124  -1.742227699695837   1.659804136724980   3.587453869960141   0.000050381542404    4.44219
   2.134742673152286   0.658443356205294   3.581105178529543   1.760568461462359   0.000040269994524    4.57325
   1.100481284724033  -3.550499142062639   2.657691632618314  -0.201840796066658  -0.000620283583989    4.57397
   0.821113390403648  -2.098145150996987  -0.129655873954397   4.007474120728348   0.000026487269228    4.59925
   0.817843594510862   4.460881057074997   0.201261288465245   0.899127608411353   0.000039994304940    4.62788
   3.921467221354480   0.575352695077556  -2.433645289431984  -0.464811660010352   0.000029364322933    4.67414
   1.583446833001215   3.059100044205283  -2.118451837600371   2.449445717136881   0.000027908819424    4.72790
  -0.780727133672497  -4.059549256695357  -2.404518139985139   0.382446176350259   0.000028040519341    4.79765
  -0.545375609877210  -2.219972581608908  -2.828974704558766   3.150072090952942   0.000027487224452    4.81163
   0.251102621055679  -3.696808890956508  -1.827725877044540  -2.866099649865455   0.000017313776970    5.02838
  -1.800498919062082  -4.398022172906439   1.791417947699286  -0.161178792064495   0.000013667301061    5.08129
   2.555221794731109   2.965619961973994  -2.399252024543458  -2.319262834643373   0.000009605441884    5.14388
   1.966320516696229  -2.624904414771774   4.136371696787609   1.725856186431711   0.000006843236174    5.55380
   3.061397204959997   0.641974853385397   4.179533873478758  -2.521851166307730   0.000134320043726    5.79763
   2.983817744480681   0.490078929964663   4.388988102320098  -2.344587018018196   0.063656333717066    5.82268
   2.984162418201408   0.490405616011051   4.388766210585786  -2.345026781482708  -0.063755502903533    5.82290
  -1.300277364635687   0.107498727987915  -2.931053103914524  -4.892966891451821   0.000002202786218    5.85102
   2.809861743741761  -3.316553625973007   3.487326515999101  -2.024425952341331   0.000003780348796    5.92913
  -2.525672214303098   5.242793979639121   0.484558447333702  -1.368181518237260   0.000002856690576    5.99772
  -5.171238072888323  -0.439067440213412   1.678905842115729   5.113563898681885   0.000000212945924    7.47675
  -5.990365142780862  -3.731852497008191  -2.643091258248970  -1.036385795450373   0.000000190962897    7.60731
  -0.157249454440404   3.561241635121966   7.065167491578314   0.984103002609909   0.000000126579566    7.97447
  -1.419795879174427   2.303988239697239   3.725436014853918   6.938888497632989   0.000000064215717    8.32774
  -5.963933797742665   2.428677045426671   5.429894755535258  -3.219788779422764   0.000000036913525    9.01764

E_n^{r^2} 4 dimensions, degree 10, asymmetric 213 point rule with points at 213 distinct radii (31 negative weights, stability factor 42.062703)
#                 x1                  x2                  x3                  x4              Weight     Radius
   0.326012904882773   0.000000000000000   0.000000000000000   0.000000000000000  18.710098239380809    0.32601
   0.333437464955669  -0.054691775429663   0.000000000000000   0.000000000000000 -18.012862964133770    0.33789
   0.195058801569856   0.060854380566191   0.549928377736602   0.000000000000000  -1.882811254131485    0.58666
  -0.116102475515562  -0.693186008145016   0.238504829886264   0.173002818216339   8.329319639800595    0.76210
  -0.018320579442589  -0.248789755348653   0.709919583907331   0.443634497858705   1.279576767734693    0.87352
  -0.246582926185997  -0.798023335447691   0.290849981078527   0.278057920150108 -21.529702622965466    0.92712
  -0.272228629106093   0.485243965169314   0.613540027356898  -0.532516232025818   0.673893160791165    0.98467
  -0.249973623999571  -0.868784738537907   0.358759267133265   0.273499910787483  10.699463060355578    1.01034
   0.819057983899365   0.184371377180526   0.547304335239810  -0.197216396217047 -18.122473170822992    1.02141
  -0.453986017128960  -0.790886054054676   0.001275503611170   0.492127909717971   8.658947026518860    1.03624
   0.959913363202011   0.272569750899267   0.295201408983780  -0.116174380311209   3.550548544721044    1.04708
   0.759328932417008  -0.058911898599193   0.723154888342057  -0.166289694431606  20.135832393117081    1.06332
   0.530255624443600  -0.530885259371238  -0.772848301329381   0.217134311349008   0.527819324302476    1.09884
   0.738597837215494   0.294266714391396   0.651535015339679  -0.404614818939800   8.989291213109652    1.10469
  -0.495978349327724  -0.815262917256552  -0.128608546210082   0.552322498957687  -4.763692826267587    1.11007
   0.462600108995171  -0.288228946025671   0.032005444994135  -1.006147095928058   0.715761626192674    1.14474
   0.405069593304113   0.310276927268687   0.278863915451162   0.995786222568004 -10.366139758652821    1.15313
   0.389624323080152   0.323352595645367   0.274612345907198   1.009588111388669   9.914390839505012    1.16234
   0.646145500664049  -0.081540408527919   0.167882538335580   0.953411128716927   0.610051228274881    1.16676
   0.599560317379077   0.116613839362492   0.829195972780057  -0.566143388599300 -12.211363020048765    1.17523
  -0.452943329307372  -0.881980670864194  -0.391112571655304  -0.506239641190207   0.147497659699766    1.17996
   0.560625200199928   0.022865918939863   0.901866600829797  -0.585480110101545   7.877355427377178    1.21284
   0.752441298549461  -0.182957980960573   0.942695496553864  -0.035604403261109 -13.083502066598980    1.22049
  -1.046735155475897  -0.275153704154271   0.469186496481469  -0.412710204873800   0.771785354923641    1.24973
   0.747454178919165   0.502859895731388   0.852984194678803   0.316228339499098   1.755906925482174    1.28029
  -0.569593705763493   0.722405280424739  -0.492948592907370   0.759589388197261   0.231568933131144    1.29084
  -0.877139141121235   0.700166204058931   0.515129628062278   0.477479812521750   0.243690983836664    1.32399
   0.774351689204425  -0.292246685446875   1.066238680228000   0.015585321275561   5.029760160922392    1.34987
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  -0.156868561779224   1.969355170734566  -0.897340185108372  -1.761572983771090   0.001875192024952    2.79488
   0.821098655566237   0.205526865005610  -2.655575472931190   0.232612313937904   0.001778099711321    2.79690
  -0.350970715013348   0.759658182072951   0.695876998479437  -2.663132062686484   1.044451470762015    2.87694
  -0.840632146912584  -0.251162283099119  -0.796525601969804   2.622774511702731   0.001567193059177    2.87805
  -2.001521026887549   0.098662158596546   0.079021917604069  -2.065009226934424   0.001514209376192    2.87860
  -0.364180694914123   0.754704862763450   0.714247375893705  -2.660576187250028  -2.084371863262444    2.87941
  -0.377234643102147   0.749440849085794   0.732410657489438  -2.657620462925655   1.043669341118546    2.88155
   2.229843771630243  -1.581508831759331   0.793174574521787   0.514537672452503   0.001365723442202    2.89262
   0.741123002912919  -2.197929302380882   1.713278912434793  -0.232506564959480   0.029592015445899    2.89302
  -1.614296988599521  -1.057290733447051  -2.097234919848137   0.575442604740305   0.001616665671532    2.90746
  -2.049836525518268   0.089188854949162  -1.556143936521235   1.389922319781432   0.001456023964965    2.92630
  -2.136770389790921   1.324897469275856   1.051066548560046   1.137325293504904   0.001149294123409    2.95286
   1.260100170952685   0.313052861467843  -2.311187741199839  -1.371148397279381   0.000809933185249    2.98454
   2.380754710689004   0.443949400227695   0.840270938667886   1.565179568669758   0.000943156063957    3.00349
  -1.336067580145918  -1.363928402541205   0.472654276279664  -2.302464539799350   0.000889429878899    3.02822
  -2.967954258237842  -0.342683720613455  -0.259145143292294   0.482964835722746   0.000806665789310    3.03753
   0.414904796381119  -2.702193565633812   1.036693275638583   0.831750100044973   0.000901585079966    3.03983
  -2.818541313129557   0.820278601811560   0.043891277895248  -0.858257479546652   0.000724680978415    3.05869
  -1.835466702143411   0.037021307350298   2.346614486135643   0.773089384332011   0.000523508419373    3.07808
   2.440075105860422  -0.201699825236468   1.845104163836748  -0.415361424853277   0.000657079171072    3.09380
  -0.732448857677667  -1.231941020820234   1.173658760514649   2.536712958638477   0.000497245892653    3.14111
   1.509491020274735   0.465589762197038   2.532223755877510   1.244909897843199   0.000397448915186    3.23377
   0.778157778996553  -2.510582019949870   1.879271775729398  -0.142722995617640  -0.006121953590395    3.23428
   0.580614846480764  -1.483612664187896  -0.091680547691789   2.833712126206429   0.000261418868933    3.25216
   0.578302751630144   3.154319245526297   0.142313221866929   0.635779229060234   0.000394727968050    3.27240
   2.772896064419329   0.406835792264660  -1.720847087160338  -0.328671476766232   0.000289814250857    3.30512
   1.119665993264377   2.163110385586452  -1.497971659981030   1.732019676739773   0.000275449007012    3.34313
  -0.552057450475165  -2.870534807967628  -1.700251082268482   0.270430284734171   0.000276748833099    3.39245
  -0.385638792038239  -1.569757666506917  -2.000387197400782   2.227437336741422   0.000271288031425    3.40233
   0.177556366123830  -2.614038635539168  -1.292397361805989  -2.026638497974120   0.000170880129387    3.55560
  -1.273144995189875  -3.109871302271482   1.266723778758136  -0.113970616852805   0.000134890854704    3.59302
   1.806814658491524   2.097009985535907  -1.696527376329376  -1.639966477735648   0.000094801911495    3.63727
   1.390398571341547  -1.856087711653876   2.924856476308169   1.220364612778227   0.000067540033860    3.92713
   2.164734723530307   0.453944772185141   2.955376744130959  -1.783218060843000   0.001325685694573    4.09954
   2.109877760943081   0.346538134693773   3.103483249702868  -1.657873379519873   0.628262831411243    4.11726
   2.110121482068293   0.346769136612480   3.103326348552862  -1.658184339247731  -0.629241592050299    4.11741
  -0.919434941954540   0.076013079538044  -2.072567525790639  -3.459850069049963   0.000021740628555    4.13730
   1.986872293191527  -2.345157559091987   2.465912227672526  -1.431485318905586   0.000037310547116    4.19253
  -1.785919949781196   3.707215175355563   0.342634563992482  -0.967450429439959   0.000028194405878    4.24103
  -3.656617508468211  -0.310467564370248   1.187165705933622   3.615835708784603   0.000002101692026    5.28686
  -4.235827814247570  -2.638818207022759  -1.868947752005274  -0.732835423885827   0.000001884728245    5.37918
  -0.111192155571421   2.518178109640637   4.995827843526854   0.695865906534044   0.000001249290241    5.63880
  -1.003947294060165   1.629165708062484   2.634281068991214   4.906535110585115   0.000000633783720    5.88860
  -4.217138030924396   1.717334008128797   3.839515402764869  -2.276734479914282   0.000000364321893    6.37643

>> # evaluating formula 1 with 22 points
# r5_22_4g.txt:4 formula 1   : problem  G, 5_22_4  (d=5 n=22 o=4 plus 0/126 of order 5) quality P
# evaluating formula 2 with 22 points
# r5_22_4g.txt:30 formula 2   : problem  S, 5_22_4  (d=5 n=22 o=4 plus 0/126 of order 5) quality PI
# evaluating formula 3 with 22 points
# r5_22_4g.txt:56 formula 3   : problem E1, 5_22_4  (d=5 n=22 o=4 plus 0/126 of order 5) quality P
# evaluating formula 4 with 22 points
# r5_22_4g.txt:82 formula 4   : problem E2, 5_22_4  (d=5 n=22 o=4 plus 0/126 of order 5) quality P
G_n 5 dimensions, degree 4, asymmetric 22 point rule with points at 3 distinct radii: 1+6+15=22

#                x1                 x2                 x3                 x4                 x5             Weight     Radius     cos1     cos2
 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.250000000000000    0.00000
  1.000000000000000  1.000000000000000  1.000000000000000  1.000000000000000  1.000000000000000  0.055555555555556    2.23607  1.00000
 -2.159591794226542  0.289897948556636  0.289897948556636  0.289897948556636  0.289897948556636  0.055555555555556    2.23607 -0.20000
  0.289897948556636 -2.159591794226542  0.289897948556636  0.289897948556636  0.289897948556636  0.055555555555556    2.23607 -0.20000
  0.289897948556636  0.289897948556636 -2.159591794226542  0.289897948556636  0.289897948556636  0.055555555555556    2.23607 -0.20000
  0.289897948556636  0.289897948556636  0.289897948556636 -2.159591794226542  0.289897948556636  0.055555555555556    2.23607 -0.20000
  0.289897948556636  0.289897948556636  0.289897948556636  0.289897948556636 -2.159591794226542  0.055555555555556    2.23607 -0.20000
 -0.579795897113272 -0.579795897113272 -0.579795897113272  1.869693845669907  1.869693845669907  0.027777777777778    2.82843  0.31623  1.00000
 -0.579795897113272 -0.579795897113272  1.869693845669907  1.869693845669907 -0.579795897113272  0.027777777777778    2.82843  0.31623  0.25000
 -0.579795897113272 -0.579795897113272  1.869693845669907 -0.579795897113272  1.869693845669907  0.027777777777778    2.82843  0.31623  0.25000
 -0.579795897113272  1.869693845669907  1.869693845669907 -0.579795897113272 -0.579795897113272  0.027777777777778    2.82843  0.31623 -0.50000
 -0.579795897113272  1.869693845669907 -0.579795897113272  1.869693845669907 -0.579795897113272  0.027777777777778    2.82843  0.31623  0.25000
 -0.579795897113272  1.869693845669907 -0.579795897113272 -0.579795897113272  1.869693845669907  0.027777777777778    2.82843  0.31623  0.25000
  1.869693845669907  1.869693845669907 -0.579795897113272 -0.579795897113272 -0.579795897113272  0.027777777777778    2.82843  0.31623 -0.50000
  1.869693845669907 -0.579795897113272  1.869693845669907 -0.579795897113272 -0.579795897113272  0.027777777777778    2.82843  0.31623 -0.50000
  1.869693845669907 -0.579795897113272 -0.579795897113272  1.869693845669907 -0.579795897113272  0.027777777777778    2.82843  0.31623  0.25000
  1.869693845669907 -0.579795897113272 -0.579795897113272 -0.579795897113272  1.869693845669907  0.027777777777778    2.82843  0.31623  0.25000
  1.159591794226543 -1.289897948556636 -1.289897948556636 -1.289897948556636 -1.289897948556636  0.027777777777778    2.82843 -0.63246 -0.50000
 -1.289897948556636  1.159591794226543 -1.289897948556636 -1.289897948556636 -1.289897948556636  0.027777777777778    2.82843 -0.63246 -0.50000
 -1.289897948556636 -1.289897948556636  1.159591794226543 -1.289897948556636 -1.289897948556636  0.027777777777778    2.82843 -0.63246 -0.50000
 -1.289897948556636 -1.289897948556636 -1.289897948556636  1.159591794226543 -1.289897948556636  0.027777777777778    2.82843 -0.63246  0.25000
 -1.289897948556636 -1.289897948556636 -1.289897948556636 -1.289897948556636  1.159591794226543  0.027777777777778    2.82843 -0.63246  0.25000

S_n 5 dimensions, degree 4, asymmetric 22 point rule with points at 3 distinct radii: 1+6+15=22

#                x1                 x2                 x3                 x4                 x5             Weight     Radius     cos1     cos2
 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.187992464782654    0.00000
  0.333333333333333  0.333333333333333  0.333333333333333  0.333333333333333  0.333333333333333  0.375984929565309    0.74536  1.00000
 -0.719863931408847  0.096632649518879  0.096632649518879  0.096632649518879  0.096632649518879  0.375984929565309    0.74536 -0.20000
  0.096632649518879 -0.719863931408847  0.096632649518879  0.096632649518879  0.096632649518879  0.375984929565309    0.74536 -0.20000
  0.096632649518879  0.096632649518879 -0.719863931408847  0.096632649518879  0.096632649518879  0.375984929565309    0.74536 -0.20000
  0.096632649518879  0.096632649518879  0.096632649518879 -0.719863931408847  0.096632649518879  0.375984929565309    0.74536 -0.20000
  0.096632649518879  0.096632649518879  0.096632649518879  0.096632649518879 -0.719863931408847  0.375984929565309    0.74536 -0.20000
 -0.193265299037757 -0.193265299037757 -0.193265299037757  0.623231281889969  0.623231281889969  0.187992464782654    0.94281  0.31623  1.00000
 -0.193265299037757 -0.193265299037757  0.623231281889969  0.623231281889969 -0.193265299037757  0.187992464782654    0.94281  0.31623  0.25000
 -0.193265299037757 -0.193265299037757  0.623231281889969 -0.193265299037757  0.623231281889969  0.187992464782654    0.94281  0.31623  0.25000
 -0.193265299037757  0.623231281889969  0.623231281889969 -0.193265299037757 -0.193265299037757  0.187992464782654    0.94281  0.31623 -0.50000
 -0.193265299037757  0.623231281889969 -0.193265299037757  0.623231281889969 -0.193265299037757  0.187992464782654    0.94281  0.31623  0.25000
 -0.193265299037757  0.623231281889969 -0.193265299037757 -0.193265299037757  0.623231281889969  0.187992464782654    0.94281  0.31623  0.25000
  0.623231281889969  0.623231281889969 -0.193265299037757 -0.193265299037757 -0.193265299037757  0.187992464782654    0.94281  0.31623 -0.50000
  0.623231281889969 -0.193265299037757  0.623231281889969 -0.193265299037757 -0.193265299037757  0.187992464782654    0.94281  0.31623 -0.50000
  0.623231281889969 -0.193265299037757 -0.193265299037757  0.623231281889969 -0.193265299037757  0.187992464782654    0.94281  0.31623  0.25000
  0.623231281889969 -0.193265299037757 -0.193265299037757 -0.193265299037757  0.623231281889969  0.187992464782654    0.94281  0.31623  0.25000
  0.386530598075514 -0.429965982852212 -0.429965982852212 -0.429965982852212 -0.429965982852212  0.187992464782654    0.94281 -0.63246 -0.50000
 -0.429965982852212  0.386530598075514 -0.429965982852212 -0.429965982852212 -0.429965982852212  0.187992464782654    0.94281 -0.63246 -0.50000
 -0.429965982852212 -0.429965982852212  0.386530598075514 -0.429965982852212 -0.429965982852212  0.187992464782654    0.94281 -0.63246 -0.50000
 -0.429965982852212 -0.429965982852212 -0.429965982852212  0.386530598075514 -0.429965982852212  0.187992464782654    0.94281 -0.63246  0.25000
 -0.429965982852212 -0.429965982852212 -0.429965982852212 -0.429965982852212  0.386530598075514  0.187992464782654    0.94281 -0.63246  0.25000

E_n^r 5 dimensions, degree 4, asymmetric 22 point rule with points at 3 distinct radii: 1+6+15=22

#                x1                 x2                 x3                 x4                 x5             Weight     Radius     cos1     cos2
 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 276.348923230502123    0.00000
  2.828427124746191  2.828427124746191  2.828427124746191  2.828427124746191  2.828427124746191 26.318945069571608    6.32456  1.00000
 -6.108248009169646  0.819955221105865  0.819955221105865  0.819955221105865  0.819955221105865 26.318945069571608    6.32456 -0.20000
  0.819955221105865 -6.108248009169646  0.819955221105865  0.819955221105865  0.819955221105865 26.318945069571608    6.32456 -0.20000
  0.819955221105865  0.819955221105865 -6.108248009169646  0.819955221105865  0.819955221105865 26.318945069571608    6.32456 -0.20000
  0.819955221105865  0.819955221105865  0.819955221105865 -6.108248009169646  0.819955221105865 26.318945069571608    6.32456 -0.20000
  0.819955221105865  0.819955221105865  0.819955221105865  0.819955221105865 -6.108248009169646 26.318945069571608    6.32456 -0.20000
 -1.639910442211728 -1.639910442211728 -1.639910442211728  5.288292788063781  5.288292788063781 13.159472534785820    8.00000  0.31623  1.00000
 -1.639910442211728 -1.639910442211728  5.288292788063781  5.288292788063781 -1.639910442211728 13.159472534785820    8.00000  0.31623  0.25000
 -1.639910442211728 -1.639910442211728  5.288292788063781 -1.639910442211728  5.288292788063781 13.159472534785820    8.00000  0.31623  0.25000
 -1.639910442211728  5.288292788063781  5.288292788063781 -1.639910442211728 -1.639910442211728 13.159472534785820    8.00000  0.31623 -0.50000
 -1.639910442211728  5.288292788063781 -1.639910442211728  5.288292788063781 -1.639910442211728 13.159472534785820    8.00000  0.31623  0.25000
 -1.639910442211728  5.288292788063781 -1.639910442211728 -1.639910442211728  5.288292788063781 13.159472534785820    8.00000  0.31623  0.25000
  5.288292788063781  5.288292788063781 -1.639910442211728 -1.639910442211728 -1.639910442211728 13.159472534785820    8.00000  0.31623 -0.50000
  5.288292788063781 -1.639910442211728  5.288292788063781 -1.639910442211728 -1.639910442211728 13.159472534785820    8.00000  0.31623 -0.50000
  5.288292788063781 -1.639910442211728 -1.639910442211728  5.288292788063781 -1.639910442211728 13.159472534785820    8.00000  0.31623  0.25000
  5.288292788063781 -1.639910442211728 -1.639910442211728 -1.639910442211728  5.288292788063781 13.159472534785820    8.00000  0.31623  0.25000
  3.279820884423455 -3.648382345852054 -3.648382345852054 -3.648382345852054 -3.648382345852054 13.159472534785820    8.00000 -0.63246 -0.50000
 -3.648382345852054  3.279820884423455 -3.648382345852054 -3.648382345852054 -3.648382345852054 13.159472534785820    8.00000 -0.63246 -0.50000
 -3.648382345852054 -3.648382345852054  3.279820884423455 -3.648382345852054 -3.648382345852054 13.159472534785820    8.00000 -0.63246 -0.50000
 -3.648382345852054 -3.648382345852054 -3.648382345852054  3.279820884423455 -3.648382345852054 13.159472534785820    8.00000 -0.63246  0.25000
 -3.648382345852054 -3.648382345852054 -3.648382345852054 -3.648382345852054  3.279820884423455 13.159472534785820    8.00000 -0.63246  0.25000

E_n^{r^2} 5 dimensions, degree 4, asymmetric 22 point rule with points at 3 distinct radii: 1+6+15=22

#                x1                 x2                 x3                 x4                 x5             Weight     Radius     cos1     cos2
 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  4.373354581906217    0.00000
  0.707106781186548  0.707106781186548  0.707106781186548  0.707106781186548  0.707106781186548  0.971856573756937    1.58114  1.00000
 -1.527062002292411  0.204988805276466  0.204988805276466  0.204988805276466  0.204988805276466  0.971856573756937    1.58114 -0.20000
  0.204988805276466 -1.527062002292411  0.204988805276466  0.204988805276466  0.204988805276466  0.971856573756937    1.58114 -0.20000
  0.204988805276466  0.204988805276466 -1.527062002292411  0.204988805276466  0.204988805276466  0.971856573756937    1.58114 -0.20000
  0.204988805276466  0.204988805276466  0.204988805276466 -1.527062002292411  0.204988805276466  0.971856573756937    1.58114 -0.20000
  0.204988805276466  0.204988805276466  0.204988805276466  0.204988805276466 -1.527062002292411  0.971856573756937    1.58114 -0.20000
 -0.409977610552932 -0.409977610552932 -0.409977610552932  1.322073197015945  1.322073197015945  0.485928286878469    2.00000  0.31623  1.00000
 -0.409977610552932 -0.409977610552932  1.322073197015945  1.322073197015945 -0.409977610552932  0.485928286878469    2.00000  0.31623  0.25000
 -0.409977610552932 -0.409977610552932  1.322073197015945 -0.409977610552932  1.322073197015945  0.485928286878469    2.00000  0.31623  0.25000
 -0.409977610552932  1.322073197015945  1.322073197015945 -0.409977610552932 -0.409977610552932  0.485928286878469    2.00000  0.31623 -0.50000
 -0.409977610552932  1.322073197015945 -0.409977610552932  1.322073197015945 -0.409977610552932  0.485928286878469    2.00000  0.31623  0.25000
 -0.409977610552932  1.322073197015945 -0.409977610552932 -0.409977610552932  1.322073197015945  0.485928286878469    2.00000  0.31623  0.25000
  1.322073197015945  1.322073197015945 -0.409977610552932 -0.409977610552932 -0.409977610552932  0.485928286878469    2.00000  0.31623 -0.50000
  1.322073197015945 -0.409977610552932  1.322073197015945 -0.409977610552932 -0.409977610552932  0.485928286878469    2.00000  0.31623 -0.50000
  1.322073197015945 -0.409977610552932 -0.409977610552932  1.322073197015945 -0.409977610552932  0.485928286878469    2.00000  0.31623  0.25000
  1.322073197015945 -0.409977610552932 -0.409977610552932 -0.409977610552932  1.322073197015945  0.485928286878469    2.00000  0.31623  0.25000
  0.819955221105864 -0.912095586463013 -0.912095586463013 -0.912095586463013 -0.912095586463013  0.485928286878469    2.00000 -0.63246 -0.50000
 -0.912095586463013  0.819955221105864 -0.912095586463013 -0.912095586463013 -0.912095586463013  0.485928286878469    2.00000 -0.63246 -0.50000
 -0.912095586463013 -0.912095586463013  0.819955221105864 -0.912095586463013 -0.912095586463013  0.485928286878469    2.00000 -0.63246 -0.50000
 -0.912095586463013 -0.912095586463013 -0.912095586463013  0.819955221105864 -0.912095586463013  0.485928286878469    2.00000 -0.63246  0.25000
 -0.912095586463013 -0.912095586463013 -0.912095586463013 -0.912095586463013  0.819955221105864  0.485928286878469    2.00000 -0.63246  0.25000

>> # evaluating formula 1 with 80 points
# r5_80_6g.txt:4 formula 1   : problem  G, 5_80_6  (d=5 n=80 o=6 plus 0/330 of order 7) quality P
# evaluating formula 2 with 80 points
# r5_80_6g.txt:88 formula 2   : problem E2, 5_80_6  (d=5 n=80 o=6 plus 0/330 of order 7) quality P
G 5 dimensions, degree 6, asymmetric 80 point rule with points at 80 distinct radii: 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=80

#                x1                 x2                 x3                 x4                 x5             Weight     Radius
  0.525978883618116  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.160717532259439    0.52598
 -0.457075404827968 -1.427571109514293  0.000000000000000  0.000000000000000  0.000000000000000  0.038997225192196    1.49896
 -0.850772987246752  0.129307841580535  1.493066988044931  0.000000000000000  0.000000000000000  0.023302417524508    1.72331
 -0.731391750529577  0.177598851775757  0.052730839245962  1.591856822426189  0.000000000000000  0.042472565646275    1.76161
 -0.663823919556601 -0.195130453079779 -1.299499589296579 -0.462406821760747  0.988183811177152  0.050468731229106    1.83242
 -0.241496414254388  1.428061212539928 -0.016399080826969 -1.183228046018092  0.166686907993302  0.044867218663080    1.87770
 -0.353243548501523 -0.271342052322487  0.234940613448662  0.245694959800685 -1.852152954069729  0.036800605996956    1.93506
 -0.997223557819864  0.660503198452008 -1.137979249801055 -0.117667401017477 -1.197024275430209  0.033474519105024    2.04265
 -0.225927345555532 -1.320590908409695  1.679014758245989 -0.562542445461301  0.209782181735079  0.027118284131642    2.23037
  0.143512179274176  1.614908250521244  0.653208251863218  1.233230456587519 -0.679206212210146  0.021108872725177    2.24441
  1.621927790456775 -0.966042927111844 -0.860960423206200 -0.784375396396712 -0.433452114344924  0.020331770861493    2.26015
 -0.300896769398391  0.041796105795071  0.759011265943552 -1.940155405737450 -0.822362311262275  0.021931134210714    2.26028
 -1.845330741951008  0.229103171318676  0.473037969044580 -0.087331330131230  1.220567760018360  0.022810263904731    2.27572
  0.121446209677222  0.452758572355129  0.493326909794623  0.788217447876192  2.090311093216363  0.018615727833664    2.33534
  0.073491074751219  1.761182943861515 -0.700553069455747  1.096415257517210  0.940920182288580  0.019282505314565    2.38441
 -0.295226998784488  1.066253099946695  1.824112133875573  0.229576139726376  1.162180773311321  0.015493632070861    2.44025
  1.904136430359638 -0.310519490938026  1.112498580150478  0.099712712948721  1.061758529691471  0.018586068942503    2.46923
  1.253972847127549 -1.004103845481670 -0.090295179022433  1.766607421258837 -0.661825572506495  0.017200635927645    2.47946
  1.138026843456055  0.796319169342854 -1.288744566038432  1.209833923194932 -1.054961997021105  0.016144595049976    2.48329
  0.365358903033166 -1.439948090099475 -1.108560711485391  1.180639348912693  1.189435457841063  0.015708054575624    2.49890
 -2.152261595222397 -0.904766332350211  0.242757434652880 -0.508621069995829 -0.809904531756512  0.016896461220056    2.53464
 -1.838285862085757  1.528212267519926 -0.650456453001555  0.620732055834782  0.363125268113575  0.012478422387724    2.57973
  0.432060136821483  0.401181079535157 -2.122816041114406 -1.050555581004263 -0.908118952272760  0.011399943983761    2.60429
 -1.744511825564231 -0.996019665603737 -0.329999591321923  1.468555065454399  0.782352454378590  0.010082590279772    2.62926
  0.383191911606296  0.173263483727912  1.002088765257195 -1.743897731468651  1.643670224197355  0.013895123884656    2.63132
 -1.362876276886903 -0.782085943569707  0.092346542842982 -1.967040287257767  0.818901520379175  0.010795997303252    2.64905
  0.527340623372767 -1.783209750872186 -0.495348327667819 -1.735947381980242  0.636480013935030  0.011567968665239    2.66869
 -1.798500076683897  1.358695376663296  0.962752211461084 -0.557386535586664 -0.921280931927919  0.010689954229883    2.67712
  0.866742920645520  1.139947870245335  2.055793092025534 -0.835315124844068 -0.499170470621832  0.012931760205756    2.68774
  1.018562041775385 -0.437722028875576  2.147763055879996  0.990068681382953 -0.705057835461789  0.010140675942211    2.70542
  1.784233812664246  1.173681475923357 -1.502291238959932 -0.181331037401504  0.690868526774279  0.009260141942865    2.70704
  1.609930482935805 -0.910074985284107  1.008090711541266 -0.140544253189852 -1.720873138578080  0.010064489191098    2.72351
 -0.244768484977980  0.250338486920300 -2.383595159724701  1.254340256705401  0.222369263964925  0.010586708952439    2.72524
  0.578558622967769  0.741640769966280 -1.096600126490888 -0.757615273225516  2.193961718806492  0.008801769709301    2.73400
 -0.261002327240031 -0.869626528484923 -0.478825420107196 -1.953409184880050 -1.616770408704415  0.008367109240572    2.73558
  0.043085866354355 -1.051585569412625  1.242868019359046  1.898230160974114  1.112868324726220  0.011193713645278    2.73755
 -1.051091390767562  0.284216644289855  2.090947072656136  1.255997850914194 -0.618843787005676  0.008684142847913    2.74192
 -0.952512476447155 -1.031100527212648 -1.385767753450186  1.454372987635966 -1.278720577828327  0.009792921916064    2.76426
  1.439346557282178  0.743483515676016 -0.187344733304161 -1.491197908499201 -1.703997055651363  0.008696589180518    2.79049
 -0.989916724051303 -1.335055659763976 -1.918838566800467 -0.956752143141531 -0.762495679447713  0.008231730405806    2.81798
 -0.407218910066817 -1.394167891547479  0.739174773828514 -0.212629764647899  2.312763690619307  0.008835484276543    2.83725
  0.667499121597262 -1.984017993905502 -1.631998041708373  0.574160126417174 -0.842717617486665  0.006944342733158    2.84344
  2.319117292767222  1.188778932168480  0.427423464144792  0.564002647627383 -0.911873892770042  0.008458726871739    2.85023
  0.147571040475811  1.455169103312398  0.910517696389863 -0.099845406853528 -2.269258022185990  0.007555711815553    2.85094
  1.816367037683986  0.196208881822375 -0.701314263227990  1.710341679375575  1.308078214714395  0.007705640803295    2.90962
  2.212564287008156  0.731875767797056 -0.022596169483833 -1.736483907257559  0.424481966518153  0.006356094769029    2.93720
  0.599663609003842  2.538369949527121 -0.925975668440697 -0.506359306038797 -0.906650129537287  0.006855420985280    2.95614
  1.535957109048902 -1.110535826708849 -0.720587349307695 -0.539523956392050  2.097985451859095  0.006128548348807    2.96721
  1.504211871753881 -0.566445195327981 -2.566388263013825  0.023889554487891  0.366817382200111  0.003984292715649    3.05041
  0.181728938603313 -2.446825677974218  0.161549219800174 -0.634474697484461 -1.693485320049263  0.005293776136457    3.05230
  1.526696423415486  2.294813261375531  0.724855206831920 -0.223726036305604  1.227449604125403  0.005396140186032    3.11112
 -0.846319562402871 -2.145929407360746  1.011954392233666  1.494953196731892 -1.091670218843651  0.005655444050782    3.12601
  0.438536700529340  0.365079011744037 -1.416965275442533 -2.792508865555734  0.516265028693607  0.004554086491130    3.22460
  1.463484785819568 -2.757142386951415  0.754468506721180  0.423310774132222  0.539203853411780  0.004288335449188    3.28371
  1.667677993813642 -1.138162836189353  1.551930381367417 -2.105276127386423 -0.264049240264549  0.003762283698200    3.31466
  1.390652494870341  1.181806509132474  1.490818604959167  2.295189301017430  0.512171246942847  0.003405783667636    3.32916
 -1.372456222944826 -2.844984718326645 -0.722027268362507  0.019865930415718  0.845543479371499  0.003261313080160    3.34877
  1.145257165412947 -0.347942026749059 -1.484374374109279  0.194144305872535 -2.928111517717829  0.002691928972888    3.49965
 -2.359153309862209  0.944166574929905 -1.197590693935497 -2.161598414234952 -0.080903184509655  0.002511802840729    3.54547
  0.272807306833399  0.125181365172404  0.736243111005387  2.538026880358109 -2.508380298008947  0.001919794989303    3.65591
 -2.758690666767411  0.456074129913178  0.489016240277986  1.722285050788152 -1.555028452802620  0.001901600135080    3.66632
 -1.283708723746440  2.236443612541097  0.047007704711448 -1.224184037860520  2.470809735599397  0.001705897036651    3.77562
 -0.924469444709625 -0.729802697697213  2.629856572282709 -0.866932554956829 -2.361099348199312  0.001701019870715    3.82489
 -1.005942574791578  3.478911669226576  1.326761301904560  0.275242573711966 -0.016232839963469  0.001273615874475    3.86666
 -1.108545960346608  0.186402871531918 -1.482893212247593  1.738464215160573  2.986179444496705  0.001353075046691    3.92455
 -0.128327743027874  0.400615519898365 -0.813905725656708  3.869600241775243  0.119450557237816  0.001156718236306    3.97838
 -0.744812023831341  2.377925780829460 -2.983526074800474 -0.677869683655410  0.856527117105110  0.001132116537532    4.03780
 -1.100476378288022  2.328264847098248 -1.445098586198112  1.895072723252798 -2.124611670822335  0.001001872888620    4.10188
 -3.357140397734372 -0.415463728579217 -2.351255886991576  0.506423631223533  0.261277314791323  0.000925544048867    4.15886
 -2.027103800425216  0.729354004373583  2.835559758683833 -2.344130595469630  0.699022075483899  0.000779905998485    4.32031
 -3.064232326708181 -1.673087208562613  2.583382585803965  0.818935230170196  1.247882601053748  0.000508043175231    4.59244
  4.440097976301273 -1.121900384395893 -0.733218134094819  0.508179034119279 -0.402654677217575  0.000426371596412    4.68307
 -1.649725448615769  1.914290623955623 -0.718252663810389 -2.472434344788752 -3.477802419190281  0.000269442273703    5.01099
 -2.873288034466189 -1.200572413446108 -1.597529083886628 -1.789045766208691  4.280424794142120  0.000092253303971    5.81137
 -2.711734020389407  2.316745109403878  2.013075880029548  3.670427325620154  2.273830130827989  0.000116660031288    5.95110
  1.096975039920008 -0.741892050835174  5.692857451292036 -0.098357360461734  2.762758075036888  0.000063296149951    6.46567
 -0.047074143235228 -3.044516562863345 -5.621846751717821 -1.774821864260280  2.535459534925816  0.000031914954015    7.10317
 -3.878501679618951 -7.778818308475994  3.221484048564351 -5.773311575380263 -0.505977241884623  0.000002487577683   10.93242
  0.947693514039050  7.041731738628084  2.581716909550937 -8.577321800360878 -0.799061381635434  0.000001946795792   11.46117
 -6.127149242631335 -3.158304666619124 -2.395672937637830 -0.539349664167283 -11.341470706791743  0.000000689287630   13.49726

E_n^{r^2} 5 dimensions, degree 6, asymmetric 80 point rule with points at 80 distinct radii: 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=80

#                x1                 x2                 x3                 x4                 x5             Weight     Radius
  0.371923235367301  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  2.811499024397909    0.37192
 -0.323201118267443 -1.009445212163556  0.000000000000000  0.000000000000000  0.000000000000000  0.682194773903675    1.05992
 -0.601587348532515  0.091434451642194  1.055757792012343  0.000000000000000  0.000000000000000  0.407638937801192    1.21856
 -0.517172066503365  0.125581352421589  0.037286334008478  1.125612753815624  0.000000000000000  0.742990358297808    1.24565
 -0.469394395032309 -0.137978066588713 -0.918884971740747 -0.326970999333946  0.698751473942129  0.882870627855219    1.29572
 -0.170763752151512  1.009791767336464 -0.011595901257975 -0.836668575029505  0.117865442977079  0.784881025270268    1.32774
 -0.249780908555825 -0.191867805218306  0.166128100945678  0.173732572178424 -1.309669913617404  0.643768395414846    1.36829
 -0.705143540093401  0.467046290620817 -0.804672844383903 -0.083203417184058 -0.846423982401616  0.585583766020260    1.44437
 -0.159754758097794 -0.933798786509800  1.187242721268031 -0.397777577890948  0.148338403276986  0.474391488642207    1.57711
  0.101478435147632  1.141912574937678  0.461887984419492  0.872025618618816 -0.480271318477824  0.369266341006112    1.58704
  1.146876139226900 -0.683095504678088 -0.608790953582347 -0.554637161787998 -0.306496929372941  0.355672173021506    1.59817
 -0.212766146078723  0.029554309834882  0.536702013145675 -1.371897043952688 -0.581497966885798  0.383650505147301    1.59826
 -1.304845881165561  0.162000406030783  0.334488355670133 -0.061752575745839  0.863071740006653  0.399029488648989    1.60918
  0.085875438412163  0.320148656752655  0.348834803257581  0.557353902442806  1.478073148802759  0.325652714467497    1.65133
  0.051966037313273  1.245344402514565 -0.495365825993210  0.775282663586809  0.665331041451537  0.337316931872341    1.68603
 -0.208757012829863  0.753954797433487  1.289842059508081  0.162334845199145  0.821785905773062  0.271036587229871    1.72552
  1.346427782211644 -0.219570437732874  0.786655290084805  0.070507535496549  0.750776656327503  0.325133879077289    1.74601
  0.886692703627688 -0.710008638155577 -0.063848333395217  1.249180087266608 -0.467981350282006  0.300897919783465    1.75325
  0.804706498180099  0.563082684631172 -0.911280021863088  0.855481771200664 -0.745970781987724  0.282424154939327    1.75595
  0.258347757901624 -1.018197059065950 -0.783870796448306  0.834838089751837  0.841057878023145  0.274787569804551    1.76699
 -1.521878768869133 -0.639766408994116  0.171655428226504 -0.359649407648408 -0.572688986518748  0.295576864378932    1.79226
 -1.299864398840198  1.080609257455816 -0.459942168783949  0.438923845980634  0.256768339503287  0.218290262897262    1.82414
  0.305512652626859  0.283677861823045 -1.501057617883580 -0.742854975341485 -0.642137069276097  0.199423989019414    1.84151
 -1.233556141716594 -0.704292259743551 -0.233344948812521  1.038425245328661  0.553206725769039  0.176378969590097    1.85917
  0.270957599192649  0.122515784276009  0.708583761264216 -1.233121911617323  1.162250361564362  0.243073214828455    1.86063
 -0.963699057305004 -0.553018274168820  0.065298866663407 -1.390907525987104  0.579050818184083  0.188858897089703    1.87316
  0.372886130782023 -1.260919707119700 -0.350264161543333 -1.227500165581260  0.450059333943169  0.202363315061884    1.88705
 -1.271731600187705  0.960742714405426  0.680768617326482 -0.394131799055411 -0.651443994344098  0.187003841246512    1.89301
  0.612879796733886  0.806064869249634  1.453665236087716 -0.590656989204929 -0.352966824744777  0.226220690991826    1.90052
  0.720232126798594 -0.309516214892657  1.518697821194685  0.700084278446309 -0.498551176583736  0.177395086381973    1.91302
  1.261643828157217  0.829918130578439 -1.062280322385710 -0.128220406186196  0.488517820190452  0.161991536779726    1.91417
  1.138392761722843 -0.643520193482643  0.712827778181999 -0.099379794487338 -1.216841065850335  0.176062319673742    1.92581
 -0.173077455548691  0.177016041693328 -1.685456301044769  0.886952501431664  0.157238814477058  0.185197728417822    1.92703
  0.409102725614460  0.524419217647570 -0.775413385691733 -0.535714897228264  1.551365209031762  0.153973039548218    1.93323
 -0.184556515496893 -0.614918815391409 -0.338580701562293 -1.381268881060767 -1.143229319616641  0.146369342138255    1.93435
  0.030466308272458 -0.743583287129579  0.878840404608674  1.342251419077629  0.786916738981628  0.195816315436494    1.93574
 -0.743233850058537  0.200971516503442  1.478522854177317  0.888124597537154 -0.437588638286873  0.151915343655398    1.93883
 -0.673528031260576 -0.729098174877085 -0.979885775614272  1.028397001931932 -0.904191991825189  0.171311679727475    1.95463
  1.017771711131745  0.525722235634919 -0.132472731338957 -1.054436153190981 -1.204907873172990  0.152133072558304    1.97318
 -0.699976828386650 -0.944026910280591 -1.356823762586885 -0.676525928330138 -0.539165865562924  0.144001103548987    1.99261
 -0.287947252735645 -0.985825570225769  0.522675495056172 -0.150351948464630  1.635370888918939  0.154562822576725    2.00624
  0.471993155317487 -1.402912577486713 -1.153996882175160  0.405992518876513 -0.595891341950187  0.121480292441527    2.01061
  1.639863564082695  0.840593644268033  0.302234029935027  0.398810096744491 -0.644792213164669  0.147972047686445    2.01542
  0.104348483427208  1.028959940725340  0.643833237507629 -0.070601364256458 -1.604607735749685  0.132175227552452    2.01592
  1.284365449470064  0.138740630865636 -0.495904071271360  1.209394199632459  0.924950975946947  0.134797998054461    2.05741
  1.564519211154650  0.517514318395406 -0.015977904670858 -1.227879546243132  0.300154077016389  0.111189824724652    2.07692
  0.424026204357419  1.794898604470774 -0.654763674368162 -0.358050099016950 -0.641098454759479  0.119924747107481    2.09031
  1.086085687420159 -0.785267413816436 -0.509532201132715 -0.381501048177412  1.483499739840292  0.107209260006764    2.09813
  1.063638414858475 -0.400537238786950 -1.814710543934638  0.016892465977918  0.259379058410798  0.069698899214559    2.15696
  0.128501764824238 -1.730167029276941  0.114232548816098 -0.448641361082535 -1.197474953646699  0.092606240487836    2.15830
  1.079537393810338  1.622678018675455  0.512550032129225 -0.158198197399684  0.867937938641814  0.094396937628759    2.19989
 -0.598438301625905 -1.517401235892410  0.715559812999937  1.057091542965632 -0.771927414563743  0.098933048608801    2.21042
  0.310092274743474  0.258149844873088 -1.001945754971279 -1.974601955358009  0.365054502678710  0.079666540089527    2.28013
  1.034840016216353 -1.949594078510209  0.533489797294231  0.299325918938228  0.381274701189394  0.075017645941826    2.32194
  1.179226418261206 -0.804802659564013  1.097380496594322 -1.488655025945086 -0.186711008358217  0.065815202599822    2.34382
  0.983339809396805  0.835663396657975  1.054167945085696  1.622943918856231  0.362159761842060  0.059578798431342    2.35407
 -0.970473102125967 -2.011707986700864 -0.510550377660726  0.014047334111541  0.597889528051657  0.057051514008603    2.36794
  0.809819107865979 -0.246032166574053 -1.049611185752205  0.137280755211233 -2.070487510248705  0.047091039630977    2.47463
 -1.668173303262255  0.667626587702613 -0.846824500767692 -1.528480896907631 -0.057207190386374  0.043940017849394    2.50702
  0.192903896619137  0.088516592191596  0.520602496393795  1.794656017934963 -1.773692718516855  0.033583776851157    2.58512
 -1.950688877667275  0.322493109985369  0.345786699610920  1.217839438548519 -1.099571163914760  0.033265486654829    2.59248
 -0.907719143629437  1.581404444169152  0.033239466769480 -0.865628834591513  1.747126319064068  0.029841970485991    2.66977
 -0.653698613353931 -0.516048436469941  1.859589415809115 -0.613013888441350 -1.669549360166871  0.029756652182020    2.70460
 -0.711308816119372  2.459962032459114  0.938161913592602  0.194625890342961 -0.011478351216092  0.022279895280894    2.73414
 -0.783860365818051  0.131806734492871 -1.048563846155779  1.229279835390184  2.111547735043499  0.023669907820428    2.77508
 -0.090741417309382  0.283277950768716 -0.575518257858414  2.736220571440381  0.084464299039376  0.020234955994899    2.81314
 -0.526661632760416  1.681447444782831 -2.109671519338299 -0.479326250073529  0.605656132775182  0.019804588186671    2.85516
 -0.778154309623068  1.646331861781429 -1.021839009783774  1.340018773453703 -1.502327319826557  0.017526181551730    2.90047
 -2.373856740633279 -0.293777219815406 -1.662588981996529  0.358095583791272  0.184750961059150  0.016190929227470    2.94076
 -1.433378843449690  0.515731162378120  2.005043533825034 -1.657550640043439  0.494283249773757  0.013643221887722    3.05492
 -2.166739457346394 -1.183051310691089  1.826727344821222  0.579074654605911  0.882386249329817  0.008887411792802    3.24734
  3.139623388175296 -0.793303369622139 -0.518463514707394  0.359336841082582 -0.284719852737019  0.007458696699056    3.31143
 -1.166532051812217  1.353607881360843 -0.507881329185619 -1.748275091238640 -2.459177674236436  0.004713466409028    3.54331
 -2.031721453473208 -0.848932894853236 -1.129623648358965 -1.265046393139258  3.026717398296907  0.001613825638479    4.10926
 -1.917485514591609  1.638186177140265  1.423459605811970  2.595384051798396  1.607840704774762  0.002040782729436    4.20807
  0.775678489519824 -0.524596900053949  4.025458108136957 -0.069549156562101  1.953564969636479  0.001107266029624    4.57192
 -0.033286445900179 -2.152798307035437 -3.975245960931260 -1.254988575616595  1.792840630570137  0.000558301641487    5.02270
 -2.742514838501975 -5.500455175541478  2.277933216224145 -4.082347764854170 -0.357779938862686  0.000043516237030    7.73039
  0.670120510263532  4.979256263680411  1.825549533847438 -6.065082409454352 -0.565021721538720  0.000034056113180    8.10427
 -4.332548778806618 -2.233258646819514 -1.693996579708805 -0.381377804963360 -8.019630845401013  0.000012057996868    9.54400

>> # evaluating formula 1 with 80 points
# r5_80_6E1d.txt:3 formula 1   : problem E1, 5_80_6  (d=5 n=80 o=6 plus 0/330 of order 7) quality P
E1 5 dimensions, degree 6, asymmetric 80 point rule with points at 80 distinct radii
#                x1                 x2                 x3                 x4                 x5             Weight     Radius
  1.054979750792653  0.039856575712741 -1.379548545674621  0.111098415942054 -1.040774267487751 99.192597589923309    2.02812
 -1.455394057161333 -2.496194669491342 -0.601795135841893  0.000000000000000  0.000000000000000 64.792202635740949    2.95149
 -2.216495495666666  2.255923390619139  0.000000000000000  0.000000000000000  0.000000000000000 67.950196090002308    3.16260
  0.257319151920844  0.665660509872070  1.764655354779092 -3.232352554932132  0.000000000000000 38.613294566113574    3.75119
  2.089435812020419 -0.781206155116966  3.294453366816909  0.919365091650658  0.842114945933117 46.037551138720090    4.16939
  0.858852341231145  1.220289925195077 -0.150115551014322  1.019869850960937  4.849743408386642 23.220053549425462    5.17778
  0.099115322328464 -1.284460439289735  0.359174149980717  4.898072639351798 -1.351488478787904 20.665483215289591    5.25417
 -4.082600258664884 -0.325588061343669  2.334431205846981  1.807961354529535  2.740132539148827 17.171762914226921    5.74458
  2.661449155512000  4.198280805128484  1.382166934019975 -1.490081843546786  2.066502390500926 16.784718168250645    5.75413
  1.013493610148740 -3.123968642356374  2.638275521853994 -3.171139875917313 -2.798632794051076 13.226170616587119    5.96953
  0.437126432768689 -2.202498218645959 -4.193985944597771  2.461729182967904  2.782060586393768 16.027617884054244    6.03586
 -0.090016938339615  2.887871184809816  3.014923311583570  3.869517843303779 -2.206046320118591 13.486129768800788    6.10553
  1.801513034905021  2.934207456094948  0.993417594354236 -1.167075527649739 -4.804621689330527 15.543151793397183    6.10642
  4.429077092909071 -3.922790895310299 -0.337483417924010 -0.127290200433244  1.468080599048191 13.076140335287235    6.10658
  1.874230959351408 -0.704860035038918 -3.089686061435060 -5.069945523963114  1.099631112662590 13.361095891404426    6.36155
 -0.484719699753026 -2.536042807283604  0.228919110541243 -2.587490576568109  5.384396611024523 10.994540355013537    6.51197
 -1.291975909403511  2.346251876571712 -4.301034549867198 -1.647364549204482  4.205675387059636  8.393590784149637    6.78782
  4.480139640603905  3.044685430859525 -4.152102624657338 -0.384769170330698  0.140340949206438  9.121358273467795    6.83736
 -3.627007243687154 -1.168978491317442 -1.122234929263367 -3.193421276145755 -4.702316634819040  9.299640480919502    6.93475
 -0.547294323287458  4.417650429322430 -3.052545074304911  4.461551084092341 -0.363896725939802  8.878465802180866    7.01221
 -3.782958745504774  0.449533410447322  5.226862248265900 -0.635875563698145 -3.119669789539815  8.714936827020146    7.20900
  4.665445840786881  2.177001186717132 -0.630149091583280  5.132185400080719  1.999694987214983  6.165760182271049    7.56577
 -4.916693672475831 -3.479131761442928  2.109748865333622 -4.046782523665232  1.352437324620750  5.156311203847886    7.67690
 -1.891121385934186 -5.675554677893953  4.444931126269748  1.826247248310511 -1.514237962150113  5.210304378624637    7.82137
 -5.595326825243171  0.866596567346940 -5.335706385787419  0.958562260541780 -1.486663537706684  4.714249054203063    7.97856
 -6.239874565036247 -2.060453401373157 -0.206253399496034  3.952116158838522 -2.197979503351574  4.589148584517468    7.97962
  0.111830546753055 -0.208105372269250 -5.478960673786349  3.162399561943994 -4.945307893728766  4.713327226610805    8.03316
 -4.748906212296611  0.426208181098297 -2.529073243149676 -5.408739205446032  2.766979970157065  3.623166013253526    8.12654
  5.996993186154720 -0.570278391130671 -0.859646782143904  2.923701042443383 -4.688892561196374  4.184491278710357    8.21960
 -1.765404209404980  4.992230477084066 -4.278846482141041 -4.103859964010148 -2.203985145363557  4.238982360538340    8.24905
 -2.041884355681607 -1.205637465185744  1.002487305119945  2.763653128369354 -7.380305161845406  3.897381839912563    8.29063
 -2.511267304851641 -4.076732655483032 -5.964764634997749 -3.161588883689853 -0.636093889710665  3.806603356566087    8.30090
  1.389073091394764 -5.909731974747973 -0.919933047910408 -0.429062570363222 -5.837580257408812  3.448948027140769    8.48305
 -0.908603421848359 -0.831346518637101  2.318206352569339  7.160175964200642  4.271377729745380  2.821141972110164    8.74091
 -2.970790863118217  2.866355818091761  4.761509411329852 -3.774964466482944  4.754506040544166  3.202362238088846    8.75039
  8.839385482712961  0.836368156583080  2.057543881903361 -0.409949986949875  0.213190201610154  2.244860716845901    9.12586
 -4.167367627512114  1.635644335596101 -3.948803971490583  5.293099312230776  4.577441129898845  1.961901753404385    9.19811
 -0.983702571281742  2.652299094166853  8.391930259004932  1.799276476509075  1.809781501308432  1.953592565644810    9.21627
 -2.052607553022388  3.075794621969075  1.491913738579726 -8.229495537801228 -1.335307542383567  2.041047832061989    9.24160
  6.463775589319365 -1.768898350214052  0.288093610290837 -5.056945637666272 -3.976691464936229  2.046798377054048    9.29404
  0.023556657645165 -4.355456139221060  6.648807763231039  0.383248277919397  5.174550026986223  1.823455850072248    9.49210
  4.491629410955860 -1.700265818300714  3.279177439730636 -6.441223693601344  4.141666940456202  1.889552670428316    9.61569
  3.661125792808315 -1.601357366266777  6.379917226959227  1.784420146493035 -5.891622520109935  1.774277886199969    9.72455
  0.752259350547534 -8.902211443355602 -0.418629399512361 -3.595483000412977  1.576431745575321  1.746199826156483    9.76745
  1.774965470394492  0.104916403193600 -5.646460649511573 -4.185727754079243 -6.548518849841303  1.667526134408839    9.76972
  3.964744102789208 -6.751822872278440  0.813345093634655  5.786319971118582 -1.417527721640434  1.547308276834364    9.87212
 -2.466017653332085 -7.811877932142302 -0.019626251486602  3.846346026088772  4.521382431023695  1.343014023010701   10.11654
  0.238288553139191  9.659306581421671 -2.636025537660576 -0.296736104126119  1.480499733258955  1.126868345514505   10.12855
 -0.716101046163137  6.875791977193795  3.424792683967967  4.421881442756130  5.019400232603449  1.273742665918626   10.21107
  5.210070904809910  7.217120798552990  3.561846059374419  2.975878093279640 -1.951363222875892  1.142494577432294   10.22654
  5.733371076480946 -5.036394509504468 -6.605087092598254 -1.106918481230787 -1.451207490491134  1.259545773504611   10.25647
 -4.299060234349412  5.758493965924544 -1.607535780354528  1.656828357700346 -7.128438430681241  1.199766425743439   10.38201
 -2.767341834978319  8.739194849066877  4.270623533134350 -2.298319854097816 -2.055269412622323  1.162896385542825   10.57243
 -7.924015590468083 -3.639906178164611 -3.672620510401475  0.310106813959209  5.092258518146467  0.967176712620779   10.74962
  7.567457292403066  0.249077530881837 -3.731789903983090 -2.130298330391536  6.516788811097264  0.899713123743860   10.87481
 -7.422314161808862  6.614569410390121 -0.825978145002857 -0.377465171370057  4.918001261054311  0.736970589056239   11.12900
 -2.223048780673501 -8.031710296791566 -5.661144293634497  3.886388145234154 -2.715483196348651  0.766889645785877   11.13448
  0.218480047167261  2.091202974892896 -11.078890837002726 -0.038436612008807  0.752255757250154  0.710556815442797   11.30177
  4.263873101684460  3.351611439571708  9.081990819283106 -4.211459803457225 -1.683935783571449  0.713604978583154   11.50950
  5.382755464605619 -4.832076557208274  0.618972184915897  4.475975939617205  7.900133754396207  0.548784440043294   11.62552
 -10.919074346162011  2.868663781964341  1.068485144413439 -3.430185476258026 -2.049911458161924  0.511750022496494   12.02353
 -1.713742844180935 -4.051536245211686  9.141192398298982 -6.628761970371828  0.405820064897210  0.403191930860625   12.12512
  6.579439269739275  6.384999470159151 -0.818237333779406 -7.791600128185736 -2.051734536924915  0.443790808056153   12.23296
 -8.521291480799258  6.136695198877183  2.821526819505626  7.662555868721208 -1.466303262510548  0.280970537435033   13.38272
  6.990076973930474 -2.017261155923851 -7.989058234922688  8.159424361794345  0.811932894896182  0.224706088801604   13.56433
 -3.494968011839038 -2.071151138729987 -5.007204806025496 11.987368419597265 -0.617010569151547  0.187328387051263   13.62550
  5.286087256227751  9.077891382027373 -4.934371795925142  2.773231265357128 -7.242522069334232  0.182057554447929   13.95865
  1.391988112755550  7.535394262774941 -1.406311183318003 -8.802845405834498  8.622541624919734  0.164679068674297   14.57861
 -0.864821632253310 -6.470116322936174 -1.172573636094449 -13.597953593362224 -3.240259580116879  0.109389231898664   15.47220
 -1.061574018088747  2.409170763277175  5.780106211305537 -9.076574384171002 -12.537802444332339  0.062461989503397   16.73085
 -11.367958991205512 -11.505052158624995  0.471704891998992 -1.998308451894194 -5.200102953356290  0.059700827399468   17.11296
  8.332368914837444  3.785687743643487  8.903329039869233  0.090231290531462 12.148257672878998  0.057224072987481   17.62434
 10.073416394953012 -0.815104870108823 11.173868503591057 11.393912942325564  1.977267019092837  0.033764650007124   18.99274
 11.556177898411073 -13.313151556926174 11.761356550830568 -2.659314799274108 -0.326148490749998  0.016667043735063   21.36102
  1.450661981710747 -9.444240585118187 -12.954765169501304 -4.871749382517416 13.728028631944278  0.016340680985101   21.70983
 -5.435495587620785 -4.320794171712275 14.316629556902699 14.390082756519305 -3.390567483372345  0.014797948498411   21.71981
 -7.346722910152848  0.350955809592479  1.865631902070385  1.355260930527904 23.889121406199219  0.006478695577358   25.10189
  6.325322351009254 12.947406773972277 -12.411633207334152  7.871196325402711 17.126086496215166  0.004220726865101   26.77596
  5.577453194220465  6.393746068094476  0.260149962892733 23.492995250963887 -15.327673428577686  0.002453761268436   29.30724
 -24.668857288977343 -5.301422709854606 16.753471446626563  3.343272565644968  8.857872994337164  0.001284855744615   31.73288
>> # evaluating formula 1 with 80 points
# refir5_80_6Sa.txt:5 formula 1   : problem  S, 5_80_6  (d=5 n=80 o=6 plus 0/330 of order 7) quality NO (5 negative weights, stability factor 1.048493)

# S 5 dimensions, 80 point rule of degree 6
#  numerically refined to high precision by refir5_80_6Sa.mac, error=5.103203814961955E-202 
#                                       x1                                       x2                                       x3                                       x4                                       x5                                   Weight        Radius
         0.4670601531231115427307806728576        0.0000000000000000000000000000000        0.0000000000000000000000000000000        0.0000000000000000000000000000000        0.0000000000000000000000000000000       0.28183981440556646322562974185308   0.467060153
        -0.3101393512078312623075100037783        0.5863029021020235441821951413953        0.0000000000000000000000000000000        0.0000000000000000000000000000000        0.0000000000000000000000000000000       0.14547485826232638588863529568104   0.663277853
        -0.1650383816057912417670417352381        0.3987138535269369817804711705136        0.5685591071355541370773434126845        0.0000000000000000000000000000000        0.0000000000000000000000000000000       0.13546967321248394709886348161162   0.713771576
        -0.3330483319538938392196129271835       -0.3077973340280823350152060984064       -0.3356105050534958983600833535538        0.4663232471592134374770850842483        0.0000000000000000000000000000000       0.17519911925037667002438428132714   0.731950936
        -0.2833050840121726146623467752480        0.0473771425493268260923761136436       -0.0313670880663095841556114570300       -0.6202352772174618115895320978121        0.3091312377524445556872542788526       0.16617411789675026705987758502684   0.750828995
        -0.5073805086678310862777992623208       -0.2669961636850106266952177273427        0.3876177372180190133690959273148        0.1070687817749318336708612623410       -0.3006261479376651856978297482301       0.14050346437111696989271139042982   0.762108422
        -0.0161705252371746337722961972010       -0.1397611039416312748551343574017        0.0498049785516937940753682269953       -0.0479361942939875809209686653546        0.7595400979096499760441021336200       0.11637463655038680094435260845517   0.775547695
         0.1481685689424835426374953502881       -0.3052520351907831730464920151077       -0.5075756115419439688576564868120       -0.4525417548547509767290502472860       -0.1761316337348433155478688201407       0.12202405194849235123504633632413   0.780116737
         0.2148209353730409920176603691386       -0.5713332642104256269265979930718        0.4668449728455803338565498281679       -0.1169112298471880253757277351210        0.0933010962057996224155830628235        0.1085278769637002758370227392447   0.782871185
         0.2793374987755835774525213589324       -0.5534282471752396023547893734392       -0.2351841422938364590343825326275        0.2678993441329827697539998856951        0.3270805404197611057064370660010       0.12141773250017882331035371989461   0.786368605
         0.2362167936160312786001124943245        0.1425581560726594951770867932458        0.0047050315418725115387056281582       -0.6201114333900916637110778686548       -0.4181984338219835653767268873247       0.10416779622605916969591492246315   0.797227357
        -0.0415031416397251392583571942554       -0.0889611515440849408386837423373       -0.6653413389876610487748224599955       -0.1098144668941038727023994689417        0.4306017402329549149400320473179       0.12904144195573915871209281990929   0.806097246
        -0.0366002318152270751268865823874       -0.0774379364374370908401450207170       -0.0256621807141937158710763998368        0.4229193025025781629602678171687       -0.6868268861227659603907509684927       0.10790581543070911814491380606268   0.811533528
        -0.3608885184835025297873973338386       -0.1180772881421435268592526066579       -0.1202057841505136429184019411116       -0.2893238450189868144264281991741       -0.6478881147604855828379247035190       0.12211904204120485386712543075796   0.813694965
         0.4866699331116869708569475533385       -0.1684676082440502261773915909336       -0.4222725414935862118307454802999        0.0704057031902580756610195512918       -0.4624798193950377815500790933161      0.075275350707893853003455555862381   0.813871983
         0.1264550004283100414023389399074       -0.2806084271357796725008037547710        0.4447928251557319010270048382110        0.5051004792293347786646497924417       -0.3477802843435244918239755028977       0.09703603644253702916789365395006   0.817710361
        -0.5859239557541538332088088788323       -0.0901341314733176645400066110636        0.3456109395878292513417153660492        0.2607108199145690513689157632544        0.3625567241265268647286081519878       0.10789130737160243130216924005211   0.818715747
         0.0146239832423966493901872999264        0.0019162603350368718896100045153        0.5737571691449318136586008560690       -0.5591570101767490652700396600735       -0.1685442207089417316940565046488        0.1196325514627657324860187542786   0.818827539
         0.0260269220252893724298240669282       -0.6236122988736170104649886685270       -0.0305780585678972944058816957452        0.0875234219148845580463246252656       -0.5279173268491148279147677694149      0.095526072809944637395710654353844   0.822716094
        -0.7062147266307512696594032800454        0.2472078761095036797283679716587       -0.2859827816370425867103237423676        0.0273634313275583382803016419980       -0.2217914983954007650923489995455       0.10055310420232325658803029514451   0.831611298
         0.3882548245796715150048094132321       -0.5667344400429707060672235244934        0.0546138556359012955973026251667       -0.3738671588991566387872704797347       -0.2838599816767797327839903934499      0.092004741952508584063217526729972   0.833825851
        -0.0153053507447669486562691164561       -0.6292301965091395419618218461371       -0.1656867232201919901958436673845       -0.3666840788005209598575153898273        0.3740991085625045732736815186590       0.10847439053115305740820616491626   0.835478510
         0.0938223006484205992577847777528        0.2137351961477354554768007905097       -0.3024168703716073675900911704688        0.7145879720100908320495150454353       -0.2260651171203243993894565022615       0.10383093308244012809928340311333   0.841238806
         0.1186630790615916705026628245112        0.4641905460348672989271302916863       -0.1530832212431279669778791253540       -0.0141547878464714423878337055367        0.6766530069161960503299893033202      0.093687258437440298883960407302481   0.843236569
         0.3811043844413522785243731699003        0.1090149286979169689219949896513       -0.6985119522013259413436723535213        0.2500421564833484673189941966767        0.0851462030649959691788530883977      0.082732794130969722267211882115988   0.845467155
        -0.7077070189719911962787782998044       -0.3792022777120437348041569188981       -0.1649689264426748622048709382221       -0.1751907082020041969190758893788        0.1231883222034468728364492210854      0.094552323185691308343790584504527   0.847186807
         0.2515564792970735508566508053013        0.3950400258754939164334048875448       -0.5546469095767809731040167179344       -0.3382298184834651452409518570553       -0.2931267539760101169231697590594      0.090323128544213037759615673706756   0.852814858
         0.3631690367933355321328432086256        0.6835196278777523571107835776152        0.2242939515221321132905742515314       -0.1856425318263387024784275712910       -0.2459026626094889536836558726346      0.085517688823492354845066916466335   0.862745546
        -0.1721378943689267262727671230289       -0.0749990352067214622812495027781       -0.7087787143307946330451395482827        0.1497145413716946638079110386449       -0.4446457945706593642149238042277      0.081878246526250431439208426332303   0.870487164
        -0.0479215517753903883135031396746        0.1778199078214298181693231820382        0.5669592114960893395356980323360       -0.2984855554884933689819903368777        0.5604238210621204374424126305280      0.075655516764927276682880194152962   0.870934916
         0.6252131145748509377953161466471        0.1429746070732047339411448874101        0.0762015950616634045159713375097        0.5641347731932530075838368598998        0.1601065416990512728123445511692      0.080088010830423897136042354048162   0.872365753
         0.2917457687532447440949466122314       -0.2908909230291617945614830607010        0.4851473199972180236426259951381        0.3063842340459712735563775248256        0.5193386363701820390304108256991      0.087180852325055923469337433084766   0.876746807
        -0.0471265283083457578207691941716        0.4060945965322997093803067953022        0.3731010974349730175225858306902        0.4942132768267164022473495171597        0.4766365564554102051262924649583      0.078378915407511188333591465862993   0.881911180
         0.2552206930284519444749884040943        0.5077975060076909147038243274719        0.1333342251814925442668489071758       -0.6046052064779553703213349117486        0.2712179568324041263285802054907       0.06990517472598214567229354983684   0.883108465
        -0.0926055603241991845225933990423       -0.2134353593301418713975986830535        0.2222156945199558535306417539951        0.8173212752035080409211272416811        0.1320824271165382065507075052780      0.076839906210676081666454859772214   0.888239884
        -0.1713420641514123108859871479867        0.6161005802793334390420387899006       -0.4613485693801822995598432222210       -0.3535217602307545483653253719173        0.2322206177112280402159041342565      0.064548156175310076426021727154731   0.894809801
        -0.3954002713125598065741935562032        0.2770548848266460884576826389370       -0.3117842779835095841886618265133        0.5687616575567314240134674223788        0.3962145691227004882548102407859      0.062286141007279472765256412989369   0.900436576
        -0.2094931294773870552113780835776        0.3235957156986641493329300338621        0.4636991949276241337814936014368       -0.0377328071855756107564457707936       -0.6725743342375308520353889268733      0.071052019213091684570185014420554   0.904100936
         0.5227788773007879256984220520864        0.0179845353904322220230575399134        0.7290907396551336775908324263663       -0.0560339303453950811307889835643       -0.1270747195402398690246429502079      0.070595473570098101906027540609256   0.908010072
         0.5744624402665781764077055331342        0.5790233680438232855938176739732       -0.3582044980385426120434098857611        0.0719724884656907889197624547902        0.1609447970498953500348738849888      0.054982715560627808225712693622879   0.908112815
        -0.3665085250330656260209300469634       -0.5746398389702189207257013172308        0.1391928569545849739737540653106       -0.5070301533599737373919827882425       -0.2928582793009554834758279020427      0.057278715043320074773595125899332   0.909263242
        -0.1047624360347649066574626052251        0.5857149131203568505649497841886       -0.2520646382920960090529361129432        0.1115486934747875082263958540067       -0.6331749693998986334018304802063      0.069729992248688692112401029694928   0.911552172
         0.2264418095489142862033287856913        0.4314337290486066280509440523958        0.4772435771872013495819466543284        0.5346914903030369564094595397024       -0.2916380131800366898262931146158      0.066013527811225864810068278240538   0.914396035
         0.0604416749152099850522701249671        0.8188303317749598318020377960737       -0.1096940616664601299801340120954        0.3871174607565742377503619233272        0.0642947125188642457346532054515      0.058654866905627347816856545583272   0.916603968
        -0.6358447601179394177144364686460        0.0267865332694424370649221648774       -0.4806941666824485507757334432818        0.0323241307126361777971472683347        0.4610272005531531577677709851220      0.036521751745297635986546873731156   0.921777570
         0.2472141739165663382257035859357        0.0070632198118480271457174141235       -0.3269374292799539950942968617367        0.5655207910060077382374093013354        0.6269554883788424331791450773454      0.054729290698440021106373890098854   0.938583917
        -0.2487894404807480494221750818267       -0.8264859175475468690795783195977        0.2512350015027970180343977220464        0.2938840568735940248387867913803        0.0527855127620380061223985170252      0.053811752694680571423084753216048   0.947231932
        -0.3413323169958604186202661961062       -0.4520656577654319922149292287954        0.5557115328647861294236831502546       -0.3674568826495726105440738067319        0.3805799933355412061406937745231      0.050259641121639522021420619067229   0.953704414
         0.5691909576927268028952067170228        0.4760514100442062527672023517904        0.4703883533079751484517161391933        0.0115553144105878063446167012432        0.3990255240755405792884852484172       0.04513121855051865790181736828554   0.964999165
        -0.5975987103216419358840722274190        0.3765045983040355715586178739026        0.2277064226614925484762852719654        0.5734496933149471232864944885947       -0.2371570553320293906600772932500      0.056082554978142683430348023621106   0.967376951
         0.7456611830998765151750097424092       -0.4303418669664008579913490071170        0.2081783496718782634252782258412        0.3411517860754548879516181981060       -0.1891126420800594057265499705446      0.041928700634537394144411319262252   0.967828022
        -0.6501718913985109278188112363867        0.4321039221882763749121806180523        0.0704092788483336609988418892514       -0.0851049473468541135860717239532        0.5620764681962956367796895487114      0.042647865613547628771242304754463   0.968280725
        -0.3412729083072302924418792036846        0.5443483852509332440206585941357       -0.0122924330912166690108586425334       -0.6459858774733294590821699018723       -0.3555057035367165086564872381353      0.041566687227857875727478507359226   0.978067240
        -0.4490240593096589506834403520192        0.0072416468682887344951315747558       -0.6539171594504266659622021832403       -0.5798746966020824884910364465846       -0.1098642681513209758457548746030      0.039940476563235303825782277801483   0.988740370
         0.7208659536596614766023917180049        0.3268212159841936859633607761967       -0.1320538412513036366799516732325        0.2441095343864635935195705955992       -0.6006138901515282417293413173891      0.034804689826399714137974778384514   1.031612600
        -0.8069288581945053875567326088449        0.1978550539743049058981371163334        0.4268747351015566894777047594155       -0.4371694644729841712485571332763       -0.0895145697760147219358696034332         0.036488356036057504825188841408   1.035197007
        -0.2805270190591886763506505337809        0.4930407545463936599280208391034       -0.8220734608415654126489184778942        0.2788848222384947194882459736611        0.0234615287219081876658160027394      0.026127013600174656631423759817624   1.037263976
        -0.1975403421745421855600681726194       -0.0639590389914603896442375813993        0.9923787435677150104866438104356        0.2618971303546645979654672769723        0.0513951935976030939251191769854      0.029631718312668532933855193862191   1.048408360
         0.5787569765102754220245412254539        0.0369007310823766778506068167735        0.2680179999260105222427459003407       -0.1518804878022572480289133674892       -0.8648527936616766774281197263786      0.039677213728729250701466963560082   1.085906528
         0.5668746661456472815914150205422        0.0611130163446552454165743622880       -0.4314979632007994944707491977688       -0.7108730604734245885785323028084        0.4455089895850933241867476008621      0.031970202164824570215061910238654   1.102311638
        -0.4385472396845102688539746858182       -0.5345074822173300284919286064495       -0.0780545667604693828571099768594        0.3566087340559565502000818760006        0.7919216652833235198353603108829      0.018998485793513025246996489750268   1.112845074
         0.6841499952730970735505684084355       -0.2278001097097101316206893282867        0.2575776593314264482915969488133       -0.7019300584578954582590296271452        0.4610158426334543922965307216028      0.034315717705729723710921325099839   1.136460193
        -0.0604506350635266678151294303840       -0.3187612265688712601703359753334       -0.0326184797206917898448484106887       -1.0833857129428643467479817032906       -0.1170838863882520591277190849873      0.013036583052618503987584271994824   1.137435802
         0.7586705662033146643961436519165       -0.6116047167543424159728232397549       -0.6782907459569692224838381554920        0.0051476614843751338457322968566        0.0093115447962507162434474028019      0.013953679135243912314112761341634   1.187363844
         0.9511331924651823505924597877884       -0.0971161654666136609825300309190       -0.1006202570056824788942436571179       -0.3206590126603577736595220279070        0.6563541752697346634652582187338      0.032601398373968436644494554703783   1.207407695
         0.0400052279654858606652646422704       -0.4424795291866488870970147699813        0.9307721190393989996905409859364       -0.2160912500552053380041238195681       -0.7329649525812506612870304541667      0.010052478728305538889795653510283   1.283611444
         1.1890836595286389308079676170083        0.0212149565161165306689740801635       -0.0466229757249667368540076721515       -0.6581012408759631860113126265545        0.2555075751584612734070949134410      0.032542274514208597667144284414131   1.383808184
         1.2237572327517001725859941597512       -0.0264957430306592050730743704805       -0.0535177073899132351383810631771       -0.7318470019544995627489690820836        0.4943380468926807328485053440355     -0.027827665178821737675155302851781   1.510337073
         0.4692036253714152025761792523618       -0.1121841628753415739975160520965       -0.4672935667769310973749298539661       -0.4067122166445273874755539512082       -1.4627458556201812756369764561751     0.0017737326979353353694061937983302   1.660162905
        -0.5158065097064187922923460651307        1.3709246838615049761196614131169        0.7259544688929678887308349113523       -0.4355926328591119221352322367110        0.2509609336339278420536049333745      0.001896940011270323894643500168255   1.710328351
         0.7492663537090621448906959038622       -1.0696196096740826276589778872924       -0.6421832758232579102178329159228        0.9035918190662309189107662619005       -0.2414718371843192754509994291508     0.0093118937308745478262978545566385   1.729934207
        -1.2297475994822069238817281675529       -0.4228110990940673549667563395762       -0.1521701735658676089543834197846        0.8499124805143366302276612158492       -0.7877284363854979630422600046918     0.0018507469593040016537290165769053   1.748448301
        -0.5156260788420730184322525673187       -1.1876408693103168932820212650347       -1.2064362006728037427432764295674        0.3571377030315719585309140557743       -0.0914346372453184276710799114848      0.071681927736187081953831047895538   1.807693842
        -0.6639529307310720065260426414409       -0.1259174043464032334171469431907       -0.3807542851347963123950437732993       -0.7768525647865198405495140197771        1.5416874703735244916609616575354    0.00059833539833730218701562163654856   1.892607375
         1.0482156518679067690828296399249        0.1779801180344446578568868895676        0.1404680092775332127050149265151       -0.1479248047700812160758035295745       -1.5837299203359312953338802605516    -0.0011805975357318528829816714377629   1.918396842
        -0.5649128276472480230739409749002       -1.2731922622287956827521949709377       -1.3640052499511121951955074260417        0.4448841252429677679865365421634       -0.0533878563030721850161104965886     -0.096107413641913082669570405351248   2.000356846
        -0.5975523377741381415366943076859       -1.3291109157554066517102728655032       -1.4790344023032560553757588657180        0.5077986525973822151639835260012       -0.0198989728156752024655661036264      0.038880671588860086815229560028056   2.137616155
         1.0305765829529541517079910981771       -1.4294713006467563682957613617580       -0.8152427451253943607550878789949        1.0138474171036607700206700149709       -0.2327182916281795806611828192162    -0.0023262239313671102859518631513649   2.202757684
         1.2327598871994371193237751999886       -1.8230851232475369614938222851615       -0.1531902404726503466596373511996        0.3639992790971912647102528281236        0.2491075695193752473237301120658    0.00025743764371628698756681154133618   2.249745233
         0.5313267063502566532965962530670       -0.1354401506077792494824750299250        1.9640570360244080887893852832004       -0.5067987009014983677056515032447       -1.0062797413470353759357794220204   -0.00018587539082656873665401071950704   2.329724444

>> # evaluating formula 1 with 220 points
# r5_220_8Sda.txt:3 formula 1   : problem  S, 5_220_8  (d=5 n=220 o=8 plus 11/715 of order 9) quality NO (13 negative weights, stability factor 2.214220)
S 5 dimensions, degree 8, asymmetric 220 point rule with points at 220 distinct radii (13 negative weights, stability factor 2.214220)
#                 x1                  x2                  x3                  x4                  x5              Weight     Radius
   0.424709337139729   0.000000000000000  -0.000000000000000  -0.000000000000000  -0.000000000000000   0.066632293245791    0.42471
  -0.179602664811563   0.423546954390886  -0.000000000000000  -0.000000000000000   0.000000000000000   0.076045303031258    0.46005
  -0.389080159352350  -0.113115334455742   0.333335442603262   0.000000000000000   0.000000000000000   0.076407358312117    0.52468
   0.149267348928262  -0.090562631137352  -0.356655613622879   0.355683039845142  -0.000000000000000   0.051323648439411    0.53310
   0.143339939545780  -0.283551141826109   0.025787031416878  -0.426344093788878   0.106098494929735   0.068758253341813    0.54281
  -0.326948374379421   0.069951211512709  -0.297261689312249  -0.029945842398733   0.338172362386769   0.053218938801043    0.56161
  -0.153512926953273   0.207782967421392  -0.188604926601996  -0.511159685935165   0.003466814032437   0.063165028172912    0.60300
  -0.079031513220402  -0.087252282928715   0.300522195482943  -0.342641541500279  -0.381712571734972   0.052475740019112    0.60604
   0.146925616004060   0.372355828832397  -0.032168207345689   0.441341532388064   0.214221782639813   0.054474981262796    0.63399
   0.147683264151571  -0.177993504406982   0.178216904538342   0.177693862565651   0.544848506586906   0.403794768592216    0.64319
  -0.320259899995798  -0.466885474446918  -0.085192628459783  -0.069907800979724   0.289471920329250   0.043351107892141    0.64536
  -0.264945866774720  -0.435810149584660   0.301235317819167   0.225275893741126   0.142654732239551   0.020019943510166    0.64959
   0.204765839633637  -0.127176575524276  -0.423549580285217  -0.010485352717461  -0.442637325095603   0.043053185348727    0.65843
   0.453108949989801   0.325676703250001   0.134006751517149  -0.283559647056547  -0.176335398762361   0.062069781874076    0.66395
   0.164499830724635  -0.160280422598887   0.217989980457734   0.165363690444003   0.576744282732602  -0.390529131922192    0.67842
  -0.021423692676284  -0.316519105892274  -0.530083390733486  -0.261989652112511   0.111894472542094   0.045581659767052    0.68029
  -0.108437560740896  -0.074898910492714   0.293155860331636   0.596895108819218  -0.085660809844632   0.046440829856414    0.68332
   0.286283674904183  -0.238222245155831   0.558684891075641   0.136649663203639  -0.103852593298621   0.058965714284565    0.69303
   0.182474551627158   0.196734792263098  -0.527498151517218  -0.298410087790985   0.220902842387003   0.041736554642140    0.69864
   0.104423903796133   0.132391666266882   0.046160206631183   0.343965271009719  -0.586868748995538   0.052934841343801    0.70235
   0.106666142242564   0.407566875421261   0.517229358547742   0.244596740151773  -0.000207827118325   0.043581309966982    0.71052
  -0.406100643195835  -0.206408753774013  -0.336060937651363   0.001542239316063  -0.442584447332080   0.066866209135514    0.71857
  -0.478440260498688   0.102880890452757  -0.160213440127580   0.501585500995922  -0.036428113510050   0.049196633207049    0.71977
   0.151256415371961   0.111743598799162   0.386102457524406  -0.176761093859485   0.551000096629827   0.062782436450440    0.72061
   0.112054192201668  -0.490161609289480  -0.000312280636933   0.124987377240387  -0.518664016566233   0.060073087125435    0.73311
  -0.044723358349940   0.277094325054455   0.473656680125192  -0.462534790655492  -0.182252815526350   0.035835535188644    0.74181
  -0.189070873005294   0.208258821346468   0.497486903527928   0.197443227828985  -0.465061348867197   0.048072193313056    0.76281
   0.360767688041254   0.536733581716572  -0.408408526177438   0.091239940451339  -0.081622878242787   0.040662560129492    0.77461
  -0.109489984331394  -0.643098720374263  -0.301723812775547   0.301363114926321  -0.064777881158314   0.043849572911296    0.78206
   0.545746211792818   0.024888487492342   0.306058164128492   0.483504579369102  -0.026935540332192   0.041280251259281    0.79160
  -0.424491975024551   0.369664107705973  -0.312491436043446  -0.210718761344804  -0.418557999266294   0.030028380852705    0.79630
   0.506358436930501  -0.122512488820229  -0.209130631906886  -0.323539884012176   0.480128566044264  -0.414916389447694    0.80644
   0.546071155810570  -0.116088524835989  -0.236572882005437  -0.260387561722345   0.471551019573087   0.317911200135910    0.81105
   0.374717108302881  -0.041535226688589  -0.143265873078519  -0.439933407983512   0.551674309706732   0.150771630171001    0.81274
   0.584833729070175  -0.475480592838733  -0.015206307164539  -0.246441429992954   0.216177293732204   0.041660986363060    0.82208
  -0.494411208500771   0.039561344122619  -0.151766933624276   0.410625550996371   0.491003149053207   0.034924184449258    0.82386
   0.043211962844791   0.659589010994899  -0.098279581989038  -0.202809269729499  -0.448593798266904   0.040253504987021    0.83003
  -0.563008241399497  -0.258162857419151   0.201140777787861  -0.511324059417468   0.094209797949338   0.039351131679846    0.83331
   0.028208902906371  -0.753132720318884   0.311683373276058  -0.178647936896534  -0.029124090682488   0.041382875963094    0.83541
  -0.142427095737147   0.539516302776855  -0.436869522408557   0.351129899276912  -0.303366119406629   0.032300209631086    0.84708
  -0.624227768238716   0.277573215212885   0.167159592353385  -0.333560710092037  -0.353885627772643   0.035103498653048    0.85507
  -0.327338431733395   0.373689798803085   0.335580893238924  -0.421596877981858   0.441221445813921   0.036425882031561    0.85547
  -0.188541951571687   0.268302788663801  -0.404580347896661   0.136210701439261  -0.667381440966462   0.028427389724643    0.85742
  -0.790668279720130   0.258507520722450  -0.106413760334426  -0.090802936140064   0.156963892184952   0.038585525008691    0.85801
   0.084024819052549   0.256973496806485  -0.580200362029306   0.154145778131066   0.550226330700504   0.043997698057677    0.85804
   0.369265097435622   0.025788105195462   0.262606599743399   0.304709725539496   0.661966151727956   0.046402887617892    0.85851
   0.027366216732922  -0.399903224329064  -0.278742868655146  -0.510811602686049  -0.487584494427001   0.038478377327412    0.85851
  -0.212343802333297   0.217285952773941  -0.795037683531710   0.089185555032214  -0.071195162908028   0.040743598415303    0.85873
   0.039045298259839  -0.067242315563938   0.533488943818613   0.207324435992440   0.641628084278976   0.037488769551142    0.86332
   0.005800449559460  -0.186083942815653  -0.701331139707891   0.429582722396028  -0.192353925822048   0.031711750387759    0.86491
   0.371641233634004   0.593486845548834  -0.104573630163191  -0.164519389263744   0.474179545852683   0.032853275079990    0.86787
  -0.078725474850981  -0.403238517992811  -0.434190771908513   0.384944675913707   0.499770744302496   0.034840984121345    0.86906
  -0.048629780673197  -0.680656948203214   0.242071407313285   0.470978642790527  -0.104246229384555   0.029369988210444    0.87003
  -0.011942034189619  -0.081676547334362  -0.317615006172404   0.623553343926773  -0.510823401687283   0.029709935159740    0.87032
  -0.471035489363432  -0.608803277573229   0.097466112906120  -0.015874460077727  -0.396764925857590   0.031258052052447    0.87160
   0.430230378689570   0.296677857544001  -0.253860099040661   0.110161540788229  -0.647182419559218   0.024797796404271    0.87667
   0.353661800054393  -0.340802843584467   0.541191729465638  -0.363281058010049  -0.323761049473359   0.034802006055455    0.87801
  -0.234417941007484  -0.043233314778793   0.392925859760021   0.650604160448635   0.375627263715379   0.024271882594036    0.88068
  -0.466408336107169   0.274910390124763   0.398212956831149   0.221677831782225   0.526243998619809   0.038589735778033    0.88191
   0.392033386799114   0.159173238982368  -0.332875012290262  -0.627221358283193  -0.314584095853504   0.034213125775554    0.88442
  -0.250636135030336  -0.298375671909298   0.751760504641776  -0.254602664576690  -0.039944142096877   0.028478915518902    0.88510
   0.671067206574984   0.003908814496650  -0.434621475696376   0.354906523530794   0.141853141669831   0.025239647254402    0.88618
  -0.282663732376979  -0.118813150528308   0.137400340736480  -0.067634041028842  -0.819038999798969   0.035340296020957    0.88786
  -0.079043712443708  -0.094976478042153   0.065722262648696   0.032810485601489   0.876299764977106   0.032284025998646    0.88801
  -0.633014306590324  -0.285908161114349  -0.498063127277829   0.231741063634314   0.078302232251276   0.027796316904760    0.88902
  -0.662816050102449   0.318221850930054   0.374982456720126   0.321269792527308  -0.089117351540846   0.033391583005426    0.89015
   0.557252256832361  -0.224610479141458  -0.054316652063124  -0.169650546077370  -0.632467870149676   0.033312322766633    0.89035
   0.205076117230743   0.560337795670047   0.408533971361849  -0.376186747679796   0.360972034937501   0.024770169015153    0.89149
  -0.657951560340632  -0.291937738748564   0.240556320122866   0.435325953168462  -0.172375206892062   0.027123276948141    0.89175
   0.069173096926965   0.108031198084196  -0.296652225713607  -0.314157183869512  -0.769910671084842   0.027617812926119    0.89214
   0.340306947067410  -0.433966060909049   0.200863232642475  -0.060451598365582   0.669943417807767   0.035974368642673    0.89273
   0.329081891734975  -0.443081561281243  -0.353439472564640  -0.338289600395267   0.504524998790895   0.033791816639885    0.89360
   0.145810211095895  -0.332544832759373   0.560857959777292  -0.492278118599481   0.331924969662678   0.027136724388889    0.89382
   0.016422518724447  -0.512259192441529   0.630256712724152   0.146673666945457   0.345186941339593   0.029465622405317    0.89475
  -0.058107996149532   0.470380298553503  -0.016763633683019   0.033205020554962   0.760135965871699   0.029490335310578    0.89656
  -0.116256814136874  -0.813929852822073  -0.173927969930150  -0.241354413632982  -0.198665245538657   0.015857321036510    0.89664
  -0.859665546390682  -0.244022352690544   0.001254974002344  -0.073852572286779   0.002172294015009   0.022234275336579    0.89668
   0.434139728591623  -0.020691057151999  -0.244565838107328  -0.642864939006232   0.378126725406745   0.059846156133790    0.89720
  -0.526423406579143   0.078069472544346  -0.032564875932281  -0.296484298616648   0.659729060795244   0.029676887136899    0.89857
   0.484319282137000  -0.728643531238632  -0.111175619507973   0.173320378645641  -0.020478946548718   0.453144462915097    0.89906
  -0.216510735194922  -0.339313641788736  -0.118480698934240   0.784771205622149   0.129012116096186   0.032399684689170    0.89920
   0.335759112549127  -0.074094327496932  -0.334254781419463   0.733248800606988   0.211575348446732   0.028884727807494    0.90131
  -0.107308984575914   0.390176834074642  -0.433145130844574   0.656203491165679   0.175860206822442   0.027578221857695    0.90161
   0.432218148798904   0.456414070548543   0.406126592075667   0.150418407283932  -0.480785628738435   0.028861121808206    0.90213
   0.185766594510195   0.181544494336091  -0.169171651766658  -0.645867702334306   0.548954672164048  -0.265935057652737    0.90254
   0.736442035854262  -0.148223582780580   0.217713058179560  -0.387941345295992   0.231142044519435   0.024586397001761    0.90313
   0.265258567078457   0.140332203051616   0.292970586157292  -0.272795642659855  -0.755244182311618   0.027444806570738    0.90592
   0.206082609898267   0.258819725255725   0.022028914463846  -0.761875390068651   0.361460939139892   0.051236571170938    0.90612
  -0.219540447347814  -0.073018833217117  -0.701620038890428  -0.411076105933396  -0.326028639148253   0.024896561222729    0.90613
   0.335861575708854  -0.407302321933785  -0.014802999074978   0.659880451113940  -0.327120894202788   0.028017411337808    0.90629
  -0.281015198222230   0.775504573486381   0.024181367813142  -0.279383380163664   0.256661601548016   0.025013699714604    0.90824
  -0.355867506789574   0.649418915415196   0.035044346992602   0.452430819703935   0.266488105922992   0.027960361125831    0.90847
   0.476144881323271  -0.755647772397551  -0.080896721055529   0.146956588859062  -0.032966537594073  -0.574303882061656    0.90937
  -0.332206309365518  -0.267599731959586   0.113917975789452   0.543749652499055  -0.580272929828938   0.029216651942120    0.90958
   0.135543658825852   0.218510441540779  -0.201705470031125  -0.625439718651384   0.573957730314428   0.214229053332197    0.90962
   0.265514902672259   0.630848782828565   0.087130622274139   0.530283163735797  -0.265952585644942   0.028252338903106    0.90994
   0.338356034716682   0.171359363369271  -0.732139437065961  -0.081960846258291  -0.376246236611733   0.027926873966764    0.91003
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   0.687667998929856   0.585757141235754  -0.662325493278286  -0.192154181245635   0.939480760872323   0.000211390244796    1.47452
   0.079044501765121   0.750236958963313   1.109508841629643  -0.405800530307340   1.560740628654814   0.000031807812370    2.09778
   0.591069669619606  -0.484058922444007  -1.020247767325830  -0.724343576289192  -1.508878982721470   0.000011698745801    2.10380
  -0.239646898519070  -0.836380510345436  -1.168234783951668   0.300088060041328  -1.865505415406412  -0.000024735200764    2.38577

>> # evaluating formula 1 with 224 points
# r5_224_8g.txt:3 formula 1   : problem  G, 5_224_8  (d=5 n=224 o=8 plus 0/715 of order 9) quality N (14 negative weights, stability factor 8.692041)
# evaluating formula 2 with 224 points
# r5_224_8g.txt:230 formula 2   : problem E2, 5_224_8  (d=5 n=224 o=8 plus 0/715 of order 9) quality N (14 negative weights, stability factor 8.692041)
G 5 dimensions, degree 8, asymmetric 224 point rule with points at 224 distinct radii (14 negative weights, stability factor 8.692041)
#                 x1                  x2                  x3                  x4                  x5              Weight     Radius
   0.180686774270343  -0.762062147000261  -1.090617540215284   0.000000000000000   0.000000000000000   0.051096142822476    1.34270
  -0.494796785965257  -1.251843866124186   0.000000000000000   0.000000000000000   0.000000000000000   0.030436293184533    1.34608
  -1.384266401025062   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.042873229102063    1.38427
   0.475259894702608   0.104184008093217   0.868233206294006  -1.121907299418323   0.000000000000000   0.036841224171274    1.49974
  -0.341083544337340  -0.402953104127186   1.215190325828727   0.739682065415955  -0.105761746721947   0.031723812042907    1.52109
   0.468104701509068   1.360686514413074   0.350800649706957   0.099363390536846  -0.379358884374787   0.038674999950522    1.53213
   1.380923052654808  -0.104446076721613  -0.503214452085614  -0.186422698268852   0.483711973124113   0.025766540545119    1.56199
   0.491636683249967  -0.264376107045471   0.346348784034897   0.280506407041702   1.449062837753554   0.034757499258337    1.61556
  -0.540655647143722   1.031489196730532   0.077211367146511  -0.295860055677788   1.143684827451427   0.041503620373569    1.66066
   0.552262722717516   0.235944387074488  -0.664209102586978   1.196800271423581  -0.893971923946795   0.424284373274742    1.74165
  -0.614385598626888   0.205593586755702  -0.334947477455929   0.428422046565933  -1.574193051437751   0.026322092460454    1.78705
   0.500082490494489   0.277548242908776  -0.820379281185785   1.273515941764057  -0.890011647642790  -0.657429476895399    1.84773
   1.249744747116979   0.133315330699713   1.298718792362343   0.529187198461513   0.088521521150920   0.019023745875575    1.88525
  -0.823160335996262   0.003085381563716  -0.413131481585094   1.583109916179952   0.498162089153990   0.018232394818515    1.89807
  -0.875596862077817   0.202448110877600   0.725165296831412  -1.156191509408033  -0.980175286362310   0.019002215875931    1.90553
  -0.303454249463475   1.129455333249302  -1.301259705955607  -0.531297280256977  -0.554003144399769   0.049409347157582    1.91056
   0.784103041011376   0.642843818923033  -0.765144483820279   1.176066868878789   0.814875041185555   0.019131322805284    1.91329
   0.229988812396943   0.093776147228218  -0.908080306183429  -1.397537864097209   1.014178609811199   0.017727687122520    1.96672
   0.458121818147802   0.291484351678408  -1.025159562494169   1.333046910716889  -0.906310268006903   0.263509332945165    1.98600
  -0.210143773492933   0.886313510685535  -0.497064263161604   1.728926677671196  -0.363448350861812   0.022801260873863    2.04892
  -0.398493090278890   0.896664021403443   1.519837409333020   0.803858329358975   0.623792207950905   0.014438107848010    2.07558
   0.382136646991357  -1.440650674124848   0.302389723552769  -1.449067533206997   0.230126334532255   0.013777234157061    2.11322
   1.027149055945396  -0.322811615280038  -0.320386479277184  -1.231334918308991  -1.315165995467940   0.016245371612560    2.12314
  -0.565383863265992   0.253397877787322  -0.373900129223502  -2.002422370784886  -0.159612075791109   0.010119938866172    2.13514
   0.181999387219089  -0.244134288620892   1.254487576865767  -0.194257822881901  -1.695351387866042   0.015446314270401    2.13972
   0.535615189529579  -1.284648530845771   0.272380299352017   1.573757210748519  -0.403851725065092   0.014347377541356    2.15667
  -0.000284010101009  -1.740856334743640   0.861241442640041   0.629497013732307   0.909669769541122   0.009890551055358    2.23519
   0.515300404241755  -1.555357340576190   0.327965001389293  -0.514928088239142  -1.554718555322458   0.010183040806685    2.33977
  -1.214094806211064  -1.014055234697926   0.313483298472022  -1.353223758239396   1.124520744304230   0.010778707542820    2.38671
  -1.064505183248227  -1.189732578421367  -0.051969694553563   0.534436408338065   1.704759028910345   0.007165684906132    2.39649
  -1.252545935720599  -0.087978220781238  -1.392973842003780   0.116519309662393   1.544723214544019   0.008274090044964    2.43243
  -0.289162546707975  -1.233779835169245   1.925527913118870  -0.882109948103819  -0.193178144075948   0.008039775620842    2.47567
  -0.899068855049183  -1.404453458451297  -0.590374872154517  -1.482896697773660  -0.960362921785921   0.009132384424797    2.50013
   2.357975185247168   0.315368963268612   0.392563933409539  -0.373385388828111  -0.593115884114421   0.005611901213578    2.51094
   1.611395971986149   1.251573898635002  -1.300330644844391  -0.525895937404141   0.506536227846937   0.007076183340600    2.52726
  -1.664424828763246  -0.162982846777677   1.820888619073273  -0.349926402578131   0.508657236367684   0.007212106519731    2.54827
  -1.712971146299826   1.543447734729623   0.843622197250817   0.522285175361502  -0.548477253257592   0.007441110425625    2.56940
  -0.303629315694119   0.836163037799711   1.456936255359203   1.610377678480494  -1.072884961394487   0.006574543604368    2.58039
  -0.339915996642153  -0.345068965471258  -2.150650561941295   1.041733608955129   0.926048277644257   0.005058917227820    2.60820
  -1.901420587577147   1.405844095753134  -1.132095649938450  -0.274157332701728  -0.155087548484693   0.007521170708795    2.64058
  -1.830987395769182  -0.672086071095561   0.632128213011998   1.090860929149536  -1.308437897696946   0.006679910421805    2.66567
  -1.083472316420084  -0.565901210686438  -1.899781852534898  -0.340070133853245  -1.388795085225214   0.004853423956394    2.67352
  -0.767116891569383   1.928401327609358  -1.360074582412605  -0.940682765967336  -0.448604821180162   0.651839568998387    2.69131
  -0.766143690269798   1.890749928000266  -1.400836854459378  -0.964960265878971  -0.493370224070912  -1.022882088754717    2.70163
   1.336580534676158   1.975739242819971   0.276045893877512  -0.741078809652300   1.010988068969383   0.005771895927355    2.70878
  -0.445926318313431  -1.215074751601486  -0.900598500108137  -1.048599503092847   1.951621635648305   0.003671562141485    2.71932
  -0.845859290737813   2.009762456135470  -0.366577452610651  -1.399657319403291  -0.758271034854748   0.009213406914999    2.72452
   1.454506076704699  -1.913461897616236  -1.068171966944342   0.754201690046981  -0.081421958930106   0.004045885740974    2.73740
  -0.755186317729745   1.832071178992934  -1.493531524671717  -1.011670790320211  -0.561940564696396   0.361708181461375    2.73801
   0.848087410213880   1.230899822771774   1.005405917540928  -1.674895358084055  -1.209491811334739   0.004051418391143    2.74105
   1.696363734083510   1.024472705585288  -0.575662221894031  -0.133672884125457  -1.812209242320457   0.004847100135334    2.74965
   2.340143619675583  -0.163431424272312  -0.561358427854453   1.276053888379484  -0.365190217655578   0.004794521463259    2.75314
   1.543078031182582   1.405513088702405   0.989716272615936   0.916141958446804   1.253086114774092   0.004552117810883    2.78310
  -0.653038362286221   0.881457660328250   1.413884420699786  -2.119437837749585   0.413111198564076   0.004067566071317    2.80449
   0.073323990030409  -0.409667649776419   1.823935376141081  -0.898463728387441   1.894940522008695   0.006736852072636    2.81033
  -1.528445936549808  -0.855825993554828  -1.857958924681266  -1.083612621591151   0.459389943640544   0.005164559779034    2.81173
  -0.652023068247898  -0.561362903522479   0.374792278852886   2.205853502218825   1.512150444616569   0.003674740930261    2.83428
   1.821365228573676   0.114238291728795   0.957602965834833  -1.662803140312114   1.013091647599550   0.003735981879707    2.83526
   1.223139042632645   1.200350695856447  -0.483214822396315  -2.166092149540596  -0.449021214468477   0.004158712038514    2.83972
   1.773923941955573  -2.033214194882978   0.964708338821765  -0.077258800803340  -0.195977392329917   0.028880160578302    2.87329
   1.397986248475831   1.789980546514489  -1.242869254206203   1.212962550629078  -0.299108737293609   0.003952514413289    2.87469
  -0.136473109810515   1.516951768251497  -2.038746507045472   0.255670539941865   1.338764754316946   0.003921751750996    2.88685
  -1.083948867715924   1.287630268942579   1.614550416057756  -0.246932742842152  -1.706373085227260   0.003087841358861    2.90041
   1.149505196770897   0.125477174224443   0.753225545399526   2.409951259707511   0.842639917541745   0.003652548126646    2.90213
   1.228190623913473  -1.400245464741936  -0.304281476963045  -1.081727252237434   1.945295803667318   0.003812499872634    2.91822
   1.734153369705728  -0.102202795858782  -2.157065512161721  -0.401267574213721  -0.878792481292421   0.003497982412126    2.93325
   0.765786978015594  -0.254609529597098  -2.455620246372829  -0.787114802180719   1.141926345545082   0.003030496590150    2.93341
   1.533411544165352   0.773335354523385   2.152423855514868  -0.614474842995080  -0.835719165285769   0.002498613081399    2.94250
  -0.018840829827278   1.472628812153335  -2.177027027771832  -0.664142403179327  -1.160955088649158  -0.213325424930487    2.94913
   0.598682484849583  -1.061481474490332  -1.201063217600161   2.219555242750396   0.925999698194110   0.003718223924377    2.95154
   0.009449653346152   1.481469910187249  -2.180219597217487  -0.659798630569877  -1.174610000445699   0.202594025172604    2.96028
  -0.138149196194011   0.244128116786168  -0.940249322220268  -1.817413759770282  -2.148407429311980   0.002769078841036    2.98017
   0.163473253096264  -2.269475282917816  -1.054935809232245   0.543930224371778   1.521187908773554   0.003249360331629    2.98329
  -0.598190709520466   2.552178076347084  -0.118682000567144   0.349776853727913  -1.376555371341860   0.002737472468833    2.98375
  -1.049979259607734   1.683120169331165  -1.606611714129105  -0.513478078692026  -1.487004922937533   0.005023199647613    2.99857
  -1.822720323685987   0.804800182536980  -0.882556680917014  -2.049757708794283   0.341722899702666   0.002869971736317    3.01118
   0.748761959338511   1.106464066684897  -0.840981922688075  -0.791200135461937   2.444427024112067   0.002536159321722    3.01552
   0.626879565813883  -1.721458131345825  -1.812032433138655  -0.549156358210509  -1.483008732527741   0.002641854035083    3.02337
   2.084993229247941  -0.962159817974236  -0.814253068649908  -1.791248673809408  -0.064811794755222   0.003269530126166    3.02469
  -1.922794774547336  -1.989123473099562  -1.093427661578433   0.441246304357556   0.395328464957358   0.002787364852691    3.03320
   1.775291967987786  -1.275810006912651   1.955830366598437  -0.783353533135858  -0.116883098126955   0.003137771846452    3.03841
  -1.770800149211773   0.586921482521378  -1.641163325060585   1.729865284255568  -0.258272506837954   0.291130930433000    3.03855
  -1.777205462426558   0.596334880149833  -1.628973664052985   1.738459612714239  -0.265286662577456  -0.294143182146880    3.04307
   0.708785206234917  -0.398079844834689  -1.384673679320286   0.779864015871794   2.485691829011737   0.002435692749613    3.06023
   0.627670307957517   0.358821376863362   0.315147999065782  -2.674852260443985   1.316871117120470   0.002087613326773    3.08400
  -2.077145406291913   1.303843252168644   0.810964483064180   0.841061408517945   1.463630668351408   0.001910713245755    3.08574
   1.974863984173933  -1.681559886270924   0.345781546008016   1.093018789239301   1.219775383647217   0.002475315982968    3.08704
  -0.866157329516312   2.175044803120069   1.727772236301592  -0.815539417498885   0.645923703822400   0.001885567984127    3.09008
  -0.795070798015688  -2.505960214470193   1.015987516919424  -0.547897388836379  -1.151769231664303   0.002444562104368    3.09370
  -2.283117215691956   0.348988060686329  -0.073841325686488  -1.431954566675478  -1.499918243832555   0.002404636045523    3.10485
   2.737105401499249   0.067884986434619   0.158656766906158  -0.051122068502777   1.462668838203660   0.002279302328553    3.10862
   1.603939604670141  -1.222797496118877   2.026204929590546   1.105275322124467   0.565248517846867   0.002098781925256    3.11681
  -1.761678376354443  -0.067739431749977   1.184520817901197   0.156962800220768   2.281986796330871   0.002161951738032    3.12142
  -2.497248910763810  -1.681558161790002   0.457250604873090  -0.723277582119699  -0.446101764378417   0.002185427057272    3.16150
  -1.096405434558426  -2.086072001456758  -0.899053921555301   1.498411112230066  -1.220511858922617   0.047686001475507    3.17758
   1.596622513134364  -2.415705702971721   1.260326492254200  -0.200048230867250   0.294377170405061   0.014133684775660    3.17804
   0.205653573460699  -1.086155118531557  -0.760148363351940  -2.890127517745764   0.098267877893983   0.001656482081052    3.18784
  -0.181191020452219  -1.671828704332512   1.299578372614782   1.445018031562263  -1.887011550477728   0.001766205660365    3.18836
  -1.963612156989657   0.883583309757347  -1.211487152871791   1.926696909994827  -0.665784161395215   0.007328464148531    3.20306
   1.774951059034469  -0.209110786436579   1.206281123901589   1.463956115922593  -1.871359106749576   0.002318154982665    3.20850
  -0.996186928528300   2.317970693600290  -0.421836650423823   0.299235709022737   1.926338653361697  -0.472533699102071    3.21615
  -2.255629886285119  -1.553391892429344   1.051434225543615   1.037283775060121   0.817502978655804   0.001895203684887    3.21725
   1.742106060994485  -2.377552605662339   1.281078871954665   0.014734669662109  -0.151866777070384  -0.320090368881171    3.21747
   0.351329120564395   1.734585730957464  -0.411922569307943   1.420968816837156  -2.246650353423675   0.002010542888681    3.22001
  -0.991406273463154   2.324554891159738  -0.417858117433344   0.297739765403547   1.928578062903508   0.465146661146575    3.22011
   1.335464171751596   1.555678649152464   0.675389528459832   2.288708324296360  -0.710197710660506   0.001695372482674    3.22526
  -0.814188808778838   0.591588560515896  -0.215425407112092   1.149041343284162   2.835835282632037   0.001780560346033    3.22824
   1.741063238208576  -2.392420177098154   1.293933064254288   0.029289893761139  -0.170012779391555   0.286960494837234    3.23404
  -0.336988078552788   0.522184604020932  -3.096108565583560  -0.360158643395565  -0.610031990459494   0.002730283735484    3.23635
   0.762862782035182   0.097126595117064  -0.638926977700025   2.960423762322320  -0.859392523606045   0.001890668254197    3.24072
  -1.547390918049215   1.784898347078834  -0.807863355798712  -0.088734235702920   2.080012424693963   0.004191352992400    3.25073
  -2.029672618696564   0.166504200083116   1.463185967059127   2.025287215193143   0.449125138116986   0.001215436677044    3.25449
  -1.119508237131313  -2.178293600736419  -0.831429490897845   1.670574298761657  -1.080519820268575  -0.201883614620823    3.26311
  -1.118314338117158  -2.201480512420481  -0.799514866082057   1.689836397418637  -1.039400090832811   0.156652070073387    3.26684
  -2.719370422693200   0.069292371562226  -0.650336291417402   1.570525555908769   0.679740376044641   0.001831942316226    3.27892
  -0.329467910564158  -0.521839730542161   2.356019415643655   1.484686765407972   1.618252283606869   0.001713000390230    3.27944
   0.252327907136677  -0.432640809532178  -2.263297853280482  -2.196614493118709  -0.749481116396398   0.001591217789171    3.28027
   0.554978582040818  -0.617963852117297   2.928996684986569   0.455214277799662  -1.153304872483535   0.001532579250574    3.28728
  -0.351520021804035  -0.190947922510669   0.060734062431276   2.190178143165248  -2.441624052880729   0.001551506065498    3.30486
   0.432832382282519   1.297022738521720   2.621240327967794  -1.040386777109802   1.054342697452039   0.005161243626404    3.30674
   0.200363696097522   2.833572736180071   1.623932593596354   0.484055387997549   0.025821449924656   0.001739226225159    3.30778
  -0.037545831938564   1.439705178223724   0.423985989185810  -1.191232813705343  -2.705120598079831   0.001399354437908    3.31521
  -0.132889851586102   1.389989922206899   2.835091970034064  -1.031930798837925   0.016159319805282   0.008347944592633    3.32455
   0.971673496718995   1.769346128385339   1.672046028856976   0.403960479168085  -2.022094349935730   0.001424993401363    3.33504
  -3.088206745008169  -0.002786405560338  -0.217937808004217  -0.630208209586888   1.072973662063443   0.001409368900108    3.33661
   1.303263013353871  -1.386839636092577  -0.874319434335415   0.861392781522029  -2.451271455294726   0.001724605388467    3.33721
  -1.200373785614907  -1.804931205934553  -1.115891389961693   2.093993805210771  -0.956961098363088   0.005990338962892    3.35328
  -2.826329811102149  -0.545797041340444  -1.306714232839853   0.048037792221374  -1.122437766967929   0.001393836027089    3.35495
  -1.972821593793756   2.217666480534735   0.817793073406017  -0.720069846574646   1.144905222271884   0.000904377227582    3.36276
  -0.974962732989373  -2.248892972271668   1.920179855398935   1.273278222176422  -0.275562842503634   0.001081667588749    3.37525
   2.491000085851635   2.024333892701768   0.576690415633510   0.694883625316468  -0.544127250527949   0.001163133596573    3.37854
  -1.814652300189897  -0.779519627700152   2.085913780808229  -0.643559739521439  -1.682111182996025   0.001336680387108    3.39047
   0.315816833682500   1.040327002208634   1.886824018362788   0.314081852231166   2.582641891242325   0.001809205888547    3.39276
  -1.384144318097961   0.548462897757235   0.449926857782321  -2.123611439600536   2.144815727864846   0.001234729667048    3.39545
  -1.208961418204124  -1.135364216979717  -0.022880709226136  -0.622990099648262  -2.906890759038791   0.001416418109494    3.40431
   0.143704022041809  -0.026381802221967  -2.023069707920425  -0.081492363489506  -2.738718575687440   0.001128119328166    3.40901
   0.615318635288798   0.184288665998131   0.104978176886415   0.038770729832604  -3.348412579698320   0.001007781087318    3.41130
   0.054975097732101   1.587795647171712   2.781067496897869  -1.184875932163490   0.331603706796344  -0.009376045184739    3.43109
   2.362552407006418  -1.202986332787767  -1.871387951321673   0.173178299606678   1.101261902957331   0.001196733477047    3.43128
  -0.953932921462569   2.328852278902380  -0.725619461861028   1.643458077271057   1.503984626121579   0.017164798199693    3.43846
  -2.549340342224049   0.681880074355174   1.462720658725793  -1.653875519495994   0.154871711526486   0.000959463656316    3.44426
  -1.238509114692418  -0.333309774006013   0.609829854891340   3.142237329720487  -0.378850450650717   0.000929305538250    3.46902
   1.975237219922858   0.817258955466397  -1.136665215647145   0.340555781294290   2.489553508808734   0.000621084736456    3.48932
  -1.079184833245272  -2.782785154572385   1.164768678935926  -0.657397448952216   1.221949663288457   0.000956613682100    3.49150
   0.519065537727025  -2.175658830088650  -2.327257651038165  -1.217817122157645   0.666095937819099   0.000965341984705    3.51366
   1.024160402134576   0.431219323538495   2.017449019367335  -0.679278501842584   2.575105446807908   0.166798376288355    3.52101
   1.050769121326101   0.394679812975755   2.072190078228667  -0.645260676425194   2.546391090725373  -0.364364619669937    3.52907
   1.079033299651421   0.362114285048138   2.112373401170405  -0.616837452864069   2.523824898326817   0.197551058413253    3.53663
  -0.562383241636139   2.336261444931746  -0.729630904402361   1.842462651756865   1.684741728037173   0.203565338684358    3.54115
  -0.584245602802506   2.344148729148653  -0.730607020092093   1.843228959089219   1.675019914869116  -0.214014291656448    3.54589
   1.396354301328830   0.370603941743416  -2.937806538140120   1.259131221106318   0.567402705141892   0.000899855851214    3.55320
  -1.216345712122600  -1.113019560537152   1.480967208469727  -2.779554112758775  -0.061578975258426   0.000792759927636    3.55546
  -0.483487108428239   1.777964251113697   0.945848785731378   2.601751632246490   1.306961287553466   0.001095873410958    3.57307
   2.388332781017261  -0.219561156898878   1.064826241768535  -0.797446020624022  -2.309571629628201   0.000789012250657    3.58556
  -0.519800929117478   2.173371114908712  -2.485094560443255   1.102023339543478  -0.738673704300452   0.000809350071757    3.59576
  -0.462431604521142  -0.211654668796357  -0.507657680340651  -1.010922581776835   3.404058553993690   0.000626113298910    3.62297
  -1.606406590605681  -0.114021205573417   2.942563457562288   1.154562625525648  -0.746883288429486   0.000645505791264    3.62534
   0.105827686183193   2.315838864546050  -0.429737548955431  -2.405349023977009   1.349269338035833   0.000775315932467    3.62839
   0.337214924129272  -0.775860118046549   1.961114563585085   2.907197569443871  -0.416621078427705   0.000714914923125    3.63139
   1.234648478332397  -0.375593611463746   0.481366967489801   1.828119530883197   2.846287987566721   0.000665743065042    3.65247
   0.366842740346481   2.321028849200667   2.227799566727430  -1.737109501640244   0.133744756945477   0.001389075189823    3.67699
  -0.244018822891929  -1.442751181941510   3.306585961801664   0.140599813708833   0.659885408345066   0.000470499598870    3.67829
  -0.816874552915229   0.912836379609252  -2.387178307683074  -1.945558617534653   1.686182219904803   0.000529269122381    3.71855
  -0.098842689576846   3.052894056672489  -0.412918330763821   2.077415830873490   0.562436307415512   0.000886370985007    3.75931
   3.065051996936164   1.104641230376216   0.480375290208230  -1.846297629489142  -0.133167246647973   0.000415585130947    3.77784
   1.024188371452936   3.554922789457908  -0.784173457799646  -0.125312375861653   0.226960377203747   0.000385624500686    3.79059
  -0.585856720951739  -2.049759850864500  -3.043919203596039   0.773787740848570  -0.039454491678378   0.000592732242923    3.79612
   2.540639788156530   0.423138758534955  -1.062484255654437   2.357190232530777   1.147784320154756   0.000400262342250    3.82577
   0.996351663942510   1.185383890044167   3.081903160564948   1.687411480058810   0.000356858862764   0.000507430514270    3.83971
  -2.175444274483998   1.010908804760963  -0.103926579917020   0.483785329490811  -2.973794165343813   0.000487425785551    3.85263
   3.216412075550873  -1.329408838284895  -0.839962514070668  -0.119712263282956  -1.470650709131583   0.000384406420525    3.87238
   1.349355199723142   1.195170919959268  -2.408992547438436  -2.435479309373621   0.262855658645827   0.000321322138213    3.87983
   1.533518558517934   3.074516837161472  -0.173789507474897  -1.035897740638469  -1.471302155010685   0.000433575743284    3.88231
   0.083964421392930  -3.836318181905642  -0.652241624959649   0.558996522304088  -0.157815978470691   0.000433078114065    3.93538
  -3.668091621240988   0.522799360857558   1.097757200979435   0.436683835831752  -0.743833385150673   0.000341893048390    3.95945
   1.150187736349236  -3.589728890377474  -0.900771518508435  -1.201625604326680  -0.122003194787833   0.000475156417938    4.05947
   1.175010692865250  -1.685995680965791  -2.707320780859572   1.714601834189336  -1.462811611708181   0.000520275837755    4.07830
   3.527759122715144  -0.044725560641031   1.563597635320437   1.391604240707916   0.076447853796858   0.000248832865800    4.10297
  -0.026095287141156  -2.624897416817819  -1.274319367974869   2.059854014219782  -2.042275131576002   0.000440699478707    4.11443
  -0.177371393343182  -2.097145314746831   1.132050419050659   0.270047176406250   3.437089303259821   0.000241954420677    4.19494
  -0.891418032462133   0.491471203865843   2.199590210396285   1.195851634368620  -3.227897356080897   0.000176706716348    4.20996
   2.808189880828896   1.748071818331266   2.650964651723147  -0.630667776723446   0.214325563018144   0.000129170175974    4.29103
  -0.003385650079347  -2.885204345030769   0.855000072103757   2.746193034009857   1.490875452931599   0.000172319802885    4.33817
   0.467311666562490  -2.049671328096768   1.320400992089759  -2.998367783701405   1.940858463294182   0.000174857311778    4.34973
  -1.589711393046326   2.340032017172191   1.208763006266283   2.809817152501997  -1.363517004127085   0.000135710416546    4.38387
  -2.696361006418286  -1.496790423087700  -0.444477625575200  -3.114641312881625   0.085087122652147   0.000121273514882    4.40642
   3.893548812795597   1.246577994070409  -1.622883617256519  -0.343523801794529  -0.125088292339207   0.000132591303192    4.41374
   0.988069741751574  -2.117851844468982  -2.439822023576682   1.740415329563306  -2.307748884736969  -0.000250110683784    4.44624
  -0.230495919866176  -1.208160990435692   1.630527983668046  -3.065699048652985  -2.520078595374850   0.000617811787962    4.46326
   2.579969570119587   0.092144815089763  -1.457494707748328  -2.489705958617413   2.261887923822288   0.000129014323203    4.48373
  -1.849255971936430  -1.622537888654323  -1.545352348407007   2.258104664096205   2.574029248046541   0.000123627497433    4.49056
   1.940033450832717  -1.951851535851880  -0.057453686841191   0.278829313289376   3.606632451943792   0.000042316112321    4.54558
  -0.498389135245937   0.987869243196579   0.006362265192450  -4.438380895482035  -1.017069270460533   0.000095274086656    4.68593
   2.912274636498776   2.598548972956378  -0.432103020976276   1.389062437694806   2.264376000060908   0.000055234124417    4.74103
   3.791451212368384  -2.422917420842755   1.243256578347946  -0.846429507640311   0.479081812993599   0.000089866401676    4.76836
   2.738097973127570   0.918095572290028  -1.680574195202315   2.107408523196371  -2.690093611289682   0.000068494691478    4.77935
  -3.464803894221715   3.208104962776365  -0.281787102160551  -0.679232728912134  -0.506685972506830   0.000047579943525    4.80565
  -1.163940106791946   0.055813701187851  -2.939072319305795   1.869157053602342  -3.211642339611962   0.000060742224243    4.87898
   0.372467624067526  -2.233060871382877   1.908645546965464  -0.003083786917109  -3.950267469330339   0.000039521782783    4.93689
   0.218917827659316  -1.518349680007122   2.385887189309765  -3.021414829032856  -2.895271256865003  -0.069880151889296    5.05542
   0.220276907849179  -1.517314449827978   2.388355280979864  -3.020999471844177  -2.896030470248106   0.069604716543736    5.05652
   1.334559966752876  -2.579099029713127  -0.599473438458428  -2.439155475637817  -3.310798518571634   0.000042590322639    5.06982
  -0.754351421745061  -1.095676520644931  -1.817728421453980  -3.921649076914754   2.354419703451956   0.000038010927304    5.09866
  -3.413330379194857  -1.993743138983897  -0.879636279988965  -0.841251649789261   3.201697001088895   0.000032963759858    5.23050
   2.775657251480596  -2.617078381058210   0.067147011909476   3.559004904736187  -0.955441821558100   0.000032248402284    5.30446
  -0.697876355430253  -1.124955574344681  -4.102065180901021  -0.039406471729075   3.428261291440459   0.000019604993471    5.50763
  -2.514340702356314   2.289901637710405   4.329980342418205   1.260735216548564   0.980395207629237   0.000015460426504    5.73279
   1.700680182228547  -1.515754958514181   2.288639948016630  -4.694836031397838  -1.666984494219259   0.000089679399577    5.93700
  -3.168393659384495  -2.161585060541928   4.000595932156341  -1.530705612721162   1.792275760509068   0.000008912154307    6.02256
   0.037292176060530  -5.474651908786809  -1.717646510233809  -1.510821367671319   1.098865236078798   0.001464501347057    6.03437
   1.983859448594651   3.612100609116273  -4.004917709202799  -0.501303591812871   1.779075215007756   0.000008051314571    6.03645
  -3.909327964830847   0.752615692139744  -4.437180252938915   0.026136151375958   1.237031268962702   0.000009753676978    6.08841
  -1.101620386105340   1.738215302073453   4.201475352444501  -1.811843000495788   3.661911485512682   0.000008280045744    6.21126
  -2.758636039194244   2.916811990764538   2.540031269889579  -3.140547779166845  -2.742483475557495   0.000006440971725    6.32091
   0.732661762524995  -0.672532776908028   4.426340662500196  -4.422129104732930  -0.364460412582541   0.000012900999341    6.34584
   0.198791570807997  -6.002196501931881  -1.909360100520857  -1.552298173792906   1.240478883029995  -0.005833109621515    6.60757
   0.221785954962613  -6.083490658165251  -1.938392877134121  -1.559677196602083   1.264646780098413   0.004604497601844    6.69682
  -3.112936748430510  -0.656813276077912  -3.492552633416494  -3.785135877915222  -2.895934731688715   0.000004121175118    6.71069
   3.641815478534538   0.839652661349862  -2.182663118660376  -3.736806337172936  -4.164360735043777   0.000003060510976    7.07372
  -3.899405371961402  -4.086457938478575  -0.742535955378293   2.989330713793162  -2.941512137396734   0.000004252305018    7.07421
  -1.931030020231582  -5.399813779479250  -3.092731022959888  -1.551827408557610  -2.448062537187362   0.000002674419971    7.13113
   1.223855556878254  -3.293196097575595   3.241919923592589  -5.507211478075852  -2.763869060169588   0.000023778898530    7.79880
  -1.395707758700073   2.643982868029289  -3.297988155926253   6.279046921729112   2.470276574693114   0.000005013899276    8.08357
   1.616099075131692  -3.037985968825171   3.711356617330245  -6.498460016724721  -2.866784159137303  -0.000014349797300    8.72145

E_n^{r^2} 5 dimensions, degree 8, asymmetric 224 point rule with points at 224 distinct radii (14 negative weights, stability factor 8.692041)
#                 x1                  x2                  x3                  x4                  x5              Weight     Radius
   0.127764843357290  -0.538859311829490  -0.771183058367261   0.000000000000000   0.000000000000000   0.893846201321523    0.94943
  -0.349874162665272  -0.885187286723168   0.000000000000000   0.000000000000000   0.000000000000000   0.532434809019388    0.95182
  -0.978824159133555   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.749999331738405    0.97882
   0.336059494370272   0.073669218613844   0.613933587821891  -0.793308259281317   0.000000000000000   0.644478946129829    1.06048
  -0.241182487152086  -0.284930872428539   0.859269319825892   0.523034204377614  -0.074784848297206   0.554957915013471    1.07557
   0.331000008742443   0.962150661410507   0.248053518252519   0.070260527250260  -0.268247239644695   0.676557952955350    1.08338
   0.976460054829062  -0.073854529118187  -0.355826351460803  -0.131820754112991   0.342036016337240   0.450744872611494    1.10449
   0.347639632606119  -0.186942138075609   0.244905573846761   0.198347982585501   1.024642158940910   0.608027474548233    1.14237
  -0.382301274382108   0.729373005728775   0.054596681293964  -0.209204651652062   0.808707297031071   0.726040193305760    1.17426
   0.390508716230097   0.166837876083318  -0.469666760564986   0.846265587649496  -0.632133609613110   7.422184031569227    1.23153
  -0.434436223052336   0.145376619363400  -0.236843632650340   0.302940134336615  -1.113122581568383   0.460463374669196    1.26364
   0.353611720181300   0.196256244667259  -0.580095752871326   0.900511758370518  -0.629333271383180 -11.500688860242787    1.30654
   0.883702985438793   0.094268174373813   0.918332864933899   0.374191856549288   0.062594167886822   0.332790344759760    1.33308
  -0.582062255586706   0.002181694226426  -0.292128072150594   1.119427757094461   0.352253791370618   0.318946909674857    1.34214
  -0.619140478760857   0.143152432039913   0.512769298870680  -0.817550856652607  -0.693088591738255   0.332413711469533    1.34741
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  -0.854864817005078  -0.802823736942834  -0.016179104652163  -0.440520524073272  -2.055482167884950   0.024777994516204    2.40721
   0.101614088469578  -0.018654751250943  -1.430526309283658  -0.057623802838376  -1.936566476630142   0.019734663331093    2.41054
   0.435095979603174   0.130311765423201   0.074230780753068   0.027415045976084  -2.367685241315085   0.017629536143117    2.41215
   0.038873264402834   1.122741069253908   1.966511685993974  -0.837833806497757   0.234479229742406  -0.164019080675017    2.42614
   1.670576827902806  -0.850639793589060  -1.323271110610376   0.122455550006261   0.778709759443483   0.020934959340652    2.42628
  -0.674532437563380   1.646747238793716  -0.513090442042911   1.162100351034222   1.063477727930833   0.300270995415880    2.43136
  -1.802655843539001   0.482162024532625   1.034299696766521  -1.169466595074089   0.109510837434310   0.016784299110090    2.43546
  -0.875758193560288  -0.235685601435352   0.431214825763789   2.221897323942775  -0.267887722710691   0.016256730534786    2.45297
   1.396703632659659   0.577889349395583  -0.803743681923016   0.240809302325760   1.760380168205521   0.010864895111714    2.46732
  -0.763098913741471  -1.967726253383409   0.823615831389328  -0.464850194088774   0.864048893179733   0.016734443318904    2.46886
   0.367034761607004  -1.538423112303945  -1.645619666617534  -0.861126745322748   0.471000954552672   0.016887131167667    2.48453
   0.724190765372097   0.304918107852717   1.426551882292661  -0.480322434967161   1.820874523708147   2.917873772780774    2.48973
   0.743005971151114   0.279080772152567   1.465259656222852  -0.456268199933299   1.800570407804784  -6.373982715672144    2.49543
   0.762991763309617   0.256053466522027   1.493673556365572  -0.436169945810042   1.784613700134210   3.455843305888086    2.50077
  -0.397665003786481   1.651986310336031  -0.515926960266200   1.302817835140406   1.191292300443120   3.561053626610359    2.50397
  -0.413124027619944   1.657563462490949  -0.516617178289633   1.303359696251593   1.184417940426566  -3.743841532036311    2.50732
   0.987371595408704   0.262056560341185  -2.077342924933092   0.890340224848043   0.401214300469314   0.015741554839842    2.51249
  -0.860086301309053  -0.787023678849031   1.047201955823998  -1.965441561806671  -0.043542910983804   0.013868081047510    2.51409
  -0.341877012985840   1.257210578669824   0.668816090367708   1.839716222124677   0.924161189177366   0.019170572012006    2.52654
   1.688806305187450  -0.155253182928349   0.752945856339921  -0.563879488813560  -1.633113760946137   0.013802521366363    2.53537
  -0.367554761845934   1.536805453386977  -1.757227215579389   0.779248176417124  -0.522321185395206   0.014158299378725    2.54259
  -0.326988523391978  -0.149662451575440  -0.358968188290153  -0.714830212829161   2.407032887084982   0.010952861858329    2.56183
  -1.135900993560101  -0.080625167659849   2.080706574914208   0.816399061813701  -0.528126238003398   0.011292102839487    2.56350
   0.074831474537411   1.637545365255779  -0.303870334996915  -1.700838605974622   0.954077498572244   0.013562925942717    2.56566
   0.238446959569207  -0.548615950722898   1.386717406594825   2.055699115602764  -0.294595589741465   0.012506305818891    2.56778
   0.873028311410429  -0.265584789636426   0.340377846951305   1.292675717107160   2.012629537218180   0.011646121935502    2.58268
   0.259396989328075   1.641215238599463   1.575292180757769  -1.228321908273424   0.094571824584497   0.024299673384102    2.60003
  -0.172547364404183  -1.020179144315744   2.338109356166203   0.099419081707061   0.466609447046972   0.008230646306007    2.60094
  -0.577617535745040   0.645472794135401  -1.687989969264124  -1.375717691654562   1.192310882010802   0.009258726165709    2.62941
  -0.069892336070425   2.158722089717354  -0.291977351759464   1.468954821354949   0.397702526959349   0.015505658434196    2.65823
   2.167319051722977   0.781099304777228   0.339676625220633  -1.305529573900436  -0.094163463136680   0.007270004546394    2.67134
   0.724210542666810   2.513710011020154  -0.554494369636453  -0.088609230738643   0.160485221781378   0.006745890707890    2.68035
  -0.414263260188840  -1.449399090350168  -2.152375910246714   0.547150558753009  -0.027898538614090   0.010368913081731    2.68426
   1.796503622757750   0.299204285543022  -0.751289822077132   1.666785197969156   0.811606076121079   0.007001956593773    2.70523
   0.704527018020284   0.838192986959513   2.179234623795634   1.193180100201560   0.000252337321842   0.008876694258331    2.71508
  -1.538271398581012   0.714820471007844  -0.073487189404807   0.342087887121583  -2.102790020167410   0.008526743170317    2.72422
   2.274346789712424  -0.940034004520601  -0.593943189642015  -0.084649353158465  -1.039907089183828   0.006724582322074    2.73819
   0.954138211953702   0.845113462180148  -1.703414966121650  -1.722143935097675   0.185867018701786   0.005621022581681    2.74345
   1.084361371803588   2.174011704429128  -0.122887739234560  -0.732490317021343  -1.040367730982468   0.007584721853977    2.74521
   0.059371811745288  -2.712686601214725  -0.461204475981077   0.395270231581062  -0.111592748556403   0.007576016617878    2.78273
  -2.593732459393138   0.369674973262517   0.776231560908983   0.308782101551199  -0.525969630712995   0.005980878118790    2.79976
   0.813305548010049  -2.538321641006639  -0.636941649036912  -0.849677613266616  -0.086269286360934   0.008312109990055    2.87048
   0.830858028891615  -1.192178979062520  -1.914364882993291   1.212406583990364  -1.034364010238008   0.009101402875601    2.88379
   2.494502398064733  -0.031625747221743   1.105630490982287   0.984012795332675   0.054056795827003   0.004352937415093    2.90123
  -0.018452154494428  -1.856082763350917  -0.901079866492353   1.456536741709163  -1.444106594586234   0.007709340337777    2.90934
  -0.125420515021725  -1.482905673191056   0.800480527955637   0.190952189677113   2.430389153878537   0.004232609897122    2.96627
  -0.630327735625952   0.347522621011337   1.555345153602685   0.845594799955139  -2.282468109459047   0.003091204510374    2.97689
   1.985690107593683   1.236073436743045   1.874515081919098  -0.445949461596921   0.151551058991791   0.002259627923774    3.03422
  -0.002394016129908  -2.040147557480271   0.604576348899472   1.941851716795865   1.054208142672485   0.003014462397997    3.06755
   0.330439248353869  -1.449336495301041   0.933664495392122  -2.120166192346709   1.372394180718800   0.003058852102568    3.07572
  -1.124095706152504   1.654652507536400   0.854724518578425   1.986840762428436  -0.964152119881430   0.002374039088061    3.09986
  -1.906615152165336  -1.058390658180310  -0.314293143129881  -2.202383993302449   0.060165681418934   0.002121488327898    3.11581
   2.753154768408744   0.881463752885136  -1.147552010838741  -0.242908009747878  -0.088450779760096   0.002319475133336    3.12098
   0.698670814678185  -1.497547400772272  -1.725214697760013   1.230659481615452  -1.631824885672906  -0.004375290819651    3.14397
  -0.162985227973234  -0.854298829101998   1.152957394165915  -2.167776586379592  -1.781964663912631   0.010807640054558    3.15600
   1.824313978286400   0.065156223601033  -1.030604391392276  -1.760487966498850   1.599396289218735   0.002256901526050    3.17047
  -1.307621437905787  -1.147307543799465  -1.092729124881032   1.596721120611101   1.820113536266032   0.002162667529391    3.17531
   1.371810808812018  -1.380167456870234  -0.040625891569458   0.197162098220532   2.550274264017401   0.000740253454835    3.21421
  -0.352414337202116   0.698529040789914   0.004498800861188  -3.138409228684212  -0.719176578079007   0.001666669453649    3.31346
   2.059289144145808   1.837451600023059  -0.305542976303536   0.982215469185279   1.601155624799234   0.000966233644382    3.35242
   2.680960862802954  -1.713261338532905   0.879115157304679  -0.598516044648637   0.338761998710866   0.001572070558125    3.37174
   1.936127644351540   0.649191604943640  -1.188345409714659   1.490162857482415  -1.902183434569412   0.001198206291255    3.37951
  -2.449986329085454   2.268472773937217  -0.199253570788620  -0.480290068617541  -0.358281087091570   0.000832335856083    3.39811
  -0.823029942407585   0.039466246592997  -2.078237967378512   1.321693627704765  -2.270974077085373   0.001062589138826    3.44996
   0.263374382750708  -1.579012484957131   1.349616209140982  -0.002180566641062  -2.793260915064102   0.000691371079281    3.49091
   0.154798280460554  -1.073635354945401   1.687077010707068  -2.136462914386896  -2.047265939103746  -1.222442729797422    3.57472
   0.155759295278983  -1.072903336665640   1.688822215063585  -2.136169212502168  -2.047802784035305   1.217624424075323    3.57550
   0.943676402391330  -1.823698413262165  -0.423891733475158  -1.724743377191893  -2.341088083624720   0.000745050330629    3.58490
  -0.533407005713780  -0.774760297734729  -1.285328093165533  -2.773024655720186   1.664826138069854   0.000664941052347    3.60530
  -2.413589057558659  -1.409789293519452  -0.621996778557796  -0.594854746250267   2.263941660774294   0.000576648840845    3.69852
   1.962686064771282  -1.850553870142777   0.047480107457504   2.516596502415019  -0.675599391053017   0.000564134791552    3.75082
  -0.493473103354649  -0.795463715152944  -2.900598106284955  -0.027864583382483   2.424146806857531   0.000342958352099    3.89448
  -1.777907360849217   1.619204976275386   3.061758462528253   0.891474420901885   0.693244099557876   0.000270455708366    4.05370
   1.202562489483379  -1.071800609782755   1.618312826937133  -3.319750394360749  -1.178736039995370   0.001568799252168    4.19810
  -2.240392642019342  -1.528471454420633   2.828848512414724  -1.082372318755275   1.267330344012270   0.000155904043500    4.25859
   0.026369550577666  -3.871163489338974  -1.214559495067718  -1.068312034241846   0.777015060041567   0.025619134705431    4.26694
   1.402800469022422   2.554140835034514  -2.831904470271710  -0.354475169203920   1.257996148773035   0.000140845013872    4.26842
  -2.764312313813990   0.532179659539320  -3.137560246200115   0.018481049871975   0.874713198823155   0.000170625151613    4.30516
  -0.778963245308676   1.229103827258211   2.970891712701032  -1.281166472096357   2.589362443511002   0.000144846303978    4.39202
  -1.950650250139774   2.062497538115645   1.796073335364684  -2.220702631289439  -1.939228662858534   0.000112674612814    4.46956
   0.518070100597469  -0.475552487121882   3.129895498295565  -3.126917477238760  -0.257712429210800   0.000225682578308    4.48718
   0.140566867761150  -4.244193848530133  -1.350121474805300  -1.097640565112348   0.877151030109301  -0.102041026760054    4.67226
   0.156826352726093  -4.301677497673588  -1.370650748025212  -1.102858322179243   0.894240314013396   0.080548402737604    4.73536
  -2.201178684220087  -0.464437121488100  -2.469607650739903  -2.676495246986291  -2.047735086650934   0.000072093440332    4.74518
   2.575152420701829   0.593724090681881  -1.543375892250445  -2.642321100995826  -2.944647715056323   0.000053538798808    5.00187
  -2.757295981109178  -2.889562119331642  -0.525052209322838   2.113776018932533  -2.079963179295842   0.000074387350541    5.00222
  -1.365444421980672  -3.818244940614037  -2.186891078721027  -1.097307683821962  -1.731041620814055   0.000046784747336    5.04247
   0.865396563461478  -2.328641292372786   2.292383562035992  -3.894186581576117  -1.954350554757602   0.000415974219359    5.51459
  -0.986914420731400   1.869578215324599  -2.332029789328271   4.439956657743183   1.746749317371724   0.000087710237492    5.71595
   1.142754615094862  -2.148180479705957   2.624325431515494  -4.595105145095599  -2.027122519124060  -0.000251027007084    6.16700

>> # evaluating formula 1 with 230 points
# r5_230_8E1a.txt:4 formula 1   : problem E1, 5_230_7  (d=5 n=230 o=7 plus 494/495 of order 8) quality N (18 negative weights, stability factor 1.453426)
E1 5 dimensions, degree 8, asymmetric 230 point rule with points at 230 distinct radii (18 negative weights, stability factor 1.453426)
This rule was refined at higher precision to meet the degree 8 constraints - see refir5_230_8E1a.txt
#                 x1                  x2                  x3                  x4                  x5              Weight     Radius
  -0.565793566255137   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000  39.525289439023858    0.56579
  -0.113623172376383   1.083913509096411   0.000000000000000   0.000000000000000   0.000000000000000  38.447894534822545    1.08985
   1.296266696005040  -1.894728358613216   1.965163720790902  -0.000000000000000  -0.000000000000000  37.955731712307788    3.02195
   0.927124699870226   2.730275274080581   0.255590610772425   2.632333426641871   0.000000000000001  28.595948175854701    3.91260
  -0.215924682511055  -3.856088062331682  -0.970716752724652   0.654869059500069   0.097934972464755  23.739014720969084    4.03693
   0.533516093230264   2.259870540386577  -2.102938245847553  -2.302917582375459  -1.088867048484703  28.983656677766781    4.03771
  -2.413624513786557  -0.418820735239728   1.522184021976696  -2.652502887186981  -1.456273444649673  25.497378237473658    4.18026
  -1.905192441978218  -0.286262506124846  -2.458410817902755   0.861629044669424   2.868093911397320  27.780401677070383    4.32711
   0.443196527893272  -1.442754575745862   0.833049636368747  -3.207640186026595   2.476375108919500  20.431529343493338    4.40379
  -2.708274658743109   0.126195237902880  -0.832228670352613   1.854294264496875  -3.128965677634489  19.473584915538535    4.61217
  -0.815883241512434  -1.612852759009969   2.228467006083751   2.622208264018273  -2.536205092574772  11.860383794995570    4.64126
   2.969902282030254   1.695338795390410  -1.724921785293483  -0.453506136153646   2.645185948454490  19.097974192143997    4.67681
   1.219557530196754  -1.001852680200312  -1.078452757985149   4.350867284065856  -0.066518335299720  14.827976623926778    4.75274
   3.226117119791389   0.671254270274952   1.778566203990497   0.129707039634539  -2.941966899874330  19.750236639612972    4.76379
  -2.375711764930217  -0.833329659556103  -3.513395553400256  -2.167614157396827  -0.671380186646503  12.528349895749965    4.88177
   0.481628145394611  -0.857334426479004  -2.677913872261507   0.152036614249586  -4.103023298717537  13.887260987429988    4.99961
   3.393720699583663   0.134684974136823   1.748950652247056   1.127135298485368   3.286670560542612  12.912279439002971    5.16400
  -0.792675517330730   2.705614572227305   3.126727373721279  -0.112969184424430   3.319994345190677  12.876666887324882    5.36286
   2.713044407729635  -3.019774825399364  -3.505614719179099  -0.459857785283369   0.916677728431775  16.003208343935977    5.46084
  -3.634170693528120   0.475710363553293   2.028547000205291   3.570590350944738   1.153531587093979  14.895971337423976    5.62390
  -1.493927979860798   2.237855221689713   0.184309856895031  -3.358119624165056   3.683664137098677  10.420726146578730    5.66746
  -2.236825577669735   2.960284463948367   4.144769604925211  -0.282205366166870  -1.114615569276397  10.096148775172162    5.68047
  -4.296104536483460  -2.349304478917725   1.887529516498718  -0.918956501458292   2.276928849490409   9.747855434502135    5.79374
   5.131453169710482  -0.178428632789701  -2.890499109535809   0.426291014459986  -1.552976474215668   9.896261349911713    6.10836
  -3.511115405999955   5.196145106919282  -0.938662374129536  -0.491484706483813  -0.048389084553421   8.012803036354935    6.36025
   0.095142664985181   0.928767962901067   5.944250221578018  -2.090574773632734   0.640894360732189   7.060713959260378    6.40211
   5.009270413835324  -2.922891413749732   0.309474020757058  -2.721754859793748  -0.866356255137079   6.666508600832779    6.47228
   0.564358148005018  -1.067665207767662   0.387101734117944  -4.329894316568764  -4.692241226096685  12.007845791684758    6.50948
  -1.312688852891905  -1.308390426257057   1.829595752164682   4.077748745210476   4.356647275728057  15.622214222349426    6.51083
  -2.173156147394829  -1.603235382553291   2.541226904672311   4.168768068289845   3.371536240855764 -12.876962200273018    6.51895
   3.067323054741458   3.529747610254716   2.727457123301126  -3.789470852028443   0.034901289331017   6.478455403301801    6.60817
   0.576780934771961   1.841951461330184  -5.990551448570823   2.088599983376201  -0.422147564858144   7.446117952486081    6.64474
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   1.841133253804415  -0.135631137146959   4.979145764854043   4.905904044212297  -0.640204151518028   4.744411177988545    7.25795
   0.200661862048464  -3.423469324917135  -2.843951560659364  -5.686742832902303  -0.758149826467434   3.575041260445796    7.26377
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   2.777603002223104   0.374688844173355  -0.562061483700451  -6.742052263782122   0.295384188860907   3.254952715924856    7.32898
   4.133169283217846  -4.512023265728929  -2.182862681756797   3.280099470782559  -2.256654864299044  10.165770966311145    7.61957
   0.591377951306888   3.615360377609632   1.416961900195763   0.293242552250307  -6.652920096876201   8.351204068778518    7.73147
   0.790771262336150  -6.414889515687047  -0.042411798319271   1.942253136909003  -3.867611608406026   3.649106942830394    7.77873
   2.999904699316984   7.078077895813291   0.289897323745211  -0.984334869346559  -0.836218369128969   2.488445155394531    7.80069
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   4.709315858187005  -2.208262847635671   6.726930891325107  -1.373491720964873  -0.058702549706934   1.430813532597820    8.61369
   2.251966668685105  -5.741298353853606  -0.701437636380156   5.176750536668207  -2.995616798875909  -9.250871277130283    8.61965
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   0.763859446910423   0.091482071788718  -4.843991073593167  -3.007847867237417   6.531396067513924   1.524821936201159    8.70416
   6.889891813227563  -4.154593988782762  -2.974909672615699   1.656132052728335   1.251827604069297   3.844601418245759    8.82560
   3.572639814487014   5.470927011510859   5.428222319483443   2.241008500509437   1.358297346023661   1.275861860513425    8.88974
   7.004191017752833   3.090061994978697  -0.251005637656623   4.523127160967221  -1.566197045490266   1.458066493075822    9.03227
   5.909298998775257  -4.518761260547503  -4.995902009579934   0.031910453898865  -1.391129642705944   5.227722185214957    9.06831
   4.362912522155828  -5.305679163695169   3.721925232238751   1.246147918575114   4.501768462730432   1.236524410116728    9.10257
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   0.107780007257870  -1.156182628207623  -1.790786703137665  -6.908111709401334  -5.690452922559809 -11.565212863658573    9.20101
   1.251616435121653   1.966870628495331   1.537711263157742   0.607653990205124  -8.746153596509830  -8.835992517037946    9.20131
  -2.230901886005507   2.362642494623936   4.935671959922372  -6.098991795847212   3.699618103033635   1.652751984414071    9.26308
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   2.644021868157481   0.458991179782588  -7.804206548668787  -4.653782612125521   1.150355679188001   1.002670256129644    9.54401
   8.443636709128649   2.184921599007758   3.178443004422851  -1.574484497868014   1.630196112993025   0.969442394661726    9.55552
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   1.837613838144700  -1.101582851022950  -3.232610481935787  -6.228844970833577  -6.277653804229770   2.873595413329965    9.65648
   2.784451786222708  -4.194778298713834   2.183191177172288   7.974277322557075   0.068171492949239   3.519363109696648    9.68036
   3.057837602556988  -4.996058343160244  -3.950482090469940   4.591092717533955   4.800566348634170   2.006245078943422    9.69747
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   4.239740343408304  -6.851097269280823   3.617099264012496   3.404855313993531  -2.838266661170857   1.014662623141561    9.88156
   3.486995357112771   1.588795215821465   4.212931411894868  -2.001563709756585   7.855239563107878   0.595842563747154    9.90673
   6.780230576356471  -1.463095825501068  -1.489155378635099  -4.843025051119210   4.962721010038853   0.686007258874656    9.92035
   0.382298054967257   4.963629682459604  -0.216211478627883   4.513024364765982  -7.301785356982974   4.162949961992374    9.92542
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   0.097750818797065  -1.674234261824842  -1.235992610060398  -8.041655619601730  -5.671861696978911   3.761090780109607   10.05875
   1.567229250064861  -1.639044050339403   1.112650763166164   2.382865166088155  -9.447977176337439   3.945789316118900   10.06593
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   0.278753314181771   8.440402002036043   0.608232710670232  -3.113733512481314   4.716208412074877   0.603833101467135   10.17969
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   4.296400445733974   7.588258876000332  -5.100220144683975   0.893541335194319  -1.334210944108635   0.619050530802335   10.22895
   1.877817872981842  -3.526522582561803   0.384748841693783   9.116337021131949  -2.508483547264715  -4.369288102089600   10.27184
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   6.495815826815284   4.448893913629336  -3.221446458161589  -5.614547229873689  -2.242723293184543   0.508007418889556   10.43642
   0.841896208333911   0.385426845350852   1.380854881998157   0.787712602780928 -10.290729633499458   6.912964747458108   10.45388
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   2.566595100962447   1.158183972106061  -6.417591959304243   7.679369285631872  -1.698278684322359   6.633838416397811   10.53428
   0.311265717330979   3.815157929154644  -1.909350321470160   0.439805527560826   9.644720974886155   0.504490570081423   10.55992
   4.259226662524286  -2.070336576326009  -4.403179370665515   5.995767093626291   5.814551710280615   3.858177892892549   10.56284
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   3.950301765955241  -2.914602889706882   5.035559558746318  -6.837688838837774   4.101207163531420   0.426273223291354   10.63158
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   6.265405548401594   6.639987989106917  -0.995848213719234   2.357451042627594   4.965851995731009   0.443678946549649   10.70298
   7.232073757896198  -0.502834757529017   3.158629246795399   6.505154146913652   3.164500576651997   0.492331622387199   10.71745
   0.063613466691542 -10.194004447616143   1.102400420469092   2.068880662602908   2.548828757886213   0.408346322550598   10.76633
   0.311943557537537   2.934192492780694   3.591022387271647   9.023106411825136   3.599028766084121   0.282839044247235   10.76902
   0.758641574919968  -0.562394238851754   6.378255703292115  -8.467836167850171  -1.714992345688862   0.371910847008514   10.78051
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   0.998114593183553   4.318734206069143   0.580742403559451  -6.963356234329926  -7.052553890831605   0.478413053344367   10.87253
   0.415534811306457  -1.429320659062340   0.881183497672438   1.687041917916916 -10.606446842169952  -7.907956526893189   10.87819
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   3.485241786754750  -3.009935535978390   2.358731599377719   9.583830250513582  -1.475489814601485   6.080259659956103   10.99077
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   0.714191058251830   1.841475627464245  -8.006874791310938   7.103436167524994  -2.120727684994857  -3.730665348971453   11.08907
   5.286337662560121   3.738378263686117  -4.119938744241121   0.015697926954517  -8.030544295735872   0.347149325378090   11.10786
   4.196029504189926  -2.590212981359514  -0.180499152590502  -0.732525153740334   9.945475876844899   0.291881665766072   11.12643
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   2.732002467137639  -2.509732362814423  -1.000524497186709  10.449453908152663   1.382998720905261   0.431406753857333   11.21906
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   3.717121698155697  -3.472473064174079   3.432302580415365   9.610158617049546  -0.517404468573275  -8.725905469784879   11.41397
   4.251431896929885   0.857964683993035  -6.746700160652514   8.151684750573324  -0.088171152340534  -6.907950353239931   11.43619
  -5.600148615737936   3.628672760378312  -8.694728178831106  -2.898375653753156  -1.719344746211272   0.290086658547614   11.46665
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   4.756651450189806   4.977268416329202   8.404453433769502   2.668221589387524  -2.577587718941789   0.183272131460798   11.48029
   7.169398534893086   3.897444574767490   2.284427527989838  -1.524496383165550  -7.613579229666800   0.293501914868522   11.49346
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   4.652847486750066  -3.663110981615930  -4.588183254525086   6.653850091502739   5.791568349989994  -5.285167887758951   11.57302
   3.440045893815157   3.223485886096246   7.751843876304986  -3.628131611460333  -6.255099174657103   0.214162483637352   11.60196
   4.257450441196276  -4.671474377468205   6.931340839877139  -3.954564846132124  -5.704745436156210   0.238472998523286   11.66939
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   5.643310408076040   5.889267531395566  -4.090034951153763  -5.010401633351178   5.437785894073536   0.220970792795779   11.74446
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  -3.839370291835160  -3.356335562132728   4.262547296117087   9.895795066485814   2.439084548886480   0.204285013647990   12.16762
   3.970605711271786  -3.792758702165675   4.406059241893425  10.001792455499279  -0.075686181633867   2.736290246100110   12.23134
   4.956628934497001   1.122878984965339  -7.738399215231867   7.959063222700950   1.687628836144920   6.912268291972525   12.32504
   5.797508702063602  -9.849253779451725   0.540101979109108  -4.445905510320648  -1.209497572229120   0.167133706753489   12.33449
 -10.488587071021881   4.308202189136010   0.333000582906034   4.362089195882369  -2.576613690161910   0.140811291349681   12.42372
   8.886346436968696  -0.975104931013910   6.392515570568591   3.600415476420597  -4.672058794976935   0.136616897922359   12.47291
   1.009131112849400  -9.325757401690122  -7.918767087298368  -0.410004550373642   2.301128466932929   0.111235423071272   12.49633
   0.004415456029956   2.262986152135515  -9.670460383745192   7.282109560929662  -2.281222263557256   0.940162908443629   12.52486
   4.820659779460422  -0.135679378081970  -8.508480151597084   7.228690475063307   2.996707210047764   4.265512309557771   12.52540
   3.403388121462557   7.087316062438212   1.534732413757508   9.544662282967657   1.484337489549476   0.122478587506008   12.54880
  -3.290032521321654  -3.285085018803269   7.486869915009442   5.801751706422795  -6.803371518594425   0.240149364143433   12.55450
   3.006768256556620   4.242431758680654   3.598745544687378   5.750604446697962   9.214848957403035   0.118309871978838   12.56872
   2.807261760605769 -10.409336750598349  -2.794456249339211   5.041821469686832  -2.929156097746437   0.185646253346997   12.57155
  -0.987902200545207  10.394546483212700  -3.354514677353977  -5.677381445936149  -2.600486848370783   0.135301019809990   12.62024
  -6.781027377716661   6.256096145843470   1.173615814015585   7.939120811649317   3.412946622968489   0.096834964861861   12.69552
   5.116524249998770  -4.533969091193795  -4.536049117176619   7.348316624216014   6.366783219823875   1.540085455070381   12.72184
  -9.135002221919850   4.391770856331202  -0.800629388469553  -7.673321059229726  -1.276061524792347   0.123578303387402   12.80176
   1.416655550644513  -1.686131134517719  -2.259627582050476 -10.623713541525603   6.456886413034209   0.079687615030740   12.82617
   4.821848648543509   0.922832103357426  -8.712373210493613   7.462057846324337   3.085259539121681  -9.834832929468650   12.85334
  -1.881025066196311   6.253394087704828  -0.797668732291190   5.807726218472129  -9.433153784870463   0.580497462058429   12.88385
  11.765820040106410   2.222465883064536  -4.286348825883051  -2.081378427056312   0.108396997220032   0.099509828761101   12.88761
   5.743319803343748   5.051697383163069   2.975500518379533  -7.302543868823173   6.739043454135657   0.091307713307387   12.88801
  -4.737532032996033  -1.391141322803254  -5.636930520063936   8.354997097205057  -6.509546801695032   0.080075032847783   12.97438
   5.509681692799058   0.229483199313968 -10.960348903562220   1.143768128790615  -4.185655194348388   0.089847867428831   13.01409
  -8.793699978979131  -0.056763263791947  -5.768512772346467   0.492418637388007  -7.758116431482810   0.106916467571453   13.07819
  -3.171372591443287  -5.533226267681936  -5.194109235304444   1.198775435932859  10.133464237171982   0.102938949694515   13.10638
  -5.068625107144623  -8.284953058819436   2.695882180854829   4.484736476650673   7.324592048442621   0.089497757219667   13.24242
   4.392300595231315   1.513031885175783  -9.248042108197453   7.386451609931129   3.713989891077975   2.771274296146839   13.24618
  12.366880981360698  -3.749958375831302   3.367850091026227   1.631382415757772  -0.353397984601398   0.054524544448249   13.45848
  -2.732188814194973  -7.356257713471767   4.514318384748792  -6.072001059150947   8.075265203041560   0.066879590065202   13.56604
  10.927900200458199  -3.980814491005052  -0.964574029645812  -1.765134324689266  -7.158237921519115   0.065984397575374   13.80407
 -10.698925530650259  -1.113439696532553  -8.114359830977932   2.107799395288953   2.162891259077631   0.064979268153910   13.80835
   6.389411818794660   0.366809892563796  10.848265062519420   1.686272279772651   5.428429495492466   0.056504105963357   13.81866
   7.247969572605868   2.654004642835670 -10.008753047801424   3.289043616991717   4.999215030445806   0.123300984169038   13.98434
  -3.666210683977246   5.901853864699465   8.355176079455832   1.623719977830091  -8.674845674381693   0.030819157889531   13.99898
   9.759157416760310  -0.177787926278104   3.569845575925636  -8.839096692381709  -3.491038116808548   0.058924433975467   14.08309
   0.356733542606138  10.915899811496983   7.511482951897970  -3.815357408598217  -3.552400910661356   0.044354266762713   14.24370
   3.794052794695659   5.639216170862332   6.263974145851419   6.762371415930749  -8.692229619693947   0.042604107409827   14.37767
   1.231150903658939  -3.177356024664294  13.811821357279062   1.792527407350966  -2.296049024527068   0.042804581763151   14.52111
 -10.683575088241186  -2.797301976613989  -0.908807009124914   8.760366737492328  -3.385182235090384   0.040990172561007   14.52560
   3.564511628380661  -7.957086860395452   1.270204213680208  -2.980932353924469 -11.231261289324898   0.038359504627646   14.58292
  -5.765185843194319 -10.274950705554282   6.907834397266398   4.671176327684358  -4.139310111757449   0.038881414834740   15.01612
  -5.352791524088708   1.929688341509131   8.593252677452657  -7.331008320397371  -8.136011099716939   0.035944842706351   15.03856
 -10.129334046194769   0.147164269040102   8.167601310531007   4.533459204730773   6.822973319499339   0.028444234889368   15.37661
   4.934682937398542 -11.579511406391472   1.014772635317184  -8.806190578051066   4.070700751126969   2.847491829819997   15.92437
   4.974293200407375 -11.658976667518594   1.125918646429932  -9.119110747073989   3.990969238195442  -3.307811951696163   16.15639
  -9.007502350729817   9.594211460622665  -8.139800508111199   4.212279679352912   2.139837442264670   0.016028016655222   16.17908
  -1.563527334644946   1.085500529873619   0.330279497119283  -9.556027935825572  13.073208707871824   0.017234577327371   16.30823
   4.123280212863643  11.244008164334744  -0.553492834779344   9.420665386622080  -6.054122591167550   0.014026482090875   16.40539
   5.163398740241578  10.581248179318228   7.398838491993591   0.024859654387441   8.780292181442402   0.010685067317534   16.44568
  -4.009335225333326   5.250840709183031  15.120693015553382   0.404959490482239  -0.433696051756110   0.013133487440888   16.51162
   5.026907994630027 -11.836549659967201   1.453688755851584 -10.148873781286753   3.702058360574687   0.567223133682218   16.85799
   3.202333885825792   6.885903003679484 -13.079183116692526  -6.218582021809963  -4.396929350975459   0.012040675599667   16.93338
  11.376537106514816  -0.486440350911353  -5.244716104985973   9.071475116608593  -7.343349819910402   0.013236694317236   17.12851
   0.342282755023197  12.967942777241454   0.446475924771812   2.347413793217623 -11.508277062766167   0.013529473165203   17.50528
   7.378034127159149  -6.316468486127063 -10.147496345394245  -3.483667317577727   9.963633987103808   0.007981437729754   17.57028
   1.869425674644961 -12.374153711811260  12.082002690455692  -0.865896621583089   2.903147730817773   0.008890378889419   17.65693
  12.999574202724828  11.506698151378567   2.786842970252633   0.438014369908770  -2.126619097134501   0.007698361523990   17.71649
 -17.237618880197342  -1.141453579255986   1.627079324072124  -2.584470941761345   2.797641391642249   0.006561574911463   17.76491
  12.419788567781275  -8.403135782426213   6.431724318502145  -5.860391548483856   5.975223778067997   0.005724862676999   18.33790
  -8.914889296270331  10.515720101653930  -1.200349854905223  -7.273399497746684   9.860761380664240   0.006440421448388   18.48333
  -4.862824370426861   1.405367369207630  -2.481936378615189  11.358682155558045  13.502117429872268   0.006234108405221   18.52320
 -11.622910514833027  -9.679651446359188   9.087268368241963  -3.312118636024536   5.118642977761987   0.005077766158847   18.66914
   3.261695090507293  -6.400928243198945  -8.852992450141338   2.152441348145766 -15.513437672299737   0.004569430414223   19.37229
   2.603885132595968   5.516180842269285   2.667451860396862 -18.291601206447986   0.919182479863371   0.003437416682799   19.48721
   5.582451684525929  -3.278896604774242  -6.898654415201797  17.145434880393736  -3.362752379584077   0.002994115897348   19.86908
  11.273780059644139  -4.808429283994175  -8.199659766366958 -13.333289108887943   0.634113932238040   0.003625578266564   19.89051
 -13.524990017539841  -7.471304418024583  -8.222531358103407  -9.294041861346114  -2.586715016667666   0.003759654771209   19.98565
  15.925303303426213   1.457173547302665  -0.576543559794772   1.996287737916368  11.863216542032735   0.003295688920275   20.01979
   0.951304324123292 -15.055003550841018 -10.613802929274883  -7.886697610630145  -4.910076044953569   0.002023815060777   20.65236
  -3.888902230771567  -8.067778615798575   7.807643620793664   2.873194076355453 -17.882376051259900   0.002093962845271   21.66118
   9.340184303714594   6.531828599058109  16.629491174766589  -8.508752964723415   1.615625684437246   0.001477291014858   21.94204
  -6.169100622236731 -11.618585246707712   6.526849429486783 -12.268468561342893 -10.770135430104173   0.001271836982021   21.95815
 -15.438773245900025  13.960523067555712  -3.285173596063157  -5.109745347864359  -4.152377396818430   0.001402524768163   22.07705
  -4.304965043392094  -5.465474209456016 -16.556439829362063 -18.404666669589702   2.388624367192006   0.000373639480608   25.82551
   4.156873166784904  -8.906996598145573  10.285910838360593   8.980650126953430  20.496520237417247   0.000367926742006   26.51742
  -8.726330651273379   6.127733902695208 -18.455712745745160  -8.345883700049580  17.069580860362336   0.000136568965425   28.55408
  11.270677404156142  21.161733347647271   4.232131236324476 -16.622194982979018  -2.379597451340463   0.000122769313074   29.57563
  -0.441727967505327  27.309306085469380  -6.801739525667683   5.408484123205437   7.729952664216020   0.000145132043516   29.68604

>> # evaluating formula 1 with 28 points
# r6_28_4g.txt:4 formula 1   : problem  G, 6_28_4  (d=6 n=28 o=4 plus 219/252 of order 5) quality P
# evaluating formula 2 with 28 points
# r6_28_4g.txt:36 formula 2   : problem  S, 6_28_4  (d=6 n=28 o=4 plus 219/252 of order 5) quality PI
# evaluating formula 3 with 28 points
# r6_28_4g.txt:68 formula 3   : problem E1, 6_28_4  (d=6 n=28 o=4 plus 219/252 of order 5) quality P
# evaluating formula 4 with 28 points
# r6_28_4g.txt:100 formula 4   : problem E2, 6_28_4  (d=6 n=28 o=4 plus 219/252 of order 5) quality P
G_n 6 dimensions, degree 4, asymmetric 28 point rule with points at 2 distinct radii: 1+27=28

#                x1                 x2                 x3                 x4                 x5                 x6             Weight     Radius     cos1
  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.250000000000000    0.00000
  0.707106781186547  1.224744871391589 -2.449489742783179  0.000000000000000 -0.000000000000000 -0.000000000000000  0.027777777777778    2.82843 -0.50000
  0.707106781186547 -1.224744871391589 -1.224744871391589 -1.224744871391589 -1.224744871391589 -1.224744871391589  0.027777777777778    2.82843  0.25000
 -1.414213562373095  0.000000000000000 -1.224744871391589 -1.224744871391589 -1.224744871391589  1.224744871391589  0.027777777777778    2.82843  0.25000
 -1.414213562373095 -0.000000000000000 -1.224744871391589 -1.224744871391589  1.224744871391589 -1.224744871391589  0.027777777777778    2.82843  0.25000
  0.707106781186547 -1.224744871391589 -1.224744871391589 -1.224744871391589  1.224744871391589  1.224744871391589  0.027777777777778    2.82843  0.25000
 -1.414213562373095 -0.000000000000000 -1.224744871391589  1.224744871391589 -1.224744871391589 -1.224744871391589  0.027777777777778    2.82843  0.25000
  0.707106781186547 -1.224744871391589 -1.224744871391589  1.224744871391589 -1.224744871391589  1.224744871391589  0.027777777777778    2.82843  0.25000
  0.707106781186547 -1.224744871391589 -1.224744871391589  1.224744871391589  1.224744871391589 -1.224744871391589  0.027777777777778    2.82843  0.25000
 -1.414213562373095 -0.000000000000000 -1.224744871391589  1.224744871391589  1.224744871391589  1.224744871391589  0.027777777777778    2.82843  0.25000
  0.707106781186547  1.224744871391589 -0.000000000000000 -2.449489742783179 -0.000000000000000 -0.000000000000000  0.027777777777778    2.82843 -0.50000
  0.707106781186547  1.224744871391589  0.000000000000000  0.000000000000000 -2.449489742783179  0.000000000000000  0.027777777777778    2.82843 -0.50000
  0.707106781186547  1.224744871391589  0.000000000000000  0.000000000000000  0.000000000000000 -2.449489742783179  0.027777777777778    2.82843 -0.50000
  2.828427124746189  0.000000000000000 -0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.027777777777778    2.82843 -0.50000
 -1.414213562373095  2.449489742783179  0.000000000000000  0.000000000000000 -0.000000000000000 -0.000000000000000  0.027777777777778    2.82843 -0.50000
 -1.414213562373095 -2.449489742783179  0.000000000000000 -0.000000000000000  0.000000000000000  0.000000000000000  0.027777777777778    2.82843  1.00000
  0.707106781186547  1.224744871391589 -0.000000000000000  0.000000000000000 -0.000000000000000  2.449489742783179  0.027777777777778    2.82843 -0.50000
  0.707106781186547  1.224744871391589 -0.000000000000000  0.000000000000000  2.449489742783179 -0.000000000000000  0.027777777777778    2.82843 -0.50000
  0.707106781186547  1.224744871391589  0.000000000000000  2.449489742783179  0.000000000000000 -0.000000000000000  0.027777777777778    2.82843 -0.50000
 -1.414213562373095  0.000000000000000  1.224744871391589 -1.224744871391589 -1.224744871391589 -1.224744871391589  0.027777777777778    2.82843  0.25000
  0.707106781186547 -1.224744871391589  1.224744871391589 -1.224744871391589 -1.224744871391589  1.224744871391589  0.027777777777778    2.82843  0.25000
  0.707106781186547 -1.224744871391589  1.224744871391589 -1.224744871391589  1.224744871391589 -1.224744871391589  0.027777777777778    2.82843  0.25000
 -1.414213562373095  0.000000000000000  1.224744871391589 -1.224744871391589  1.224744871391589  1.224744871391589  0.027777777777778    2.82843  0.25000
  0.707106781186547 -1.224744871391589  1.224744871391589  1.224744871391589 -1.224744871391589 -1.224744871391589  0.027777777777778    2.82843  0.25000
 -1.414213562373095 -0.000000000000000  1.224744871391589  1.224744871391589 -1.224744871391589  1.224744871391589  0.027777777777778    2.82843  0.25000
 -1.414213562373095  0.000000000000000  1.224744871391589  1.224744871391589  1.224744871391589 -1.224744871391589  0.027777777777778    2.82843  0.25000
  0.707106781186547 -1.224744871391589  1.224744871391589  1.224744871391589  1.224744871391589  1.224744871391589  0.027777777777778    2.82843  0.25000
  0.707106781186547  1.224744871391589  2.449489742783179  0.000000000000000 -0.000000000000000  0.000000000000000  0.027777777777778    2.82843 -0.50000

S_n 6 dimensions, degree 4, asymmetric 28 point rule with points at 2 distinct radii: 1+27=28

#                x1                 x2                 x3                 x4                 x5                 x6             Weight     Radius     cos1
  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.322982048753126    0.00000
 -0.447213595499958 -0.774596669241484  0.000000000000000 -0.000000000000000  0.000000000000000  0.000000000000000  0.179434471529513    0.89443  1.00000
 -0.447213595499958 -0.000000000000000 -0.387298334620742 -0.387298334620742  0.387298334620742 -0.387298334620742  0.179434471529513    0.89443  0.25000
 -0.447213595499958 -0.000000000000000  0.387298334620742  0.387298334620742 -0.387298334620742  0.387298334620742  0.179434471529513    0.89443  0.25000
  0.223606797749979 -0.387298334620742  0.387298334620742  0.387298334620742 -0.387298334620742 -0.387298334620742  0.179434471529513    0.89443  0.25000
  0.223606797749979 -0.387298334620742 -0.387298334620742  0.387298334620742 -0.387298334620742  0.387298334620742  0.179434471529513    0.89443  0.25000
  0.223606797749979 -0.387298334620742  0.387298334620742 -0.387298334620742 -0.387298334620742  0.387298334620742  0.179434471529513    0.89443  0.25000
  0.223606797749979 -0.387298334620742  0.387298334620742  0.387298334620742  0.387298334620742  0.387298334620742  0.179434471529513    0.89443  0.25000
  0.223606797749979 -0.387298334620742 -0.387298334620742  0.387298334620742  0.387298334620742 -0.387298334620742  0.179434471529513    0.89443  0.25000
  0.223606797749979 -0.387298334620742 -0.387298334620742 -0.387298334620742 -0.387298334620742 -0.387298334620742  0.179434471529513    0.89443  0.25000
  0.223606797749979 -0.387298334620742  0.387298334620742 -0.387298334620742  0.387298334620742 -0.387298334620742  0.179434471529513    0.89443  0.25000
  0.223606797749979 -0.387298334620742 -0.387298334620742 -0.387298334620742  0.387298334620742  0.387298334620742  0.179434471529513    0.89443  0.25000
 -0.447213595499958 -0.000000000000000 -0.387298334620742  0.387298334620742 -0.387298334620742 -0.387298334620742  0.179434471529513    0.89443  0.25000
 -0.447213595499958  0.000000000000000  0.387298334620742 -0.387298334620742 -0.387298334620742 -0.387298334620742  0.179434471529513    0.89443  0.25000
 -0.447213595499958  0.000000000000000  0.387298334620742  0.387298334620742  0.387298334620742 -0.387298334620742  0.179434471529513    0.89443  0.25000
 -0.447213595499958  0.000000000000000  0.387298334620742 -0.387298334620742  0.387298334620742  0.387298334620742  0.179434471529513    0.89443  0.25000
 -0.447213595499958 -0.000000000000000 -0.387298334620742  0.387298334620742  0.387298334620742  0.387298334620742  0.179434471529513    0.89443  0.25000
 -0.447213595499958  0.000000000000000 -0.387298334620742 -0.387298334620742 -0.387298334620742  0.387298334620742  0.179434471529513    0.89443  0.25000
  0.894427190999916  0.000000000000000 -0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.179434471529513    0.89443 -0.50000
 -0.447213595499958  0.774596669241484  0.000000000000000  0.000000000000000 -0.000000000000000 -0.000000000000000  0.179434471529513    0.89443 -0.50000
  0.223606797749979  0.387298334620742  0.774596669241484  0.000000000000000 -0.000000000000000  0.000000000000000  0.179434471529513    0.89443 -0.50000
  0.223606797749979  0.387298334620742  0.000000000000000  0.774596669241484  0.000000000000000 -0.000000000000000  0.179434471529513    0.89443 -0.50000
  0.223606797749979  0.387298334620742  0.000000000000000  0.000000000000000 -0.774596669241484  0.000000000000000  0.179434471529513    0.89443 -0.50000
  0.223606797749979  0.387298334620742 -0.774596669241484  0.000000000000000 -0.000000000000000 -0.000000000000000  0.179434471529513    0.89443 -0.50000
  0.223606797749979  0.387298334620742 -0.000000000000000 -0.774596669241484 -0.000000000000000 -0.000000000000000  0.179434471529513    0.89443 -0.50000
  0.223606797749979  0.387298334620742 -0.000000000000000  0.000000000000000  0.774596669241484 -0.000000000000000  0.179434471529513    0.89443 -0.50000
  0.223606797749979  0.387298334620742 -0.000000000000000  0.000000000000000 -0.000000000000000  0.774596669241484  0.179434471529513    0.89443 -0.50000
  0.223606797749979  0.387298334620742  0.000000000000000  0.000000000000000  0.000000000000000 -0.774596669241484  0.179434471529513    0.89443 -0.50000

E_n^r 6 dimensions, degree 4, asymmetric 28 point rule with points at 2 distinct radii: 1+27=28

#                x1                 x2                 x3                 x4                 x5                 x6             Weight     Radius     cos1
  0.000000000000001  0.000000000000001  0.000000000000001  0.000000000000001  0.000000000000001  0.000000000000001 1550.313834014991471    0.00000
 -4.242640687119284 -7.348469228349535  0.000000000000001 -0.000000000000001  0.000000000000001  0.000000000000001 80.386643245221791    8.48528  1.00000
 -4.242640687119284 -0.000000000000001 -3.674234614174767 -3.674234614174767  3.674234614174767 -3.674234614174767 80.386643245221791    8.48528  0.25000
 -4.242640687119284 -0.000000000000001  3.674234614174767  3.674234614174767 -3.674234614174767  3.674234614174767 80.386643245221791    8.48528  0.25000
  2.121320343559642 -3.674234614174767  3.674234614174767  3.674234614174767 -3.674234614174767 -3.674234614174767 80.386643245221791    8.48528  0.25000
  2.121320343559642 -3.674234614174767 -3.674234614174767  3.674234614174767 -3.674234614174767  3.674234614174767 80.386643245221791    8.48528  0.25000
  2.121320343559642 -3.674234614174767  3.674234614174767 -3.674234614174767 -3.674234614174767  3.674234614174767 80.386643245221791    8.48528  0.25000
  2.121320343559642 -3.674234614174767  3.674234614174767  3.674234614174767  3.674234614174767  3.674234614174767 80.386643245221791    8.48528  0.25000
  2.121320343559642 -3.674234614174767 -3.674234614174767  3.674234614174767  3.674234614174767 -3.674234614174767 80.386643245221791    8.48528  0.25000
  2.121320343559642 -3.674234614174767 -3.674234614174767 -3.674234614174767 -3.674234614174767 -3.674234614174767 80.386643245221791    8.48528  0.25000
  2.121320343559642 -3.674234614174767  3.674234614174767 -3.674234614174767  3.674234614174767 -3.674234614174767 80.386643245221791    8.48528  0.25000
  2.121320343559642 -3.674234614174767 -3.674234614174767 -3.674234614174767  3.674234614174767  3.674234614174767 80.386643245221791    8.48528  0.25000
 -4.242640687119284 -0.000000000000001 -3.674234614174767  3.674234614174767 -3.674234614174767 -3.674234614174767 80.386643245221791    8.48528  0.25000
 -4.242640687119284  0.000000000000001  3.674234614174767 -3.674234614174767 -3.674234614174767 -3.674234614174767 80.386643245221791    8.48528  0.25000
 -4.242640687119284  0.000000000000001  3.674234614174767  3.674234614174767  3.674234614174767 -3.674234614174767 80.386643245221791    8.48528  0.25000
 -4.242640687119284  0.000000000000001  3.674234614174767 -3.674234614174767  3.674234614174767  3.674234614174767 80.386643245221791    8.48528  0.25000
 -4.242640687119284 -0.000000000000001 -3.674234614174767  3.674234614174767  3.674234614174767  3.674234614174767 80.386643245221791    8.48528  0.25000
 -4.242640687119284  0.000000000000001 -3.674234614174767 -3.674234614174767 -3.674234614174767  3.674234614174767 80.386643245221791    8.48528  0.25000
  8.485281374238568  0.000000000000001 -0.000000000000001  0.000000000000001  0.000000000000001  0.000000000000001 80.386643245221791    8.48528 -0.50000
 -4.242640687119284  7.348469228349535  0.000000000000001  0.000000000000001 -0.000000000000001 -0.000000000000001 80.386643245221791    8.48528 -0.50000
  2.121320343559642  3.674234614174767  7.348469228349535  0.000000000000001 -0.000000000000001  0.000000000000001 80.386643245221791    8.48528 -0.50000
  2.121320343559642  3.674234614174767  0.000000000000001  7.348469228349535  0.000000000000001 -0.000000000000001 80.386643245221791    8.48528 -0.50000
  2.121320343559642  3.674234614174767  0.000000000000001  0.000000000000001 -7.348469228349535  0.000000000000001 80.386643245221791    8.48528 -0.50000
  2.121320343559642  3.674234614174767 -7.348469228349535  0.000000000000001 -0.000000000000001 -0.000000000000001 80.386643245221791    8.48528 -0.50000
  2.121320343559642  3.674234614174767 -0.000000000000001 -7.348469228349535 -0.000000000000001 -0.000000000000001 80.386643245221791    8.48528 -0.50000
  2.121320343559642  3.674234614174767 -0.000000000000001  0.000000000000001  7.348469228349535 -0.000000000000001 80.386643245221791    8.48528 -0.50000
  2.121320343559642  3.674234614174767 -0.000000000000001  0.000000000000001 -0.000000000000001  7.348469228349535 80.386643245221791    8.48528 -0.50000
  2.121320343559642  3.674234614174767  0.000000000000001  0.000000000000001  0.000000000000001 -7.348469228349535 80.386643245221791    8.48528 -0.50000

E_n^{r^2} 6 dimensions, degree 4, asymmetric 28 point rule with points at 2 distinct radii: 1+27=28

#                x1                 x2                 x3                 x4                 x5                 x6             Weight     Radius     cos1
  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  7.751569170074958    0.00000
 -1.000000000000000 -1.732050807568877  0.000000000000000 -0.000000000000000  0.000000000000000  0.000000000000000  0.861285463341662    2.00000  1.00000
 -1.000000000000000 -0.000000000000000 -0.866025403784438 -0.866025403784438  0.866025403784438 -0.866025403784438  0.861285463341662    2.00000  0.25000
 -1.000000000000000 -0.000000000000000  0.866025403784438  0.866025403784438 -0.866025403784438  0.866025403784438  0.861285463341662    2.00000  0.25000
  0.500000000000000 -0.866025403784438  0.866025403784438  0.866025403784438 -0.866025403784438 -0.866025403784438  0.861285463341662    2.00000  0.25000
  0.500000000000000 -0.866025403784438 -0.866025403784438  0.866025403784438 -0.866025403784438  0.866025403784438  0.861285463341662    2.00000  0.25000
  0.500000000000000 -0.866025403784438  0.866025403784438 -0.866025403784438 -0.866025403784438  0.866025403784438  0.861285463341662    2.00000  0.25000
  0.500000000000000 -0.866025403784438  0.866025403784438  0.866025403784438  0.866025403784438  0.866025403784438  0.861285463341662    2.00000  0.25000
  0.500000000000000 -0.866025403784438 -0.866025403784438  0.866025403784438  0.866025403784438 -0.866025403784438  0.861285463341662    2.00000  0.25000
  0.500000000000000 -0.866025403784438 -0.866025403784438 -0.866025403784438 -0.866025403784438 -0.866025403784438  0.861285463341662    2.00000  0.25000
  0.500000000000000 -0.866025403784438  0.866025403784438 -0.866025403784438  0.866025403784438 -0.866025403784438  0.861285463341662    2.00000  0.25000
  0.500000000000000 -0.866025403784438 -0.866025403784438 -0.866025403784438  0.866025403784438  0.866025403784438  0.861285463341662    2.00000  0.25000
 -1.000000000000000 -0.000000000000000 -0.866025403784438  0.866025403784438 -0.866025403784438 -0.866025403784438  0.861285463341662    2.00000  0.25000
 -1.000000000000000  0.000000000000000  0.866025403784438 -0.866025403784438 -0.866025403784438 -0.866025403784438  0.861285463341662    2.00000  0.25000
 -1.000000000000000  0.000000000000000  0.866025403784438  0.866025403784438  0.866025403784438 -0.866025403784438  0.861285463341662    2.00000  0.25000
 -1.000000000000000  0.000000000000000  0.866025403784438 -0.866025403784438  0.866025403784438  0.866025403784438  0.861285463341662    2.00000  0.25000
 -1.000000000000000 -0.000000000000000 -0.866025403784438  0.866025403784438  0.866025403784438  0.866025403784438  0.861285463341662    2.00000  0.25000
 -1.000000000000000  0.000000000000000 -0.866025403784438 -0.866025403784438 -0.866025403784438  0.866025403784438  0.861285463341662    2.00000  0.25000
  1.999999999999999  0.000000000000000 -0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.861285463341662    2.00000 -0.50000
 -1.000000000000000  1.732050807568877  0.000000000000000  0.000000000000000 -0.000000000000000 -0.000000000000000  0.861285463341662    2.00000 -0.50000
  0.500000000000000  0.866025403784438  1.732050807568877  0.000000000000000 -0.000000000000000  0.000000000000000  0.861285463341662    2.00000 -0.50000
  0.500000000000000  0.866025403784438  0.000000000000000  1.732050807568877  0.000000000000000 -0.000000000000000  0.861285463341662    2.00000 -0.50000
  0.500000000000000  0.866025403784438  0.000000000000000  0.000000000000000 -1.732050807568877  0.000000000000000  0.861285463341662    2.00000 -0.50000
  0.500000000000000  0.866025403784438 -1.732050807568877  0.000000000000000 -0.000000000000000 -0.000000000000000  0.861285463341662    2.00000 -0.50000
  0.500000000000000  0.866025403784438 -0.000000000000000 -1.732050807568877 -0.000000000000000 -0.000000000000000  0.861285463341662    2.00000 -0.50000
  0.500000000000000  0.866025403784438 -0.000000000000000  0.000000000000000  1.732050807568877 -0.000000000000000  0.861285463341662    2.00000 -0.50000
  0.500000000000000  0.866025403784438 -0.000000000000000  0.000000000000000 -0.000000000000000  1.732050807568877  0.861285463341662    2.00000 -0.50000
  0.500000000000000  0.866025403784438  0.000000000000000  0.000000000000000  0.000000000000000 -1.732050807568877  0.861285463341662    2.00000 -0.50000

>> # evaluating formula 1 with 44 points
# r6_44_5E1da.txt:4 formula 1   : problem E1, 6_44_5  (d=6 n=44 o=5 plus 405/462 of order 6) quality P
E1 6 dimensions, degree 5, centrally symmetric 44 point rule with points at 2 distinct radii: 12+32=44

#                 x1                  x2                  x3                  x4                  x5                  x6              Weight     Radius     cos1     cos2
   5.405789201738854  -0.000000000000000   0.000000000000000   0.000000000000000  -0.000000000000000   0.000000000000000 274.495347525855161    5.40579  1.00000  0.40825
   0.000000000000001   5.405789201738854  -0.000000000000000   0.000000000000000  -0.000000000000000   0.000000000000000 274.495347525855161    5.40579  0.00000  0.40825
  -0.000000000000001  -0.000000000000001   5.405789201738853   0.000000000000001   0.000000000000001  -0.000000000000000 274.495347525855161    5.40579 -0.00000 -0.40825
  -0.000000000000001  -0.000000000000000   0.000000000000002   5.405789201738857   0.000000000000002   0.000000000000000 274.495347525855161    5.40579 -0.00000  0.40825
  -0.000000000000001   0.000000000000001  -0.000000000000000   0.000000000000001   5.405789201738856  -0.000000000000000 274.495347525855161    5.40579 -0.00000  0.40825
  -0.000000000000001  -0.000000000000000   0.000000000000001  -0.000000000000001   0.000000000000001   5.405789201738854 274.495347525855161    5.40579 -0.00000  0.40825
   0.000000000000001   0.000000000000001  -0.000000000000001   0.000000000000001  -0.000000000000001  -5.405789201738854 274.495347525855161    5.40579  0.00000 -0.40825
   0.000000000000001  -0.000000000000001   0.000000000000000  -0.000000000000001  -5.405789201738856   0.000000000000000 274.495347525855161    5.40579  0.00000 -0.40825
   0.000000000000001   0.000000000000001  -0.000000000000001  -5.405789201738856  -0.000000000000002  -0.000000000000000 274.495347525855161    5.40579  0.00000 -0.40825
   0.000000000000001   0.000000000000001  -5.405789201738853  -0.000000000000001  -0.000000000000001   0.000000000000000 274.495347525855161    5.40579  0.00000  0.40825
  -0.000000000000000  -5.405789201738855  -0.000000000000001   0.000000000000001   0.000000000000001   0.000000000000000 274.495347525855161    5.40579 -0.00000 -0.40825
  -5.405789201738854   0.000000000000000  -0.000000000000001  -0.000000000000000   0.000000000000000  -0.000000000000001 274.495347525855161    5.40579 -1.00000 -0.40825
  -4.840992984344200  -4.840992984344200  -4.840992984344200  -4.840992984344200  -4.840992984344200   4.840992984344200  13.337782228928730   11.85796 -0.40825 -0.33333
  -4.840992984344200  -4.840992984344200  -4.840992984344200  -4.840992984344200   4.840992984344200  -4.840992984344200  13.337782228928730   11.85796 -0.40825 -0.33333
  -4.840992984344200  -4.840992984344200  -4.840992984344200   4.840992984344200  -4.840992984344200  -4.840992984344200  13.337782228928730   11.85796 -0.40825 -0.33333
  -4.840992984344200  -4.840992984344200  -4.840992984344200   4.840992984344200   4.840992984344200   4.840992984344200  13.337782228928730   11.85796 -0.40825  0.33333
  -4.840992984344200  -4.840992984344200   4.840992984344200  -4.840992984344200  -4.840992984344200  -4.840992984344200  13.337782228928730   11.85796 -0.40825 -1.00000
  -4.840992984344200  -4.840992984344200   4.840992984344200  -4.840992984344200   4.840992984344200   4.840992984344200  13.337782228928730   11.85796 -0.40825 -0.33333
  -4.840992984344200  -4.840992984344200   4.840992984344200   4.840992984344200  -4.840992984344200   4.840992984344200  13.337782228928730   11.85796 -0.40825 -0.33333
  -4.840992984344200  -4.840992984344200   4.840992984344200   4.840992984344200   4.840992984344200  -4.840992984344200  13.337782228928730   11.85796 -0.40825 -0.33333
  -4.840992984344200   4.840992984344200  -4.840992984344200  -4.840992984344200  -4.840992984344200  -4.840992984344200  13.337782228928730   11.85796 -0.40825 -0.33333
  -4.840992984344200   4.840992984344200  -4.840992984344200  -4.840992984344200   4.840992984344200   4.840992984344200  13.337782228928730   11.85796 -0.40825  0.33333
  -4.840992984344200   4.840992984344200  -4.840992984344200   4.840992984344200  -4.840992984344200   4.840992984344200  13.337782228928730   11.85796 -0.40825  0.33333
  -4.840992984344200   4.840992984344200  -4.840992984344200   4.840992984344200   4.840992984344200  -4.840992984344200  13.337782228928730   11.85796 -0.40825  0.33333
  -4.840992984344200   4.840992984344200   4.840992984344200  -4.840992984344200  -4.840992984344200   4.840992984344200  13.337782228928730   11.85796 -0.40825 -0.33333
  -4.840992984344200   4.840992984344200   4.840992984344200  -4.840992984344200   4.840992984344200  -4.840992984344200  13.337782228928730   11.85796 -0.40825 -0.33333
  -4.840992984344200   4.840992984344200   4.840992984344200   4.840992984344200  -4.840992984344200  -4.840992984344200  13.337782228928730   11.85796 -0.40825 -0.33333
  -4.840992984344200   4.840992984344200   4.840992984344200   4.840992984344200   4.840992984344200   4.840992984344200  13.337782228928730   11.85796 -0.40825  0.33333
   4.840992984344200  -4.840992984344200  -4.840992984344200  -4.840992984344200  -4.840992984344200  -4.840992984344200  13.337782228928730   11.85796  0.40825 -0.33333
   4.840992984344200  -4.840992984344200  -4.840992984344200  -4.840992984344200   4.840992984344200   4.840992984344200  13.337782228928730   11.85796  0.40825  0.33333
   4.840992984344200  -4.840992984344200  -4.840992984344200   4.840992984344200  -4.840992984344200   4.840992984344200  13.337782228928730   11.85796  0.40825  0.33333
   4.840992984344200  -4.840992984344200  -4.840992984344200   4.840992984344200   4.840992984344200  -4.840992984344200  13.337782228928730   11.85796  0.40825  0.33333
   4.840992984344200  -4.840992984344200   4.840992984344200  -4.840992984344200  -4.840992984344200   4.840992984344200  13.337782228928730   11.85796  0.40825 -0.33333
   4.840992984344200  -4.840992984344200   4.840992984344200  -4.840992984344200   4.840992984344200  -4.840992984344200  13.337782228928730   11.85796  0.40825 -0.33333
   4.840992984344200  -4.840992984344200   4.840992984344200   4.840992984344200  -4.840992984344200  -4.840992984344200  13.337782228928730   11.85796  0.40825 -0.33333
   4.840992984344200  -4.840992984344200   4.840992984344200   4.840992984344200   4.840992984344200   4.840992984344200  13.337782228928730   11.85796  0.40825  0.33333
   4.840992984344200   4.840992984344200  -4.840992984344200  -4.840992984344200  -4.840992984344200   4.840992984344200  13.337782228928730   11.85796  0.40825  0.33333
   4.840992984344200   4.840992984344200  -4.840992984344200  -4.840992984344200   4.840992984344200  -4.840992984344200  13.337782228928730   11.85796  0.40825  0.33333
   4.840992984344200   4.840992984344200  -4.840992984344200   4.840992984344200  -4.840992984344200  -4.840992984344200  13.337782228928730   11.85796  0.40825  0.33333
   4.840992984344200   4.840992984344200  -4.840992984344200   4.840992984344200   4.840992984344200   4.840992984344200  13.337782228928730   11.85796  0.40825  1.00000
   4.840992984344200   4.840992984344200   4.840992984344200  -4.840992984344200  -4.840992984344200  -4.840992984344200  13.337782228928730   11.85796  0.40825 -0.33333
   4.840992984344200   4.840992984344200   4.840992984344200  -4.840992984344200   4.840992984344200   4.840992984344200  13.337782228928730   11.85796  0.40825  0.33333
   4.840992984344200   4.840992984344200   4.840992984344200   4.840992984344200  -4.840992984344200   4.840992984344200  13.337782228928730   11.85796  0.40825  0.33333
   4.840992984344200   4.840992984344200   4.840992984344200   4.840992984344200   4.840992984344200  -4.840992984344200  13.337782228928730   11.85796  0.40825  0.33333

>> # evaluating formula 1 with 127 points
# r6_127_7g.txt:4 formula 1   : problem  G, 6_127_7  (d=6 n=127 o=7 plus 1155/1287 of order 8) quality P
# evaluating formula 2 with 127 points
# r6_127_7g.txt:135 formula 2   : problem  S, 6_127_7  (d=6 n=127 o=7 plus 1160/1287 of order 8) quality PB
# evaluating formula 3 with 127 points
# r6_127_7g.txt:266 formula 3   : problem E2, 6_127_7  (d=6 n=127 o=7 plus 1155/1287 of order 8) quality P
G_n 6 dimensions, degree 7, symmetric 127 point rule with points at 3 distinct radii: 1+54+72=127

#                x1                 x2                 x3                 x4                 x5                 x6             Weight     Radius     cos1     cos2
  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.135505102572168    0.00000  0.00000  0.00000
  2.490389734332217  0.000000000000000  0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.014904024783905    2.49039  1.00000  0.61237
  1.245194867166108  2.156740775255680 -0.000000000000000  0.000000000000000 -0.000000000000000 -0.000000000000000  0.014904024783905    2.49039  0.50000  0.61237
  1.245194867166108 -0.000000000000000  2.156740775255680  0.000000000000000  0.000000000000000  0.000000000000000  0.014904024783905    2.49039  0.50000  0.61237
  1.245194867166108 -0.000000000000000 -0.000000000000000  2.156740775255680 -0.000000000000000 -0.000000000000000  0.014904024783905    2.49039  0.50000  0.61237
  1.245194867166108 -0.000000000000000 -0.000000000000000 -0.000000000000000  2.156740775255680  0.000000000000000  0.014904024783905    2.49039  0.50000  0.61237
  1.245194867166108  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  2.156740775255680  0.014904024783905    2.49039  0.50000 -0.00000
  1.245194867166108 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -2.156740775255680  0.014904024783905    2.49039  0.50000  0.61237
  1.245194867166108 -0.000000000000000  0.000000000000000 -0.000000000000000 -2.156740775255680  0.000000000000000  0.014904024783905    2.49039  0.50000 -0.00000
  1.245194867166108  0.000000000000000  0.000000000000000 -2.156740775255680 -0.000000000000000  0.000000000000000  0.014904024783905    2.49039  0.50000 -0.00000
  1.245194867166108 -0.000000000000000 -2.156740775255680 -0.000000000000000 -0.000000000000000  0.000000000000000  0.014904024783905    2.49039  0.50000 -0.00000
  1.245194867166108 -2.156740775255680  0.000000000000000 -0.000000000000000 -0.000000000000000  0.000000000000000  0.014904024783905    2.49039  0.50000 -0.00000
  0.622597433583054  1.078370387627840  1.078370387627840  1.078370387627840  1.078370387627840  1.078370387627840  0.014904024783905    2.49039  0.25000  0.61237
  0.622597433583054  1.078370387627840  1.078370387627840  1.078370387627840 -1.078370387627840 -1.078370387627840  0.014904024783905    2.49039  0.25000  0.61237
  0.622597433583054  1.078370387627840  1.078370387627840 -1.078370387627840  1.078370387627840 -1.078370387627840  0.014904024783905    2.49039  0.25000  0.61237
  0.622597433583054  1.078370387627840  1.078370387627840 -1.078370387627840 -1.078370387627840  1.078370387627840  0.014904024783905    2.49039  0.25000 -0.00000
  0.622597433583054  1.078370387627840 -1.078370387627840  1.078370387627840  1.078370387627840 -1.078370387627840  0.014904024783905    2.49039  0.25000  0.61237
  0.622597433583054  1.078370387627840 -1.078370387627840  1.078370387627840 -1.078370387627840  1.078370387627840  0.014904024783905    2.49039  0.25000 -0.00000
  0.622597433583054  1.078370387627840 -1.078370387627840 -1.078370387627840  1.078370387627840  1.078370387627840  0.014904024783905    2.49039  0.25000 -0.00000
  0.622597433583054  1.078370387627840 -1.078370387627840 -1.078370387627840 -1.078370387627840 -1.078370387627840  0.014904024783905    2.49039  0.25000 -0.00000
  0.622597433583054 -1.078370387627840  1.078370387627840  1.078370387627840  1.078370387627840 -1.078370387627840  0.014904024783905    2.49039  0.25000  0.61237
  0.622597433583054 -1.078370387627840  1.078370387627840  1.078370387627840 -1.078370387627840  1.078370387627840  0.014904024783905    2.49039  0.25000 -0.00000
  0.622597433583054 -1.078370387627840  1.078370387627840 -1.078370387627840  1.078370387627840  1.078370387627840  0.014904024783905    2.49039  0.25000 -0.00000
  0.622597433583054 -1.078370387627840  1.078370387627840 -1.078370387627840 -1.078370387627840 -1.078370387627840  0.014904024783905    2.49039  0.25000 -0.00000
  0.622597433583054 -1.078370387627840 -1.078370387627840  1.078370387627840  1.078370387627840  1.078370387627840  0.014904024783905    2.49039  0.25000 -0.00000
  0.622597433583054 -1.078370387627840 -1.078370387627840  1.078370387627840 -1.078370387627840 -1.078370387627840  0.014904024783905    2.49039  0.25000 -0.00000
  0.622597433583054 -1.078370387627840 -1.078370387627840 -1.078370387627840  1.078370387627840 -1.078370387627840  0.014904024783905    2.49039  0.25000 -0.00000
  0.622597433583054 -1.078370387627840 -1.078370387627840 -1.078370387627840 -1.078370387627840  1.078370387627840  0.014904024783905    2.49039  0.25000 -0.61237
 -0.622597433583054  1.078370387627840  1.078370387627840  1.078370387627840  1.078370387627840 -1.078370387627840  0.014904024783905    2.49039 -0.25000  0.61237
 -0.622597433583054  1.078370387627840  1.078370387627840  1.078370387627840 -1.078370387627840  1.078370387627840  0.014904024783905    2.49039 -0.25000  0.00000
 -0.622597433583054  1.078370387627840  1.078370387627840 -1.078370387627840  1.078370387627840  1.078370387627840  0.014904024783905    2.49039 -0.25000  0.00000
 -0.622597433583054  1.078370387627840  1.078370387627840 -1.078370387627840 -1.078370387627840 -1.078370387627840  0.014904024783905    2.49039 -0.25000  0.00000
 -0.622597433583054  1.078370387627840 -1.078370387627840  1.078370387627840  1.078370387627840  1.078370387627840  0.014904024783905    2.49039 -0.25000  0.00000
 -0.622597433583054  1.078370387627840 -1.078370387627840  1.078370387627840 -1.078370387627840 -1.078370387627840  0.014904024783905    2.49039 -0.25000  0.00000
 -0.622597433583054  1.078370387627840 -1.078370387627840 -1.078370387627840  1.078370387627840 -1.078370387627840  0.014904024783905    2.49039 -0.25000  0.00000
 -0.622597433583054  1.078370387627840 -1.078370387627840 -1.078370387627840 -1.078370387627840  1.078370387627840  0.014904024783905    2.49039 -0.25000 -0.61237
 -0.622597433583054 -1.078370387627840  1.078370387627840  1.078370387627840  1.078370387627840  1.078370387627840  0.014904024783905    2.49039 -0.25000  0.00000
 -0.622597433583054 -1.078370387627840  1.078370387627840  1.078370387627840 -1.078370387627840 -1.078370387627840  0.014904024783905    2.49039 -0.25000  0.00000
 -0.622597433583054 -1.078370387627840  1.078370387627840 -1.078370387627840  1.078370387627840 -1.078370387627840  0.014904024783905    2.49039 -0.25000  0.00000
 -0.622597433583054 -1.078370387627840  1.078370387627840 -1.078370387627840 -1.078370387627840  1.078370387627840  0.014904024783905    2.49039 -0.25000 -0.61237
 -0.622597433583054 -1.078370387627840 -1.078370387627840  1.078370387627840  1.078370387627840 -1.078370387627840  0.014904024783905    2.49039 -0.25000  0.00000
 -0.622597433583054 -1.078370387627840 -1.078370387627840  1.078370387627840 -1.078370387627840  1.078370387627840  0.014904024783905    2.49039 -0.25000 -0.61237
 -0.622597433583054 -1.078370387627840 -1.078370387627840 -1.078370387627840  1.078370387627840  1.078370387627840  0.014904024783905    2.49039 -0.25000 -0.61237
 -0.622597433583054 -1.078370387627840 -1.078370387627840 -1.078370387627840 -1.078370387627840 -1.078370387627840  0.014904024783905    2.49039 -0.25000 -0.61237
 -1.245194867166108  2.156740775255680 -0.000000000000000  0.000000000000000  0.000000000000000 -0.000000000000000  0.014904024783905    2.49039 -0.50000  0.00000
 -1.245194867166108  0.000000000000000  2.156740775255680  0.000000000000000  0.000000000000000 -0.000000000000000  0.014904024783905    2.49039 -0.50000  0.00000
 -1.245194867166108 -0.000000000000000 -0.000000000000000  2.156740775255680  0.000000000000000 -0.000000000000000  0.014904024783905    2.49039 -0.50000  0.00000
 -1.245194867166108  0.000000000000000 -0.000000000000000  0.000000000000000  2.156740775255680 -0.000000000000000  0.014904024783905    2.49039 -0.50000  0.00000
 -1.245194867166108  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  2.156740775255680  0.014904024783905    2.49039 -0.50000 -0.61237
 -1.245194867166108 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -2.156740775255680  0.014904024783905    2.49039 -0.50000  0.00000
 -1.245194867166108  0.000000000000000  0.000000000000000  0.000000000000000 -2.156740775255680 -0.000000000000000  0.014904024783905    2.49039 -0.50000 -0.61237
 -1.245194867166108  0.000000000000000  0.000000000000000 -2.156740775255680  0.000000000000000  0.000000000000000  0.014904024783905    2.49039 -0.50000 -0.61237
 -1.245194867166108  0.000000000000000 -2.156740775255680 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.014904024783905    2.49039 -0.50000 -0.61237
 -1.245194867166108 -2.156740775255680  0.000000000000000 -0.000000000000000  0.000000000000000  0.000000000000000  0.014904024783905    2.49039 -0.50000 -0.61237
 -2.490389734332217 -0.000000000000000 -0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.014904024783905    2.49039 -1.00000 -0.61237
  2.517363165514142  1.453400301257639  1.453400301257639  1.453400301257639  1.453400301257639 -1.453400301257639  0.000828854987458    4.11084  0.61237  1.00000
  2.517363165514142  1.453400301257639  1.453400301257639  1.453400301257639 -1.453400301257639  1.453400301257639  0.000828854987458    4.11084  0.61237  0.50000
  2.517363165514142  1.453400301257639  1.453400301257639 -1.453400301257639  1.453400301257639  1.453400301257639  0.000828854987458    4.11084  0.61237  0.50000
  2.517363165514142  1.453400301257639  1.453400301257639 -1.453400301257639 -1.453400301257639 -1.453400301257639  0.000828854987458    4.11084  0.61237  0.50000
  2.517363165514142  1.453400301257639 -1.453400301257639  1.453400301257639  1.453400301257639  1.453400301257639  0.000828854987458    4.11084  0.61237  0.50000
  2.517363165514142  1.453400301257639 -1.453400301257639  1.453400301257639 -1.453400301257639 -1.453400301257639  0.000828854987458    4.11084  0.61237  0.50000
  2.517363165514142  1.453400301257639 -1.453400301257639 -1.453400301257639  1.453400301257639 -1.453400301257639  0.000828854987458    4.11084  0.61237  0.50000
  2.517363165514142  1.453400301257639 -1.453400301257639 -1.453400301257639 -1.453400301257639  1.453400301257639  0.000828854987458    4.11084  0.61237 -0.00000
  2.517363165514142 -1.453400301257639  1.453400301257639  1.453400301257639  1.453400301257639  1.453400301257639  0.000828854987458    4.11084  0.61237  0.50000
  2.517363165514142 -1.453400301257639  1.453400301257639  1.453400301257639 -1.453400301257639 -1.453400301257639  0.000828854987458    4.11084  0.61237  0.50000
  2.517363165514142 -1.453400301257639  1.453400301257639 -1.453400301257639  1.453400301257639 -1.453400301257639  0.000828854987458    4.11084  0.61237  0.50000
  2.517363165514142 -1.453400301257639  1.453400301257639 -1.453400301257639 -1.453400301257639  1.453400301257639  0.000828854987458    4.11084  0.61237 -0.00000
  2.517363165514142 -1.453400301257639 -1.453400301257639  1.453400301257639  1.453400301257639 -1.453400301257639  0.000828854987458    4.11084  0.61237  0.50000
  2.517363165514142 -1.453400301257639 -1.453400301257639  1.453400301257639 -1.453400301257639  1.453400301257639  0.000828854987458    4.11084  0.61237 -0.00000
  2.517363165514142 -1.453400301257639 -1.453400301257639 -1.453400301257639  1.453400301257639  1.453400301257639  0.000828854987458    4.11084  0.61237 -0.00000
  2.517363165514142 -1.453400301257639 -1.453400301257639 -1.453400301257639 -1.453400301257639 -1.453400301257639  0.000828854987458    4.11084  0.61237 -0.00000
 -0.000000000000000  2.906800602515279  2.906800602515279  0.000000000000000  0.000000000000000 -0.000000000000000  0.000828854987458    4.11084  0.00000  0.50000
  0.000000000000000  2.906800602515279 -0.000000000000000  2.906800602515279  0.000000000000000 -0.000000000000000  0.000828854987458    4.11084  0.00000  0.50000
 -0.000000000000000  2.906800602515279 -0.000000000000000  0.000000000000000  2.906800602515279 -0.000000000000000  0.000828854987458    4.11084 -0.00000  0.50000
  0.000000000000000  2.906800602515279 -0.000000000000000  0.000000000000000  0.000000000000000  2.906800602515279  0.000828854987458    4.11084  0.00000  0.00000
  0.000000000000000  2.906800602515279 -0.000000000000000  0.000000000000000 -0.000000000000000 -2.906800602515279  0.000828854987458    4.11084  0.00000  0.50000
  0.000000000000000  2.906800602515279  0.000000000000000  0.000000000000000 -2.906800602515279 -0.000000000000000  0.000828854987458    4.11084  0.00000  0.00000
  0.000000000000000  2.906800602515279  0.000000000000000 -2.906800602515279 -0.000000000000000 -0.000000000000000  0.000828854987458    4.11084  0.00000  0.00000
  0.000000000000000  2.906800602515279 -2.906800602515279  0.000000000000000 -0.000000000000000 -0.000000000000000  0.000828854987458    4.11084  0.00000  0.00000
 -0.000000000000000 -0.000000000000000  2.906800602515279  2.906800602515279  0.000000000000000 -0.000000000000000  0.000828854987458    4.11084 -0.00000  0.50000
 -0.000000000000000  0.000000000000000  2.906800602515279  0.000000000000000  2.906800602515279 -0.000000000000000  0.000828854987458    4.11084 -0.00000  0.50000
  0.000000000000000  0.000000000000000  2.906800602515279  0.000000000000000  0.000000000000000  2.906800602515279  0.000828854987458    4.11084  0.00000  0.00000
  0.000000000000000 -0.000000000000000  2.906800602515279  0.000000000000000  0.000000000000000 -2.906800602515279  0.000828854987458    4.11084  0.00000  0.50000
  0.000000000000000 -0.000000000000000  2.906800602515279  0.000000000000000 -2.906800602515279  0.000000000000000  0.000828854987458    4.11084  0.00000  0.00000
 -0.000000000000000  0.000000000000000  2.906800602515279 -2.906800602515279  0.000000000000000  0.000000000000000  0.000828854987458    4.11084  0.00000  0.00000
 -0.000000000000000 -0.000000000000000 -0.000000000000000  2.906800602515279  2.906800602515279 -0.000000000000000  0.000828854987458    4.11084 -0.00000  0.50000
  0.000000000000000 -0.000000000000000 -0.000000000000000  2.906800602515279  0.000000000000000  2.906800602515279  0.000828854987458    4.11084 -0.00000  0.00000
  0.000000000000000 -0.000000000000000 -0.000000000000000  2.906800602515279 -0.000000000000000 -2.906800602515279  0.000828854987458    4.11084  0.00000  0.50000
  0.000000000000000 -0.000000000000000  0.000000000000000  2.906800602515279 -2.906800602515279 -0.000000000000000  0.000828854987458    4.11084  0.00000  0.00000
  0.000000000000000  0.000000000000000 -0.000000000000000 -0.000000000000000  2.906800602515279  2.906800602515279  0.000828854987458    4.11084 -0.00000  0.00000
  0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  2.906800602515279 -2.906800602515279  0.000828854987458    4.11084  0.00000  0.50000
 -0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 -2.906800602515279  2.906800602515279  0.000828854987458    4.11084 -0.00000 -0.50000
 -0.000000000000000 -0.000000000000000  0.000000000000000  0.000000000000000 -2.906800602515279 -2.906800602515279  0.000828854987458    4.11084  0.00000  0.00000
 -0.000000000000000  0.000000000000000 -0.000000000000000 -2.906800602515279  2.906800602515279  0.000000000000000  0.000828854987458    4.11084 -0.00000 -0.00000
 -0.000000000000000  0.000000000000000  0.000000000000000 -2.906800602515279  0.000000000000000  2.906800602515279  0.000828854987458    4.11084 -0.00000 -0.50000
 -0.000000000000000  0.000000000000000  0.000000000000000 -2.906800602515279 -0.000000000000000 -2.906800602515279  0.000828854987458    4.11084  0.00000 -0.00000
  0.000000000000000  0.000000000000000  0.000000000000000 -2.906800602515279 -2.906800602515279  0.000000000000000  0.000828854987458    4.11084  0.00000 -0.50000
  0.000000000000000 -0.000000000000000 -2.906800602515279  2.906800602515279 -0.000000000000000 -0.000000000000000  0.000828854987458    4.11084 -0.00000  0.00000
  0.000000000000000  0.000000000000000 -2.906800602515279 -0.000000000000000  2.906800602515279  0.000000000000000  0.000828854987458    4.11084 -0.00000 -0.00000
 -0.000000000000000  0.000000000000000 -2.906800602515279 -0.000000000000000 -0.000000000000000  2.906800602515279  0.000828854987458    4.11084 -0.00000 -0.50000
 -0.000000000000000 -0.000000000000000 -2.906800602515279 -0.000000000000000 -0.000000000000000 -2.906800602515279  0.000828854987458    4.11084 -0.00000 -0.00000
  0.000000000000000 -0.000000000000000 -2.906800602515279 -0.000000000000000 -2.906800602515279  0.000000000000000  0.000828854987458    4.11084  0.00000 -0.50000
  0.000000000000000  0.000000000000000 -2.906800602515279 -2.906800602515279 -0.000000000000000  0.000000000000000  0.000828854987458    4.11084  0.00000 -0.50000
 -0.000000000000000 -2.906800602515279  2.906800602515279 -0.000000000000000  0.000000000000000  0.000000000000000  0.000828854987458    4.11084 -0.00000 -0.00000
  0.000000000000000 -2.906800602515279 -0.000000000000000  2.906800602515279  0.000000000000000  0.000000000000000  0.000828854987458    4.11084 -0.00000  0.00000
 -0.000000000000000 -2.906800602515279 -0.000000000000000 -0.000000000000000  2.906800602515279  0.000000000000000  0.000828854987458    4.11084 -0.00000 -0.00000
 -0.000000000000000 -2.906800602515279  0.000000000000000 -0.000000000000000  0.000000000000000  2.906800602515279  0.000828854987458    4.11084 -0.00000 -0.50000
 -0.000000000000000 -2.906800602515279  0.000000000000000 -0.000000000000000 -0.000000000000000 -2.906800602515279  0.000828854987458    4.11084 -0.00000 -0.00000
  0.000000000000000 -2.906800602515279  0.000000000000000 -0.000000000000000 -2.906800602515279  0.000000000000000  0.000828854987458    4.11084  0.00000 -0.50000
 -0.000000000000000 -2.906800602515279  0.000000000000000 -2.906800602515279 -0.000000000000000  0.000000000000000  0.000828854987458    4.11084 -0.00000 -0.50000
  0.000000000000000 -2.906800602515279 -2.906800602515279 -0.000000000000000 -0.000000000000000  0.000000000000000  0.000828854987458    4.11084 -0.00000 -0.50000
 -2.517363165514142  1.453400301257639  1.453400301257639  1.453400301257639  1.453400301257639  1.453400301257639  0.000828854987458    4.11084 -0.61237  0.00000
 -2.517363165514142  1.453400301257639  1.453400301257639  1.453400301257639 -1.453400301257639 -1.453400301257639  0.000828854987458    4.11084 -0.61237  0.00000
 -2.517363165514142  1.453400301257639  1.453400301257639 -1.453400301257639  1.453400301257639 -1.453400301257639  0.000828854987458    4.11084 -0.61237  0.00000
 -2.517363165514142  1.453400301257639  1.453400301257639 -1.453400301257639 -1.453400301257639  1.453400301257639  0.000828854987458    4.11084 -0.61237 -0.50000
 -2.517363165514142  1.453400301257639 -1.453400301257639  1.453400301257639  1.453400301257639 -1.453400301257639  0.000828854987458    4.11084 -0.61237  0.00000
 -2.517363165514142  1.453400301257639 -1.453400301257639  1.453400301257639 -1.453400301257639  1.453400301257639  0.000828854987458    4.11084 -0.61237 -0.50000
 -2.517363165514142  1.453400301257639 -1.453400301257639 -1.453400301257639  1.453400301257639  1.453400301257639  0.000828854987458    4.11084 -0.61237 -0.50000
 -2.517363165514142  1.453400301257639 -1.453400301257639 -1.453400301257639 -1.453400301257639 -1.453400301257639  0.000828854987458    4.11084 -0.61237 -0.50000
 -2.517363165514142 -1.453400301257639  1.453400301257639  1.453400301257639  1.453400301257639 -1.453400301257639  0.000828854987458    4.11084 -0.61237  0.00000
 -2.517363165514142 -1.453400301257639  1.453400301257639  1.453400301257639 -1.453400301257639  1.453400301257639  0.000828854987458    4.11084 -0.61237 -0.50000
 -2.517363165514142 -1.453400301257639  1.453400301257639 -1.453400301257639  1.453400301257639  1.453400301257639  0.000828854987458    4.11084 -0.61237 -0.50000
 -2.517363165514142 -1.453400301257639  1.453400301257639 -1.453400301257639 -1.453400301257639 -1.453400301257639  0.000828854987458    4.11084 -0.61237 -0.50000
 -2.517363165514142 -1.453400301257639 -1.453400301257639  1.453400301257639  1.453400301257639  1.453400301257639  0.000828854987458    4.11084 -0.61237 -0.50000
 -2.517363165514142 -1.453400301257639 -1.453400301257639  1.453400301257639 -1.453400301257639 -1.453400301257639  0.000828854987458    4.11084 -0.61237 -0.50000
 -2.517363165514142 -1.453400301257639 -1.453400301257639 -1.453400301257639  1.453400301257639 -1.453400301257639  0.000828854987458    4.11084 -0.61237 -0.50000
 -2.517363165514142 -1.453400301257639 -1.453400301257639 -1.453400301257639 -1.453400301257639  1.453400301257639  0.000828854987458    4.11084 -0.61237 -1.00000

S_n 6 dimensions, degree 7, symmetric 127 point rule with points at 3 distinct radii: 1+54+72=127

#                x1                 x2                 x3                 x4                 x5                 x6             Weight     Radius     cos1     cos2
  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.129192819501248    0.00000  0.00000 -0.00000
  0.816496580927726  0.000000000000000  0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.064596409750625    0.81650  1.00000 -0.61237
  0.408248290463863  0.707106781186548 -0.000000000000000  0.000000000000000 -0.000000000000000 -0.000000000000000  0.064596409750625    0.81650  0.50000 -0.61237
  0.408248290463863 -0.000000000000000  0.707106781186548  0.000000000000000  0.000000000000000  0.000000000000000  0.064596409750625    0.81650  0.50000 -0.61237
  0.408248290463863 -0.000000000000000 -0.000000000000000  0.707106781186548 -0.000000000000000 -0.000000000000000  0.064596409750625    0.81650  0.50000 -0.61237
  0.408248290463863 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.707106781186548  0.000000000000000  0.064596409750625    0.81650  0.50000 -0.61237
  0.408248290463863  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.707106781186548  0.064596409750625    0.81650  0.50000  0.00000
  0.408248290463863 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.707106781186548  0.064596409750625    0.81650  0.50000 -0.61237
  0.408248290463863 -0.000000000000000  0.000000000000000 -0.000000000000000 -0.707106781186548  0.000000000000000  0.064596409750625    0.81650  0.50000  0.00000
  0.408248290463863  0.000000000000000  0.000000000000000 -0.707106781186548 -0.000000000000000  0.000000000000000  0.064596409750625    0.81650  0.50000  0.00000
  0.408248290463863 -0.000000000000000 -0.707106781186548 -0.000000000000000 -0.000000000000000  0.000000000000000  0.064596409750625    0.81650  0.50000  0.00000
  0.408248290463863 -0.707106781186548  0.000000000000000 -0.000000000000000 -0.000000000000000  0.000000000000000  0.064596409750625    0.81650  0.50000  0.00000
  0.204124145231931  0.353553390593274  0.353553390593274  0.353553390593274  0.353553390593274  0.353553390593274  0.064596409750625    0.81650  0.25000 -0.61237
  0.204124145231931  0.353553390593274  0.353553390593274  0.353553390593274 -0.353553390593274 -0.353553390593274  0.064596409750625    0.81650  0.25000 -0.61237
  0.204124145231931  0.353553390593274  0.353553390593274 -0.353553390593274  0.353553390593274 -0.353553390593274  0.064596409750625    0.81650  0.25000 -0.61237
  0.204124145231931  0.353553390593274  0.353553390593274 -0.353553390593274 -0.353553390593274  0.353553390593274  0.064596409750625    0.81650  0.25000  0.00000
  0.204124145231931  0.353553390593274 -0.353553390593274  0.353553390593274  0.353553390593274 -0.353553390593274  0.064596409750625    0.81650  0.25000 -0.61237
  0.204124145231931  0.353553390593274 -0.353553390593274  0.353553390593274 -0.353553390593274  0.353553390593274  0.064596409750625    0.81650  0.25000  0.00000
  0.204124145231931  0.353553390593274 -0.353553390593274 -0.353553390593274  0.353553390593274  0.353553390593274  0.064596409750625    0.81650  0.25000  0.00000
  0.204124145231931  0.353553390593274 -0.353553390593274 -0.353553390593274 -0.353553390593274 -0.353553390593274  0.064596409750625    0.81650  0.25000  0.00000
  0.204124145231931 -0.353553390593274  0.353553390593274  0.353553390593274  0.353553390593274 -0.353553390593274  0.064596409750625    0.81650  0.25000 -0.61237
  0.204124145231931 -0.353553390593274  0.353553390593274  0.353553390593274 -0.353553390593274  0.353553390593274  0.064596409750625    0.81650  0.25000  0.00000
  0.204124145231931 -0.353553390593274  0.353553390593274 -0.353553390593274  0.353553390593274  0.353553390593274  0.064596409750625    0.81650  0.25000  0.00000
  0.204124145231931 -0.353553390593274  0.353553390593274 -0.353553390593274 -0.353553390593274 -0.353553390593274  0.064596409750625    0.81650  0.25000  0.00000
  0.204124145231931 -0.353553390593274 -0.353553390593274  0.353553390593274  0.353553390593274  0.353553390593274  0.064596409750625    0.81650  0.25000  0.00000
  0.204124145231931 -0.353553390593274 -0.353553390593274  0.353553390593274 -0.353553390593274 -0.353553390593274  0.064596409750625    0.81650  0.25000  0.00000
  0.204124145231931 -0.353553390593274 -0.353553390593274 -0.353553390593274  0.353553390593274 -0.353553390593274  0.064596409750625    0.81650  0.25000  0.00000
  0.204124145231931 -0.353553390593274 -0.353553390593274 -0.353553390593274 -0.353553390593274  0.353553390593274  0.064596409750625    0.81650  0.25000  0.61237
 -0.204124145231931  0.353553390593274  0.353553390593274  0.353553390593274  0.353553390593274 -0.353553390593274  0.064596409750625    0.81650 -0.25000 -0.61237
 -0.204124145231931  0.353553390593274  0.353553390593274  0.353553390593274 -0.353553390593274  0.353553390593274  0.064596409750625    0.81650 -0.25000 -0.00000
 -0.204124145231931  0.353553390593274  0.353553390593274 -0.353553390593274  0.353553390593274  0.353553390593274  0.064596409750625    0.81650 -0.25000 -0.00000
 -0.204124145231931  0.353553390593274  0.353553390593274 -0.353553390593274 -0.353553390593274 -0.353553390593274  0.064596409750625    0.81650 -0.25000 -0.00000
 -0.204124145231931  0.353553390593274 -0.353553390593274  0.353553390593274  0.353553390593274  0.353553390593274  0.064596409750625    0.81650 -0.25000 -0.00000
 -0.204124145231931  0.353553390593274 -0.353553390593274  0.353553390593274 -0.353553390593274 -0.353553390593274  0.064596409750625    0.81650 -0.25000 -0.00000
 -0.204124145231931  0.353553390593274 -0.353553390593274 -0.353553390593274  0.353553390593274 -0.353553390593274  0.064596409750625    0.81650 -0.25000 -0.00000
 -0.204124145231931  0.353553390593274 -0.353553390593274 -0.353553390593274 -0.353553390593274  0.353553390593274  0.064596409750625    0.81650 -0.25000  0.61237
 -0.204124145231931 -0.353553390593274  0.353553390593274  0.353553390593274  0.353553390593274  0.353553390593274  0.064596409750625    0.81650 -0.25000 -0.00000
 -0.204124145231931 -0.353553390593274  0.353553390593274  0.353553390593274 -0.353553390593274 -0.353553390593274  0.064596409750625    0.81650 -0.25000 -0.00000
 -0.204124145231931 -0.353553390593274  0.353553390593274 -0.353553390593274  0.353553390593274 -0.353553390593274  0.064596409750625    0.81650 -0.25000 -0.00000
 -0.204124145231931 -0.353553390593274  0.353553390593274 -0.353553390593274 -0.353553390593274  0.353553390593274  0.064596409750625    0.81650 -0.25000  0.61237
 -0.204124145231931 -0.353553390593274 -0.353553390593274  0.353553390593274  0.353553390593274 -0.353553390593274  0.064596409750625    0.81650 -0.25000 -0.00000
 -0.204124145231931 -0.353553390593274 -0.353553390593274  0.353553390593274 -0.353553390593274  0.353553390593274  0.064596409750625    0.81650 -0.25000  0.61237
 -0.204124145231931 -0.353553390593274 -0.353553390593274 -0.353553390593274  0.353553390593274  0.353553390593274  0.064596409750625    0.81650 -0.25000  0.61237
 -0.204124145231931 -0.353553390593274 -0.353553390593274 -0.353553390593274 -0.353553390593274 -0.353553390593274  0.064596409750625    0.81650 -0.25000  0.61237
 -0.408248290463863  0.707106781186548 -0.000000000000000  0.000000000000000  0.000000000000000 -0.000000000000000  0.064596409750625    0.81650 -0.50000 -0.00000
 -0.408248290463863  0.000000000000000  0.707106781186548  0.000000000000000  0.000000000000000 -0.000000000000000  0.064596409750625    0.81650 -0.50000 -0.00000
 -0.408248290463863 -0.000000000000000 -0.000000000000000  0.707106781186548  0.000000000000000 -0.000000000000000  0.064596409750625    0.81650 -0.50000 -0.00000
 -0.408248290463863  0.000000000000000 -0.000000000000000  0.000000000000000  0.707106781186548 -0.000000000000000  0.064596409750625    0.81650 -0.50000 -0.00000
 -0.408248290463863  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.707106781186548  0.064596409750625    0.81650 -0.50000  0.61237
 -0.408248290463863 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.707106781186548  0.064596409750625    0.81650 -0.50000 -0.00000
 -0.408248290463863  0.000000000000000  0.000000000000000  0.000000000000000 -0.707106781186548 -0.000000000000000  0.064596409750625    0.81650 -0.50000  0.61237
 -0.408248290463863  0.000000000000000  0.000000000000000 -0.707106781186548  0.000000000000000  0.000000000000000  0.064596409750625    0.81650 -0.50000  0.61237
 -0.408248290463863  0.000000000000000 -0.707106781186548 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.064596409750625    0.81650 -0.50000  0.61237
 -0.408248290463863 -0.707106781186548  0.000000000000000 -0.000000000000000  0.000000000000000  0.000000000000000  0.064596409750625    0.81650 -0.50000  0.61237
 -0.816496580927726 -0.000000000000000 -0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.064596409750625    0.81650 -1.00000  0.61237
 -0.612372435695794 -0.353553390593274 -0.353553390593274 -0.353553390593274 -0.353553390593274  0.353553390593274  0.021532136583541    1.00000 -0.61237  1.00000
 -0.612372435695794 -0.353553390593274 -0.353553390593274 -0.353553390593274  0.353553390593274 -0.353553390593274  0.021532136583541    1.00000 -0.61237  0.50000
 -0.612372435695794 -0.353553390593274 -0.353553390593274  0.353553390593274 -0.353553390593274 -0.353553390593274  0.021532136583541    1.00000 -0.61237  0.50000
 -0.612372435695794 -0.353553390593274 -0.353553390593274  0.353553390593274  0.353553390593274  0.353553390593274  0.021532136583541    1.00000 -0.61237  0.50000
 -0.612372435695794 -0.353553390593274  0.353553390593274 -0.353553390593274 -0.353553390593274 -0.353553390593274  0.021532136583541    1.00000 -0.61237  0.50000
 -0.612372435695794 -0.353553390593274  0.353553390593274 -0.353553390593274  0.353553390593274  0.353553390593274  0.021532136583541    1.00000 -0.61237  0.50000
 -0.612372435695794 -0.353553390593274  0.353553390593274  0.353553390593274 -0.353553390593274  0.353553390593274  0.021532136583541    1.00000 -0.61237  0.50000
 -0.612372435695794 -0.353553390593274  0.353553390593274  0.353553390593274  0.353553390593274 -0.353553390593274  0.021532136583541    1.00000 -0.61237 -0.00000
 -0.612372435695794  0.353553390593274 -0.353553390593274 -0.353553390593274 -0.353553390593274 -0.353553390593274  0.021532136583541    1.00000 -0.61237  0.50000
 -0.612372435695794  0.353553390593274 -0.353553390593274 -0.353553390593274  0.353553390593274  0.353553390593274  0.021532136583541    1.00000 -0.61237  0.50000
 -0.612372435695794  0.353553390593274 -0.353553390593274  0.353553390593274 -0.353553390593274  0.353553390593274  0.021532136583541    1.00000 -0.61237  0.50000
 -0.612372435695794  0.353553390593274 -0.353553390593274  0.353553390593274  0.353553390593274 -0.353553390593274  0.021532136583541    1.00000 -0.61237 -0.00000
 -0.612372435695794  0.353553390593274  0.353553390593274 -0.353553390593274 -0.353553390593274  0.353553390593274  0.021532136583541    1.00000 -0.61237  0.50000
 -0.612372435695794  0.353553390593274  0.353553390593274 -0.353553390593274  0.353553390593274 -0.353553390593274  0.021532136583541    1.00000 -0.61237 -0.00000
 -0.612372435695794  0.353553390593274  0.353553390593274  0.353553390593274 -0.353553390593274 -0.353553390593274  0.021532136583541    1.00000 -0.61237 -0.00000
 -0.612372435695794  0.353553390593274  0.353553390593274  0.353553390593274  0.353553390593274  0.353553390593274  0.021532136583541    1.00000 -0.61237 -0.00000
  0.000000000000000 -0.707106781186548 -0.707106781186548 -0.000000000000000 -0.000000000000000  0.000000000000000  0.021532136583541    1.00000 -0.00000  0.50000
 -0.000000000000000 -0.707106781186548  0.000000000000000 -0.707106781186548 -0.000000000000000  0.000000000000000  0.021532136583541    1.00000 -0.00000  0.50000
  0.000000000000000 -0.707106781186548  0.000000000000000 -0.000000000000000 -0.707106781186548  0.000000000000000  0.021532136583541    1.00000  0.00000  0.50000
 -0.000000000000000 -0.707106781186548  0.000000000000000 -0.000000000000000 -0.000000000000000 -0.707106781186548  0.021532136583541    1.00000 -0.00000  0.00000
 -0.000000000000000 -0.707106781186548  0.000000000000000 -0.000000000000000  0.000000000000000  0.707106781186548  0.021532136583541    1.00000 -0.00000  0.50000
 -0.000000000000000 -0.707106781186548 -0.000000000000000 -0.000000000000000  0.707106781186548  0.000000000000000  0.021532136583541    1.00000 -0.00000  0.00000
 -0.000000000000000 -0.707106781186548 -0.000000000000000  0.707106781186548  0.000000000000000  0.000000000000000  0.021532136583541    1.00000 -0.00000  0.00000
 -0.000000000000000 -0.707106781186548  0.707106781186548 -0.000000000000000  0.000000000000000  0.000000000000000  0.021532136583541    1.00000 -0.00000  0.00000
  0.000000000000000  0.000000000000000 -0.707106781186548 -0.707106781186548 -0.000000000000000  0.000000000000000  0.021532136583541    1.00000  0.00000  0.50000
  0.000000000000000 -0.000000000000000 -0.707106781186548 -0.000000000000000 -0.707106781186548  0.000000000000000  0.021532136583541    1.00000  0.00000  0.50000
 -0.000000000000000 -0.000000000000000 -0.707106781186548 -0.000000000000000 -0.000000000000000 -0.707106781186548  0.021532136583541    1.00000 -0.00000  0.00000
 -0.000000000000000  0.000000000000000 -0.707106781186548 -0.000000000000000 -0.000000000000000  0.707106781186548  0.021532136583541    1.00000 -0.00000  0.50000
 -0.000000000000000  0.000000000000000 -0.707106781186548 -0.000000000000000  0.707106781186548 -0.000000000000000  0.021532136583541    1.00000 -0.00000 -0.00000
  0.000000000000000 -0.000000000000000 -0.707106781186548  0.707106781186548 -0.000000000000000 -0.000000000000000  0.021532136583541    1.00000 -0.00000  0.00000
  0.000000000000000  0.000000000000000  0.000000000000000 -0.707106781186548 -0.707106781186548  0.000000000000000  0.021532136583541    1.00000  0.00000  0.50000
 -0.000000000000000  0.000000000000000  0.000000000000000 -0.707106781186548 -0.000000000000000 -0.707106781186548  0.021532136583541    1.00000  0.00000  0.00000
 -0.000000000000000  0.000000000000000  0.000000000000000 -0.707106781186548  0.000000000000000  0.707106781186548  0.021532136583541    1.00000 -0.00000  0.50000
 -0.000000000000000  0.000000000000000 -0.000000000000000 -0.707106781186548  0.707106781186548  0.000000000000000  0.021532136583541    1.00000 -0.00000  0.00000
 -0.000000000000000 -0.000000000000000  0.000000000000000  0.000000000000000 -0.707106781186548 -0.707106781186548  0.021532136583541    1.00000  0.00000  0.00000
 -0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 -0.707106781186548  0.707106781186548  0.021532136583541    1.00000 -0.00000  0.50000
  0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.707106781186548 -0.707106781186548  0.021532136583541    1.00000  0.00000 -0.50000
  0.000000000000000  0.000000000000000 -0.000000000000000 -0.000000000000000  0.707106781186548  0.707106781186548  0.021532136583541    1.00000 -0.00000  0.00000
  0.000000000000000 -0.000000000000000  0.000000000000000  0.707106781186548 -0.707106781186548 -0.000000000000000  0.021532136583541    1.00000  0.00000 -0.00000
  0.000000000000000 -0.000000000000000 -0.000000000000000  0.707106781186548 -0.000000000000000 -0.707106781186548  0.021532136583541    1.00000  0.00000 -0.50000
  0.000000000000000 -0.000000000000000 -0.000000000000000  0.707106781186548  0.000000000000000  0.707106781186548  0.021532136583541    1.00000 -0.00000  0.00000
 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.707106781186548  0.707106781186548 -0.000000000000000  0.021532136583541    1.00000 -0.00000 -0.50000
 -0.000000000000000  0.000000000000000  0.707106781186548 -0.707106781186548  0.000000000000000  0.000000000000000  0.021532136583541    1.00000  0.00000  0.00000
 -0.000000000000000 -0.000000000000000  0.707106781186548  0.000000000000000 -0.707106781186548 -0.000000000000000  0.021532136583541    1.00000  0.00000  0.00000
  0.000000000000000 -0.000000000000000  0.707106781186548  0.000000000000000  0.000000000000000 -0.707106781186548  0.021532136583541    1.00000  0.00000 -0.50000
  0.000000000000000  0.000000000000000  0.707106781186548  0.000000000000000  0.000000000000000  0.707106781186548  0.021532136583541    1.00000  0.00000 -0.00000
 -0.000000000000000  0.000000000000000  0.707106781186548  0.000000000000000  0.707106781186548 -0.000000000000000  0.021532136583541    1.00000 -0.00000 -0.50000
 -0.000000000000000 -0.000000000000000  0.707106781186548  0.707106781186548  0.000000000000000 -0.000000000000000  0.021532136583541    1.00000 -0.00000 -0.50000
  0.000000000000000  0.707106781186548 -0.707106781186548  0.000000000000000 -0.000000000000000 -0.000000000000000  0.021532136583541    1.00000  0.00000 -0.00000
 -0.000000000000000  0.707106781186548  0.000000000000000 -0.707106781186548 -0.000000000000000 -0.000000000000000  0.021532136583541    1.00000  0.00000  0.00000
  0.000000000000000  0.707106781186548  0.000000000000000  0.000000000000000 -0.707106781186548 -0.000000000000000  0.021532136583541    1.00000  0.00000 -0.00000
  0.000000000000000  0.707106781186548 -0.000000000000000  0.000000000000000 -0.000000000000000 -0.707106781186548  0.021532136583541    1.00000  0.00000 -0.50000
  0.000000000000000  0.707106781186548 -0.000000000000000  0.000000000000000  0.000000000000000  0.707106781186548  0.021532136583541    1.00000  0.00000 -0.00000
 -0.000000000000000  0.707106781186548 -0.000000000000000  0.000000000000000  0.707106781186548 -0.000000000000000  0.021532136583541    1.00000 -0.00000 -0.50000
  0.000000000000000  0.707106781186548 -0.000000000000000  0.707106781186548  0.000000000000000 -0.000000000000000  0.021532136583541    1.00000  0.00000 -0.50000
 -0.000000000000000  0.707106781186548  0.707106781186548  0.000000000000000  0.000000000000000 -0.000000000000000  0.021532136583541    1.00000  0.00000 -0.50000
  0.612372435695794 -0.353553390593274 -0.353553390593274 -0.353553390593274 -0.353553390593274 -0.353553390593274  0.021532136583541    1.00000  0.61237  0.00000
  0.612372435695794 -0.353553390593274 -0.353553390593274 -0.353553390593274  0.353553390593274  0.353553390593274  0.021532136583541    1.00000  0.61237  0.00000
  0.612372435695794 -0.353553390593274 -0.353553390593274  0.353553390593274 -0.353553390593274  0.353553390593274  0.021532136583541    1.00000  0.61237  0.00000
  0.612372435695794 -0.353553390593274 -0.353553390593274  0.353553390593274  0.353553390593274 -0.353553390593274  0.021532136583541    1.00000  0.61237 -0.50000
  0.612372435695794 -0.353553390593274  0.353553390593274 -0.353553390593274 -0.353553390593274  0.353553390593274  0.021532136583541    1.00000  0.61237  0.00000
  0.612372435695794 -0.353553390593274  0.353553390593274 -0.353553390593274  0.353553390593274 -0.353553390593274  0.021532136583541    1.00000  0.61237 -0.50000
  0.612372435695794 -0.353553390593274  0.353553390593274  0.353553390593274 -0.353553390593274 -0.353553390593274  0.021532136583541    1.00000  0.61237 -0.50000
  0.612372435695794 -0.353553390593274  0.353553390593274  0.353553390593274  0.353553390593274  0.353553390593274  0.021532136583541    1.00000  0.61237 -0.50000
  0.612372435695794  0.353553390593274 -0.353553390593274 -0.353553390593274 -0.353553390593274  0.353553390593274  0.021532136583541    1.00000  0.61237  0.00000
  0.612372435695794  0.353553390593274 -0.353553390593274 -0.353553390593274  0.353553390593274 -0.353553390593274  0.021532136583541    1.00000  0.61237 -0.50000
  0.612372435695794  0.353553390593274 -0.353553390593274  0.353553390593274 -0.353553390593274 -0.353553390593274  0.021532136583541    1.00000  0.61237 -0.50000
  0.612372435695794  0.353553390593274 -0.353553390593274  0.353553390593274  0.353553390593274  0.353553390593274  0.021532136583541    1.00000  0.61237 -0.50000
  0.612372435695794  0.353553390593274  0.353553390593274 -0.353553390593274 -0.353553390593274 -0.353553390593274  0.021532136583541    1.00000  0.61237 -0.50000
  0.612372435695794  0.353553390593274  0.353553390593274 -0.353553390593274  0.353553390593274  0.353553390593274  0.021532136583541    1.00000  0.61237 -0.50000
  0.612372435695794  0.353553390593274  0.353553390593274  0.353553390593274 -0.353553390593274  0.353553390593274  0.021532136583541    1.00000  0.61237 -0.50000
  0.612372435695794  0.353553390593274  0.353553390593274  0.353553390593274  0.353553390593274 -0.353553390593274  0.021532136583541    1.00000  0.61237 -1.00000

E_n^{r^2} 6 dimensions, degree 7, symmetric 127 point rule with points at 3 distinct radii: 1+54+72=127

#                x1                 x2                 x3                 x4                 x5                 x6             Weight     Radius     cos1     cos2
  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  4.201508701945053    0.00000  0.00000  0.00000
  1.760971468943675  0.000000000000000  0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.462118316099807    1.76097  1.00000  0.61237
  0.880485734471837  1.525046027444823 -0.000000000000000  0.000000000000000 -0.000000000000000 -0.000000000000000  0.462118316099807    1.76097  0.50000  0.61237
  0.880485734471837 -0.000000000000000  1.525046027444823  0.000000000000000  0.000000000000000  0.000000000000000  0.462118316099807    1.76097  0.50000  0.61237
  0.880485734471837 -0.000000000000000 -0.000000000000000  1.525046027444823 -0.000000000000000 -0.000000000000000  0.462118316099807    1.76097  0.50000  0.61237
  0.880485734471837 -0.000000000000000 -0.000000000000000 -0.000000000000000  1.525046027444823  0.000000000000000  0.462118316099807    1.76097  0.50000  0.61237
  0.880485734471837  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  1.525046027444823  0.462118316099807    1.76097  0.50000 -0.00000
  0.880485734471837 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -1.525046027444823  0.462118316099807    1.76097  0.50000  0.61237
  0.880485734471837 -0.000000000000000  0.000000000000000 -0.000000000000000 -1.525046027444823  0.000000000000000  0.462118316099807    1.76097  0.50000 -0.00000
  0.880485734471837  0.000000000000000  0.000000000000000 -1.525046027444823 -0.000000000000000  0.000000000000000  0.462118316099807    1.76097  0.50000 -0.00000
  0.880485734471837 -0.000000000000000 -1.525046027444823 -0.000000000000000 -0.000000000000000  0.000000000000000  0.462118316099807    1.76097  0.50000 -0.00000
  0.880485734471837 -1.525046027444823  0.000000000000000 -0.000000000000000 -0.000000000000000  0.000000000000000  0.462118316099807    1.76097  0.50000 -0.00000
  0.440242867235919  0.762523013722411  0.762523013722411  0.762523013722411  0.762523013722411  0.762523013722411  0.462118316099807    1.76097  0.25000  0.61237
  0.440242867235919  0.762523013722411  0.762523013722411  0.762523013722411 -0.762523013722411 -0.762523013722411  0.462118316099807    1.76097  0.25000  0.61237
  0.440242867235919  0.762523013722411  0.762523013722411 -0.762523013722411  0.762523013722411 -0.762523013722411  0.462118316099807    1.76097  0.25000  0.61237
  0.440242867235919  0.762523013722411  0.762523013722411 -0.762523013722411 -0.762523013722411  0.762523013722411  0.462118316099807    1.76097  0.25000 -0.00000
  0.440242867235919  0.762523013722411 -0.762523013722411  0.762523013722411  0.762523013722411 -0.762523013722411  0.462118316099807    1.76097  0.25000  0.61237
  0.440242867235919  0.762523013722411 -0.762523013722411  0.762523013722411 -0.762523013722411  0.762523013722411  0.462118316099807    1.76097  0.25000 -0.00000
  0.440242867235919  0.762523013722411 -0.762523013722411 -0.762523013722411  0.762523013722411  0.762523013722411  0.462118316099807    1.76097  0.25000 -0.00000
  0.440242867235919  0.762523013722411 -0.762523013722411 -0.762523013722411 -0.762523013722411 -0.762523013722411  0.462118316099807    1.76097  0.25000 -0.00000
  0.440242867235919 -0.762523013722411  0.762523013722411  0.762523013722411  0.762523013722411 -0.762523013722411  0.462118316099807    1.76097  0.25000  0.61237
  0.440242867235919 -0.762523013722411  0.762523013722411  0.762523013722411 -0.762523013722411  0.762523013722411  0.462118316099807    1.76097  0.25000 -0.00000
  0.440242867235919 -0.762523013722411  0.762523013722411 -0.762523013722411  0.762523013722411  0.762523013722411  0.462118316099807    1.76097  0.25000 -0.00000
  0.440242867235919 -0.762523013722411  0.762523013722411 -0.762523013722411 -0.762523013722411 -0.762523013722411  0.462118316099807    1.76097  0.25000 -0.00000
  0.440242867235919 -0.762523013722411 -0.762523013722411  0.762523013722411  0.762523013722411  0.762523013722411  0.462118316099807    1.76097  0.25000 -0.00000
  0.440242867235919 -0.762523013722411 -0.762523013722411  0.762523013722411 -0.762523013722411 -0.762523013722411  0.462118316099807    1.76097  0.25000 -0.00000
  0.440242867235919 -0.762523013722411 -0.762523013722411 -0.762523013722411  0.762523013722411 -0.762523013722411  0.462118316099807    1.76097  0.25000 -0.00000
  0.440242867235919 -0.762523013722411 -0.762523013722411 -0.762523013722411 -0.762523013722411  0.762523013722411  0.462118316099807    1.76097  0.25000 -0.61237
 -0.440242867235919  0.762523013722411  0.762523013722411  0.762523013722411  0.762523013722411 -0.762523013722411  0.462118316099807    1.76097 -0.25000  0.61237
 -0.440242867235919  0.762523013722411  0.762523013722411  0.762523013722411 -0.762523013722411  0.762523013722411  0.462118316099807    1.76097 -0.25000  0.00000
 -0.440242867235919  0.762523013722411  0.762523013722411 -0.762523013722411  0.762523013722411  0.762523013722411  0.462118316099807    1.76097 -0.25000  0.00000
 -0.440242867235919  0.762523013722411  0.762523013722411 -0.762523013722411 -0.762523013722411 -0.762523013722411  0.462118316099807    1.76097 -0.25000  0.00000
 -0.440242867235919  0.762523013722411 -0.762523013722411  0.762523013722411  0.762523013722411  0.762523013722411  0.462118316099807    1.76097 -0.25000  0.00000
 -0.440242867235919  0.762523013722411 -0.762523013722411  0.762523013722411 -0.762523013722411 -0.762523013722411  0.462118316099807    1.76097 -0.25000  0.00000
 -0.440242867235919  0.762523013722411 -0.762523013722411 -0.762523013722411  0.762523013722411 -0.762523013722411  0.462118316099807    1.76097 -0.25000  0.00000
 -0.440242867235919  0.762523013722411 -0.762523013722411 -0.762523013722411 -0.762523013722411  0.762523013722411  0.462118316099807    1.76097 -0.25000 -0.61237
 -0.440242867235919 -0.762523013722411  0.762523013722411  0.762523013722411  0.762523013722411  0.762523013722411  0.462118316099807    1.76097 -0.25000  0.00000
 -0.440242867235919 -0.762523013722411  0.762523013722411  0.762523013722411 -0.762523013722411 -0.762523013722411  0.462118316099807    1.76097 -0.25000  0.00000
 -0.440242867235919 -0.762523013722411  0.762523013722411 -0.762523013722411  0.762523013722411 -0.762523013722411  0.462118316099807    1.76097 -0.25000  0.00000
 -0.440242867235919 -0.762523013722411  0.762523013722411 -0.762523013722411 -0.762523013722411  0.762523013722411  0.462118316099807    1.76097 -0.25000 -0.61237
 -0.440242867235919 -0.762523013722411 -0.762523013722411  0.762523013722411  0.762523013722411 -0.762523013722411  0.462118316099807    1.76097 -0.25000  0.00000
 -0.440242867235919 -0.762523013722411 -0.762523013722411  0.762523013722411 -0.762523013722411  0.762523013722411  0.462118316099807    1.76097 -0.25000 -0.61237
 -0.440242867235919 -0.762523013722411 -0.762523013722411 -0.762523013722411  0.762523013722411  0.762523013722411  0.462118316099807    1.76097 -0.25000 -0.61237
 -0.440242867235919 -0.762523013722411 -0.762523013722411 -0.762523013722411 -0.762523013722411 -0.762523013722411  0.462118316099807    1.76097 -0.25000 -0.61237
 -0.880485734471837  1.525046027444823 -0.000000000000000  0.000000000000000  0.000000000000000 -0.000000000000000  0.462118316099807    1.76097 -0.50000  0.00000
 -0.880485734471837  0.000000000000000  1.525046027444823  0.000000000000000  0.000000000000000 -0.000000000000000  0.462118316099807    1.76097 -0.50000  0.00000
 -0.880485734471837 -0.000000000000000 -0.000000000000000  1.525046027444823  0.000000000000000 -0.000000000000000  0.462118316099807    1.76097 -0.50000  0.00000
 -0.880485734471837  0.000000000000000 -0.000000000000000  0.000000000000000  1.525046027444823 -0.000000000000000  0.462118316099807    1.76097 -0.50000  0.00000
 -0.880485734471837  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  1.525046027444823  0.462118316099807    1.76097 -0.50000 -0.61237
 -0.880485734471837 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -1.525046027444823  0.462118316099807    1.76097 -0.50000  0.00000
 -0.880485734471837  0.000000000000000  0.000000000000000  0.000000000000000 -1.525046027444823 -0.000000000000000  0.462118316099807    1.76097 -0.50000 -0.61237
 -0.880485734471837  0.000000000000000  0.000000000000000 -1.525046027444823  0.000000000000000  0.000000000000000  0.462118316099807    1.76097 -0.50000 -0.61237
 -0.880485734471837  0.000000000000000 -1.525046027444823 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.462118316099807    1.76097 -0.50000 -0.61237
 -0.880485734471837 -1.525046027444823  0.000000000000000 -0.000000000000000  0.000000000000000  0.000000000000000  0.462118316099807    1.76097 -0.50000 -0.61237
 -1.760971468943675 -0.000000000000000 -0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.462118316099807    1.76097 -1.00000 -0.61237
  1.780044565044283  1.027709208797848  1.027709208797848  1.027709208797848  1.027709208797848 -1.027709208797848  0.025699707068961    2.90680  0.61237  1.00000
  1.780044565044283  1.027709208797848  1.027709208797848  1.027709208797848 -1.027709208797848  1.027709208797848  0.025699707068961    2.90680  0.61237  0.50000
  1.780044565044283  1.027709208797848  1.027709208797848 -1.027709208797848  1.027709208797848  1.027709208797848  0.025699707068961    2.90680  0.61237  0.50000
  1.780044565044283  1.027709208797848  1.027709208797848 -1.027709208797848 -1.027709208797848 -1.027709208797848  0.025699707068961    2.90680  0.61237  0.50000
  1.780044565044283  1.027709208797848 -1.027709208797848  1.027709208797848  1.027709208797848  1.027709208797848  0.025699707068961    2.90680  0.61237  0.50000
  1.780044565044283  1.027709208797848 -1.027709208797848  1.027709208797848 -1.027709208797848 -1.027709208797848  0.025699707068961    2.90680  0.61237  0.50000
  1.780044565044283  1.027709208797848 -1.027709208797848 -1.027709208797848  1.027709208797848 -1.027709208797848  0.025699707068961    2.90680  0.61237  0.50000
  1.780044565044283  1.027709208797848 -1.027709208797848 -1.027709208797848 -1.027709208797848  1.027709208797848  0.025699707068961    2.90680  0.61237 -0.00000
  1.780044565044283 -1.027709208797848  1.027709208797848  1.027709208797848  1.027709208797848  1.027709208797848  0.025699707068961    2.90680  0.61237  0.50000
  1.780044565044283 -1.027709208797848  1.027709208797848  1.027709208797848 -1.027709208797848 -1.027709208797848  0.025699707068961    2.90680  0.61237  0.50000
  1.780044565044283 -1.027709208797848  1.027709208797848 -1.027709208797848  1.027709208797848 -1.027709208797848  0.025699707068961    2.90680  0.61237  0.50000
  1.780044565044283 -1.027709208797848  1.027709208797848 -1.027709208797848 -1.027709208797848  1.027709208797848  0.025699707068961    2.90680  0.61237 -0.00000
  1.780044565044283 -1.027709208797848 -1.027709208797848  1.027709208797848  1.027709208797848 -1.027709208797848  0.025699707068961    2.90680  0.61237  0.50000
  1.780044565044283 -1.027709208797848 -1.027709208797848  1.027709208797848 -1.027709208797848  1.027709208797848  0.025699707068961    2.90680  0.61237 -0.00000
  1.780044565044283 -1.027709208797848 -1.027709208797848 -1.027709208797848  1.027709208797848  1.027709208797848  0.025699707068961    2.90680  0.61237 -0.00000
  1.780044565044283 -1.027709208797848 -1.027709208797848 -1.027709208797848 -1.027709208797848 -1.027709208797848  0.025699707068961    2.90680  0.61237 -0.00000
 -0.000000000000000  2.055418417595695  2.055418417595695  0.000000000000000  0.000000000000000 -0.000000000000000  0.025699707068961    2.90680  0.00000  0.50000
  0.000000000000000  2.055418417595695 -0.000000000000000  2.055418417595695  0.000000000000000 -0.000000000000000  0.025699707068961    2.90680  0.00000  0.50000
 -0.000000000000000  2.055418417595695 -0.000000000000000  0.000000000000000  2.055418417595695 -0.000000000000000  0.025699707068961    2.90680 -0.00000  0.50000
  0.000000000000000  2.055418417595695 -0.000000000000000  0.000000000000000  0.000000000000000  2.055418417595695  0.025699707068961    2.90680  0.00000  0.00000
  0.000000000000000  2.055418417595695 -0.000000000000000  0.000000000000000 -0.000000000000000 -2.055418417595695  0.025699707068961    2.90680  0.00000  0.50000
  0.000000000000000  2.055418417595695  0.000000000000000  0.000000000000000 -2.055418417595695 -0.000000000000000  0.025699707068961    2.90680  0.00000  0.00000
  0.000000000000000  2.055418417595695  0.000000000000000 -2.055418417595695 -0.000000000000000 -0.000000000000000  0.025699707068961    2.90680  0.00000  0.00000
  0.000000000000000  2.055418417595695 -2.055418417595695  0.000000000000000 -0.000000000000000 -0.000000000000000  0.025699707068961    2.90680  0.00000  0.00000
 -0.000000000000000 -0.000000000000000  2.055418417595695  2.055418417595695  0.000000000000000 -0.000000000000000  0.025699707068961    2.90680 -0.00000  0.50000
 -0.000000000000000  0.000000000000000  2.055418417595695  0.000000000000000  2.055418417595695 -0.000000000000000  0.025699707068961    2.90680 -0.00000  0.50000
  0.000000000000000  0.000000000000000  2.055418417595695  0.000000000000000  0.000000000000000  2.055418417595695  0.025699707068961    2.90680  0.00000  0.00000
  0.000000000000000 -0.000000000000000  2.055418417595695  0.000000000000000  0.000000000000000 -2.055418417595695  0.025699707068961    2.90680  0.00000  0.50000
  0.000000000000000 -0.000000000000000  2.055418417595695  0.000000000000000 -2.055418417595695  0.000000000000000  0.025699707068961    2.90680  0.00000  0.00000
 -0.000000000000000  0.000000000000000  2.055418417595695 -2.055418417595695  0.000000000000000  0.000000000000000  0.025699707068961    2.90680  0.00000  0.00000
 -0.000000000000000 -0.000000000000000 -0.000000000000000  2.055418417595695  2.055418417595695 -0.000000000000000  0.025699707068961    2.90680 -0.00000  0.50000
  0.000000000000000 -0.000000000000000 -0.000000000000000  2.055418417595695  0.000000000000000  2.055418417595695  0.025699707068961    2.90680 -0.00000  0.00000
  0.000000000000000 -0.000000000000000 -0.000000000000000  2.055418417595695 -0.000000000000000 -2.055418417595695  0.025699707068961    2.90680  0.00000  0.50000
  0.000000000000000 -0.000000000000000  0.000000000000000  2.055418417595695 -2.055418417595695 -0.000000000000000  0.025699707068961    2.90680  0.00000  0.00000
  0.000000000000000  0.000000000000000 -0.000000000000000 -0.000000000000000  2.055418417595695  2.055418417595695  0.025699707068961    2.90680 -0.00000  0.00000
  0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  2.055418417595695 -2.055418417595695  0.025699707068961    2.90680  0.00000  0.50000
 -0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 -2.055418417595695  2.055418417595695  0.025699707068961    2.90680 -0.00000 -0.50000
 -0.000000000000000 -0.000000000000000  0.000000000000000  0.000000000000000 -2.055418417595695 -2.055418417595695  0.025699707068961    2.90680  0.00000  0.00000
 -0.000000000000000  0.000000000000000 -0.000000000000000 -2.055418417595695  2.055418417595695  0.000000000000000  0.025699707068961    2.90680 -0.00000 -0.00000
 -0.000000000000000  0.000000000000000  0.000000000000000 -2.055418417595695  0.000000000000000  2.055418417595695  0.025699707068961    2.90680 -0.00000 -0.50000
 -0.000000000000000  0.000000000000000  0.000000000000000 -2.055418417595695 -0.000000000000000 -2.055418417595695  0.025699707068961    2.90680  0.00000 -0.00000
  0.000000000000000  0.000000000000000  0.000000000000000 -2.055418417595695 -2.055418417595695  0.000000000000000  0.025699707068961    2.90680  0.00000 -0.50000
  0.000000000000000 -0.000000000000000 -2.055418417595695  2.055418417595695 -0.000000000000000 -0.000000000000000  0.025699707068961    2.90680 -0.00000  0.00000
  0.000000000000000  0.000000000000000 -2.055418417595695 -0.000000000000000  2.055418417595695  0.000000000000000  0.025699707068961    2.90680 -0.00000 -0.00000
 -0.000000000000000  0.000000000000000 -2.055418417595695 -0.000000000000000 -0.000000000000000  2.055418417595695  0.025699707068961    2.90680 -0.00000 -0.50000
 -0.000000000000000 -0.000000000000000 -2.055418417595695 -0.000000000000000 -0.000000000000000 -2.055418417595695  0.025699707068961    2.90680 -0.00000 -0.00000
  0.000000000000000 -0.000000000000000 -2.055418417595695 -0.000000000000000 -2.055418417595695  0.000000000000000  0.025699707068961    2.90680  0.00000 -0.50000
  0.000000000000000  0.000000000000000 -2.055418417595695 -2.055418417595695 -0.000000000000000  0.000000000000000  0.025699707068961    2.90680  0.00000 -0.50000
 -0.000000000000000 -2.055418417595695  2.055418417595695 -0.000000000000000  0.000000000000000  0.000000000000000  0.025699707068961    2.90680 -0.00000 -0.00000
  0.000000000000000 -2.055418417595695 -0.000000000000000  2.055418417595695  0.000000000000000  0.000000000000000  0.025699707068961    2.90680 -0.00000  0.00000
 -0.000000000000000 -2.055418417595695 -0.000000000000000 -0.000000000000000  2.055418417595695  0.000000000000000  0.025699707068961    2.90680 -0.00000 -0.00000
 -0.000000000000000 -2.055418417595695  0.000000000000000 -0.000000000000000  0.000000000000000  2.055418417595695  0.025699707068961    2.90680 -0.00000 -0.50000
 -0.000000000000000 -2.055418417595695  0.000000000000000 -0.000000000000000 -0.000000000000000 -2.055418417595695  0.025699707068961    2.90680 -0.00000 -0.00000
  0.000000000000000 -2.055418417595695  0.000000000000000 -0.000000000000000 -2.055418417595695  0.000000000000000  0.025699707068961    2.90680  0.00000 -0.50000
 -0.000000000000000 -2.055418417595695  0.000000000000000 -2.055418417595695 -0.000000000000000  0.000000000000000  0.025699707068961    2.90680 -0.00000 -0.50000
  0.000000000000000 -2.055418417595695 -2.055418417595695 -0.000000000000000 -0.000000000000000  0.000000000000000  0.025699707068961    2.90680 -0.00000 -0.50000
 -1.780044565044283  1.027709208797848  1.027709208797848  1.027709208797848  1.027709208797848  1.027709208797848  0.025699707068961    2.90680 -0.61237  0.00000
 -1.780044565044283  1.027709208797848  1.027709208797848  1.027709208797848 -1.027709208797848 -1.027709208797848  0.025699707068961    2.90680 -0.61237  0.00000
 -1.780044565044283  1.027709208797848  1.027709208797848 -1.027709208797848  1.027709208797848 -1.027709208797848  0.025699707068961    2.90680 -0.61237  0.00000
 -1.780044565044283  1.027709208797848  1.027709208797848 -1.027709208797848 -1.027709208797848  1.027709208797848  0.025699707068961    2.90680 -0.61237 -0.50000
 -1.780044565044283  1.027709208797848 -1.027709208797848  1.027709208797848  1.027709208797848 -1.027709208797848  0.025699707068961    2.90680 -0.61237  0.00000
 -1.780044565044283  1.027709208797848 -1.027709208797848  1.027709208797848 -1.027709208797848  1.027709208797848  0.025699707068961    2.90680 -0.61237 -0.50000
 -1.780044565044283  1.027709208797848 -1.027709208797848 -1.027709208797848  1.027709208797848  1.027709208797848  0.025699707068961    2.90680 -0.61237 -0.50000
 -1.780044565044283  1.027709208797848 -1.027709208797848 -1.027709208797848 -1.027709208797848 -1.027709208797848  0.025699707068961    2.90680 -0.61237 -0.50000
 -1.780044565044283 -1.027709208797848  1.027709208797848  1.027709208797848  1.027709208797848 -1.027709208797848  0.025699707068961    2.90680 -0.61237  0.00000
 -1.780044565044283 -1.027709208797848  1.027709208797848  1.027709208797848 -1.027709208797848  1.027709208797848  0.025699707068961    2.90680 -0.61237 -0.50000
 -1.780044565044283 -1.027709208797848  1.027709208797848 -1.027709208797848  1.027709208797848  1.027709208797848  0.025699707068961    2.90680 -0.61237 -0.50000
 -1.780044565044283 -1.027709208797848  1.027709208797848 -1.027709208797848 -1.027709208797848 -1.027709208797848  0.025699707068961    2.90680 -0.61237 -0.50000
 -1.780044565044283 -1.027709208797848 -1.027709208797848  1.027709208797848  1.027709208797848  1.027709208797848  0.025699707068961    2.90680 -0.61237 -0.50000
 -1.780044565044283 -1.027709208797848 -1.027709208797848  1.027709208797848 -1.027709208797848 -1.027709208797848  0.025699707068961    2.90680 -0.61237 -0.50000
 -1.780044565044283 -1.027709208797848 -1.027709208797848 -1.027709208797848  1.027709208797848 -1.027709208797848  0.025699707068961    2.90680 -0.61237 -0.50000
 -1.780044565044283 -1.027709208797848 -1.027709208797848 -1.027709208797848 -1.027709208797848  1.027709208797848  0.025699707068961    2.90680 -0.61237 -1.00000
>> # evaluating formula 1 with 38 points
# r7_38_4dg.txt:4 formula 1   : problem  G, 7_38_4  (d=7 n=38 o=4 plus 0/462 of order 5) quality N (2 negative weights, stability factor 7.180984)
# evaluating formula 2 with 38 points
# r7_38_4dg.txt:46 formula 2   : problem E2, 7_38_4  (d=7 n=38 o=4 plus 0/462 of order 5) quality N (2 negative weights, stability factor 7.180984)
# evaluating formula 3 with 38 points
# r7_38_4dg.txt:88 formula 3   : problem  S, 7_38_4  (d=7 n=38 o=4 plus 0/462 of order 5) quality NO (2 negative weights, stability factor 8.554536)
G_n 7 dimensions, degree 4, asymmetric 38 point rule with points at 6 distinct radii: 1+1+1+7+7+21=38
 (2 negative weights, inflation 7.180984)
#                x1                 x2                 x3                 x4                 x5                 x6                 x7             Weight     Radius     cos1     cos2     cos3
 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  1.088145887545156    0.00000  0.00000  0.00000  0.00000
  0.440920353809594  0.440920353809594  0.440920353809594  0.440920353809594  0.440920353809594  0.440920353809594  0.440920353809594 -1.454646247156015    1.16657 -0.70967  0.75729 -0.00236
 -0.366396933652386 -0.366396933652386 -0.366396933652386 -0.366396933652386 -0.366396933652386 -0.366396933652386 -0.366396933652386 -1.635845762853535    0.96940  0.70967 -0.75729  0.00236
  0.637222908005327 -0.625436431345467 -0.625436431345467 -0.625436431345467 -0.625436431345467 -0.625436431345467 -0.625436431345467  0.212194672740512    1.65924  1.00000 -0.07731 -0.45310
 -0.625436431345467  0.637222908005327 -0.625436431345467 -0.625436431345467 -0.625436431345467 -0.625436431345467 -0.625436431345467  0.212194672740512    1.65924  0.42090 -0.61411 -0.45310
 -0.625436431345467 -0.625436431345467  0.637222908005327 -0.625436431345467 -0.625436431345467 -0.625436431345467 -0.625436431345467  0.212194672740512    1.65924  0.42090 -0.61411  0.18359
 -0.625436431345467 -0.625436431345467 -0.625436431345467  0.637222908005327 -0.625436431345467 -0.625436431345467 -0.625436431345467  0.212194672740512    1.65924  0.42090 -0.61411  0.18359
 -0.625436431345467 -0.625436431345467 -0.625436431345467 -0.625436431345467  0.637222908005327 -0.625436431345467 -0.625436431345467  0.212194672740512    1.65924  0.42090 -0.61411  0.18359
 -0.625436431345467 -0.625436431345467 -0.625436431345467 -0.625436431345467 -0.625436431345467  0.637222908005327 -0.625436431345467  0.212194672740512    1.65924  0.42090 -0.61411  0.18359
 -0.625436431345467 -0.625436431345467 -0.625436431345467 -0.625436431345467 -0.625436431345467 -0.625436431345467  0.637222908005327  0.212194672740512    1.65924  0.42090 -0.61411  0.18359
  1.553072976400314  0.323312790189201  0.323312790189201  0.323312790189201  0.323312790189201  0.323312790189201  0.323312790189201  0.201409207764857    1.74334 -0.07731  1.00000 -0.42335
  0.323312790189201  1.553072976400314  0.323312790189201  0.323312790189201  0.323312790189201  0.323312790189201  0.323312790189201  0.201409207764857    1.74334 -0.61411  0.50240 -0.42335
  0.323312790189201  0.323312790189201  1.553072976400314  0.323312790189201  0.323312790189201  0.323312790189201  0.323312790189201  0.201409207764857    1.74334 -0.61411  0.50240  0.16684
  0.323312790189201  0.323312790189201  0.323312790189201  1.553072976400314  0.323312790189201  0.323312790189201  0.323312790189201  0.201409207764857    1.74334 -0.61411  0.50240  0.16684
  0.323312790189201  0.323312790189201  0.323312790189201  0.323312790189201  1.553072976400314  0.323312790189201  0.323312790189201  0.201409207764857    1.74334 -0.61411  0.50240  0.16684
  0.323312790189201  0.323312790189201  0.323312790189201  0.323312790189201  0.323312790189201  1.553072976400314  0.323312790189201  0.201409207764857    1.74334 -0.61411  0.50240  0.16684
  0.323312790189201  0.323312790189201  0.323312790189201  0.323312790189201  0.323312790189201  0.323312790189201  1.553072976400314  0.201409207764857    1.74334 -0.61411  0.50240  0.16684
 -2.676753314369268 -2.676753314369268  1.065112745681246  1.065112745681246  1.065112745681246  1.065112745681246  1.065112745681246  0.005100902806039    4.47240 -0.45310 -0.42335  1.00000
 -2.676753314369268  1.065112745681246 -2.676753314369268  1.065112745681246  1.065112745681246  1.065112745681246  1.065112745681246  0.005100902806039    4.47240 -0.45310 -0.42335  0.30000
 -2.676753314369268  1.065112745681246  1.065112745681246 -2.676753314369268  1.065112745681246  1.065112745681246  1.065112745681246  0.005100902806039    4.47240 -0.45310 -0.42335  0.30000
 -2.676753314369268  1.065112745681246  1.065112745681246  1.065112745681246 -2.676753314369268  1.065112745681246  1.065112745681246  0.005100902806039    4.47240 -0.45310 -0.42335  0.30000
 -2.676753314369268  1.065112745681246  1.065112745681246  1.065112745681246  1.065112745681246 -2.676753314369268  1.065112745681246  0.005100902806039    4.47240 -0.45310 -0.42335  0.30000
 -2.676753314369268  1.065112745681246  1.065112745681246  1.065112745681246  1.065112745681246  1.065112745681246 -2.676753314369268  0.005100902806039    4.47240 -0.45310 -0.42335  0.30000
  1.065112745681246 -2.676753314369268 -2.676753314369268  1.065112745681246  1.065112745681246  1.065112745681246  1.065112745681246  0.005100902806039    4.47240  0.18359  0.16684  0.30000
  1.065112745681246 -2.676753314369268  1.065112745681246 -2.676753314369268  1.065112745681246  1.065112745681246  1.065112745681246  0.005100902806039    4.47240  0.18359  0.16684  0.30000
  1.065112745681246 -2.676753314369268  1.065112745681246  1.065112745681246 -2.676753314369268  1.065112745681246  1.065112745681246  0.005100902806039    4.47240  0.18359  0.16684  0.30000
  1.065112745681246 -2.676753314369268  1.065112745681246  1.065112745681246  1.065112745681246 -2.676753314369268  1.065112745681246  0.005100902806039    4.47240  0.18359  0.16684  0.30000
  1.065112745681246 -2.676753314369268  1.065112745681246  1.065112745681246  1.065112745681246  1.065112745681246 -2.676753314369268  0.005100902806039    4.47240  0.18359  0.16684  0.30000
  1.065112745681246  1.065112745681246 -2.676753314369268 -2.676753314369268  1.065112745681246  1.065112745681246  1.065112745681246  0.005100902806039    4.47240  0.18359  0.16684 -0.39999
  1.065112745681246  1.065112745681246 -2.676753314369268  1.065112745681246 -2.676753314369268  1.065112745681246  1.065112745681246  0.005100902806039    4.47240  0.18359  0.16684 -0.39999
  1.065112745681246  1.065112745681246 -2.676753314369268  1.065112745681246  1.065112745681246 -2.676753314369268  1.065112745681246  0.005100902806039    4.47240  0.18359  0.16684 -0.39999
  1.065112745681246  1.065112745681246 -2.676753314369268  1.065112745681246  1.065112745681246  1.065112745681246 -2.676753314369268  0.005100902806039    4.47240  0.18359  0.16684 -0.39999
  1.065112745681246  1.065112745681246  1.065112745681246 -2.676753314369268 -2.676753314369268  1.065112745681246  1.065112745681246  0.005100902806039    4.47240  0.18359  0.16684 -0.39999
  1.065112745681246  1.065112745681246  1.065112745681246 -2.676753314369268  1.065112745681246 -2.676753314369268  1.065112745681246  0.005100902806039    4.47240  0.18359  0.16684 -0.39999
  1.065112745681246  1.065112745681246  1.065112745681246 -2.676753314369268  1.065112745681246  1.065112745681246 -2.676753314369268  0.005100902806039    4.47240  0.18359  0.16684 -0.39999
  1.065112745681246  1.065112745681246  1.065112745681246  1.065112745681246 -2.676753314369268 -2.676753314369268  1.065112745681246  0.005100902806039    4.47240  0.18359  0.16684 -0.39999
  1.065112745681246  1.065112745681246  1.065112745681246  1.065112745681246 -2.676753314369268  1.065112745681246 -2.676753314369268  0.005100902806039    4.47240  0.18359  0.16684 -0.39999
  1.065112745681246  1.065112745681246  1.065112745681246  1.065112745681246  1.065112745681246 -2.676753314369268 -2.676753314369268  0.005100902806039    4.47240  0.18359  0.16684 -0.39999

E_n^{r^2} 7 dimensions, degree 4, asymmetric 38 point rule with points at 6 distinct radii: 1+1+1+7+7+21=38
 (2 negative weights, inflation 7.180984)
#                x1                 x2                 x3                 x4                 x5                 x6                 x7             Weight     Radius     cos1     cos2     cos3
 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 59.801445190807272    0.00000  0.00000  0.00000  0.00000
  0.311777772141935  0.311777772141935  0.311777772141935  0.311777772141935  0.311777772141935  0.311777772141935  0.311777772141935 -79.943276739814863    0.82489 -0.70967  0.75729 -0.00236
 -0.259081756391560 -0.259081756391560 -0.259081756391560 -0.259081756391560 -0.259081756391560 -0.259081756391560 -0.259081756391560 -89.901493768077330    0.68547  0.70967 -0.75729  0.00236
  0.450584639377978 -0.442250341805495 -0.442250341805495 -0.442250341805495 -0.442250341805495 -0.442250341805495 -0.442250341805495 11.661623902563727    1.17326  1.00000 -0.07731 -0.45310
 -0.442250341805495  0.450584639377978 -0.442250341805495 -0.442250341805495 -0.442250341805495 -0.442250341805495 -0.442250341805495 11.661623902563727    1.17326  0.42090 -0.61411 -0.45310
 -0.442250341805495 -0.442250341805495  0.450584639377978 -0.442250341805495 -0.442250341805495 -0.442250341805495 -0.442250341805495 11.661623902563727    1.17326  0.42090 -0.61411  0.18359
 -0.442250341805495 -0.442250341805495 -0.442250341805495  0.450584639377978 -0.442250341805495 -0.442250341805495 -0.442250341805495 11.661623902563727    1.17326  0.42090 -0.61411  0.18359
 -0.442250341805495 -0.442250341805495 -0.442250341805495 -0.442250341805495  0.450584639377978 -0.442250341805495 -0.442250341805495 11.661623902563727    1.17326  0.42090 -0.61411  0.18359
 -0.442250341805495 -0.442250341805495 -0.442250341805495 -0.442250341805495 -0.442250341805495  0.450584639377978 -0.442250341805495 11.661623902563727    1.17326  0.42090 -0.61411  0.18359
 -0.442250341805495 -0.442250341805495 -0.442250341805495 -0.442250341805495 -0.442250341805495 -0.442250341805495  0.450584639377978 11.661623902563727    1.17326  0.42090 -0.61411  0.18359
  1.098188433290237  0.228616666387128  0.228616666387128  0.228616666387128  0.228616666387128  0.228616666387128  0.228616666387128 11.068885006077970    1.23273 -0.07731  1.00000 -0.42335
  0.228616666387128  1.098188433290237  0.228616666387128  0.228616666387128  0.228616666387128  0.228616666387128  0.228616666387128 11.068885006077970    1.23273 -0.61411  0.50240 -0.42335
  0.228616666387128  0.228616666387128  1.098188433290237  0.228616666387128  0.228616666387128  0.228616666387128  0.228616666387128 11.068885006077970    1.23273 -0.61411  0.50240  0.16684
  0.228616666387128  0.228616666387128  0.228616666387128  1.098188433290237  0.228616666387128  0.228616666387128  0.228616666387128 11.068885006077970    1.23273 -0.61411  0.50240  0.16684
  0.228616666387128  0.228616666387128  0.228616666387128  0.228616666387128  1.098188433290237  0.228616666387128  0.228616666387128 11.068885006077970    1.23273 -0.61411  0.50240  0.16684
  0.228616666387128  0.228616666387128  0.228616666387128  0.228616666387128  0.228616666387128  1.098188433290237  0.228616666387128 11.068885006077970    1.23273 -0.61411  0.50240  0.16684
  0.228616666387128  0.228616666387128  0.228616666387128  0.228616666387128  0.228616666387128  0.228616666387128  1.098188433290237 11.068885006077970    1.23273 -0.61411  0.50240  0.16684
 -1.892750420154076 -1.892750420154076  0.753148445199432  0.753148445199432  0.753148445199432  0.753148445199432  0.753148445199432  0.280331307658684    3.16246 -0.45310 -0.42335  1.00000
 -1.892750420154076  0.753148445199432 -1.892750420154076  0.753148445199432  0.753148445199432  0.753148445199432  0.753148445199432  0.280331307658684    3.16246 -0.45310 -0.42335  0.30000
 -1.892750420154076  0.753148445199432  0.753148445199432 -1.892750420154076  0.753148445199432  0.753148445199432  0.753148445199432  0.280331307658684    3.16246 -0.45310 -0.42335  0.30000
 -1.892750420154076  0.753148445199432  0.753148445199432  0.753148445199432 -1.892750420154076  0.753148445199432  0.753148445199432  0.280331307658684    3.16246 -0.45310 -0.42335  0.30000
 -1.892750420154076  0.753148445199432  0.753148445199432  0.753148445199432  0.753148445199432 -1.892750420154076  0.753148445199432  0.280331307658684    3.16246 -0.45310 -0.42335  0.30000
 -1.892750420154076  0.753148445199432  0.753148445199432  0.753148445199432  0.753148445199432  0.753148445199432 -1.892750420154076  0.280331307658684    3.16246 -0.45310 -0.42335  0.30000
  0.753148445199432 -1.892750420154076 -1.892750420154076  0.753148445199432  0.753148445199432  0.753148445199432  0.753148445199432  0.280331307658684    3.16246  0.18359  0.16684  0.30000
  0.753148445199432 -1.892750420154076  0.753148445199432 -1.892750420154076  0.753148445199432  0.753148445199432  0.753148445199432  0.280331307658684    3.16246  0.18359  0.16684  0.30000
  0.753148445199432 -1.892750420154076  0.753148445199432  0.753148445199432 -1.892750420154076  0.753148445199432  0.753148445199432  0.280331307658684    3.16246  0.18359  0.16684  0.30000
  0.753148445199432 -1.892750420154076  0.753148445199432  0.753148445199432  0.753148445199432 -1.892750420154076  0.753148445199432  0.280331307658684    3.16246  0.18359  0.16684  0.30000
  0.753148445199432 -1.892750420154076  0.753148445199432  0.753148445199432  0.753148445199432  0.753148445199432 -1.892750420154076  0.280331307658684    3.16246  0.18359  0.16684  0.30000
  0.753148445199432  0.753148445199432 -1.892750420154076 -1.892750420154076  0.753148445199432  0.753148445199432  0.753148445199432  0.280331307658684    3.16246  0.18359  0.16684 -0.39999
  0.753148445199432  0.753148445199432 -1.892750420154076  0.753148445199432 -1.892750420154076  0.753148445199432  0.753148445199432  0.280331307658684    3.16246  0.18359  0.16684 -0.39999
  0.753148445199432  0.753148445199432 -1.892750420154076  0.753148445199432  0.753148445199432 -1.892750420154076  0.753148445199432  0.280331307658684    3.16246  0.18359  0.16684 -0.39999
  0.753148445199432  0.753148445199432 -1.892750420154076  0.753148445199432  0.753148445199432  0.753148445199432 -1.892750420154076  0.280331307658684    3.16246  0.18359  0.16684 -0.39999
  0.753148445199432  0.753148445199432  0.753148445199432 -1.892750420154076 -1.892750420154076  0.753148445199432  0.753148445199432  0.280331307658684    3.16246  0.18359  0.16684 -0.39999
  0.753148445199432  0.753148445199432  0.753148445199432 -1.892750420154076  0.753148445199432 -1.892750420154076  0.753148445199432  0.280331307658684    3.16246  0.18359  0.16684 -0.39999
  0.753148445199432  0.753148445199432  0.753148445199432 -1.892750420154076  0.753148445199432  0.753148445199432 -1.892750420154076  0.280331307658684    3.16246  0.18359  0.16684 -0.39999
  0.753148445199432  0.753148445199432  0.753148445199432  0.753148445199432 -1.892750420154076 -1.892750420154076  0.753148445199432  0.280331307658684    3.16246  0.18359  0.16684 -0.39999
  0.753148445199432  0.753148445199432  0.753148445199432  0.753148445199432 -1.892750420154076  0.753148445199432 -1.892750420154076  0.280331307658684    3.16246  0.18359  0.16684 -0.39999
  0.753148445199432  0.753148445199432  0.753148445199432  0.753148445199432  0.753148445199432 -1.892750420154076 -1.892750420154076  0.280331307658684    3.16246  0.18359  0.16684 -0.39999

S_n 7 dimensions, degree 4, asymmetric 38 point rule with points at 6 distinct radii: 1+1+1+7+7+21=38
 (2 negative weights, inflation 8.554536)
#                x1                 x2                 x3                 x4                 x5                 x6                 x7             Weight     Radius     cos1     cos2     cos3
 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  5.233783257984700    0.00000  0.00000  0.00000  0.00000
  0.132942488728833  0.132942488728833  0.132942488728833  0.132942488728833  0.132942488728833  0.132942488728833  0.132942488728833 -8.400165995751491    0.35173 -0.70967  0.75729 -0.00236
 -0.110472832114700 -0.110472832114700 -0.110472832114700 -0.110472832114700 -0.110472832114700 -0.110472832114700 -0.110472832114700 -9.446541369272817    0.29228  0.70967 -0.75729  0.00236
  0.192129935788438 -0.188576179362889 -0.188576179362889 -0.188576179362889 -0.188576179362889 -0.188576179362889 -0.188576179362889  1.225363539705552    0.50028  1.00000 -0.07731 -0.45310
 -0.188576179362889  0.192129935788438 -0.188576179362889 -0.188576179362889 -0.188576179362889 -0.188576179362889 -0.188576179362889  1.225363539705552    0.50028  0.42090 -0.61411 -0.45310
 -0.188576179362889 -0.188576179362889  0.192129935788438 -0.188576179362889 -0.188576179362889 -0.188576179362889 -0.188576179362889  1.225363539705552    0.50028  0.42090 -0.61411  0.18359
 -0.188576179362889 -0.188576179362889 -0.188576179362889  0.192129935788438 -0.188576179362889 -0.188576179362889 -0.188576179362889  1.225363539705552    0.50028  0.42090 -0.61411  0.18359
 -0.188576179362889 -0.188576179362889 -0.188576179362889 -0.188576179362889  0.192129935788438 -0.188576179362889 -0.188576179362889  1.225363539705552    0.50028  0.42090 -0.61411  0.18359
 -0.188576179362889 -0.188576179362889 -0.188576179362889 -0.188576179362889 -0.188576179362889  0.192129935788438 -0.188576179362889  1.225363539705552    0.50028  0.42090 -0.61411  0.18359
 -0.188576179362889 -0.188576179362889 -0.188576179362889 -0.188576179362889 -0.188576179362889 -0.188576179362889  0.192129935788438  1.225363539705552    0.50028  0.42090 -0.61411  0.18359
  0.468269121341849  0.097482474089135  0.097482474089135  0.097482474089135  0.097482474089135  0.097482474089135  0.097482474089135  1.163080564505197    0.52564 -0.07731  1.00000 -0.42335
  0.097482474089135  0.468269121341849  0.097482474089135  0.097482474089135  0.097482474089135  0.097482474089135  0.097482474089135  1.163080564505197    0.52564 -0.61411  0.50240 -0.42335
  0.097482474089135  0.097482474089135  0.468269121341849  0.097482474089135  0.097482474089135  0.097482474089135  0.097482474089135  1.163080564505197    0.52564 -0.61411  0.50240  0.16684
  0.097482474089135  0.097482474089135  0.097482474089135  0.468269121341849  0.097482474089135  0.097482474089135  0.097482474089135  1.163080564505197    0.52564 -0.61411  0.50240  0.16684
  0.097482474089135  0.097482474089135  0.097482474089135  0.097482474089135  0.468269121341849  0.097482474089135  0.097482474089135  1.163080564505197    0.52564 -0.61411  0.50240  0.16684
  0.097482474089135  0.097482474089135  0.097482474089135  0.097482474089135  0.097482474089135  0.468269121341849  0.097482474089135  1.163080564505197    0.52564 -0.61411  0.50240  0.16684
  0.097482474089135  0.097482474089135  0.097482474089135  0.097482474089135  0.097482474089135  0.097482474089135  0.468269121341849  1.163080564505197    0.52564 -0.61411  0.50240  0.16684
 -0.807071490918465 -0.807071490918465  0.321143576077267  0.321143576077267  0.321143576077267  0.321143576077267  0.321143576077267  0.029456254661703    1.34848 -0.45310 -0.42335  1.00000
 -0.807071490918465  0.321143576077267 -0.807071490918465  0.321143576077267  0.321143576077267  0.321143576077267  0.321143576077267  0.029456254661703    1.34848 -0.45310 -0.42335  0.30000
 -0.807071490918465  0.321143576077267  0.321143576077267 -0.807071490918465  0.321143576077267  0.321143576077267  0.321143576077267  0.029456254661703    1.34848 -0.45310 -0.42335  0.30000
 -0.807071490918465  0.321143576077267  0.321143576077267  0.321143576077267 -0.807071490918465  0.321143576077267  0.321143576077267  0.029456254661703    1.34848 -0.45310 -0.42335  0.30000
 -0.807071490918465  0.321143576077267  0.321143576077267  0.321143576077267  0.321143576077267 -0.807071490918465  0.321143576077267  0.029456254661703    1.34848 -0.45310 -0.42335  0.30000
 -0.807071490918465  0.321143576077267  0.321143576077267  0.321143576077267  0.321143576077267  0.321143576077267 -0.807071490918465  0.029456254661703    1.34848 -0.45310 -0.42335  0.30000
  0.321143576077267 -0.807071490918465 -0.807071490918465  0.321143576077267  0.321143576077267  0.321143576077267  0.321143576077267  0.029456254661703    1.34848  0.18359  0.16684  0.30000
  0.321143576077267 -0.807071490918465  0.321143576077267 -0.807071490918465  0.321143576077267  0.321143576077267  0.321143576077267  0.029456254661703    1.34848  0.18359  0.16684  0.30000
  0.321143576077267 -0.807071490918465  0.321143576077267  0.321143576077267 -0.807071490918465  0.321143576077267  0.321143576077267  0.029456254661703    1.34848  0.18359  0.16684  0.30000
  0.321143576077267 -0.807071490918465  0.321143576077267  0.321143576077267  0.321143576077267 -0.807071490918465  0.321143576077267  0.029456254661703    1.34848  0.18359  0.16684  0.30000
  0.321143576077267 -0.807071490918465  0.321143576077267  0.321143576077267  0.321143576077267  0.321143576077267 -0.807071490918465  0.029456254661703    1.34848  0.18359  0.16684  0.30000
  0.321143576077267  0.321143576077267 -0.807071490918465 -0.807071490918465  0.321143576077267  0.321143576077267  0.321143576077267  0.029456254661703    1.34848  0.18359  0.16684 -0.39999
  0.321143576077267  0.321143576077267 -0.807071490918465  0.321143576077267 -0.807071490918465  0.321143576077267  0.321143576077267  0.029456254661703    1.34848  0.18359  0.16684 -0.39999
  0.321143576077267  0.321143576077267 -0.807071490918465  0.321143576077267  0.321143576077267 -0.807071490918465  0.321143576077267  0.029456254661703    1.34848  0.18359  0.16684 -0.39999
  0.321143576077267  0.321143576077267 -0.807071490918465  0.321143576077267  0.321143576077267  0.321143576077267 -0.807071490918465  0.029456254661703    1.34848  0.18359  0.16684 -0.39999
  0.321143576077267  0.321143576077267  0.321143576077267 -0.807071490918465 -0.807071490918465  0.321143576077267  0.321143576077267  0.029456254661703    1.34848  0.18359  0.16684 -0.39999
  0.321143576077267  0.321143576077267  0.321143576077267 -0.807071490918465  0.321143576077267 -0.807071490918465  0.321143576077267  0.029456254661703    1.34848  0.18359  0.16684 -0.39999
  0.321143576077267  0.321143576077267  0.321143576077267 -0.807071490918465  0.321143576077267  0.321143576077267 -0.807071490918465  0.029456254661703    1.34848  0.18359  0.16684 -0.39999
  0.321143576077267  0.321143576077267  0.321143576077267  0.321143576077267 -0.807071490918465 -0.807071490918465  0.321143576077267  0.029456254661703    1.34848  0.18359  0.16684 -0.39999
  0.321143576077267  0.321143576077267  0.321143576077267  0.321143576077267 -0.807071490918465  0.321143576077267 -0.807071490918465  0.029456254661703    1.34848  0.18359  0.16684 -0.39999
  0.321143576077267  0.321143576077267  0.321143576077267  0.321143576077267  0.321143576077267 -0.807071490918465 -0.807071490918465  0.029456254661703    1.34848  0.18359  0.16684 -0.39999

>> # evaluating formula 1 with 46 points
# r7_46_4E1ac.txt:4 formula 1   : problem E1, 7_46_4  (d=7 n=46 o=4 plus 2/462 of order 5) quality P
E1 7 dimensions, degree 4, asymmetric 46 point rule with points at 46 distinct radii: 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=46

#                x1                 x2                 x3                 x4                 x5                 x6                 x7             Weight     Radius
 -2.919553035887271  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 2999.034977168079877    2.91955
  3.460272140619591  2.583441257134286  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 2933.953409298860606    4.31829
  0.338095865881977 -3.746906006678980  4.806380318665463  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 1568.044072890766984    6.10368
 -0.534912267648242 -0.196914607156561 -3.279602680537424  5.745734188314676  0.000000000000000  0.000000000000000  0.000000000000000 1144.030722463451184    6.64034
  1.518699806514466 -2.823922301173129 -0.202809056712693 -1.254076393327084  5.901805046518621  0.000000000000000  0.000000000000000 884.544649725011141    6.83565
 -5.415590340027627 -0.048078695664352  0.096726701228047  0.369770514483796 -3.516880671250262  2.693521507329656  0.000000000000000 800.495989675229225    7.00718
  4.664074490359573 -2.708043025543082 -4.220846882562807 -1.814537626656763 -0.942654930018356 -1.963700784713051 -0.908704435199011 835.729228943092835    7.46764
 -1.104600464929036 -1.692960643167798 -3.899395944044414 -3.131212573785864  1.648726123973702  3.877888034695359  2.636728305537779 856.118073551059865    7.33517
 -0.295752894512359  2.228407216645166  1.292224528514038  2.533051964223611  6.175866997067353 -2.323975132446184  1.697318223647296 586.547534212821688    7.71768
  2.927890363152324 -2.516262691115253 -0.236256517442942  2.003445879284297 -1.423268463449071  4.032093486258658  4.451634702163247 774.510269961093513    7.55475
 -4.297901575001005 -3.430311816669233 -1.566351526253944  0.040043074569610  1.534564662289855 -4.466265407984937 -3.088711783579138 599.481155014485580    8.03347
  0.979799073108664 -0.588128102520957 -0.167523523269194  3.148894457714540 -3.454408895106525 -1.447452549977068 -5.979856999927430 641.160825070313194    7.81257
  0.243579817386688  0.587304278960320  1.288364805580139  0.385866663667970 -0.671957751388690 -7.783456345628222  0.696640203773969 641.529145385322636    7.98324
 -2.228082561683264  1.014548577712437  0.951119509028293 -3.557587953579833  0.875910769511972  4.102385984599250 -5.113388846653047 613.031606717792670    7.95602
 -0.533032423467265  2.294842430428465 -5.648477459223726 -0.033515479179962 -0.118396911522582 -3.121482840074381  4.234147585557904 614.238183072376387    8.07109
  1.777165014413612  1.352109890925839  4.037998910535731 -1.807775167292112 -5.951660240281170 -2.240589786833456 -1.794376499628287 440.547589965106738    8.25968
 -0.028395540401855  7.476075236122988 -0.453339587562253  0.050225879107612 -0.261322318085375 -1.142990502237824 -3.883074096400874 412.837454447678226    8.51784
  3.317396315173248 -0.600232064600033  1.366705727369727 -5.587869230492290 -3.425478993241517  3.890772337690870 -0.948626194163415 463.178659590021937    8.49879
 -0.158662980319278 -3.277198020933084 -0.955142830598206  1.412186736140929 -6.834227104069266 -2.047337923531370  2.791246348982541 544.405375651027271    8.50653
 -0.665212644318767  3.268412548305686 -0.324671330587257 -5.955387851767826  3.766247337933778 -2.399398232217628  0.610051987941441 556.333101623213679    8.18602
  0.495224219491350  3.206395252819042  4.134028827805176  5.338838410843163 -1.330341034834764 -0.829940437863599  4.117122741129768 461.858550061091364    8.69074
 -2.798518187470626  1.730295422407928  4.655683398296175  3.877979705155694  3.771098043000528 -0.752625193988528 -5.345559356133258 341.025418740075736    9.53427
  5.344456689712915 -0.161698281739340  0.349114034806083  2.492546011171815  3.309880401919465  5.416968207392238 -3.883443469250468 345.404257282468279    9.50284
 -0.863254202496270  0.737806574260579 -6.656287938370104  0.338867866443526  4.420339671127929  1.202229786628011 -4.819716117614499 335.056752028678545    9.48288
  0.237973373208471  1.860173194859048  5.482919678813818 -2.733964999203808  3.624521531268027  5.177896781268993  2.978951088160948 346.059339656366944    9.48028
 -4.935995886268918 -1.731777089020379  1.673624585119255  0.819114504847907  1.913998418905321 -1.220888300718874  7.816676696029949 301.546728931161056    9.85340
 -0.573257136594081  5.119632636170982  0.229844678850686 -3.534030951481633 -4.654372620246384  1.208552961135218  5.721643061086603 326.897765310777004    9.74384
 -0.270746275672038 -7.974933978282901 -1.612687134752644  0.202729445743067 -2.054941054295125  3.719089417391816 -4.374423708742726 288.370089488020824   10.17373
 -2.557131524509879  6.981691868343130 -1.572159849539561  1.947798625456387  2.769094947804708  5.753760370194108  1.875131735250818 256.040653293349010   10.28777
 -2.422675080603962  1.930909220820904 -5.064845021389149 -4.928646203403488 -4.552806828509736 -2.539178119655451 -3.617495038811867 291.027329099906410    9.99018
 -5.269057505714842  3.689825064719201  7.195622689920227 -3.527253850160038 -0.806901413201097 -2.674074945660751  0.275005100867829 214.706258462200907   10.65240
  0.272427671733328  2.257097254751843  5.480311635278646  4.581290772486221 -5.060679896675725  6.178146816801061 -2.192489318691736 187.827909066215227   11.17040
 -2.490160688891322 -5.147131024141959  0.294220326636772 -7.541049098161200 -1.768159544631592 -2.215975530959362  2.313814832418768 276.924409198172782   10.15079
  6.432755489642124 -3.900268343402488  2.556110064253327  6.949954764499851  1.437780068062515 -3.761710489618014 -0.932591844376443 169.579753767411916   11.33646
  3.634581165013035 -1.758207244702635  3.007182444432214 -5.217045614346344  2.732414215860388 -3.926983681193258 -7.359187087493790 183.537509256631751   11.38451
  6.484486253182901 -1.315959482335569  2.989494777547369 -4.106708142757876  0.970646889177948 -3.748315845573231  7.575754931651016 159.383389906770191   11.91497
 -4.841693179891881 -4.290245794951406  1.049314994111712  6.435187263892226  4.742151943791355  6.753850430176566  0.325975521138660 127.804418215005626   12.35191
  1.686947423498991  2.891575623845853 -6.886017738261515  1.300085044517386 -6.207060244863746  6.460505227078424 -1.637160456519439 153.781412043443055   11.96915
  0.253738431259582 -8.951231938726687 -3.882292046108168  3.409020188318928  3.692599049092748 -4.202581999637646  4.393793225445719 102.812374507239539   12.54930
 -9.430714310256510  9.684487706956718 -2.163883071301173  7.740045935838257 -6.579728359469339 -6.683130955405911 -0.945911778435046 25.818951669378105   18.33494
 13.893721282092377  6.643030919241416 -10.183162139307518  7.060089213150079 13.898680766513804  4.340571583263330 15.524198589598768  4.233005436894884   29.04689
 -26.396062842095873 10.097186866513024 -9.199352194885217 -2.316860067298825 14.732567431742797 -4.114897461930931  2.191842632305810  2.228130615747574   33.57806
 34.365373783380718 25.883951807942175 44.328869180569960 -4.012491083676773 14.069873738631669 -5.554043200695000 -8.589354902974481  0.184291049106823   64.30157
 14.174331517452597 13.367233701151351 -15.773367106794947  9.768360808790160 16.138267014497000 -24.237040151467532 -14.772474328398085  0.955676675369633   42.30743
 107.259132693021158 73.914747484284831 -45.344058076800380 67.684859720784885 -92.711141649351489 -38.076672221570860 24.834321446722061  0.002721755075385   185.11393
 -109.123971035356362 -90.863991929880783 85.754354795710825 123.213369476452300 -50.666110680366700 -61.231651140476181  3.826684930615778  0.001370526901394   221.42869

>> # evaluating formula 1 with 57 points
# t7_57_5.txt:4 formula 1   : problem  G, 7_57_5  (d=7 n=57 o=5 plus 263/924 of order 6) quality P
# evaluating formula 2 with 57 points
# t7_57_5.txt:65 formula 2   : problem E2, 7_57_5  (d=7 n=57 o=5 plus 263/924 of order 6) quality P
# evaluating formula 3 with 57 points
# t7_57_5.txt:126 formula 3   : problem  S, 7_57_5  (d=7 n=57 o=5 plus 242/924 of order 6) quality PI
# G 7 dimensions, degree 5, symmetric 57 point rule with points at 2 distinct radii: 1+56=57
# "E_n^{r^2}: 5-1", A.H. Stroud. Approximate Calculation of Multiple Integrals. Prentice Hall, Englewood Cliffs, NH, 1971.
#                x1                 x2                 x3                 x4                 x5                 x6                 x7             Weight     Radius     cos1
 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.222222222222222    0.00000
  3.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.013888888888889    3.00000  1.00000
 -3.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.013888888888889    3.00000 -1.00000
  1.000000000000000 -1.115355071650411 -1.115355071650411 -1.115355071650411 -1.115355071650411 -1.115355071650411  1.334134671132768  0.013888888888889    3.00000  0.33333
  1.000000000000000 -1.115355071650411 -1.115355071650411 -1.115355071650411 -1.115355071650411  1.334134671132768 -1.115355071650411  0.013888888888889    3.00000  0.33333
  1.000000000000000 -1.115355071650411 -1.115355071650411 -1.115355071650411  1.334134671132768 -1.115355071650411 -1.115355071650411  0.013888888888889    3.00000  0.33333
  1.000000000000000 -1.115355071650411 -1.115355071650411  1.334134671132768 -1.115355071650411 -1.115355071650411 -1.115355071650411  0.013888888888889    3.00000  0.33333
  1.000000000000000 -1.115355071650411  1.334134671132768 -1.115355071650411 -1.115355071650411 -1.115355071650411 -1.115355071650411  0.013888888888889    3.00000  0.33333
  1.000000000000000  1.334134671132768 -1.115355071650411 -1.115355071650411 -1.115355071650411 -1.115355071650411 -1.115355071650411  0.013888888888889    3.00000  0.33333
 -1.000000000000000  1.115355071650411  1.115355071650411  1.115355071650411  1.115355071650411  1.115355071650411 -1.334134671132768  0.013888888888889    3.00000 -0.33333
 -1.000000000000000  1.115355071650411  1.115355071650411  1.115355071650411  1.115355071650411 -1.334134671132768  1.115355071650411  0.013888888888889    3.00000 -0.33333
 -1.000000000000000  1.115355071650411  1.115355071650411  1.115355071650411 -1.334134671132768  1.115355071650411  1.115355071650411  0.013888888888889    3.00000 -0.33333
 -1.000000000000000  1.115355071650411  1.115355071650411 -1.334134671132768  1.115355071650411  1.115355071650411  1.115355071650411  0.013888888888889    3.00000 -0.33333
 -1.000000000000000  1.115355071650411 -1.334134671132768  1.115355071650411  1.115355071650411  1.115355071650411  1.115355071650411  0.013888888888889    3.00000 -0.33333
 -1.000000000000000 -1.334134671132768  1.115355071650411  1.115355071650411  1.115355071650411  1.115355071650411  1.115355071650411  0.013888888888889    3.00000 -0.33333
  1.000000000000000 -1.632993161855452 -1.632993161855452  0.816496580927726  0.816496580927726  0.816496580927726  0.816496580927726  0.013888888888889    3.00000  0.33333
  1.000000000000000 -1.632993161855452  0.816496580927726 -1.632993161855452  0.816496580927726  0.816496580927726  0.816496580927726  0.013888888888889    3.00000  0.33333
  1.000000000000000 -1.632993161855452  0.816496580927726  0.816496580927726 -1.632993161855452  0.816496580927726  0.816496580927726  0.013888888888889    3.00000  0.33333
  1.000000000000000 -1.632993161855452  0.816496580927726  0.816496580927726  0.816496580927726 -1.632993161855452  0.816496580927726  0.013888888888889    3.00000  0.33333
  1.000000000000000 -1.632993161855452  0.816496580927726  0.816496580927726  0.816496580927726  0.816496580927726 -1.632993161855452  0.013888888888889    3.00000  0.33333
  1.000000000000000  0.816496580927726 -1.632993161855452 -1.632993161855452  0.816496580927726  0.816496580927726  0.816496580927726  0.013888888888889    3.00000  0.33333
  1.000000000000000  0.816496580927726 -1.632993161855452  0.816496580927726 -1.632993161855452  0.816496580927726  0.816496580927726  0.013888888888889    3.00000  0.33333
  1.000000000000000  0.816496580927726 -1.632993161855452  0.816496580927726  0.816496580927726 -1.632993161855452  0.816496580927726  0.013888888888889    3.00000  0.33333
  1.000000000000000  0.816496580927726 -1.632993161855452  0.816496580927726  0.816496580927726  0.816496580927726 -1.632993161855452  0.013888888888889    3.00000  0.33333
  1.000000000000000  0.816496580927726  0.816496580927726 -1.632993161855452 -1.632993161855452  0.816496580927726  0.816496580927726  0.013888888888889    3.00000  0.33333
  1.000000000000000  0.816496580927726  0.816496580927726 -1.632993161855452  0.816496580927726 -1.632993161855452  0.816496580927726  0.013888888888889    3.00000  0.33333
  1.000000000000000  0.816496580927726  0.816496580927726 -1.632993161855452  0.816496580927726  0.816496580927726 -1.632993161855452  0.013888888888889    3.00000  0.33333
  1.000000000000000  0.816496580927726  0.816496580927726  0.816496580927726 -1.632993161855452 -1.632993161855452  0.816496580927726  0.013888888888889    3.00000  0.33333
  1.000000000000000  0.816496580927726  0.816496580927726  0.816496580927726 -1.632993161855452  0.816496580927726 -1.632993161855452  0.013888888888889    3.00000  0.33333
  1.000000000000000  0.816496580927726  0.816496580927726  0.816496580927726  0.816496580927726 -1.632993161855452 -1.632993161855452  0.013888888888889    3.00000  0.33333
 -1.000000000000000  1.632993161855452  1.632993161855452 -0.816496580927726 -0.816496580927726 -0.816496580927726 -0.816496580927726  0.013888888888889    3.00000 -0.33333
 -1.000000000000000  1.632993161855452 -0.816496580927726  1.632993161855452 -0.816496580927726 -0.816496580927726 -0.816496580927726  0.013888888888889    3.00000 -0.33333
 -1.000000000000000  1.632993161855452 -0.816496580927726 -0.816496580927726  1.632993161855452 -0.816496580927726 -0.816496580927726  0.013888888888889    3.00000 -0.33333
 -1.000000000000000  1.632993161855452 -0.816496580927726 -0.816496580927726 -0.816496580927726  1.632993161855452 -0.816496580927726  0.013888888888889    3.00000 -0.33333
 -1.000000000000000  1.632993161855452 -0.816496580927726 -0.816496580927726 -0.816496580927726 -0.816496580927726  1.632993161855452  0.013888888888889    3.00000 -0.33333
 -1.000000000000000 -0.816496580927726  1.632993161855452  1.632993161855452 -0.816496580927726 -0.816496580927726 -0.816496580927726  0.013888888888889    3.00000 -0.33333
 -1.000000000000000 -0.816496580927726  1.632993161855452 -0.816496580927726  1.632993161855452 -0.816496580927726 -0.816496580927726  0.013888888888889    3.00000 -0.33333
 -1.000000000000000 -0.816496580927726  1.632993161855452 -0.816496580927726 -0.816496580927726  1.632993161855452 -0.816496580927726  0.013888888888889    3.00000 -0.33333
 -1.000000000000000 -0.816496580927726  1.632993161855452 -0.816496580927726 -0.816496580927726 -0.816496580927726  1.632993161855452  0.013888888888889    3.00000 -0.33333
 -1.000000000000000 -0.816496580927726 -0.816496580927726  1.632993161855452  1.632993161855452 -0.816496580927726 -0.816496580927726  0.013888888888889    3.00000 -0.33333
 -1.000000000000000 -0.816496580927726 -0.816496580927726  1.632993161855452 -0.816496580927726  1.632993161855452 -0.816496580927726  0.013888888888889    3.00000 -0.33333
 -1.000000000000000 -0.816496580927726 -0.816496580927726  1.632993161855452 -0.816496580927726 -0.816496580927726  1.632993161855452  0.013888888888889    3.00000 -0.33333
 -1.000000000000000 -0.816496580927726 -0.816496580927726 -0.816496580927726  1.632993161855452  1.632993161855452 -0.816496580927726  0.013888888888889    3.00000 -0.33333
 -1.000000000000000 -0.816496580927726 -0.816496580927726 -0.816496580927726  1.632993161855452 -0.816496580927726  1.632993161855452  0.013888888888889    3.00000 -0.33333
 -1.000000000000000 -0.816496580927726 -0.816496580927726 -0.816496580927726 -0.816496580927726  1.632993161855452  1.632993161855452  0.013888888888889    3.00000 -0.33333
  1.000000000000000  0.298858490722685  0.298858490722685  0.298858490722685  0.298858490722685  0.298858490722685  2.748348233505863  0.013888888888889    3.00000  0.33333
  1.000000000000000  0.298858490722685  0.298858490722685  0.298858490722685  0.298858490722685  2.748348233505863  0.298858490722685  0.013888888888889    3.00000  0.33333
  1.000000000000000  0.298858490722685  0.298858490722685  0.298858490722685  2.748348233505863  0.298858490722685  0.298858490722685  0.013888888888889    3.00000  0.33333
  1.000000000000000  0.298858490722685  0.298858490722685  2.748348233505863  0.298858490722685  0.298858490722685  0.298858490722685  0.013888888888889    3.00000  0.33333
  1.000000000000000  0.298858490722685  2.748348233505863  0.298858490722685  0.298858490722685  0.298858490722685  0.298858490722685  0.013888888888889    3.00000  0.33333
  1.000000000000000  2.748348233505863  0.298858490722685  0.298858490722685  0.298858490722685  0.298858490722685  0.298858490722685  0.013888888888889    3.00000  0.33333
 -1.000000000000000 -0.298858490722685 -0.298858490722685 -0.298858490722685 -0.298858490722685 -0.298858490722685 -2.748348233505863  0.013888888888889    3.00000 -0.33333
 -1.000000000000000 -0.298858490722685 -0.298858490722685 -0.298858490722685 -0.298858490722685 -2.748348233505863 -0.298858490722685  0.013888888888889    3.00000 -0.33333
 -1.000000000000000 -0.298858490722685 -0.298858490722685 -0.298858490722685 -2.748348233505863 -0.298858490722685 -0.298858490722685  0.013888888888889    3.00000 -0.33333
 -1.000000000000000 -0.298858490722685 -0.298858490722685 -2.748348233505863 -0.298858490722685 -0.298858490722685 -0.298858490722685  0.013888888888889    3.00000 -0.33333
 -1.000000000000000 -0.298858490722685 -2.748348233505863 -0.298858490722685 -0.298858490722685 -0.298858490722685 -0.298858490722685  0.013888888888889    3.00000 -0.33333
 -1.000000000000000 -2.748348233505863 -0.298858490722685 -0.298858490722685 -0.298858490722685 -0.298858490722685 -0.298858490722685  0.013888888888889    3.00000 -0.33333

# E2 7 dimensions, degree 5, symmetric 57 point rule with points at 2 distinct radii: 1+56=57
# "E_n^{r^2}: 5-1", A.H. Stroud. Approximate Calculation of Multiple Integrals. Prentice Hall, Englewood Cliffs, NH, 1971.
#                x1                 x2                 x3                 x4                 x5                 x6                 x7             Weight     Radius     cos1
 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 12.212709889830958    0.00000
  2.121320343559642 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.763294368114435    2.12132  1.00000
 -2.121320343559642 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.763294368114435    2.12132 -1.00000
  0.707106781186548 -0.788675134594813 -0.788675134594813 -0.788675134594813 -0.788675134594813 -0.788675134594813  0.943375672974064  0.763294368114435    2.12132  0.33333
  0.707106781186548 -0.788675134594813 -0.788675134594813 -0.788675134594813 -0.788675134594813  0.943375672974064 -0.788675134594813  0.763294368114435    2.12132  0.33333
  0.707106781186548 -0.788675134594813 -0.788675134594813 -0.788675134594813  0.943375672974064 -0.788675134594813 -0.788675134594813  0.763294368114435    2.12132  0.33333
  0.707106781186548 -0.788675134594813 -0.788675134594813  0.943375672974064 -0.788675134594813 -0.788675134594813 -0.788675134594813  0.763294368114435    2.12132  0.33333
  0.707106781186548 -0.788675134594813  0.943375672974064 -0.788675134594813 -0.788675134594813 -0.788675134594813 -0.788675134594813  0.763294368114435    2.12132  0.33333
  0.707106781186548  0.943375672974064 -0.788675134594813 -0.788675134594813 -0.788675134594813 -0.788675134594813 -0.788675134594813  0.763294368114435    2.12132  0.33333
 -0.707106781186548  0.788675134594813  0.788675134594813  0.788675134594813  0.788675134594813  0.788675134594813 -0.943375672974064  0.763294368114435    2.12132 -0.33333
 -0.707106781186548  0.788675134594813  0.788675134594813  0.788675134594813  0.788675134594813 -0.943375672974064  0.788675134594813  0.763294368114435    2.12132 -0.33333
 -0.707106781186548  0.788675134594813  0.788675134594813  0.788675134594813 -0.943375672974064  0.788675134594813  0.788675134594813  0.763294368114435    2.12132 -0.33333
 -0.707106781186548  0.788675134594813  0.788675134594813 -0.943375672974064  0.788675134594813  0.788675134594813  0.788675134594813  0.763294368114435    2.12132 -0.33333
 -0.707106781186548  0.788675134594813 -0.943375672974064  0.788675134594813  0.788675134594813  0.788675134594813  0.788675134594813  0.763294368114435    2.12132 -0.33333
 -0.707106781186548 -0.943375672974064  0.788675134594813  0.788675134594813  0.788675134594813  0.788675134594813  0.788675134594813  0.763294368114435    2.12132 -0.33333
  0.707106781186548 -1.154700538379252 -1.154700538379252  0.577350269189626  0.577350269189626  0.577350269189626  0.577350269189626  0.763294368114435    2.12132  0.33333
  0.707106781186548 -1.154700538379252  0.577350269189626 -1.154700538379252  0.577350269189626  0.577350269189626  0.577350269189626  0.763294368114435    2.12132  0.33333
  0.707106781186548 -1.154700538379252  0.577350269189626  0.577350269189626 -1.154700538379252  0.577350269189626  0.577350269189626  0.763294368114435    2.12132  0.33333
  0.707106781186548 -1.154700538379252  0.577350269189626  0.577350269189626  0.577350269189626 -1.154700538379252  0.577350269189626  0.763294368114435    2.12132  0.33333
  0.707106781186548 -1.154700538379252  0.577350269189626  0.577350269189626  0.577350269189626  0.577350269189626 -1.154700538379252  0.763294368114435    2.12132  0.33333
  0.707106781186548  0.577350269189626 -1.154700538379252 -1.154700538379252  0.577350269189626  0.577350269189626  0.577350269189626  0.763294368114435    2.12132  0.33333
  0.707106781186548  0.577350269189626 -1.154700538379252  0.577350269189626 -1.154700538379252  0.577350269189626  0.577350269189626  0.763294368114435    2.12132  0.33333
  0.707106781186548  0.577350269189626 -1.154700538379252  0.577350269189626  0.577350269189626 -1.154700538379252  0.577350269189626  0.763294368114435    2.12132  0.33333
  0.707106781186548  0.577350269189626 -1.154700538379252  0.577350269189626  0.577350269189626  0.577350269189626 -1.154700538379252  0.763294368114435    2.12132  0.33333
  0.707106781186548  0.577350269189626  0.577350269189626 -1.154700538379252 -1.154700538379252  0.577350269189626  0.577350269189626  0.763294368114435    2.12132  0.33333
  0.707106781186548  0.577350269189626  0.577350269189626 -1.154700538379252  0.577350269189626 -1.154700538379252  0.577350269189626  0.763294368114435    2.12132  0.33333
  0.707106781186548  0.577350269189626  0.577350269189626 -1.154700538379252  0.577350269189626  0.577350269189626 -1.154700538379252  0.763294368114435    2.12132  0.33333
  0.707106781186548  0.577350269189626  0.577350269189626  0.577350269189626 -1.154700538379252 -1.154700538379252  0.577350269189626  0.763294368114435    2.12132  0.33333
  0.707106781186548  0.577350269189626  0.577350269189626  0.577350269189626 -1.154700538379252  0.577350269189626 -1.154700538379252  0.763294368114435    2.12132  0.33333
  0.707106781186548  0.577350269189626  0.577350269189626  0.577350269189626  0.577350269189626 -1.154700538379252 -1.154700538379252  0.763294368114435    2.12132  0.33333
 -0.707106781186548  1.154700538379252  1.154700538379252 -0.577350269189626 -0.577350269189626 -0.577350269189626 -0.577350269189626  0.763294368114435    2.12132 -0.33333
 -0.707106781186548  1.154700538379252 -0.577350269189626  1.154700538379252 -0.577350269189626 -0.577350269189626 -0.577350269189626  0.763294368114435    2.12132 -0.33333
 -0.707106781186548  1.154700538379252 -0.577350269189626 -0.577350269189626  1.154700538379252 -0.577350269189626 -0.577350269189626  0.763294368114435    2.12132 -0.33333
 -0.707106781186548  1.154700538379252 -0.577350269189626 -0.577350269189626 -0.577350269189626  1.154700538379252 -0.577350269189626  0.763294368114435    2.12132 -0.33333
 -0.707106781186548  1.154700538379252 -0.577350269189626 -0.577350269189626 -0.577350269189626 -0.577350269189626  1.154700538379252  0.763294368114435    2.12132 -0.33333
 -0.707106781186548 -0.577350269189626  1.154700538379252  1.154700538379252 -0.577350269189626 -0.577350269189626 -0.577350269189626  0.763294368114435    2.12132 -0.33333
 -0.707106781186548 -0.577350269189626  1.154700538379252 -0.577350269189626  1.154700538379252 -0.577350269189626 -0.577350269189626  0.763294368114435    2.12132 -0.33333
 -0.707106781186548 -0.577350269189626  1.154700538379252 -0.577350269189626 -0.577350269189626  1.154700538379252 -0.577350269189626  0.763294368114435    2.12132 -0.33333
 -0.707106781186548 -0.577350269189626  1.154700538379252 -0.577350269189626 -0.577350269189626 -0.577350269189626  1.154700538379252  0.763294368114435    2.12132 -0.33333
 -0.707106781186548 -0.577350269189626 -0.577350269189626  1.154700538379252  1.154700538379252 -0.577350269189626 -0.577350269189626  0.763294368114435    2.12132 -0.33333
 -0.707106781186548 -0.577350269189626 -0.577350269189626  1.154700538379252 -0.577350269189626  1.154700538379252 -0.577350269189626  0.763294368114435    2.12132 -0.33333
 -0.707106781186548 -0.577350269189626 -0.577350269189626  1.154700538379252 -0.577350269189626 -0.577350269189626  1.154700538379252  0.763294368114435    2.12132 -0.33333
 -0.707106781186548 -0.577350269189626 -0.577350269189626 -0.577350269189626  1.154700538379252  1.154700538379252 -0.577350269189626  0.763294368114435    2.12132 -0.33333
 -0.707106781186548 -0.577350269189626 -0.577350269189626 -0.577350269189626  1.154700538379252 -0.577350269189626  1.154700538379252  0.763294368114435    2.12132 -0.33333
 -0.707106781186548 -0.577350269189626 -0.577350269189626 -0.577350269189626 -0.577350269189626  1.154700538379252  1.154700538379252  0.763294368114435    2.12132 -0.33333
  0.707106781186548  0.211324865405187  0.211324865405187  0.211324865405187  0.211324865405187  0.211324865405187  1.943375672974064  0.763294368114435    2.12132  0.33333
  0.707106781186548  0.211324865405187  0.211324865405187  0.211324865405187  0.211324865405187  1.943375672974064  0.211324865405187  0.763294368114435    2.12132  0.33333
  0.707106781186548  0.211324865405187  0.211324865405187  0.211324865405187  1.943375672974064  0.211324865405187  0.211324865405187  0.763294368114435    2.12132  0.33333
  0.707106781186548  0.211324865405187  0.211324865405187  1.943375672974064  0.211324865405187  0.211324865405187  0.211324865405187  0.763294368114435    2.12132  0.33333
  0.707106781186548  0.211324865405187  1.943375672974064  0.211324865405187  0.211324865405187  0.211324865405187  0.211324865405187  0.763294368114435    2.12132  0.33333
  0.707106781186548  1.943375672974064  0.211324865405187  0.211324865405187  0.211324865405187  0.211324865405187  0.211324865405187  0.763294368114435    2.12132  0.33333
 -0.707106781186548 -0.211324865405187 -0.211324865405187 -0.211324865405187 -0.211324865405187 -0.211324865405187 -1.943375672974064  0.763294368114435    2.12132 -0.33333
 -0.707106781186548 -0.211324865405187 -0.211324865405187 -0.211324865405187 -0.211324865405187 -1.943375672974064 -0.211324865405187  0.763294368114435    2.12132 -0.33333
 -0.707106781186548 -0.211324865405187 -0.211324865405187 -0.211324865405187 -1.943375672974064 -0.211324865405187 -0.211324865405187  0.763294368114435    2.12132 -0.33333
 -0.707106781186548 -0.211324865405187 -0.211324865405187 -1.943375672974064 -0.211324865405187 -0.211324865405187 -0.211324865405187  0.763294368114435    2.12132 -0.33333
 -0.707106781186548 -0.211324865405187 -1.943375672974064 -0.211324865405187 -0.211324865405187 -0.211324865405187 -0.211324865405187  0.763294368114435    2.12132 -0.33333
 -0.707106781186548 -1.943375672974064 -0.211324865405187 -0.211324865405187 -0.211324865405187 -0.211324865405187 -0.211324865405187  0.763294368114435    2.12132 -0.33333

# S 7 dimensions, degree 5, symmetric 57 point rule with points at 2 distinct radii: 1+56=57
# "S_n: 5-1", A.H. Stroud. Approximate Calculation of Multiple Integrals. Prentice Hall, Englewood Cliffs, NH, 1971.
#                x1                 x2                 x3                 x4                 x5                 x6                 x7             Weight     Radius     cos1
 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.233321776312662    0.00000
  0.904534033733291 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.080204360607477    0.90453  1.00000
 -0.904534033733291 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.080204360607477    0.90453 -1.00000
  0.301511344577764 -0.336292207334943 -0.336292207334943 -0.336292207334943 -0.336292207334943 -0.336292207334943  0.402256738541053  0.080204360607477    0.90453  0.33333
  0.301511344577764 -0.336292207334943 -0.336292207334943 -0.336292207334943 -0.336292207334943  0.402256738541053 -0.336292207334943  0.080204360607477    0.90453  0.33333
  0.301511344577764 -0.336292207334943 -0.336292207334943 -0.336292207334943  0.402256738541053 -0.336292207334943 -0.336292207334943  0.080204360607477    0.90453  0.33333
  0.301511344577764 -0.336292207334943 -0.336292207334943  0.402256738541053 -0.336292207334943 -0.336292207334943 -0.336292207334943  0.080204360607477    0.90453  0.33333
  0.301511344577764 -0.336292207334943  0.402256738541053 -0.336292207334943 -0.336292207334943 -0.336292207334943 -0.336292207334943  0.080204360607477    0.90453  0.33333
  0.301511344577764  0.402256738541053 -0.336292207334943 -0.336292207334943 -0.336292207334943 -0.336292207334943 -0.336292207334943  0.080204360607477    0.90453  0.33333
 -0.301511344577764  0.336292207334943  0.336292207334943  0.336292207334943  0.336292207334943  0.336292207334943 -0.402256738541053  0.080204360607477    0.90453 -0.33333
 -0.301511344577764  0.336292207334943  0.336292207334943  0.336292207334943  0.336292207334943 -0.402256738541053  0.336292207334943  0.080204360607477    0.90453 -0.33333
 -0.301511344577764  0.336292207334943  0.336292207334943  0.336292207334943 -0.402256738541053  0.336292207334943  0.336292207334943  0.080204360607477    0.90453 -0.33333
 -0.301511344577764  0.336292207334943  0.336292207334943 -0.402256738541053  0.336292207334943  0.336292207334943  0.336292207334943  0.080204360607477    0.90453 -0.33333
 -0.301511344577764  0.336292207334943 -0.402256738541053  0.336292207334943  0.336292207334943  0.336292207334943  0.336292207334943  0.080204360607477    0.90453 -0.33333
 -0.301511344577764 -0.402256738541053  0.336292207334943  0.336292207334943  0.336292207334943  0.336292207334943  0.336292207334943  0.080204360607477    0.90453 -0.33333
  0.301511344577764 -0.492365963917331 -0.492365963917331  0.246182981958665  0.246182981958665  0.246182981958665  0.246182981958665  0.080204360607477    0.90453  0.33333
  0.301511344577764 -0.492365963917331  0.246182981958665 -0.492365963917331  0.246182981958665  0.246182981958665  0.246182981958665  0.080204360607477    0.90453  0.33333
  0.301511344577764 -0.492365963917331  0.246182981958665  0.246182981958665 -0.492365963917331  0.246182981958665  0.246182981958665  0.080204360607477    0.90453  0.33333
  0.301511344577764 -0.492365963917331  0.246182981958665  0.246182981958665  0.246182981958665 -0.492365963917331  0.246182981958665  0.080204360607477    0.90453  0.33333
  0.301511344577764 -0.492365963917331  0.246182981958665  0.246182981958665  0.246182981958665  0.246182981958665 -0.492365963917331  0.080204360607477    0.90453  0.33333
  0.301511344577764  0.246182981958665 -0.492365963917331 -0.492365963917331  0.246182981958665  0.246182981958665  0.246182981958665  0.080204360607477    0.90453  0.33333
  0.301511344577764  0.246182981958665 -0.492365963917331  0.246182981958665 -0.492365963917331  0.246182981958665  0.246182981958665  0.080204360607477    0.90453  0.33333
  0.301511344577764  0.246182981958665 -0.492365963917331  0.246182981958665  0.246182981958665 -0.492365963917331  0.246182981958665  0.080204360607477    0.90453  0.33333
  0.301511344577764  0.246182981958665 -0.492365963917331  0.246182981958665  0.246182981958665  0.246182981958665 -0.492365963917331  0.080204360607477    0.90453  0.33333
  0.301511344577764  0.246182981958665  0.246182981958665 -0.492365963917331 -0.492365963917331  0.246182981958665  0.246182981958665  0.080204360607477    0.90453  0.33333
  0.301511344577764  0.246182981958665  0.246182981958665 -0.492365963917331  0.246182981958665 -0.492365963917331  0.246182981958665  0.080204360607477    0.90453  0.33333
  0.301511344577764  0.246182981958665  0.246182981958665 -0.492365963917331  0.246182981958665  0.246182981958665 -0.492365963917331  0.080204360607477    0.90453  0.33333
  0.301511344577764  0.246182981958665  0.246182981958665  0.246182981958665 -0.492365963917331 -0.492365963917331  0.246182981958665  0.080204360607477    0.90453  0.33333
  0.301511344577764  0.246182981958665  0.246182981958665  0.246182981958665 -0.492365963917331  0.246182981958665 -0.492365963917331  0.080204360607477    0.90453  0.33333
  0.301511344577764  0.246182981958665  0.246182981958665  0.246182981958665  0.246182981958665 -0.492365963917331 -0.492365963917331  0.080204360607477    0.90453  0.33333
 -0.301511344577764  0.492365963917331  0.492365963917331 -0.246182981958665 -0.246182981958665 -0.246182981958665 -0.246182981958665  0.080204360607477    0.90453 -0.33333
 -0.301511344577764  0.492365963917331 -0.246182981958665  0.492365963917331 -0.246182981958665 -0.246182981958665 -0.246182981958665  0.080204360607477    0.90453 -0.33333
 -0.301511344577764  0.492365963917331 -0.246182981958665 -0.246182981958665  0.492365963917331 -0.246182981958665 -0.246182981958665  0.080204360607477    0.90453 -0.33333
 -0.301511344577764  0.492365963917331 -0.246182981958665 -0.246182981958665 -0.246182981958665  0.492365963917331 -0.246182981958665  0.080204360607477    0.90453 -0.33333
 -0.301511344577764  0.492365963917331 -0.246182981958665 -0.246182981958665 -0.246182981958665 -0.246182981958665  0.492365963917331  0.080204360607477    0.90453 -0.33333
 -0.301511344577764 -0.246182981958665  0.492365963917331  0.492365963917331 -0.246182981958665 -0.246182981958665 -0.246182981958665  0.080204360607477    0.90453 -0.33333
 -0.301511344577764 -0.246182981958665  0.492365963917331 -0.246182981958665  0.492365963917331 -0.246182981958665 -0.246182981958665  0.080204360607477    0.90453 -0.33333
 -0.301511344577764 -0.246182981958665  0.492365963917331 -0.246182981958665 -0.246182981958665  0.492365963917331 -0.246182981958665  0.080204360607477    0.90453 -0.33333
 -0.301511344577764 -0.246182981958665  0.492365963917331 -0.246182981958665 -0.246182981958665 -0.246182981958665  0.492365963917331  0.080204360607477    0.90453 -0.33333
 -0.301511344577764 -0.246182981958665 -0.246182981958665  0.492365963917331  0.492365963917331 -0.246182981958665 -0.246182981958665  0.080204360607477    0.90453 -0.33333
 -0.301511344577764 -0.246182981958665 -0.246182981958665  0.492365963917331 -0.246182981958665  0.492365963917331 -0.246182981958665  0.080204360607477    0.90453 -0.33333
 -0.301511344577764 -0.246182981958665 -0.246182981958665  0.492365963917331 -0.246182981958665 -0.246182981958665  0.492365963917331  0.080204360607477    0.90453 -0.33333
 -0.301511344577764 -0.246182981958665 -0.246182981958665 -0.246182981958665  0.492365963917331  0.492365963917331 -0.246182981958665  0.080204360607477    0.90453 -0.33333
 -0.301511344577764 -0.246182981958665 -0.246182981958665 -0.246182981958665  0.492365963917331 -0.246182981958665  0.492365963917331  0.080204360607477    0.90453 -0.33333
 -0.301511344577764 -0.246182981958665 -0.246182981958665 -0.246182981958665 -0.246182981958665  0.492365963917331  0.492365963917331  0.080204360607477    0.90453 -0.33333
  0.301511344577764  0.090109225376278  0.090109225376278  0.090109225376278  0.090109225376278  0.090109225376278  0.828658171252274  0.080204360607477    0.90453  0.33333
  0.301511344577764  0.090109225376278  0.090109225376278  0.090109225376278  0.090109225376278  0.828658171252274  0.090109225376278  0.080204360607477    0.90453  0.33333
  0.301511344577764  0.090109225376278  0.090109225376278  0.090109225376278  0.828658171252274  0.090109225376278  0.090109225376278  0.080204360607477    0.90453  0.33333
  0.301511344577764  0.090109225376278  0.090109225376278  0.828658171252274  0.090109225376278  0.090109225376278  0.090109225376278  0.080204360607477    0.90453  0.33333
  0.301511344577764  0.090109225376278  0.828658171252274  0.090109225376278  0.090109225376278  0.090109225376278  0.090109225376278  0.080204360607477    0.90453  0.33333
  0.301511344577764  0.828658171252274  0.090109225376278  0.090109225376278  0.090109225376278  0.090109225376278  0.090109225376278  0.080204360607477    0.90453  0.33333
 -0.301511344577764 -0.090109225376278 -0.090109225376278 -0.090109225376278 -0.090109225376278 -0.090109225376278 -0.828658171252274  0.080204360607477    0.90453 -0.33333
 -0.301511344577764 -0.090109225376278 -0.090109225376278 -0.090109225376278 -0.090109225376278 -0.828658171252274 -0.090109225376278  0.080204360607477    0.90453 -0.33333
 -0.301511344577764 -0.090109225376278 -0.090109225376278 -0.090109225376278 -0.828658171252274 -0.090109225376278 -0.090109225376278  0.080204360607477    0.90453 -0.33333
 -0.301511344577764 -0.090109225376278 -0.090109225376278 -0.828658171252274 -0.090109225376278 -0.090109225376278 -0.090109225376278  0.080204360607477    0.90453 -0.33333
 -0.301511344577764 -0.090109225376278 -0.828658171252274 -0.090109225376278 -0.090109225376278 -0.090109225376278 -0.090109225376278  0.080204360607477    0.90453 -0.33333
 -0.301511344577764 -0.828658171252274 -0.090109225376278 -0.090109225376278 -0.090109225376278 -0.090109225376278 -0.090109225376278  0.080204360607477    0.90453 -0.33333

>> # evaluating formula 1 with 223 points
# r7_223_6E1.txt:3 formula 1   : problem E1, 7_223_6  (d=7 n=223 o=6 plus 0/1716 of order 7) quality P
E1 7 dimensions, degree 6, asymmetric 223 point rule with points at 223 distinct radii
#                x1                 x2                 x3                 x4                 x5                 x6                 x7             Weight     Radius
  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 1289.279563279358626    0.00000
 -1.626638181046178  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 1057.600249368575987    1.62664
  0.070237625591580  3.317291395208870  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 1020.574639292272764    3.31803
 -0.956636388132960  1.897042033866215 -0.136144278505743 -1.207574648873586 -1.346300648261875 -0.605145016697405  1.700443120066101 671.901311517167414    3.32580
  3.658168266030613 -0.360700069715079 -0.299657492539754  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 793.164998521913731    3.68810
 -0.634260428813467 -2.008213201261728 -0.725755166041949 -1.732073225147905 -0.187831358365720  0.371773101854152  3.135498286774040 847.499480618595044    4.23873
 -1.271679991659528 -3.582635568624053  2.993924019415889 -0.344455359021431  0.000000000000000  0.000000000000000  0.000000000000000 615.995363000148700    4.85126
  2.055683888422273 -1.358053012544990 -0.575079991137853 -0.716209250446015 -3.385993641651390 -1.179606716683682 -2.094995245575060 514.893062565125319    4.91521
 -0.122460661365846  0.268466604112167  2.410122140201628  3.052761759089337  0.191675890803897 -3.632691193227495  0.681541421084963 534.502176720145030    5.37706
 -1.118448630753122  0.433601203400047 -1.412545539687637  4.315167073146621  0.127953642890339  1.777147560509801 -2.219086009881569 564.720906382725957    5.49125
  1.045829617911560 -2.151241791896272 -0.247022912357223 -0.696356073352389  4.252300627280125  2.876788773432701 -0.831833116674962 475.985366746003194    5.77213
  0.598014170967791 -3.634482999512554 -3.950456158927434 -2.320759161270762  1.122393921202960  0.459238604408045 -0.468370801256134 564.891555743446816    6.02073
  0.824929772179276  3.119966155834680 -0.444440007818099  0.987498270076829  4.053600208643047 -0.636870555245149 -3.009128103376873 348.506622253303419    6.12205
  1.136399341202882 -0.498588134034496 -1.627094884632518 -0.186066751939791  0.248374518696028 -2.994892260658773 -5.124090641505276 445.957035130658824    6.28565
  0.376843035527294 -0.405058985549304  2.404902052065237  0.879004219343801 -0.951022619364683  5.674093364730682  1.208339003927199 527.972602268778473    6.43600
 -2.221587343959733  1.232703251400031  1.159940208543615 -4.467458573980045  2.677448133483573 -2.542686378112048 -1.340860047866071 416.035613723002712    6.57195
 -4.631353117105665  1.635168918501671  1.367473056530349 -1.760072991614965  0.424073820661307  3.776421253553288 -0.511869974577167 338.665836843607508    6.61772
  5.474293197146212 -0.414448755985364  2.327190436734376  3.803694891625492  0.047964714388113  0.000000000000000  0.000000000000000 279.400664978684802    7.07290
 -2.190508507706777  1.949847026149891 -5.310569280882980  3.291092030191674  0.458118671563059 -1.019549705239207  1.409442865599944 260.620624582638300    7.13229
  1.257715754591049 -3.256016372979610 -1.281018239148523  3.439545840936135  4.975166141744100 -1.740069611521801  0.343688294875845 288.964538816217157    7.31801
  4.094968389258043  2.499360967139422  3.348123113724260 -4.378471421482422 -0.416850118497405  0.477743705303356 -0.317496042664624 289.451264115735626    7.34162
 -5.406854912720318 -0.896501444949322 -3.394239488592135  0.529741282782574 -1.942141171911798 -0.031916805726328 -2.951384846643533 329.167554477148713    7.37041
 -2.296525594000695  1.873921192197941 -3.743843728053084 -2.378778173861169 -0.435012090921532 -4.313920319262399  3.174965343816635 218.090998121259304    7.57233
  0.404036231602862  0.413784526133098  4.892681857748561  5.440158241709566 -1.065391057548950  1.165988901178349  1.464625644146103 242.892444292536908    7.64904
  2.907123143123941 -0.697007740924753 -3.384240998277012  4.233493907895613  0.590080726297829 -2.077794667036060  4.022448305504979 230.349378152980677    7.69144
 -2.936426161530213  1.247197838993260  0.310193140450769  3.839813587277785 -3.329322641297575  0.924635103352671  4.825068011155362 239.866853091643549    7.76139
  5.408095219397954  2.319686411259170 -3.641227778208358 -2.207312221471261  2.420155149745030  0.213657049822283  1.276708909558319 212.411362859312675    7.76479
 -2.532064987850742 -0.650873789694057  5.218728882459812 -0.934789939397951 -3.845792971527148 -3.124659239938188  1.003627611629899 252.695080244298651    7.77849
  2.638498784465658 -3.321743292902568 -1.116439217309653  0.919492556638582 -5.939855700666652 -2.011562680646352  1.091492278821628 225.952767942128588    7.78506
  2.841737788650021  1.733564398928277 -4.632218987853087  2.457430014550406 -2.445614256751402  3.897609908540196  0.968963387714297 258.967014561953135    7.79028
  3.276233443877734  0.137501346615799  0.934267097120707  1.292115442557164 -2.536167908863398  3.912355009687807 -5.139285370427670 227.665424863284017    7.83875
  1.721498849799956 -1.720007493766914  6.341433137715900  0.407321212850070  1.799789050431302 -2.072704409203427 -3.332673426137438 228.616101302279532    8.05877
 -0.832098758950359 -1.696498196546426 -3.396120591617885  4.267526745790499 -3.167355862277105 -4.395706282342536 -1.641046619754965 163.821679101597510    8.08476
  1.666992814368332  1.981959560331296 -2.229649430676662 -6.573169409244288 -0.391280048552340  2.735380256288053  1.772014820825658 188.724573203694746    8.10311
 -0.705170263297912  1.345042378657968  4.910809146632523 -3.090229374239468  4.777224770704606  2.393269362762210  1.181685835749245 235.898434208387954    8.11899
 -3.153737675179453  2.026479922002730  2.200867626021963  3.223473350994866  4.140944608572277 -0.980354915162157  4.362923909385833 236.455023512064287    8.15052
  0.549212930216030  3.866407280008722 -0.554053101302856  2.753415846285098  5.026567311807129  4.287806743646270  0.760556763823538 154.464283035773576    8.20787
 -0.730659691009983 -1.688521955219323  1.116412313876941 -5.407118047697591 -4.897988126377584  0.504695539018010 -3.075807583008996 211.944864841700166    8.22033
  3.644919553752873  5.678329580829508  2.076653299723944  0.831959154602171 -2.706549655829192  0.244047813070563  3.207000548853117 177.358734103712806    8.25853
 -0.498410923999104 -4.767205523317473  0.964304507511827 -5.869659889180840  0.431762618681517  2.174117539477745 -2.608252309242276 109.775690587335589    8.37100
  3.943370816622712 -0.088367408932477  1.927029047949976 -2.354721282453736  4.842414151328058 -4.514109561879156  1.561503239980324 188.121100447818520    8.43093
 -1.339785604801031 -5.033255074777249 -1.144017273059332  4.698964327922714 -2.777698230496075  3.595626195424826 -0.023027164376139 154.885424178358221    8.43578
  3.609135280974866  3.143597498162326 -2.787911397853591  0.693782992135738  0.340859217167987 -6.346877130219085 -1.003695451549302 157.573023152448570    8.51870
 -2.407437309582982  4.368566605380406 -1.828207176250876 -0.969536769243136 -6.278702953975417  2.010745697471497  0.421651848521573 164.788486443129045    8.53261
  2.817673933341632  0.709644211928781  1.582565421244573 -4.277444623516277 -2.798193872017845 -5.708974672196677  1.991794127425053 176.530925977772000    8.58099
 -1.351702258403987 -6.906732782595799  2.141099383106305  3.021286523658113 -1.341190315869046 -1.290621009432373 -2.652262100144227 160.447339423222161    8.58729
 -2.715558702928515  1.065293864068853  3.923513126748495 -1.105962132335804  0.286675533000703  3.917767599757628 -5.764752892736297 119.256844095913650    8.59009
 -5.173296043548782 -1.829642069218625 -3.891094275098334 -0.976159354226348  5.153506119420341 -0.407620191325266  1.596177118944045 161.773922577606271    8.68773
 -1.091166702329592 -1.702495343446036  3.049124478832635 -3.007085235494373 -1.781062342505188  0.919164710734457  7.070187572259412 130.715978660913834    8.74262
  0.596242629914420  5.158607595153480 -1.132248687412236 -3.474693897307577 -1.985825749263824  1.799824990330592 -5.386268544042233 156.463287685563984    8.74740
 -4.101254832032167  0.231399044443830  1.928897172662568 -0.645407289214162 -0.618452788775951 -1.242653932894297 -7.341496415127974 126.045204913668442    8.76557
  1.916355345771389  6.624145986886511  2.787621298435953  2.493340576360688  1.666368364470367  1.376374731283088 -3.328569908939246 123.916692191805339    8.79147
  2.545940412811195 -5.141164028617955  2.896928183977783  0.838303946110001  1.679262617504411  0.247307866358099  5.717012188341543 96.573246302691828    8.80759
  4.748601654406284  1.847982818435917  1.976210159907392  1.421027525480682  4.722213137515718  1.985626538022426  4.661247928442161 114.550025605492920    8.93634
 -3.049150817304905 -1.944251532502896  1.753839902245469  1.370375507961515 -7.489934107300979  1.678331256732789 -1.800035068165546 129.836092589392621    8.95474
  0.833323019314227  0.025833067185144 -2.117889998692419 -0.939065308828594  5.070942966054729  1.186732667925057  6.872023016249303 104.111189169758347    8.96716
 -5.020640015635700 -1.605020434842301  0.863312587251509  2.920729398575475  3.285272764897128 -4.836998941998234 -3.049144150898237 149.464290075106504    8.97473
 -1.630635347290327  4.446862311831713 -3.839021598415001 -4.180319328085313  4.400324134734277  2.451650577247714  0.874043135706430 125.941989390383100    8.98800
 -2.057690814639543 -1.211534928587023 -2.924664919411092  1.788182883794555  0.585877290115300 -7.559907530946953  2.469358917832467 100.547247867031061    9.00258
 -4.063637762215866 -2.751594856206326  2.630443914472522  3.338098773042477  5.461819924304644  2.880794227179436 -1.611430671759811 121.660078589261545    9.10350
  1.746522019497172  3.394404158244877 -1.524735225504699  3.568124167123273 -6.386299467344882 -3.113935069140017  1.784168960622393 105.808258157361237    9.12652
 -1.751145638867457 -3.740564982960292 -4.536420865098382  0.723735606356864 -3.755936095834154  3.662580275136149  4.247889347341108 107.822164987555908    9.15027
 -1.028097272797212  4.921310388149483  2.599142580868237 -0.299042712574643 -4.826403632762936 -3.754531989429300 -3.775270165150077 128.937034052396058    9.15230
  5.207264123810746 -2.022832468268474  5.144181782425702 -1.865544719390729 -4.018746794238552  1.162177324481698  2.460406390307985 114.541593877551335    9.20353
 -2.191779320588748 -5.873669573481704 -0.224173679232905 -1.983037266871139 -1.680275533690779 -6.191850080160757  1.648100267851491 113.345461605586834    9.33623
 -1.269717213362609  0.746109710281135  3.318914108424910  5.999407694875576 -3.596521093315204 -0.821169734473376 -5.247178633075912 96.104115742090940    9.50364
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  1.659115978376486 -3.257768035596520 -2.683976817474304 -9.174810273061446  9.284572726915499  1.005809804911389  0.488731337979859 12.910150891597100   13.86364
 12.004062652081194  1.144547687645390 -1.401798349345760  0.112848982373361 -4.315901341791065 -2.229282119176134  5.111905670317928 12.073638257173037   14.03971
 -7.473286395897037  6.854425619443140 -9.197261262679437 -2.270906670203728 -2.435392453349849  1.551917975239570  0.843229477102532  9.263154428064359   14.19966
  8.683955574299063  8.237969604994518  1.972817997771078  2.468450415472007  4.572409669721377 -5.087319660480198  1.654956592604212  8.878664006755924   14.24033
 -3.313228164849936  8.555147451002828 -1.359570216191457  1.281154403116583 -4.150478684178668 -8.497819358109686  5.363100975937473 10.244262723749291   14.34782
 -6.099994129551080 -4.364179954853316  1.771096219938776  1.433322330716724 -3.782856892307889  8.607515525562519 -7.592980560725279  8.756450382744976   14.40486
 -9.115956687780535  2.361761919063050  2.161971628634002 -4.561912238962607  6.822913109822497  3.701144347201293  6.113850436841234  9.136768093857313   14.55313
 -1.278346181133534  2.873622133878557  2.423347271090556 -8.248248608877715 -8.888024531221721 -3.148208137093627  6.291733856782377  7.871551332026524   14.57025
  9.494402069463018 -8.054430113190461  1.820156734758076  4.498384773528599 -3.999971199973464  2.111832975510060 -3.954148986799370  8.316982429520376   14.65131
  3.968154166042676 -3.448559234674264 -1.832056130510768 12.435354561667380 -5.388554849212228 -1.292853789241353  0.219515181481940  9.542358746513830   14.71018
 -4.731071731019690 -1.892416207938478  5.196312766985694  7.372540857438841 -5.589702553398147 -8.334000766929295  3.316889032966444  6.184542298367428   14.79941
  8.540748213395233  8.670339668410543 -0.041278403643109 -0.933314523178503 -2.656356217794105  7.971401206483842 -0.198946119591743  8.233767645857920   14.81995
  4.148928362322408  4.787317774971355  1.197303342454226 10.828741716199445  0.477176824864151 -6.925979729636247  3.832890358106456  6.072357273302627   14.89010
  4.788445924614876 -6.801386358432208  6.867012988337144 -1.637586462169488  8.949335946166087  4.891217234843724  1.094206733330674  7.102504746685228   14.97456
 -1.342239940140098  5.751290342857212  7.982206945165186  5.749823068812624  4.241373072834135  8.429662953230938  2.779698989178932  7.735424310754727   15.11391
  4.974580635607601 -6.054737645282366 -5.932129972858884  5.061226324760121  5.948387610285462  8.365851106878010 -2.177224675736071  5.931896811434769   15.24216
  0.126869239190656 -5.974604828329713  8.039811457636691  5.233238129011187 -8.982190367968816  1.888639558378697  5.006856563070829  6.633597442349509   15.39651
 67.501055403817517 40.474033211915412 -26.906996183179373 17.620781424731824 18.553126111359109 57.442126900561412 -113.348375156421923  0.000005326953312   154.01522
 -2.401865020702746 -6.036270567640578 -6.960134010583245 -0.789904561821758  3.981952546423721 -2.764097884240398 12.006386226371630  5.140127284011376   16.09107
  0.660732543204649  0.776667970724293  4.671263035529241 -12.221604076555547 -0.936416656425599  9.684442663374659  0.765350733596504  4.322825754061479   16.35479
 -1.110793838367071 10.575845703744463 -1.062340704353705 -6.772815167112933  4.069932702191050 -7.565902629307453 -6.083662373015709  3.658170102181132   16.45904
  0.856119743849459 -10.110455509972290 -5.869583782830493 -1.288958106502920 -9.868606035866136  1.584905713728100 -5.773533578709115  4.506611849155931   16.50160
 -0.431093027179412  6.513638094823246  7.313060356519151  1.923644382995177 -11.334455697434207 -1.346112150877843  6.708099564206393  3.156897700961073   16.58539
  9.849820724524971 -1.536464621024288 -11.538046874004321  4.674283802776551 -1.067131763400667 -4.516938499967734 -0.342469465114971  4.303857162172521   16.61367
 -0.377423090583939 -6.222255491259959  1.093478010692622  3.971399900017214 -7.594288449474683 -10.082898239376592 -7.821874042269495  3.782671245832061   16.62367
 -0.677129150676518  1.628707702256462 -5.557996421503515  2.690368684178666 -10.402301462007298  0.023469590828212 -11.283813321521743  4.739849155947745   16.63651
  7.763455405530010 -3.293888188294773 -7.981528814585253  0.327980262279977 11.874004497137545 -0.733592278782226  3.422161886193160  3.227300855305107   16.97571
  7.669446025034145  5.860763413552168  1.271886174927874 -6.585219516965031 -12.234873582314178 -0.201553573435067 -3.366957763971073  3.585689816684502   17.29800
 -3.183540583747575  3.600969868291974 10.026621180170554 -11.217061485796753 -1.599080341303199 -3.273914126150420 -6.888492388273114  3.025366382619355   17.61205
  6.312889139548196  8.862093163334938 10.655506334922636  8.095730246050151 -3.753335858150086 -0.055381236776981 -2.530191897378212  2.138926195293966   17.83150
 -3.680944235722931 12.634122281416030  5.580763031323727 -5.270311751882285  5.181289148067921  5.045655022477655 -5.856705375979306  2.643199112872948   17.85208
  7.600084826511505 10.244725601979765  2.082374125307221 -7.029009635358940 10.253615951754822  3.440417277681473  0.000000000000000  2.734349628127563   18.26012
 -0.558911695129064 -16.711601332688126 -2.535153165588368 -1.521575289317830  6.542356866163530  1.400724949843690  3.433210394548540  2.536796568473942   18.57104
 -6.564003012902286  0.499057962566487 -9.400884170311551  9.820710958862707 -10.405767782639636  4.214680639203897  0.663746191751065  2.157028189476655   18.83195
 -12.385355122221876  3.306101969174838 -6.509695272749435 10.220196384646156  4.494496178023662 -4.552233911766608  5.095437822798039  1.701752445942768   19.44332
  5.044011318956876 -3.792589778485197 -14.373573959247414 -5.365827993129209  2.420130482418419  8.706340255134561  6.739815391425485  1.253002290681452   20.05742
 -12.717147107042578 -8.522638982011939 10.819709381021752 -1.818997531204005 -6.420690993843712 -6.063329143078413 -8.525744393746121  0.695056285524023   22.48141
  1.794366510412947 -1.848891051529528  0.013736741034149 12.624404114935620 -2.901636832961829 18.859523372839082 -2.734267820885057  0.651119099346208   23.18601
 21.620652795457303 -0.560569968856728  6.363460511614537 -0.862742052115699  3.039594014947471 -4.634127409975959 -0.279003607105722  0.429641175034340   23.23353
 -1.698364187797962 -0.044728005850316 -1.774538002877459  0.673684571060674 22.911577496078863  6.597660225822024  2.299300215529342  0.467580992205509   24.08829
 -4.778809105054096  0.639790229845399 -15.805224731837249  4.992668258588109  1.306237057726930 -14.147379887138008 -11.667542358652845  0.355855876971423   25.21833
  3.970125102915609 -2.348414886785279  5.532725662409906 18.432986198735538 11.894720036698880 -0.191166802428182 11.217174994624783  0.234736496084941   25.67117
  0.831922190550165 -7.241874527452677 16.517429159653112 -4.839880782332330  3.449188984302681 -17.766012559577504  3.228564593289752  0.206813126203001   26.21714
 -4.548978428461385 -10.048374297635378 13.577602530862023 16.111306503265631  5.976780173554302 -9.731155084605309  0.529621088418835  0.276808413015945   26.38724
 -11.403333691511165 -0.788448728741747  3.168369096787193  1.500155527761309 -13.445917689424858 17.361628774913100 10.085455354666806  0.252605885016155   26.96075
 -4.257188548161186 11.072282239196115  3.090428947594977  6.481121930710950  5.566540286765989 -8.272595903882554 -23.542158919928564  0.141188676256618   29.08488
  3.905355707024317 -6.045055944029207 -2.509739673247523 -9.410691893473365 -2.897009506707166 -1.977863211017327 -26.973695018489003  0.128617638410892   29.77481
  1.003297336493006 -18.220013910974913  7.209757311194568  1.787275678728750 16.445031575162471 -7.807717043425064 -13.775867496077392  0.116971714152570   30.15501
 -1.578775234276323  6.089050505508843 -23.545072869737030 13.413950433620013 -10.519614210893000 -5.563669053449818 19.677296717239198  0.034813417026653   36.09275
  9.466413160537908 -18.423640747017803 -23.131117293653173 -19.830588062765418  5.673030914896745 10.656090083738665 -15.058923556071804  0.016508711186484   41.59148
 -29.540982366576472 -2.321557269643545 -19.414957897328108 -12.832428289800193 10.954485602422890 -21.106578896480080 -3.475763600228245  0.010178662457093   44.69050
 -29.197874864381475 13.951942720366409 -0.582108856949991 -12.438558673834109 -19.186938885843595  6.444511418502323 -20.371147350276598  0.011458962867154   45.02092
 -25.053100748524024 -13.279873273609796 -6.216849672492415 23.069931206926409  0.063463949015252 -0.047479653855594 -25.935676928860676  0.009684339978011   45.24986
  8.422439774712313 -40.774310779723912 31.526569262495563 -33.259303066455729 -45.159857016545800 -23.014069619140916  1.150807986199197  0.000317937178946   80.02482
  6.844739891673697 -24.405240070527931 56.615131553896163 44.164985634761237 -17.101482008778280 17.420367649526309 -31.077970712702434  0.000188378864368   85.79077
 -4.932332649352047 -6.530257318381608 -14.914297008216570 25.546392110832048 47.201520079724688 -58.798452736278449 37.485750724766774  0.000175001554478   89.62393
 -44.141747838663115 -29.801902635593724 -66.074684079822021 31.570938757978421 12.031132326109217 34.249979649525137 -11.716023486579536  0.000071745167432   98.25635

>> # evaluating formula 1 with 183 points
# r7_183_7g.txt:4 formula 1   : problem  G, 7_183_7  (d=7 n=183 o=7 plus 2702/3003 of order 8) quality P
# evaluating formula 2 with 183 points
# r7_183_7g.txt:191 formula 2   : problem  S, 7_183_7  (d=7 n=183 o=7 plus 2702/3003 of order 8) quality PI
# evaluating formula 3 with 183 points
# r7_183_7g.txt:378 formula 3   : problem E2, 7_183_7  (d=7 n=183 o=7 plus 2702/3003 of order 8) quality P
G_n 7 dimensions, degree 7, symmetric 183 point rule with points at 3 distinct radii: 1+56+126=183

#                x1                 x2                 x3                 x4                 x5                 x6                 x7             Weight     Radius     cos1     cos2
  0.000000000000000 -0.000000000000000 -0.000000000000000  0.000000000000000  0.000000000000000 -0.000000000000000 -0.000000000000000  0.076564023631843    0.00000 -0.00000 -0.00000
 -2.493068452564726  0.000000000000000  0.000000000000000  0.000000000000000 -0.000000000000000 -0.000000000000000  0.000000000000000  0.014056220399624    2.49307  1.00000 -0.57735
 -0.831022817521575  2.350487478361027  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.014056220399624    2.49307  0.33333  0.57735
 -0.831022817521575 -1.175243739180513  2.035581867537875 -0.000000000000000  0.000000000000000  0.000000000000000 -0.000000000000000  0.014056220399624    2.49307  0.33333 -0.57735
 -0.831022817521575 -1.175243739180513  0.000000000000000  2.035581867537875 -0.000000000000000  0.000000000000000  0.000000000000000  0.014056220399624    2.49307  0.33333 -0.57735
 -0.831022817521575 -1.175243739180513  0.000000000000000  0.000000000000000  2.035581867537875  0.000000000000000  0.000000000000000  0.014056220399624    2.49307  0.33333 -0.57735
 -0.831022817521575 -1.175243739180513  0.000000000000000 -0.000000000000000  0.000000000000000  2.035581867537875  0.000000000000000  0.014056220399624    2.49307  0.33333 -0.57735
 -0.831022817521575 -1.175243739180513 -0.000000000000000  0.000000000000000 -0.000000000000000  0.000000000000000  2.035581867537875  0.014056220399624    2.49307  0.33333 -0.57735
 -0.831022817521575 -1.175243739180513 -0.000000000000000  0.000000000000000 -0.000000000000000  0.000000000000000 -2.035581867537875  0.014056220399624    2.49307  0.33333 -0.57735
 -0.831022817521575 -1.175243739180513 -0.000000000000000  0.000000000000000 -0.000000000000000 -2.035581867537875  0.000000000000000  0.014056220399624    2.49307  0.33333 -0.57735
 -0.831022817521575 -1.175243739180513 -0.000000000000000  0.000000000000000 -2.035581867537875  0.000000000000000  0.000000000000000  0.014056220399624    2.49307  0.33333 -0.57735
 -0.831022817521575 -1.175243739180513 -0.000000000000000 -2.035581867537875 -0.000000000000000  0.000000000000000 -0.000000000000000  0.014056220399624    2.49307  0.33333 -0.57735
 -0.831022817521575 -1.175243739180513 -2.035581867537875  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.014056220399624    2.49307  0.33333 -0.57735
 -0.831022817521575  0.587621869590257  1.017790933768937  1.017790933768937  1.017790933768937  1.017790933768937  1.017790933768937  0.014056220399624    2.49307  0.33333 -0.00000
 -0.831022817521575  0.587621869590257  1.017790933768937  1.017790933768937  1.017790933768937 -1.017790933768937 -1.017790933768937  0.014056220399624    2.49307  0.33333  0.00000
 -0.831022817521575  0.587621869590257  1.017790933768937  1.017790933768937 -1.017790933768937  1.017790933768937 -1.017790933768937  0.014056220399624    2.49307  0.33333  0.00000
 -0.831022817521575  0.587621869590257  1.017790933768937  1.017790933768937 -1.017790933768937 -1.017790933768937  1.017790933768937  0.014056220399624    2.49307  0.33333  0.00000
 -0.831022817521575  0.587621869590257  1.017790933768937 -1.017790933768937  1.017790933768937  1.017790933768937 -1.017790933768937  0.014056220399624    2.49307  0.33333  0.00000
 -0.831022817521575  0.587621869590257  1.017790933768937 -1.017790933768937  1.017790933768937 -1.017790933768937  1.017790933768937  0.014056220399624    2.49307  0.33333  0.00000
 -0.831022817521575  0.587621869590257  1.017790933768937 -1.017790933768937 -1.017790933768937  1.017790933768937  1.017790933768937  0.014056220399624    2.49307  0.33333  0.00000
 -0.831022817521575  0.587621869590257  1.017790933768937 -1.017790933768937 -1.017790933768937 -1.017790933768937 -1.017790933768937  0.014056220399624    2.49307  0.33333  0.00000
 -0.831022817521575  0.587621869590257 -1.017790933768937  1.017790933768937  1.017790933768937  1.017790933768937 -1.017790933768937  0.014056220399624    2.49307  0.33333 -0.00000
 -0.831022817521575  0.587621869590257 -1.017790933768937  1.017790933768937  1.017790933768937 -1.017790933768937  1.017790933768937  0.014056220399624    2.49307  0.33333 -0.00000
 -0.831022817521575  0.587621869590257 -1.017790933768937  1.017790933768937 -1.017790933768937  1.017790933768937  1.017790933768937  0.014056220399624    2.49307  0.33333 -0.00000
 -0.831022817521575  0.587621869590257 -1.017790933768937  1.017790933768937 -1.017790933768937 -1.017790933768937 -1.017790933768937  0.014056220399624    2.49307  0.33333  0.00000
 -0.831022817521575  0.587621869590257 -1.017790933768937 -1.017790933768937  1.017790933768937  1.017790933768937  1.017790933768937  0.014056220399624    2.49307  0.33333 -0.00000
 -0.831022817521575  0.587621869590257 -1.017790933768937 -1.017790933768937  1.017790933768937 -1.017790933768937 -1.017790933768937  0.014056220399624    2.49307  0.33333  0.00000
 -0.831022817521575  0.587621869590257 -1.017790933768937 -1.017790933768937 -1.017790933768937  1.017790933768937 -1.017790933768937  0.014056220399624    2.49307  0.33333  0.00000
 -0.831022817521575  0.587621869590257 -1.017790933768937 -1.017790933768937 -1.017790933768937 -1.017790933768937  1.017790933768937  0.014056220399624    2.49307  0.33333  0.00000
  0.831022817521575  1.175243739180513  2.035581867537875 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.014056220399624    2.49307 -0.33333  0.57735
  0.831022817521575  1.175243739180513  0.000000000000000  2.035581867537875 -0.000000000000000 -0.000000000000000  0.000000000000000  0.014056220399624    2.49307 -0.33333  0.57735
  0.831022817521575  1.175243739180513  0.000000000000000 -0.000000000000000  2.035581867537875 -0.000000000000000 -0.000000000000000  0.014056220399624    2.49307 -0.33333  0.57735
  0.831022817521575  1.175243739180513  0.000000000000000 -0.000000000000000  0.000000000000000  2.035581867537875  0.000000000000000  0.014056220399624    2.49307 -0.33333  0.57735
  0.831022817521575  1.175243739180513  0.000000000000000 -0.000000000000000  0.000000000000000 -0.000000000000000  2.035581867537875  0.014056220399624    2.49307 -0.33333  0.57735
  0.831022817521575  1.175243739180513  0.000000000000000 -0.000000000000000 -0.000000000000000  0.000000000000000 -2.035581867537875  0.014056220399624    2.49307 -0.33333  0.57735
  0.831022817521575  1.175243739180513 -0.000000000000000  0.000000000000000 -0.000000000000000 -2.035581867537875 -0.000000000000000  0.014056220399624    2.49307 -0.33333  0.57735
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 -0.000000000000000  0.000000000000000 -2.780656542539707  0.000000000000000 -2.780656542539707  0.000000000000000 -0.000000000000000  0.001081647888803    3.93244  0.00000  0.00000
 -0.000000000000000  0.000000000000000 -2.780656542539707 -2.780656542539707  0.000000000000000  0.000000000000000  0.000000000000000  0.001081647888803    3.93244 -0.00000  0.00000
  0.000000000000000 -2.408119205038791  1.390328271269853  1.390328271269853  1.390328271269853  1.390328271269853  1.390328271269853  0.001081647888803    3.93244 -0.00000 -0.50000
 -0.000000000000000 -2.408119205038791  1.390328271269853  1.390328271269853  1.390328271269853 -1.390328271269853 -1.390328271269853  0.001081647888803    3.93244  0.00000 -0.50000
  0.000000000000000 -2.408119205038791  1.390328271269853  1.390328271269853 -1.390328271269853  1.390328271269853 -1.390328271269853  0.001081647888803    3.93244 -0.00000 -0.50000
  0.000000000000000 -2.408119205038791  1.390328271269853  1.390328271269853 -1.390328271269853 -1.390328271269853  1.390328271269853  0.001081647888803    3.93244  0.00000 -0.50000
 -0.000000000000000 -2.408119205038791  1.390328271269853 -1.390328271269853  1.390328271269853  1.390328271269853 -1.390328271269853  0.001081647888803    3.93244 -0.00000 -0.50000
 -0.000000000000000 -2.408119205038791  1.390328271269853 -1.390328271269853  1.390328271269853 -1.390328271269853  1.390328271269853  0.001081647888803    3.93244  0.00000 -0.50000
  0.000000000000000 -2.408119205038791  1.390328271269853 -1.390328271269853 -1.390328271269853  1.390328271269853  1.390328271269853  0.001081647888803    3.93244 -0.00000 -0.50000
 -0.000000000000000 -2.408119205038791  1.390328271269853 -1.390328271269853 -1.390328271269853 -1.390328271269853 -1.390328271269853  0.001081647888803    3.93244  0.00000 -0.50000
 -0.000000000000000 -2.408119205038791 -1.390328271269853  1.390328271269853  1.390328271269853  1.390328271269853 -1.390328271269853  0.001081647888803    3.93244 -0.00000 -0.50000
  0.000000000000000 -2.408119205038791 -1.390328271269853  1.390328271269853  1.390328271269853 -1.390328271269853  1.390328271269853  0.001081647888803    3.93244 -0.00000 -0.50000
  0.000000000000000 -2.408119205038791 -1.390328271269853  1.390328271269853 -1.390328271269853  1.390328271269853  1.390328271269853  0.001081647888803    3.93244 -0.00000 -0.50000
 -0.000000000000000 -2.408119205038791 -1.390328271269853  1.390328271269853 -1.390328271269853 -1.390328271269853 -1.390328271269853  0.001081647888803    3.93244  0.00000 -0.50000
  0.000000000000000 -2.408119205038791 -1.390328271269853 -1.390328271269853  1.390328271269853  1.390328271269853  1.390328271269853  0.001081647888803    3.93244 -0.00000 -0.50000
 -0.000000000000000 -2.408119205038791 -1.390328271269853 -1.390328271269853  1.390328271269853 -1.390328271269853 -1.390328271269853  0.001081647888803    3.93244 -0.00000 -0.50000
  0.000000000000000 -2.408119205038791 -1.390328271269853 -1.390328271269853 -1.390328271269853  1.390328271269853 -1.390328271269853  0.001081647888803    3.93244 -0.00000 -0.50000
  0.000000000000000 -2.408119205038791 -1.390328271269853 -1.390328271269853 -1.390328271269853 -1.390328271269853  1.390328271269853  0.001081647888803    3.93244 -0.00000 -0.50000
 -2.270396559717982  1.605412803359194  2.780656542539707 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.000000000000000  0.001081647888803    3.93244  0.57735  0.00000
 -2.270396559717982  1.605412803359194  0.000000000000000  2.780656542539707  0.000000000000000 -0.000000000000000  0.000000000000000  0.001081647888803    3.93244  0.57735 -0.00000
 -2.270396559717982  1.605412803359194  0.000000000000000 -0.000000000000000  2.780656542539707  0.000000000000000  0.000000000000000  0.001081647888803    3.93244  0.57735 -0.00000
 -2.270396559717982  1.605412803359194  0.000000000000000 -0.000000000000000  0.000000000000000  2.780656542539707  0.000000000000000  0.001081647888803    3.93244  0.57735 -0.00000
 -2.270396559717982  1.605412803359194  0.000000000000000 -0.000000000000000 -0.000000000000000  0.000000000000000  2.780656542539707  0.001081647888803    3.93244  0.57735 -0.00000
 -2.270396559717982  1.605412803359194  0.000000000000000  0.000000000000000 -0.000000000000000  0.000000000000000 -2.780656542539707  0.001081647888803    3.93244  0.57735  0.00000
 -2.270396559717982  1.605412803359194 -0.000000000000000 -0.000000000000000 -0.000000000000000 -2.780656542539707  0.000000000000000  0.001081647888803    3.93244  0.57735  0.00000
 -2.270396559717982  1.605412803359194 -0.000000000000000  0.000000000000000 -2.780656542539707 -0.000000000000000  0.000000000000000  0.001081647888803    3.93244  0.57735  0.00000
 -2.270396559717982  1.605412803359194 -0.000000000000000 -2.780656542539707 -0.000000000000000  0.000000000000000 -0.000000000000000  0.001081647888803    3.93244  0.57735  0.00000
 -2.270396559717982  1.605412803359194 -2.780656542539707  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.001081647888803    3.93244  0.57735 -0.00000
 -2.270396559717982 -0.802706401679597  1.390328271269853  1.390328271269853  1.390328271269853  1.390328271269853 -1.390328271269853  0.001081647888803    3.93244  0.57735 -0.50000
 -2.270396559717982 -0.802706401679597  1.390328271269853  1.390328271269853  1.390328271269853 -1.390328271269853  1.390328271269853  0.001081647888803    3.93244  0.57735 -0.50000
 -2.270396559717982 -0.802706401679597  1.390328271269853  1.390328271269853 -1.390328271269853  1.390328271269853  1.390328271269853  0.001081647888803    3.93244  0.57735 -0.50000
 -2.270396559717982 -0.802706401679597  1.390328271269853  1.390328271269853 -1.390328271269853 -1.390328271269853 -1.390328271269853  0.001081647888803    3.93244  0.57735 -0.50000
 -2.270396559717982 -0.802706401679597  1.390328271269853 -1.390328271269853  1.390328271269853  1.390328271269853  1.390328271269853  0.001081647888803    3.93244  0.57735 -0.50000
 -2.270396559717982 -0.802706401679597  1.390328271269853 -1.390328271269853  1.390328271269853 -1.390328271269853 -1.390328271269853  0.001081647888803    3.93244  0.57735 -0.50000
 -2.270396559717982 -0.802706401679597  1.390328271269853 -1.390328271269853 -1.390328271269853  1.390328271269853 -1.390328271269853  0.001081647888803    3.93244  0.57735 -0.50000
 -2.270396559717982 -0.802706401679597  1.390328271269853 -1.390328271269853 -1.390328271269853 -1.390328271269853  1.390328271269853  0.001081647888803    3.93244  0.57735 -0.50000
 -2.270396559717982 -0.802706401679597 -1.390328271269853  1.390328271269853  1.390328271269853  1.390328271269853  1.390328271269853  0.001081647888803    3.93244  0.57735 -0.50000
 -2.270396559717982 -0.802706401679597 -1.390328271269853  1.390328271269853  1.390328271269853 -1.390328271269853 -1.390328271269853  0.001081647888803    3.93244  0.57735 -0.50000
 -2.270396559717982 -0.802706401679597 -1.390328271269853  1.390328271269853 -1.390328271269853  1.390328271269853 -1.390328271269853  0.001081647888803    3.93244  0.57735 -0.50000
 -2.270396559717982 -0.802706401679597 -1.390328271269853  1.390328271269853 -1.390328271269853 -1.390328271269853  1.390328271269853  0.001081647888803    3.93244  0.57735 -0.50000
 -2.270396559717982 -0.802706401679597 -1.390328271269853 -1.390328271269853  1.390328271269853  1.390328271269853 -1.390328271269853  0.001081647888803    3.93244  0.57735 -0.50000
 -2.270396559717982 -0.802706401679597 -1.390328271269853 -1.390328271269853  1.390328271269853 -1.390328271269853  1.390328271269853  0.001081647888803    3.93244  0.57735 -0.50000
 -2.270396559717982 -0.802706401679597 -1.390328271269853 -1.390328271269853 -1.390328271269853  1.390328271269853  1.390328271269853  0.001081647888803    3.93244  0.57735 -0.50000
 -2.270396559717982 -0.802706401679597 -1.390328271269853 -1.390328271269853 -1.390328271269853 -1.390328271269853 -1.390328271269853  0.001081647888803    3.93244  0.57735 -0.50000
 -2.270396559717982 -3.210825606718387 -0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.001081647888803    3.93244  0.57735 -1.00000

S_n 7 dimensions, degree 7, symmetric 183 point rule with points at 3 distinct radii: 1+56+126=183

#                x1                 x2                 x3                 x4                 x5                 x6                 x7             Weight     Radius     cos1     cos2
  0.000000000000000 -0.000000000000000 -0.000000000000000  0.000000000000000  0.000000000000000 -0.000000000000000 -0.000000000000000  0.067567634767907    0.00000 -0.00000 -0.00000
 -0.806174562985883  0.000000000000000  0.000000000000000  0.000000000000000 -0.000000000000000 -0.000000000000000  0.000000000000000  0.045133705087381    0.80617  1.00000 -0.57735
 -0.268724854328628  0.760068667076559  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.045133705087381    0.80617  0.33333  0.57735
 -0.268724854328628 -0.380034333538280  0.658238774308877 -0.000000000000000  0.000000000000000  0.000000000000000 -0.000000000000000  0.045133705087381    0.80617  0.33333 -0.57735
 -0.268724854328628 -0.380034333538280  0.000000000000000  0.658238774308877 -0.000000000000000  0.000000000000000  0.000000000000000  0.045133705087381    0.80617  0.33333 -0.57735
 -0.268724854328628 -0.380034333538280  0.000000000000000  0.000000000000000  0.658238774308877  0.000000000000000  0.000000000000000  0.045133705087381    0.80617  0.33333 -0.57735
 -0.268724854328628 -0.380034333538280  0.000000000000000 -0.000000000000000  0.000000000000000  0.658238774308877  0.000000000000000  0.045133705087381    0.80617  0.33333 -0.57735
 -0.268724854328628 -0.380034333538280 -0.000000000000000  0.000000000000000 -0.000000000000000  0.000000000000000  0.658238774308877  0.045133705087381    0.80617  0.33333 -0.57735
 -0.268724854328628 -0.380034333538280 -0.000000000000000  0.000000000000000 -0.000000000000000  0.000000000000000 -0.658238774308877  0.045133705087381    0.80617  0.33333 -0.57735
 -0.268724854328628 -0.380034333538280 -0.000000000000000  0.000000000000000 -0.000000000000000 -0.658238774308877  0.000000000000000  0.045133705087381    0.80617  0.33333 -0.57735
 -0.268724854328628 -0.380034333538280 -0.000000000000000  0.000000000000000 -0.658238774308877  0.000000000000000  0.000000000000000  0.045133705087381    0.80617  0.33333 -0.57735
 -0.268724854328628 -0.380034333538280 -0.000000000000000 -0.658238774308877 -0.000000000000000  0.000000000000000 -0.000000000000000  0.045133705087381    0.80617  0.33333 -0.57735
 -0.268724854328628 -0.380034333538280 -0.658238774308877  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.045133705087381    0.80617  0.33333 -0.57735
 -0.268724854328628  0.190017166769140  0.329119387154439  0.329119387154439  0.329119387154439  0.329119387154439  0.329119387154439  0.045133705087381    0.80617  0.33333 -0.00000
 -0.268724854328628  0.190017166769140  0.329119387154439  0.329119387154439  0.329119387154439 -0.329119387154439 -0.329119387154439  0.045133705087381    0.80617  0.33333  0.00000
 -0.268724854328628  0.190017166769140  0.329119387154439  0.329119387154439 -0.329119387154439  0.329119387154439 -0.329119387154439  0.045133705087381    0.80617  0.33333  0.00000
 -0.268724854328628  0.190017166769140  0.329119387154439  0.329119387154439 -0.329119387154439 -0.329119387154439  0.329119387154439  0.045133705087381    0.80617  0.33333  0.00000
 -0.268724854328628  0.190017166769140  0.329119387154439 -0.329119387154439  0.329119387154439  0.329119387154439 -0.329119387154439  0.045133705087381    0.80617  0.33333  0.00000
 -0.268724854328628  0.190017166769140  0.329119387154439 -0.329119387154439  0.329119387154439 -0.329119387154439  0.329119387154439  0.045133705087381    0.80617  0.33333  0.00000
 -0.268724854328628  0.190017166769140  0.329119387154439 -0.329119387154439 -0.329119387154439  0.329119387154439  0.329119387154439  0.045133705087381    0.80617  0.33333  0.00000
 -0.268724854328628  0.190017166769140  0.329119387154439 -0.329119387154439 -0.329119387154439 -0.329119387154439 -0.329119387154439  0.045133705087381    0.80617  0.33333  0.00000
 -0.268724854328628  0.190017166769140 -0.329119387154439  0.329119387154439  0.329119387154439  0.329119387154439 -0.329119387154439  0.045133705087381    0.80617  0.33333 -0.00000
 -0.268724854328628  0.190017166769140 -0.329119387154439  0.329119387154439  0.329119387154439 -0.329119387154439  0.329119387154439  0.045133705087381    0.80617  0.33333 -0.00000
 -0.268724854328628  0.190017166769140 -0.329119387154439  0.329119387154439 -0.329119387154439  0.329119387154439  0.329119387154439  0.045133705087381    0.80617  0.33333 -0.00000
 -0.268724854328628  0.190017166769140 -0.329119387154439  0.329119387154439 -0.329119387154439 -0.329119387154439 -0.329119387154439  0.045133705087381    0.80617  0.33333  0.00000
 -0.268724854328628  0.190017166769140 -0.329119387154439 -0.329119387154439  0.329119387154439  0.329119387154439  0.329119387154439  0.045133705087381    0.80617  0.33333 -0.00000
 -0.268724854328628  0.190017166769140 -0.329119387154439 -0.329119387154439  0.329119387154439 -0.329119387154439 -0.329119387154439  0.045133705087381    0.80617  0.33333  0.00000
 -0.268724854328628  0.190017166769140 -0.329119387154439 -0.329119387154439 -0.329119387154439  0.329119387154439 -0.329119387154439  0.045133705087381    0.80617  0.33333  0.00000
 -0.268724854328628  0.190017166769140 -0.329119387154439 -0.329119387154439 -0.329119387154439 -0.329119387154439  0.329119387154439  0.045133705087381    0.80617  0.33333  0.00000
  0.268724854328628  0.380034333538280  0.658238774308877 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.045133705087381    0.80617 -0.33333  0.57735
  0.268724854328628  0.380034333538280  0.000000000000000  0.658238774308877 -0.000000000000000 -0.000000000000000  0.000000000000000  0.045133705087381    0.80617 -0.33333  0.57735
  0.268724854328628  0.380034333538280  0.000000000000000 -0.000000000000000  0.658238774308877 -0.000000000000000 -0.000000000000000  0.045133705087381    0.80617 -0.33333  0.57735
  0.268724854328628  0.380034333538280  0.000000000000000 -0.000000000000000  0.000000000000000  0.658238774308877  0.000000000000000  0.045133705087381    0.80617 -0.33333  0.57735
  0.268724854328628  0.380034333538280  0.000000000000000 -0.000000000000000  0.000000000000000 -0.000000000000000  0.658238774308877  0.045133705087381    0.80617 -0.33333  0.57735
  0.268724854328628  0.380034333538280  0.000000000000000 -0.000000000000000 -0.000000000000000  0.000000000000000 -0.658238774308877  0.045133705087381    0.80617 -0.33333  0.57735
  0.268724854328628  0.380034333538280 -0.000000000000000  0.000000000000000 -0.000000000000000 -0.658238774308877 -0.000000000000000  0.045133705087381    0.80617 -0.33333  0.57735
  0.268724854328628  0.380034333538280 -0.000000000000000 -0.000000000000000 -0.658238774308877 -0.000000000000000  0.000000000000000  0.045133705087381    0.80617 -0.33333  0.57735
  0.268724854328628  0.380034333538280 -0.000000000000000 -0.658238774308877  0.000000000000000  0.000000000000000  0.000000000000000  0.045133705087381    0.80617 -0.33333  0.57735
  0.268724854328628  0.380034333538280 -0.658238774308877  0.000000000000000  0.000000000000000  0.000000000000000 -0.000000000000000  0.045133705087381    0.80617 -0.33333  0.57735
  0.268724854328628 -0.190017166769140  0.329119387154439  0.329119387154439  0.329119387154439  0.329119387154439 -0.329119387154439  0.045133705087381    0.80617 -0.33333 -0.00000
  0.268724854328628 -0.190017166769140  0.329119387154439  0.329119387154439  0.329119387154439 -0.329119387154439  0.329119387154439  0.045133705087381    0.80617 -0.33333 -0.00000
  0.268724854328628 -0.190017166769140  0.329119387154439  0.329119387154439 -0.329119387154439  0.329119387154439  0.329119387154439  0.045133705087381    0.80617 -0.33333 -0.00000
  0.268724854328628 -0.190017166769140  0.329119387154439  0.329119387154439 -0.329119387154439 -0.329119387154439 -0.329119387154439  0.045133705087381    0.80617 -0.33333  0.00000
  0.268724854328628 -0.190017166769140  0.329119387154439 -0.329119387154439  0.329119387154439  0.329119387154439  0.329119387154439  0.045133705087381    0.80617 -0.33333 -0.00000
  0.268724854328628 -0.190017166769140  0.329119387154439 -0.329119387154439  0.329119387154439 -0.329119387154439 -0.329119387154439  0.045133705087381    0.80617 -0.33333  0.00000
  0.268724854328628 -0.190017166769140  0.329119387154439 -0.329119387154439 -0.329119387154439  0.329119387154439 -0.329119387154439  0.045133705087381    0.80617 -0.33333  0.00000
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  0.000000000000000 -0.598183241476405 -0.345361255491125  0.345361255491125 -0.345361255491125  0.345361255491125  0.345361255491125  0.016902467068811    0.97683 -0.00000 -0.50000
 -0.000000000000000 -0.598183241476405 -0.345361255491125  0.345361255491125 -0.345361255491125 -0.345361255491125 -0.345361255491125  0.016902467068811    0.97683  0.00000 -0.50000
  0.000000000000000 -0.598183241476405 -0.345361255491125 -0.345361255491125  0.345361255491125  0.345361255491125  0.345361255491125  0.016902467068811    0.97683 -0.00000 -0.50000
 -0.000000000000000 -0.598183241476405 -0.345361255491125 -0.345361255491125  0.345361255491125 -0.345361255491125 -0.345361255491125  0.016902467068811    0.97683 -0.00000 -0.50000
  0.000000000000000 -0.598183241476405 -0.345361255491125 -0.345361255491125 -0.345361255491125  0.345361255491125 -0.345361255491125  0.016902467068811    0.97683 -0.00000 -0.50000
  0.000000000000000 -0.598183241476405 -0.345361255491125 -0.345361255491125 -0.345361255491125 -0.345361255491125  0.345361255491125  0.016902467068811    0.97683 -0.00000 -0.50000
 -0.563972568586821  0.398788827650937  0.690722510982251 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.000000000000000  0.016902467068811    0.97683  0.57735  0.00000
 -0.563972568586821  0.398788827650937  0.000000000000000  0.690722510982251  0.000000000000000 -0.000000000000000  0.000000000000000  0.016902467068811    0.97683  0.57735 -0.00000
 -0.563972568586821  0.398788827650937  0.000000000000000 -0.000000000000000  0.690722510982251  0.000000000000000  0.000000000000000  0.016902467068811    0.97683  0.57735 -0.00000
 -0.563972568586821  0.398788827650937  0.000000000000000 -0.000000000000000  0.000000000000000  0.690722510982251  0.000000000000000  0.016902467068811    0.97683  0.57735 -0.00000
 -0.563972568586821  0.398788827650937  0.000000000000000 -0.000000000000000 -0.000000000000000  0.000000000000000  0.690722510982251  0.016902467068811    0.97683  0.57735 -0.00000
 -0.563972568586821  0.398788827650937  0.000000000000000  0.000000000000000 -0.000000000000000  0.000000000000000 -0.690722510982251  0.016902467068811    0.97683  0.57735  0.00000
 -0.563972568586821  0.398788827650937 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.690722510982251  0.000000000000000  0.016902467068811    0.97683  0.57735  0.00000
 -0.563972568586821  0.398788827650937 -0.000000000000000  0.000000000000000 -0.690722510982251 -0.000000000000000  0.000000000000000  0.016902467068811    0.97683  0.57735  0.00000
 -0.563972568586821  0.398788827650937 -0.000000000000000 -0.690722510982251 -0.000000000000000  0.000000000000000 -0.000000000000000  0.016902467068811    0.97683  0.57735  0.00000
 -0.563972568586821  0.398788827650937 -0.690722510982251  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.016902467068811    0.97683  0.57735 -0.00000
 -0.563972568586821 -0.199394413825468  0.345361255491125  0.345361255491125  0.345361255491125  0.345361255491125 -0.345361255491125  0.016902467068811    0.97683  0.57735 -0.50000
 -0.563972568586821 -0.199394413825468  0.345361255491125  0.345361255491125  0.345361255491125 -0.345361255491125  0.345361255491125  0.016902467068811    0.97683  0.57735 -0.50000
 -0.563972568586821 -0.199394413825468  0.345361255491125  0.345361255491125 -0.345361255491125  0.345361255491125  0.345361255491125  0.016902467068811    0.97683  0.57735 -0.50000
 -0.563972568586821 -0.199394413825468  0.345361255491125  0.345361255491125 -0.345361255491125 -0.345361255491125 -0.345361255491125  0.016902467068811    0.97683  0.57735 -0.50000
 -0.563972568586821 -0.199394413825468  0.345361255491125 -0.345361255491125  0.345361255491125  0.345361255491125  0.345361255491125  0.016902467068811    0.97683  0.57735 -0.50000
 -0.563972568586821 -0.199394413825468  0.345361255491125 -0.345361255491125  0.345361255491125 -0.345361255491125 -0.345361255491125  0.016902467068811    0.97683  0.57735 -0.50000
 -0.563972568586821 -0.199394413825468  0.345361255491125 -0.345361255491125 -0.345361255491125  0.345361255491125 -0.345361255491125  0.016902467068811    0.97683  0.57735 -0.50000
 -0.563972568586821 -0.199394413825468  0.345361255491125 -0.345361255491125 -0.345361255491125 -0.345361255491125  0.345361255491125  0.016902467068811    0.97683  0.57735 -0.50000
 -0.563972568586821 -0.199394413825468 -0.345361255491125  0.345361255491125  0.345361255491125  0.345361255491125  0.345361255491125  0.016902467068811    0.97683  0.57735 -0.50000
 -0.563972568586821 -0.199394413825468 -0.345361255491125  0.345361255491125  0.345361255491125 -0.345361255491125 -0.345361255491125  0.016902467068811    0.97683  0.57735 -0.50000
 -0.563972568586821 -0.199394413825468 -0.345361255491125  0.345361255491125 -0.345361255491125  0.345361255491125 -0.345361255491125  0.016902467068811    0.97683  0.57735 -0.50000
 -0.563972568586821 -0.199394413825468 -0.345361255491125  0.345361255491125 -0.345361255491125 -0.345361255491125  0.345361255491125  0.016902467068811    0.97683  0.57735 -0.50000
 -0.563972568586821 -0.199394413825468 -0.345361255491125 -0.345361255491125  0.345361255491125  0.345361255491125 -0.345361255491125  0.016902467068811    0.97683  0.57735 -0.50000
 -0.563972568586821 -0.199394413825468 -0.345361255491125 -0.345361255491125  0.345361255491125 -0.345361255491125  0.345361255491125  0.016902467068811    0.97683  0.57735 -0.50000
 -0.563972568586821 -0.199394413825468 -0.345361255491125 -0.345361255491125 -0.345361255491125  0.345361255491125  0.345361255491125  0.016902467068811    0.97683  0.57735 -0.50000
 -0.563972568586821 -0.199394413825468 -0.345361255491125 -0.345361255491125 -0.345361255491125 -0.345361255491125 -0.345361255491125  0.016902467068811    0.97683  0.57735 -0.50000
 -0.563972568586821 -0.797577655301873 -0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.016902467068811    0.97683  0.57735 -1.00000

E_n^{r^2} 7 dimensions, degree 7, symmetric 183 point rule with points at 3 distinct radii: 1+56+126=183

#                x1                 x2                 x3                 x4                 x5                 x6                 x7             Weight     Radius     cos1     cos2
  0.000000000000000 -0.000000000000000 -0.000000000000000  0.000000000000000  0.000000000000000 -0.000000000000000 -0.000000000000000  4.207743938762985    0.00000 -0.00000 -0.00000
 -1.762865608770769  0.000000000000000  0.000000000000000  0.000000000000000 -0.000000000000000 -0.000000000000000  0.000000000000000  0.772490438496569    1.76287  1.00000 -0.57735
 -0.587621869590256  1.662045635043150  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.772490438496569    1.76287  0.33333  0.57735
 -0.587621869590256 -0.831022817521575  1.439373742196407 -0.000000000000000  0.000000000000000  0.000000000000000 -0.000000000000000  0.772490438496569    1.76287  0.33333 -0.57735
 -0.587621869590256 -0.831022817521575  0.000000000000000  1.439373742196407 -0.000000000000000  0.000000000000000  0.000000000000000  0.772490438496569    1.76287  0.33333 -0.57735
 -0.587621869590256 -0.831022817521575  0.000000000000000  0.000000000000000  1.439373742196407  0.000000000000000  0.000000000000000  0.772490438496569    1.76287  0.33333 -0.57735
 -0.587621869590256 -0.831022817521575  0.000000000000000 -0.000000000000000  0.000000000000000  1.439373742196407  0.000000000000000  0.772490438496569    1.76287  0.33333 -0.57735
 -0.587621869590256 -0.831022817521575 -0.000000000000000  0.000000000000000 -0.000000000000000  0.000000000000000  1.439373742196407  0.772490438496569    1.76287  0.33333 -0.57735
 -0.587621869590256 -0.831022817521575 -0.000000000000000  0.000000000000000 -0.000000000000000  0.000000000000000 -1.439373742196407  0.772490438496569    1.76287  0.33333 -0.57735
 -0.587621869590256 -0.831022817521575 -0.000000000000000  0.000000000000000 -0.000000000000000 -1.439373742196407  0.000000000000000  0.772490438496569    1.76287  0.33333 -0.57735
 -0.587621869590256 -0.831022817521575 -0.000000000000000  0.000000000000000 -1.439373742196407  0.000000000000000  0.000000000000000  0.772490438496569    1.76287  0.33333 -0.57735
 -0.587621869590256 -0.831022817521575 -0.000000000000000 -1.439373742196407 -0.000000000000000  0.000000000000000 -0.000000000000000  0.772490438496569    1.76287  0.33333 -0.57735
 -0.587621869590256 -0.831022817521575 -1.439373742196407  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.772490438496569    1.76287  0.33333 -0.57735
 -0.587621869590256  0.415511408760787  0.719686871098204  0.719686871098204  0.719686871098204  0.719686871098204  0.719686871098204  0.772490438496569    1.76287  0.33333 -0.00000
 -0.587621869590256  0.415511408760787  0.719686871098204  0.719686871098204  0.719686871098204 -0.719686871098204 -0.719686871098204  0.772490438496569    1.76287  0.33333  0.00000
 -0.587621869590256  0.415511408760787  0.719686871098204  0.719686871098204 -0.719686871098204  0.719686871098204 -0.719686871098204  0.772490438496569    1.76287  0.33333  0.00000
 -0.587621869590256  0.415511408760787  0.719686871098204  0.719686871098204 -0.719686871098204 -0.719686871098204  0.719686871098204  0.772490438496569    1.76287  0.33333  0.00000
 -0.587621869590256  0.415511408760787  0.719686871098204 -0.719686871098204  0.719686871098204  0.719686871098204 -0.719686871098204  0.772490438496569    1.76287  0.33333  0.00000
 -0.587621869590256  0.415511408760787  0.719686871098204 -0.719686871098204  0.719686871098204 -0.719686871098204  0.719686871098204  0.772490438496569    1.76287  0.33333  0.00000
 -0.587621869590256  0.415511408760787  0.719686871098204 -0.719686871098204 -0.719686871098204  0.719686871098204  0.719686871098204  0.772490438496569    1.76287  0.33333  0.00000
 -0.587621869590256  0.415511408760787  0.719686871098204 -0.719686871098204 -0.719686871098204 -0.719686871098204 -0.719686871098204  0.772490438496569    1.76287  0.33333  0.00000
 -0.587621869590256  0.415511408760787 -0.719686871098204  0.719686871098204  0.719686871098204  0.719686871098204 -0.719686871098204  0.772490438496569    1.76287  0.33333 -0.00000
 -0.587621869590256  0.415511408760787 -0.719686871098204  0.719686871098204  0.719686871098204 -0.719686871098204  0.719686871098204  0.772490438496569    1.76287  0.33333 -0.00000
 -0.587621869590256  0.415511408760787 -0.719686871098204  0.719686871098204 -0.719686871098204  0.719686871098204  0.719686871098204  0.772490438496569    1.76287  0.33333 -0.00000
 -0.587621869590256  0.415511408760787 -0.719686871098204  0.719686871098204 -0.719686871098204 -0.719686871098204 -0.719686871098204  0.772490438496569    1.76287  0.33333  0.00000
 -0.587621869590256  0.415511408760787 -0.719686871098204 -0.719686871098204  0.719686871098204  0.719686871098204  0.719686871098204  0.772490438496569    1.76287  0.33333 -0.00000
 -0.587621869590256  0.415511408760787 -0.719686871098204 -0.719686871098204  0.719686871098204 -0.719686871098204 -0.719686871098204  0.772490438496569    1.76287  0.33333  0.00000
 -0.587621869590256  0.415511408760787 -0.719686871098204 -0.719686871098204 -0.719686871098204  0.719686871098204 -0.719686871098204  0.772490438496569    1.76287  0.33333  0.00000
 -0.587621869590256  0.415511408760787 -0.719686871098204 -0.719686871098204 -0.719686871098204 -0.719686871098204  0.719686871098204  0.772490438496569    1.76287  0.33333  0.00000
  0.587621869590256  0.831022817521575  1.439373742196407 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.772490438496569    1.76287 -0.33333  0.57735
  0.587621869590256  0.831022817521575  0.000000000000000  1.439373742196407 -0.000000000000000 -0.000000000000000  0.000000000000000  0.772490438496569    1.76287 -0.33333  0.57735
  0.587621869590256  0.831022817521575  0.000000000000000 -0.000000000000000  1.439373742196407 -0.000000000000000 -0.000000000000000  0.772490438496569    1.76287 -0.33333  0.57735
  0.587621869590256  0.831022817521575  0.000000000000000 -0.000000000000000  0.000000000000000  1.439373742196407  0.000000000000000  0.772490438496569    1.76287 -0.33333  0.57735
  0.587621869590256  0.831022817521575  0.000000000000000 -0.000000000000000  0.000000000000000 -0.000000000000000  1.439373742196407  0.772490438496569    1.76287 -0.33333  0.57735
  0.587621869590256  0.831022817521575  0.000000000000000 -0.000000000000000 -0.000000000000000  0.000000000000000 -1.439373742196407  0.772490438496569    1.76287 -0.33333  0.57735
  0.587621869590256  0.831022817521575 -0.000000000000000  0.000000000000000 -0.000000000000000 -1.439373742196407 -0.000000000000000  0.772490438496569    1.76287 -0.33333  0.57735
  0.587621869590256  0.831022817521575 -0.000000000000000 -0.000000000000000 -1.439373742196407 -0.000000000000000  0.000000000000000  0.772490438496569    1.76287 -0.33333  0.57735
  0.587621869590256  0.831022817521575 -0.000000000000000 -1.439373742196407  0.000000000000000  0.000000000000000  0.000000000000000  0.772490438496569    1.76287 -0.33333  0.57735
  0.587621869590256  0.831022817521575 -1.439373742196407  0.000000000000000  0.000000000000000  0.000000000000000 -0.000000000000000  0.772490438496569    1.76287 -0.33333  0.57735
  0.587621869590256 -0.415511408760787  0.719686871098204  0.719686871098204  0.719686871098204  0.719686871098204 -0.719686871098204  0.772490438496569    1.76287 -0.33333 -0.00000
  0.587621869590256 -0.415511408760787  0.719686871098204  0.719686871098204  0.719686871098204 -0.719686871098204  0.719686871098204  0.772490438496569    1.76287 -0.33333 -0.00000
  0.587621869590256 -0.415511408760787  0.719686871098204  0.719686871098204 -0.719686871098204  0.719686871098204  0.719686871098204  0.772490438496569    1.76287 -0.33333 -0.00000
  0.587621869590256 -0.415511408760787  0.719686871098204  0.719686871098204 -0.719686871098204 -0.719686871098204 -0.719686871098204  0.772490438496569    1.76287 -0.33333  0.00000
  0.587621869590256 -0.415511408760787  0.719686871098204 -0.719686871098204  0.719686871098204  0.719686871098204  0.719686871098204  0.772490438496569    1.76287 -0.33333 -0.00000
  0.587621869590256 -0.415511408760787  0.719686871098204 -0.719686871098204  0.719686871098204 -0.719686871098204 -0.719686871098204  0.772490438496569    1.76287 -0.33333  0.00000
  0.587621869590256 -0.415511408760787  0.719686871098204 -0.719686871098204 -0.719686871098204  0.719686871098204 -0.719686871098204  0.772490438496569    1.76287 -0.33333  0.00000
  0.587621869590256 -0.415511408760787  0.719686871098204 -0.719686871098204 -0.719686871098204 -0.719686871098204  0.719686871098204  0.772490438496569    1.76287 -0.33333  0.00000
  0.587621869590256 -0.415511408760787 -0.719686871098204  0.719686871098204  0.719686871098204  0.719686871098204  0.719686871098204  0.772490438496569    1.76287 -0.33333 -0.00000
  0.587621869590256 -0.415511408760787 -0.719686871098204  0.719686871098204  0.719686871098204 -0.719686871098204 -0.719686871098204  0.772490438496569    1.76287 -0.33333 -0.00000
  0.587621869590256 -0.415511408760787 -0.719686871098204  0.719686871098204 -0.719686871098204  0.719686871098204 -0.719686871098204  0.772490438496569    1.76287 -0.33333 -0.00000
  0.587621869590256 -0.415511408760787 -0.719686871098204  0.719686871098204 -0.719686871098204 -0.719686871098204  0.719686871098204  0.772490438496569    1.76287 -0.33333 -0.00000
  0.587621869590256 -0.415511408760787 -0.719686871098204 -0.719686871098204  0.719686871098204  0.719686871098204 -0.719686871098204  0.772490438496569    1.76287 -0.33333 -0.00000
  0.587621869590256 -0.415511408760787 -0.719686871098204 -0.719686871098204  0.719686871098204 -0.719686871098204  0.719686871098204  0.772490438496569    1.76287 -0.33333 -0.00000
  0.587621869590256 -0.415511408760787 -0.719686871098204 -0.719686871098204 -0.719686871098204  0.719686871098204  0.719686871098204  0.772490438496569    1.76287 -0.33333 -0.00000
  0.587621869590256 -0.415511408760787 -0.719686871098204 -0.719686871098204 -0.719686871098204 -0.719686871098204 -0.719686871098204  0.772490438496569    1.76287 -0.33333  0.00000
  0.587621869590256 -1.662045635043150 -0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 -0.000000000000000  0.772490438496569    1.76287 -0.33333 -0.57735
  1.762865608770769 -0.000000000000000 -0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 -0.000000000000000  0.772490438496569    1.76287 -1.00000  0.57735
  1.605412803359194  2.270396559717982  0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000 -0.000000000000000  0.059444333410068    2.78066 -0.57735  1.00000
  1.605412803359194  0.567599139929496  0.983110548690283  0.983110548690283  0.983110548690283  0.983110548690283  0.983110548690283  0.059444333410068    2.78066 -0.57735  0.50000
  1.605412803359194  0.567599139929496  0.983110548690283  0.983110548690283  0.983110548690283 -0.983110548690283 -0.983110548690283  0.059444333410068    2.78066 -0.57735  0.50000
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 -1.605412803359194  1.135198279858991 -0.000000000000000 -0.000000000000000 -0.000000000000000 -1.966221097380567  0.000000000000000  0.059444333410068    2.78066  0.57735 -0.00000
 -1.605412803359194  1.135198279858991 -0.000000000000000  0.000000000000000 -1.966221097380567 -0.000000000000000  0.000000000000000  0.059444333410068    2.78066  0.57735 -0.00000
 -1.605412803359194  1.135198279858991 -0.000000000000000 -1.966221097380567 -0.000000000000000  0.000000000000000 -0.000000000000000  0.059444333410068    2.78066  0.57735 -0.00000
 -1.605412803359194  1.135198279858991 -1.966221097380567  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.059444333410068    2.78066  0.57735 -0.00000
 -1.605412803359194 -0.567599139929496  0.983110548690283  0.983110548690283  0.983110548690283  0.983110548690283 -0.983110548690283  0.059444333410068    2.78066  0.57735 -0.50000
 -1.605412803359194 -0.567599139929496  0.983110548690283  0.983110548690283  0.983110548690283 -0.983110548690283  0.983110548690283  0.059444333410068    2.78066  0.57735 -0.50000
 -1.605412803359194 -0.567599139929496  0.983110548690283  0.983110548690283 -0.983110548690283  0.983110548690283  0.983110548690283  0.059444333410068    2.78066  0.57735 -0.50000
 -1.605412803359194 -0.567599139929496  0.983110548690283  0.983110548690283 -0.983110548690283 -0.983110548690283 -0.983110548690283  0.059444333410068    2.78066  0.57735 -0.50000
 -1.605412803359194 -0.567599139929496  0.983110548690283 -0.983110548690283  0.983110548690283  0.983110548690283  0.983110548690283  0.059444333410068    2.78066  0.57735 -0.50000
 -1.605412803359194 -0.567599139929496  0.983110548690283 -0.983110548690283  0.983110548690283 -0.983110548690283 -0.983110548690283  0.059444333410068    2.78066  0.57735 -0.50000
 -1.605412803359194 -0.567599139929496  0.983110548690283 -0.983110548690283 -0.983110548690283  0.983110548690283 -0.983110548690283  0.059444333410068    2.78066  0.57735 -0.50000
 -1.605412803359194 -0.567599139929496  0.983110548690283 -0.983110548690283 -0.983110548690283 -0.983110548690283  0.983110548690283  0.059444333410068    2.78066  0.57735 -0.50000
 -1.605412803359194 -0.567599139929496 -0.983110548690283  0.983110548690283  0.983110548690283  0.983110548690283  0.983110548690283  0.059444333410068    2.78066  0.57735 -0.50000
 -1.605412803359194 -0.567599139929496 -0.983110548690283  0.983110548690283  0.983110548690283 -0.983110548690283 -0.983110548690283  0.059444333410068    2.78066  0.57735 -0.50000
 -1.605412803359194 -0.567599139929496 -0.983110548690283  0.983110548690283 -0.983110548690283  0.983110548690283 -0.983110548690283  0.059444333410068    2.78066  0.57735 -0.50000
 -1.605412803359194 -0.567599139929496 -0.983110548690283  0.983110548690283 -0.983110548690283 -0.983110548690283  0.983110548690283  0.059444333410068    2.78066  0.57735 -0.50000
 -1.605412803359194 -0.567599139929496 -0.983110548690283 -0.983110548690283  0.983110548690283  0.983110548690283 -0.983110548690283  0.059444333410068    2.78066  0.57735 -0.50000
 -1.605412803359194 -0.567599139929496 -0.983110548690283 -0.983110548690283  0.983110548690283 -0.983110548690283  0.983110548690283  0.059444333410068    2.78066  0.57735 -0.50000
 -1.605412803359194 -0.567599139929496 -0.983110548690283 -0.983110548690283 -0.983110548690283  0.983110548690283  0.983110548690283  0.059444333410068    2.78066  0.57735 -0.50000
 -1.605412803359194 -0.567599139929496 -0.983110548690283 -0.983110548690283 -0.983110548690283 -0.983110548690283 -0.983110548690283  0.059444333410068    2.78066  0.57735 -0.50000
 -1.605412803359194 -2.270396559717982 -0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.059444333410068    2.78066  0.57735 -1.00000

>> # evaluating formula 1 with 57 points
# r8_57_4bgg.txt:4 formula 1   : problem  G, 8_57_4  (d=8 n=57 o=4 plus 0/792 of order 5) quality N (1 negative weight, stability factor 5.000000)
# evaluating formula 2 with 57 points
# r8_57_4bgg.txt:65 formula 2   : problem E2, 8_57_4  (d=8 n=57 o=4 plus 0/792 of order 5) quality N (1 negative weight, stability factor 5.000000)
# evaluating formula 3 with 57 points
# r8_57_4bgg.txt:126 formula 3   : problem  S, 8_57_4  (d=8 n=57 o=4 plus 0/792 of order 5) quality NO (1 negative weight, stability factor 6.200000)
G 8 dimensions, degree 4, asymmetric 57 point rule with points at 57 distinct radii: 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=57
 (1 negative weight, stability factor 5.000000)
#                x1                 x2                 x3                 x4                 x5                 x6                 x7                 x8             Weight     Radius
  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 -2.000000000000001    0.00000
 -0.512695880335069  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.824409645463610    0.51270
  0.536697124212146  0.632104535207456  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.621272492115347    0.82922
  0.436723840527592 -0.819927275728243  0.076504536478602  0.388784328291937  0.245441827566712 -0.290146958585328  0.967877469006504 -0.255951446592592  0.197119759425936    1.47198
  0.313357840510192 -1.033970025845479  0.325539430602675 -0.174815763153084 -0.459685670155962  0.586608779419588 -0.189062180921904  0.800474244825415  0.129343835645145    1.59240
  0.074744031040348 -0.233668177285440  0.296540913191477  0.200379317070431  0.860801685918572  0.968562504875422 -0.643510614518465 -0.769141802716527  0.131190794435333    1.69501
  0.144523985081080 -0.238027792315532 -0.543293794533932  1.390136499173835  0.151846160003958  0.206015928362233 -0.337938322972113  0.808768696789944  0.105961526206743    1.77172
 -0.099773069431616 -0.363201376581598 -1.287449164248975  0.463657614034658 -0.612455620891363  0.109652796727390 -0.271968092653296 -0.892070676869512  0.096429287830291    1.80866
  0.066805673195018 -0.935961032436271  0.287409759033078  0.028175525899905  0.152993863461156 -0.788577001223247 -1.319809528839459  0.000000000000000  0.095581541275421    1.83059
  0.089799054906423 -0.218098901023475  0.190892423031146 -0.501845718943913 -1.570199110908117 -0.763172824041974  0.097088387419188 -0.093504237960311  0.096249315536805    1.84663
 -0.598159218258745 -0.025984723036666  0.706231164252858 -0.573740590625690 -0.403475203488541  0.747586704613377  1.186299324685754 -0.736109853125123  0.070744226361639    1.96399
  0.390458938304125 -0.135334766934607 -0.448499934029720 -1.056014242604715  0.359265973344023 -0.850115609443658 -0.069141969208407 -1.260945103956052  0.073432833546906    1.98334
 -0.512194434084648 -0.419092533603873 -0.345153547878913 -0.299915540086711  1.641022064185145  0.118805450066720  0.281421429050192  0.773030066505658  0.070242790666983    2.00771
 -0.171793446458569  0.377330451512213  0.688005989380405 -0.292334440300279  0.513496104594611 -1.502043280257233  0.274474454647140  0.894491722295697  0.067523924652325    2.03125
  0.666908971207723 -0.233300069883441 -1.016822939894064 -0.817138589147791 -0.048267662439722  1.411829927250457  0.441235309500869 -0.051577427830829  0.061655150831783    2.09614
  0.889957345397163 -0.108085600237775  2.161372245511079  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.042263711263447    2.33992
 -0.273463523248480  0.280934745695092  0.555504529706849 -2.149874264994999  0.025289671056037  0.292960641068397 -0.482608476430959  0.463571964056473  0.045103303488133    2.37034
 -0.972069879205366  0.552460039348831 -1.330121459912128 -0.330238421591483 -1.027487164032085  0.122862850159050 -0.015309966552254  1.481624213106122  0.032456359043493    2.52877
 -1.625412136069220  1.392785029190181 -0.438510241129815  0.235481466290066  0.619208781224536 -0.790177573376994  0.254671768612202 -1.078260023576126  0.026537456380010    2.65798
  1.387485272846826 -0.513864259697958 -1.316195591089951 -0.603459953410654 -0.172578651685263 -1.088457383887672 -0.016294388161084  1.272293328242901  0.028375352701802    2.66819
 -0.509982282437061 -0.246390926697350  0.963831871418028  1.684623662257526 -0.859033429008538 -0.820913381843135 -0.382686975260206 -1.392862287012997  0.024368649424669    2.75428
  0.137334770126599  0.502692030082052  0.657659413106092  1.079906588127543 -1.771351511050159  1.660835439374490  0.000000000000000  0.000000000000000  0.025241849176079    2.78681
 -0.693666597872279  1.327214378142791  0.624007778454622  0.784765833383653 -0.669916058050492 -0.641345993662896 -1.761660001345310  0.928388043011148  0.020014522135005    2.84137
  0.144804740852674  1.447863579272630 -0.595005173986524  1.455612474157385 -1.097059523248267 -0.726240813284751  1.956593644976572  0.138541561399049  0.013954102666779    3.18881
 -0.445175403857415  0.679844514803370 -1.934595714928515 -0.883029793545003  1.132292135885396 -0.317361324386234 -1.964317532330144  0.265381267044006  0.013753204399285    3.23953
  0.324055242820848  0.484065534905730  0.591840286936513 -0.184524787320696  0.010818755911240  0.824384892104191  1.999935838338655  2.295201800756691  0.013838601110233    3.26666
 -0.768895150564860  0.911124707482602  1.700710308254624  2.324180067636009  1.397438112168506  0.288506937993741  0.954297509444164  0.091103266701002  0.009589384093440    3.55958
  1.305641646953143  0.197698858164424 -0.481000200986742 -0.771095001919941 -1.351014875135335  1.076045008804960 -2.754700479320605 -0.021048055996370  0.008282400610130    3.62514
 -1.710354790548624  0.055953049566387  2.253150495371548  0.210868222897741  0.457539778673537  1.387320326546612 -1.093580198627980  1.653491097487263  0.006533412537135    3.75680
  1.309285790257385  0.658000099433099  0.021322588672539  1.734291489389102  2.386098350492311 -1.963782505637904 -0.932148056117276 -0.965777126216369  0.006034845274698    4.06287
  0.063266007314474  2.091504775479921  1.821438202606521 -0.866983211919670 -0.642818271338108 -0.185909438539005 -1.744772144445908 -2.544079778749083  0.004530752168270    4.29093
 -0.941931804934553  0.321431933382452 -1.786764323636822 -2.152933738624745 -0.066548917603710 -1.054734280266779  2.924466764759406  0.095102632215426  0.004734257474051    4.30077
 -1.036812626408213  3.086734155691938 -0.209375605806671 -0.295273718445964  0.828010073760389  2.580351076745107 -0.019742400903012  0.725910771433008  0.004657695917052    4.31336
  0.972155191918535  1.340410988788592 -3.032851530996379  0.786781532591739  2.231048160548488  0.205268690817767  1.574291569598598 -0.240357770753879  0.003881006573679    4.48496
 -1.821027773813606 -3.407113464087185 -1.679435818432737 -1.720502516955551  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.003961890293169    4.55030
  2.791605820304827 -1.714074296753682  0.731054798088975 -2.241567263252140  2.412859912559353  0.000000000000000  0.000000000000000  0.000000000000000  0.002903728107131    4.70235
 -3.060189971510309 -0.382769547742197  0.053046344273397 -0.760466118827020 -1.651607796852932  1.690609818771469 -2.189451554516620 -1.292333403952045  0.003243146732187    4.70555
  3.972898130028620 -0.774516329934580 -0.084822276717997  1.724204597821748 -1.138928380931892 -0.180041696169377 -0.895398571595162 -1.414121148307710  0.002961076712919    4.84716
 -2.971084769101551 -1.792810679452342  1.235495104295641  1.308703817938542 -1.590331751728417 -0.989087406286655  1.483460169926940  1.853799499615260  0.002847008499105    4.94220
 -1.471958431926998 -1.261396650328954 -2.393545630236100  1.732187262698054  0.272932162462174 -3.810783262164672  0.598323857816890  0.397038058733581  0.002177442453504    5.25352
  2.672962820260247  1.245775204479000  0.754488852813354  0.066074723670785  2.417676364851559  1.095317970405905 -2.143196074240190  3.177169366317212  0.001790117049506    5.56802
 -2.762630968001818 -2.088777789129957  3.144898594414010 -1.386682738638049  1.715110566207596 -1.743892980497047  0.206204186699346 -2.016163556185538  0.001536857617436    5.82225
 -3.029105759775534 -0.502523234781923 -2.006562454722260  2.140110631416240  0.396295379798910  3.092648481195553  2.617813826646908 -0.196309279470321  0.001468747995472    5.88620
  0.822732142868169  2.613363076838404  2.023655802228812 -2.092309809842348  4.109832681191673  0.534350581486466  3.174442418547489 -1.429480606713545  0.000869126155024    6.72876
  1.914030705899718  2.312355236390146 -0.170477656962491  2.137322632385549 -0.245838373849610  2.200683986654554  3.138008985281361 -6.552393368521155  0.000338395878095    8.44347
  2.047467392801197 -4.232337758034305  1.809823170518728 -2.893406604265212 -2.803321229844988  2.039981129708656 -0.602966677786048 -5.051839234878264  0.000342962154001    8.46504
 -0.912131097103851  6.707011988097325 -4.689069507382798 -4.329390811583404 -6.147142998990231  2.256512735086997  0.488306569767246 -4.303444483036914  0.000080490767041   12.17310
  2.609655844904665  5.457670606090463 -4.669241162611304  2.649417031489651 -4.333133744179332 -7.232687402687318 -3.932318637669908 -1.427544887489181  0.000069073063446   12.40994
  4.572797986706415 -0.811969221864783  3.862094155764671  6.247350655246941 -4.536663631034259 -4.852989254623379  0.347220953873488  6.201932719456257  0.000070675125078   12.57904
 15.151917272664743  4.665886704105898  2.850092425084515 -9.182439146068495 -7.783368901403663  1.384706567608352  9.749486234284824 -1.018261816297314  0.000007234368223   22.41381
 12.350402194813876 -1.514304530063808  2.168568870320086  9.808292253578465  6.278698447586772 14.187037567695540  7.337766412765735  1.592502847699351  0.000005815592236   23.51178
 -8.808065855521518 13.422640583748995 12.429598682783753 -3.819448952853720 -8.462590925810048 -3.117972867842429  6.791080127696172  1.912096987494341  0.000005863305677   23.62085
 -3.944742306011838 -17.639435484239485  4.646669663990654 11.400878505437618 -2.810817227731727  8.701545488931389 -1.019289455597920 -4.876941233926675  0.000004879440651   24.22237
 -1.451541245316696 11.698234243954346 -8.095322827158842 13.903751866620338  2.428199654161203  7.861084560313775 -10.936127096961108 -7.304244995111868  0.000004215436489   25.26753
 -7.261810024404456 -10.780934672312286 -6.275119345583393  7.525003405862936 16.165911645968045 -1.916414414995426  5.225060233327370 -17.934470741474648  0.000001949120321   29.64660
  8.521569421847198 -14.760881913216890 -14.715525912128653  7.004336767595158 -24.116618535574190  5.485235344408488 19.181647907581951  2.598429770654889  0.000000708455807   39.27461
  7.888988904559925  7.695822143121796 12.969238988079999 -0.704893935362517 -3.680864225620637 -28.134667886822903 16.467236562149971 -17.139388728971841  0.000000605245828   40.74551

# E_n^{r^2} 8 dimensions, degree 4, asymmetric 57 point rule with points at 57 distinct radii: 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=57
 (1 negative weight, stability factor 5.000000)
#                x1                 x2                 x3                 x4                 x5                 x6                 x7                 x8             Weight     Radius
  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 -194.818182068004916    0.00000
 -0.362530733671334  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 80.304994204274436    0.36253
  0.379502175973727  0.446965403263963  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 60.517588741385381    0.58634
  0.308810389142893 -0.579776136747253  0.054096876535553  0.274912034954286  0.173553580659241 -0.205164881956338  0.684392721692171 -0.180985003540128 19.201256590521655    1.04085
  0.221577453962729 -0.731127216818968  0.230191138922759 -0.123613411583847 -0.325046854581563  0.414795045831154 -0.133687150195796  0.566020766681231 12.599265461044977    1.12600
  0.052852011201848 -0.165228352706035  0.209686090616945  0.141689573910031  0.608678709369835  0.684877115200439 -0.455030719291529 -0.543865384394902 12.779176037974448    1.19855
  0.102193889894935 -0.168311066057176 -0.384166726291514  0.982974945340746  0.107371449435936  0.145675259977377 -0.238958479796391  0.571885829911576 10.321615952374462    1.25280
 -0.070550213974892 -0.256822156317137 -0.910364034473403  0.327855443032682 -0.433071522708100  0.077536236142008 -0.192310482581517 -0.630789224912105  9.393089276604838    1.27892
  0.047238744537930 -0.661824392962049  0.203229389591481  0.019923105427320  0.108182998333312 -0.557608145052710 -0.933246267717004  0.000000000000000  9.310511055267744    1.29442
  0.063497520668475 -0.154219211883033  0.134981326802454 -0.354858510974679 -1.110298439136217 -0.539644679097368  0.068651857118575 -0.066117480731417  9.375558339085062    1.30577
 -0.422962439460003 -0.018373973866481  0.499380845328466 -0.405695862273400 -0.285300052427369  0.528623628357023  0.838840297002319 -0.520508268843008  6.891130785790967    1.38875
  0.276096163049747 -0.095696131429762 -0.317137344714134 -0.746714831975370  0.254039406001144 -0.601122512230145 -0.048890755291856 -0.891622833711300  7.153025567855313    1.40243
 -0.362176157627261 -0.296343172455950 -0.244060414255775 -0.212072312178539  1.160377829662062  0.084008139384097  0.198995000852600  0.546614802087239  6.842286390562522    1.41967
 -0.121476310954262  0.266812921012468  0.486493700587844 -0.206711665110701  0.363096577671726 -1.062104989105575  0.194082748143472  0.632501162550521  6.577444123431445    1.43631
  0.471575855975125 -0.164968061465877 -0.719002396065134 -0.577804237555611 -0.034130391423151  0.998314515440908  0.312000479447009 -0.036470748975339  6.005772200088300    1.48219
  0.629294873897112 -0.076428060876749  1.528320971469279  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  4.116869697895902    1.65457
 -0.193367911696165  0.198650863751918  0.392801019935557 -1.520190671476408  0.017882497897701  0.207154455920222 -0.341255726342439  0.327794879352299  4.393471795409786    1.67609
 -0.687357203373302  0.390648240158145 -0.940537904105616 -0.233513827315680 -0.726543141269222  0.086877154503371 -0.010825781168838  1.047666528257521  3.161544432699877    1.78811
 -1.149339943637457  0.984847738875480 -0.310073565122640  0.166510541657457  0.437846728174127 -0.558739920476403  0.180080134562459 -0.762444974553045  2.584989504331262    1.87948
  0.981100245226458 -0.363356902641831 -0.930690827827540 -0.426710625231191 -0.122031534894681 -0.769655597179542 -0.011521872363988  0.899647240058957  2.764017314451757    1.88669
 -0.360611930196239 -0.174224695090534  0.681532052203408  1.191208815329613 -0.607428362917870 -0.580473419068062 -0.270600555278260 -0.984902368405893  2.373727990183273    1.94757
  0.097110347249214  0.355456943319451  0.465035430718483  0.763609271513013 -1.252534665328605  1.174388001616641  0.000000000000000  0.000000000000000  2.458785584259238    1.97058
 -0.490496355238090  0.938482286873054  0.441240131658416  0.554913242429093 -0.473702187473264 -0.453500101205858 -1.245681733096371  0.656469480785691  1.949596408650758    2.00915
  0.102392414204886  1.023794155136703 -0.420732193366953  1.029273451256415 -0.775738228254130 -0.513529803848081  1.383520634389438  0.097963677541440  1.359256456966091    2.25483
 -0.314786546885038  0.480722666569941 -1.367965748880390 -0.624396355005429  0.800651447568763 -0.224408344559850 -1.388982247514270  0.187652893526695  1.339687139339195    2.29069
  0.229141659677675  0.342286022270535  0.418494280272200 -0.130478728411470  0.007650015668840  0.582928147514614  1.414168193227266  1.622952757506631  1.348005555329933    2.30988
 -0.543690974985864  0.644262459167557  1.202583791800708  1.643443486524030  0.988137965402878  0.204005212274741  0.674790240197402  0.064419737672525  0.934093188117912    2.51701
  0.923228062360140  0.139794203240902 -0.340118503869818 -0.545246504796644 -0.955311779692092  0.760878722587925 -1.947867389065433 -0.014883223125827  0.806781115012230    2.56336
 -1.209403470631829  0.039564780776459  1.593217994311050  0.149106350347749  0.323529480162650  0.980983610579045 -0.773277974221176  1.169194767664830  0.636413776592476    2.65646
  0.925804860802184  0.465276332330567  0.015077347042804  1.226329272701151  1.687226324211148 -1.388603926512071 -0.659128211550384 -0.682907555062451  0.587848792739177    2.87289
  0.044735822790662  1.478917209625900  1.287951304575307 -0.613049708323292 -0.454541158733790 -0.131457824677514 -1.233740214963096 -1.798936063433048  0.441336450411516    3.03414
 -0.666046366684507  0.227286699784634 -1.263433169625792 -1.522354046026863 -0.047057190918208 -0.745809761926552  2.067910280716060  0.067247716148218  0.461159717268240    3.04111
 -0.733137238953082  2.182650653209901 -0.148050910680939 -0.208790048619308  0.585491538046744  1.824583744208474 -0.013959985555423  0.513296429016638  0.453701925592820    3.05001
  0.687417528571306  0.947813699749379 -2.144549883899542  0.556338557007963  1.577589283477609  0.145146883242528  1.113192244427982 -0.169958609610949  0.378045322639059    3.17135
 -1.287661087592643 -2.409193034728037 -1.187540455781368 -1.216578996787793  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.385924132234030    3.21755
  1.973963405937378 -1.212033558692091  0.516933805147677 -1.585027412331359  1.706149606223899  0.000000000000000  0.000000000000000  0.000000000000000  0.282849515525515    3.32506
 -2.163881080574007 -0.270658942840215  0.037509429752875 -0.537730749485201 -1.167863073015282  1.195441667193866 -1.548176041278130 -0.913817713488385  0.315911975272231    3.32733
  2.809263208706591 -0.547665749036459 -0.059978407062977  1.219196763272782 -0.805343981442756 -0.127308704257695 -0.633142401839687 -0.999934653387689  0.288435791087391    3.42746
 -2.100874187711774 -1.267708588824413  0.873626966370229  0.925393344229068 -1.124534365983445 -0.699390412171508  1.048964745775487  1.310834197138179  0.277324510063898    3.49466
 -1.040831788840297 -0.891942125213600 -1.692492346219375  1.224841359738757  0.192992182880912 -2.694630686308832  0.423078857208019  0.280748303719658  0.212102690174673    3.71480
  1.890070136065539  0.880896094921159  0.533504184153981  0.046721885172639  1.709555352300979  0.774506764429502 -1.515468477507626  2.246598003901066  0.174373674636850    3.93719
 -1.953475091390041 -1.476988939085637  2.223779122254188 -0.980532767845297  1.212766311850090 -1.233118552173082  0.145808378724164 -1.425642922559979  0.149703903563123    4.11695
 -2.141901223668509 -0.355337587018097 -1.418853918608435  1.513286739963847  0.280223150408708  2.186832712879652  1.851073908705934 -0.138811622723309  0.143069407196941    4.16217
  0.581759477322222  1.847926753334976  1.430940740543496 -1.479486454882660  2.906090558412722  0.377842919700055  2.244669760641154 -1.010795430581808  0.084660788754765    4.75795
  1.353424091540965  1.635082068163694 -0.120545907278971  1.511315326943304 -0.173833981224933  1.556118570212081  2.218907432916767 -4.633241783883073  0.032962834894887    5.97043
  1.447778077708067 -2.992714728977926  1.279738236622330 -2.045947430605872 -1.982247451467603  1.442484490309584 -0.426361826692038 -3.572189780446680  0.033407631680301    5.98568
 -0.644974084093258  4.742573658283086 -3.315672846125440 -3.061341601277355 -4.346686499509402  1.595595456813819  0.345284886780362 -3.042994776415238  0.007840532454094    8.60768
  1.845305344495197  3.859155895049061 -3.301652089077812  1.873420749157465 -3.063988254297460 -5.114282308642720 -2.780569174482638 -1.009426670391787  0.006728344325209    8.77515
  3.233456465396298 -0.574148942895352  2.730912967122133  4.417544012775332 -3.207905617466710 -3.431581610969640  0.245522291054005  4.385428682390245  0.006884399692562    8.89473
 10.714023451478818  3.299280128721430  2.015319680785673 -6.492964988017842 -5.503672930659018  0.979135403909414  6.893927829347695 -0.720019835327161  0.000704693232770   15.84896
  8.733053142334111 -1.070775001989627  1.533409753673383  6.935509964364816  4.439710249314055 10.031750469065820  5.188584389229538  1.126069562667099  0.000566491553497   16.62534
 -6.228243095576953  9.491240178198673  8.789053516023770 -2.700758254958723 -5.983955430048027 -2.204739758407048  4.802018809875168  1.352056746143617  0.000571139276422   16.70246
 -2.789354034614429 -12.472964447208350  3.285691629341607  8.061638502678889 -1.987547922405076  6.152921822026597 -0.720746486045234 -3.448518217957840  0.000475301878540   17.12780
 -1.026394657735402  8.271900761808801 -5.724257666978271  9.831437228822358  1.716996441532216  5.558626200078739 -7.733009630179151 -5.164881167491502  0.000410621836738   17.86684
 -5.134875111944838 -7.623272014321186 -4.437179442016907  5.320980936737548 11.431025748926585 -1.355109628406916  3.694675523093947 -12.681585878288452  0.000189862038790   20.96331
  6.025659524540081 -10.437519697129522 -10.405448161192524  4.952814026080799 -17.053024505793694  3.878647108435369 13.563473309783946  1.837367311267077  0.000069010036163   27.77134
  5.578357551119756  5.441768024207010  9.170636835300325 -0.498435281712108 -2.602764054563322 -19.894214449203865 11.644094640499294 -12.119377995648270  0.000058956445965   28.81143

S 8 dimensions, degree 4, asymmetric 57 point rule with points at 57 distinct radii: 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=57
 (1 negative weight, stability factor 6.200000)
#                x1                 x2                 x3                 x4                 x5                 x6                 x7                 x8             Weight     Radius
  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 -10.552651528683604    0.00000
 -0.163029484889856  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  3.745599319221864    0.16303
  0.140460588907545  0.179203240006769  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  3.275117981928214    0.22769
  0.137145840397292 -0.265043748587360 -0.015313465000648  0.045074157497601  0.112625755102779 -0.127066999130574  0.173665270224417  0.020362746998598  1.220398738967149    0.38824
  0.067098656025230 -0.263484868473970  0.099258988360656 -0.177701391084117 -0.146882809240265  0.177868113006653 -0.080707523910437  0.233799379460912  0.552963279269194    0.47932
  0.019983112190407 -0.079561142700060  0.074628316180318  0.021236725072453  0.258227800300071  0.270362887791922 -0.192559082669329 -0.201934683519315  0.676301603830545    0.47998
  0.046739686776296 -0.086233096707496 -0.173353649952476  0.245789811941945  0.046447551954613  0.046957583038099 -0.225975331821332  0.307137648327770  0.553083999510173    0.49985
 -0.020311972228932 -0.133667709565015 -0.386528965737222  0.070347463431329 -0.132638110459074  0.000327231827311 -0.121476307640518 -0.207927530046142  0.541289855944000    0.49821
 -0.039385824990589 -0.207477234241511  0.128417920727832 -0.180615474078780  0.023420380291267 -0.226935918844664 -0.474447038462210  0.000000000000000  0.296679091873070    0.60898
  0.016233380351812 -0.056745337221375  0.055060734634404 -0.148151539985817 -0.457740352128159 -0.223496954259142  0.058733424081468 -0.058548950713410  0.442749371571693    0.54297
 -0.122190618055887 -0.088344346138101  0.156672302134103 -0.018381135022113 -0.075961664542584  0.174183367543929  0.377940726296004 -0.200379008120648  0.460691431549137    0.51645
  0.064829672818646  0.019624878586899 -0.113311480337022 -0.329740633689139  0.127642465699831 -0.264946882444128  0.017630754264427 -0.390638784269076  0.300021250330102    0.60461
 -0.222183797603887 -0.056509395559105 -0.073610771067535 -0.195518099802660  0.506002104907517  0.051470802593833  0.046094823653931  0.287690420484471  0.219737754478256    0.66316
 -0.106429716687880  0.182852121628430  0.258277684436586 -0.117610616057190  0.119687160687684 -0.438158247068510  0.068294130500787  0.280515427203222  0.241680618280589    0.64418
  0.177419668258685 -0.040839912633333 -0.304733542750778 -0.272588360866272  0.004975949333493  0.397036865132426  0.161965734962926 -0.025997170443888  0.276737289669393    0.62039
  0.257237722745995 -0.051753533072918  0.584817122258298  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.245409202910074    0.64098
 -0.202425937280444  0.267748399428630  0.291240322511958 -0.707852026969714 -0.072771505653224  0.185746571185025  0.036398909686908 -0.009725305163499  0.098637516418839    0.86009
 -0.359893433479455  0.239928480602975 -0.390888588751840 -0.130154105454662 -0.386576149950770  0.082358495356097  0.031587900484461  0.420470259802152  0.100154256359829    0.83117
 -0.467155505505096  0.348208629430010 -0.131175791975651  0.234841409283128  0.194113088879087 -0.235061740767354  0.106659089944360 -0.308977748723030  0.120280032943183    0.78206
  0.360301881366590  0.002536787182789 -0.388349740356469 -0.458481337848338 -0.083052628010294 -0.354972419926674 -0.083013142136070  0.440700337932789  0.076705230972183    0.90822
 -0.064841541972597 -0.189832612721151  0.181631655868892  0.428552267105684 -0.168993419709818 -0.238566216086867 -0.175204795087767 -0.275571825372613  0.214419757956602    0.67007
  0.107242276518950 -0.000328476583788  0.103946550327013  0.327906715700830 -0.420490342639390  0.395785290663444  0.000000000000000  0.000000000000000  0.219580094651414    0.68065
 -0.265589127529366  0.410432460699572  0.268772863878036  0.210162145875955 -0.263104260158319 -0.075992374023917 -0.508199231637954  0.229477503807964  0.082343431371211    0.86100
  0.100932490322251  0.199045062953409 -0.204261261403909  0.438644775027159 -0.210569115298685 -0.225165626421887  0.381831500130157  0.120717121998320  0.151835630267095    0.73440
 -0.340267556014602  0.507649802512063 -0.595328288228060 -0.499544093313799  0.329816249885081 -0.021031232309020 -0.670586645647358 -0.004599887672373  0.023427111046808    1.23951
  0.104872855668310  0.118589294048663  0.160350427679685 -0.020706352373360 -0.014562714021272  0.228944036099943  0.551686269877773  0.674986293790611  0.071072891009924    0.92941
 -0.103435105387010  0.053866154771234  0.346037143847456  0.629257978996891  0.360737736259334  0.037306274799430  0.115861642126743  0.137080498058697  0.100560321116868    0.83249
  0.345597306013267  0.224508745597260 -0.101405660999437 -0.422778560983267 -0.513682301807228  0.432879680297747 -0.803803042745502 -0.171534331308150  0.022757833540122    1.21887
 -0.607558780696187 -0.024403445284904  0.848331934533782  0.060321789719103  0.097577498624779  0.634847410837404 -0.255176938813033  0.483380323988907  0.014041103827290    1.34326
  0.324618696575634  0.182228473041065  0.003293445390312  0.318762449136066  0.667051404446356 -0.550137221367906 -0.428974670402805 -0.127382580983865  0.038702127184512    1.08998
  0.012064951883072  0.532013713169306  0.508415906417143 -0.004398219847745 -0.188931064854887 -0.006128348352418 -0.274508945836380 -0.827196428751145  0.028623299624958    1.15630
 -0.334829489174054  0.136118331150806 -0.525528550500012 -0.501304298896444  0.004912579280157 -0.356651728288319  0.986359050512209  0.027893789932466  0.017931938310496    1.32629
 -0.289923781926582  0.829694436235160 -0.036063449726896  0.160231181453712  0.177696333578518  0.783918156661481  0.151259575469572  0.100660988673877  0.024821290813904    1.21595
  0.244779931502606  0.323948011736303 -0.820230150979541  0.172417096714377  0.642172980939627 -0.009476864377770  0.286636537524618  0.075857177246397  0.027793328379060    1.16951
 -0.834874421022490 -1.140088929583227 -0.600604111374614 -0.972639159388747  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.005503402392052    1.81757
  0.831255827828310 -0.329026936682870  0.336839871048119 -1.077910980629854  0.844573897076257  0.000000000000000  0.000000000000000  0.000000000000000  0.006363598205520    1.66970
 -0.993780709630508 -0.138493099924914  0.042535578241067 -0.121855865302831 -0.580977502191352  0.621314917703882 -0.490000223900797 -0.598074282205398  0.009964097349375    1.53127
  0.986227767812183 -0.237434600702564 -0.094909767414932  0.201152313672336 -0.192582201865229 -0.116280989674839 -0.375110302257164 -0.234000509861345  0.030315657964818    1.15090
 -0.787542790768034 -0.635615303283042  0.314064428176582  0.352149383107359 -0.462612896510424 -0.300366211654602  0.305611380710823  0.625880462610904  0.013855943656348    1.42697
 -0.483979800468777 -0.368071304108655 -0.731166532013897  0.269042470926107  0.116979631023846 -1.206459238713030 -0.107858245337805  0.331472836460167  0.008572877144926    1.60232
  0.801214793485522  0.751521429889107  0.406337108861757 -0.336368154934292  0.714703961140297  0.526543670322065 -0.831466592938320  1.075778136083809  0.003506987671630    2.03019
 -0.908740217991629 -0.666149983542717  1.041442195641005 -0.332085319104939  0.555637163896230 -0.545326002349732  0.146619509327557 -0.644534594498817  0.004909875284247    1.87283
 -0.585161796736870 -0.356788029822281 -0.580922347016780  0.608719259213936  0.178532343586984  0.639976363268056  0.507891396670183  0.107561088756190  0.016232532612917    1.37430
  0.206845528554416  0.613018090434431  0.519093857869316 -0.182400997096599  1.075511695558638  0.107484159054808  0.940506120125518 -0.352669711940018  0.007080050031653    1.70250
  0.471140970537362  0.068943895613816 -0.182172590032218  0.628691701631187  0.125455541058782  0.223108112345967  0.491909355245870 -0.946904210192742  0.015850339899495    1.36356
  0.592282662741546 -1.174198337607549  0.407126366793165 -0.787237364416221 -0.620120968919037  0.460533384324856  0.011983690660189 -1.437023812129551  0.002213111948943    2.27527
 -0.209253503409994  1.545111433846568 -1.154294349446661 -0.346631873454155 -1.490959279273967  0.580838658922683  0.690180683402565 -1.425145615012609  0.000742276746724    2.99189
  0.391597098761719  1.246086050026683 -0.845005025562978  0.498120499188656 -0.956250806208892 -1.442061296761593 -0.994449295786216 -0.258464729352646  0.001217243506070    2.59190
  1.145529043634417 -0.289873575839817  0.801777977855559  0.992033408774575 -1.064666817317427 -1.156925508002084 -0.400533837430461  1.661103963024050  0.000839219876387    2.90085
  2.856970906840430  0.847590001809408  0.446963318917442 -1.256311157237072 -1.317673729315951  0.121787484511127  2.191828604958582 -0.383389320441745  0.000203746319493    4.16665
  1.782874512373745 -0.545533046872921  0.019455216867795  1.053306507729311  0.982685406206356  1.553567489767337  0.518151276723068  0.578758109139885  0.000805879148830    2.92725
 -1.510619120862646  2.175068406165149  2.415009076738170  0.725686187224986 -1.794199595395216 -0.446840204366312  2.028127756426484 -0.075951926717033  0.000140584589290    4.57271
 -0.293707509780290 -3.489262369616953  0.426939583614479  1.376237786533533 -0.193900908693444  1.204673496197071 -0.750382870620567 -0.334426756513362  0.000207258553060    4.06218
 -0.055663889320545  1.360943619220674 -1.331378711160419  2.161352167382942  0.415830633522581  1.155719604633251 -1.789727371526896 -0.973849691022996  0.000295635978460    3.73623
 -0.972344663549202 -2.148489224256933 -1.250149935537000  1.066948115732610  2.996731768377888 -0.664069088369067  0.254342938046988 -2.130043707073561  0.000102007408718    4.72079
  1.365582814523147 -2.246471147502215 -2.166335931839509  0.526847046376701 -2.509954351000443  0.245607165791236  1.810116060271314  0.753440004561719  0.000116147162773    4.69962
  0.967568881963284  0.430076728926457  1.194879031897045  0.546048158651858 -0.143377912614204 -3.123413142308697  1.656453603931385 -1.550685315002170  0.000177196520891    4.21566
>> # evaluating formula 1 with 59 points
# r8_59_4E1s.txt:3 formula 1   : problem E1, 8_59_4  (d=8 n=59 o=4 plus 0/792 of order 5) quality P
E1 8 dimensions, degree 4, asymmetric 59 point rule with points at 59 distinct radii
#                 x1                  x2                  x3                  x4                  x5                  x6                  x7                  x8              Weight     Radius
   3.652079397144845   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000 21494.171227605831518    3.65208
  -1.775671828460144  -1.015626350680032   5.835299963841991   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000 8103.176425967953037    6.18346
  -0.827371156306984  -0.630313110264136  -0.789847723946868  -1.145737974685842   1.684711222821143  -1.189058775477756   5.913179518524787   0.453837860512862 9808.247096428467557    6.51477
  -2.418098588114169   1.376254622286297   2.264012649876577   5.629045097257035   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000 8566.523182190008811    6.67482
  -0.954935989182608  -2.137174512989915  -2.757820721815824   0.391621608550681  -1.267554654416587   5.741632316307806   0.000000000000000   0.000000000000000 7134.420952159338412    6.91458
  -1.241317999645009   3.187736965080495  -3.156197337338499  -3.087405802597674  -4.380844833451626   0.000000000000000   0.000000000000000   0.000000000000000 7710.860594547371875    7.09845
  -4.295884926326958   1.565084887003153  -2.426330691102684   0.075301123312411   1.470014361124516  -4.555927549668847  -1.065200285891913   0.833999296747432 7388.802440708512222    7.17945
  -2.129014427514809   0.406798395418792   1.316514628917672  -1.545167012759411  -1.172397239449412  -1.934673577307312   0.264025199257294  -6.177556089869372 6916.509469606057792    7.22276
  -4.749263334407461  -5.749949306221940   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000 5386.088581578979756    7.45771
   2.144022781848736   3.008279264284806   2.168495435828966   0.980439880486363   4.284912169347661   3.855220680423145  -3.379896259375410   0.000000000000000 4889.781392407697240    7.99732
   3.687211937483834  -2.843381195302373   2.384174856767193  -2.924075895391292  -4.989423275093220  -2.686239590841398  -0.332430730870998  -0.239482128303897 4412.969758416630611    8.25790
   0.518960677297354  -2.786277900332738  -3.608732177027717   1.671979813074975  -3.721225693148428  -1.867486130568287   2.213795279591802   5.369105264239217 4092.397022086177003    8.65531
  -2.462640730247877  -2.062127435844344   0.867942122640886  -1.302876857553885   5.327813650960258   0.982375750698299  -0.558118055079367   5.710733352813695 3730.612643367428973    8.66270
  -1.400817094011336  -0.023447982140079   1.111874924679582  -4.682904472193457  -0.884296775007179   1.026577299021040  -6.983847794052847   0.372892353429080 3607.646572267741703    8.71078
   2.169547256686611  -4.524672173427840  -1.186232962026212   3.724810658000538   2.928151758368778  -0.552617201051082   2.345786791085339  -4.684326153202614 3464.127384260132203    8.76276
  -0.666828835493714   5.008955140313057  -1.646113604481261   2.515416243736751  -0.036707706948202   3.464214103875084   3.122207201967091  -4.859688873176284 3455.377220144331659    8.94082
   2.990811516150595   1.124669855663592  -1.651646728582952  -5.749348577429338   0.700002569333187   4.160277557493413  -0.423737100117965   4.571108577589075 2392.686824956917008    9.21224
   0.111892800391079  -1.540009033152955  -3.949305737235438   4.501510039225703  -5.369553986918596  -0.885796943621956  -2.767871559039439  -3.067437413853765 3122.458363393766376    9.21584
   3.592873831622134  -1.973923944407077  -2.082217115079956   3.156159364601210   5.760368091734183  -1.973922524878462  -3.290490538395923   2.456043503132776 2684.815528297900073    9.22170
  -0.511747719801552   0.772633551982190  -2.590805857095811  -6.296374899045841   5.189283491619019   1.460819761138724   0.262887581120421  -3.280996140887002 2956.507613288682933    9.33339
  -4.631930060262106   2.029254778936127   1.745490738100394   1.161898577868891  -4.300264266257466   2.456461088012532   4.801448489226148   3.707785352909898 2340.790291379644259    9.55497
   0.130795093476417  -5.318109813210506  -4.679053523265372  -3.177555282517428  -0.078315321635864  -2.312888637535773  -5.070991096266837   0.835427405847397 2481.477995602147530    9.59470
  -1.667229657613323   7.168133559041237   5.253742191934413  -3.027298435531343   1.211824769613094  -1.519075361894944  -0.984743398357237   0.640140008395785 2421.111042666070716    9.80223
   0.048494407244594   1.609852125963849   2.246046904666386   0.913891702938363  -1.593758875155609  -4.117517218328015  -3.691897230674595   7.533331369823270 2256.579072715807342    9.91711
  -0.143334046849369  -0.134136534169971  -8.768106569823633   1.106028200639110   4.146013861664549   1.955002530164041   1.049028477440012   0.222320684186087 2198.692987039813943   10.01513
   3.670662604720773   3.295905358314256  -3.674336827264038   6.698988300029740  -0.299470159470335  -4.154168769677975   1.807005856451181   0.404864141677329 1921.251595561425120   10.17300
  -3.397561069286526   3.001167166825627  -3.264974232112068   3.619837783917446  -0.741376430753985   3.323812041142454  -5.686039011704286   3.972163459881100 2163.735602081063462   10.19903
   2.279800169032920   1.368283796007796   2.625750888487165   2.255478221075442  -0.744347093824469  -5.838094929294397  -6.897882586341475  -2.975110968044155 1927.740303748451197   10.49385
  -0.314912114597454  -2.488425155572032   3.865921457531239  -2.695141907215195  -3.823943383121912   5.117680923610530  -0.266662885936806   6.508906873323869 1482.114138246921357   10.57122
   1.534574320865677  -2.725424513481166   4.169711449997745  -4.476296013862525   6.388193211216014  -5.298728028514899  -1.893203665236969  -1.637422783692539 1399.916644572550467   11.06153
  -4.318855051188908  -2.158637278839181  -1.341121455463050   3.041555906575202   4.831345800761379   1.371680791885755  -5.755106646722270  -6.045997845876627 1492.400479868083039   11.36929
   2.725764987708858   2.877368458500697   4.867163708947348  -5.838043859208004  -1.259176328920480   4.851277165437327   5.355161124048111  -1.618582306195544 1419.688859606247433   11.39733
   5.356628512515668   3.716796000449950  -2.346599157816336  -5.251028854055936   1.936971012307177  -6.103516227055342   0.238049324384406   3.643973574101115 1345.322977163561745   11.39859
   4.741779653130944   6.156986520539191   2.948039700011382   2.358199595578014  -7.057245564010047   2.040028441017440  -2.025632049869320   1.654956633218957 1413.919549230625307   11.63845
   0.158704570730056   7.890948737607141  -2.258174401833273   0.734337551392302   2.937807077232937   1.928343852727910   4.044831944421190   6.292190894070819 1359.389607588319905   11.67186
   7.214658520874869   4.330166629817951   2.445829438237365  -0.887409657228802   2.826713476025028  -2.716237117396290   3.988253091201400  -5.635037791376527 936.656754552183315   11.85746
   2.426296796319098  -6.874653460788903   5.847516893547740  -3.866279470432533   3.093845341815185   3.698933468344079  -1.271389562508973  -3.963014734376672 927.634176720020719   11.95263
   1.986338943123323   7.978815764880413  -5.223715890191353  -0.350369917342929   1.651683829734329  -1.398673611198314  -5.283720389077734  -4.019629639859181 1082.247694638345820   11.99068
   2.815416064747566  -6.943645006254051   3.336640074533257   5.363294495350896  -1.609827086243591   2.601495457417371  -5.835647420947494   2.528836857670321 1288.593361176268900   12.07675
   1.551637375781216  -4.376415231917600   3.040866919906969   3.965452607753432  -6.797980851737476   1.799701078344624   6.586786793471856  -3.441791883062558 1139.816885246537595   12.29697
  -1.359440276477423  -2.176683434130922   3.667762561497792   1.939382494028166   6.572750588126547   8.000078828142337   4.971140776349835  -1.580826801900489 898.736425170669690   12.57829
  -1.829247933215294   1.409095151191264   4.581637179278139   0.082272676455170  -5.416437994448470   7.329080649095259  -4.339291456281515  -5.535981168254303 919.859713356623843   12.60395
   5.180630655639066  -0.207557335747302   7.589099376464091   2.841008396873807   2.571987719164229  -2.273750564917720   5.260343545066194   5.736527839274845 974.890906741541357   12.84180
   6.737464194382478   0.076833194382771  -0.558371184779825   6.283983645674287  -0.452878991062995   7.338718718601074   3.773786832108064   3.823048192164370 769.606572124065110   12.96606
   7.904799154523937  -1.863191300681658  -3.317179796688848  -2.085213782327851  -1.306551943534510   4.825387125727102  -4.148920406635476  -7.107301797157628 822.982345212524592   13.19196
 -10.696503003708312   3.546473585905758   0.418184934192037  -3.749660295533721   2.550664243457014   5.151646446819903   0.100031963734456  -0.347699784012694 861.847230726922248   13.20620
  -0.963425933811157  -7.211315513610956   3.106216753980427   4.219213802096403   0.363350279875346 -10.347973204558309   1.745537497417784   0.617310856871944 700.942342375574185   13.82108
  -0.384314871563245   5.701987229053662   2.854974213432608   1.518658527866515  -5.957252224736659  -8.564497980781098   6.100632982020540  -1.437753144121250 721.885371494261449   13.82902
  -3.054151747894882  -6.577817385543407  -3.071143483669699  -7.618828858359826  -4.761717087830055   3.325230452506785   4.063335581800209  -4.673465043726643 596.146677981926700   13.86207
  -2.598489955376567   4.711916680477454   2.097911680394311   3.718553114406612  11.078001302067593  -4.772111785620909   3.161573987823906  -2.504451968660501 561.925466413992353   14.45497
  -4.312259908050087  -1.940879738022427   3.547178330522565 -10.639488268487849  -1.896371111658189  -5.624310048382019   3.700154768614716   4.318164758582800 556.622864585449406   14.68709
   2.864717913575654  -3.416581473715193  -8.526101253753806  -3.610240900012938  -0.843090446580107  -9.444871984901654   2.428315958758655  -6.575197100804896 411.678599880856439   15.64143
   8.828218497784311 -12.563376199053099  -2.242299692601777  -5.260639908178818   3.831683745611066   1.839168772493174   5.739924061988365   5.023338338213016 223.389802851671305   18.56672
 -10.992642892685357  -2.424752538103925   3.711469971517661   0.925238715597187 -12.564708422954263  -4.302669986368941  -5.458630204549351   0.771833107318412 216.968166370295080   18.65813
  -9.098808724702836  -9.697959746215657  -4.677569252240382  20.528101712026849   8.648375354416407   3.843528602453201   7.570370617781276  12.086425488725514  29.364268972429823   30.21722
  14.719498678701470   3.834791636749858 -15.636194282486645  -4.710849925464913 -10.772317309873998   4.211049570154920  16.655925384527706  -3.592611042879606  31.432392494792058   30.36700
 -19.870981333557218  -0.946857360480288 -15.552096329678042   9.716782904651682  -4.879549711949712  -2.554565571342080  12.927736089392141  -8.867999612155657  26.808694558898893   31.75121
  21.279886411382481   3.189380577457336  32.554007407122192  24.455275493833042   1.897060733352672   0.142644911485015  -3.531434569070653 -27.472542383237890   3.026980522504329   53.77416
  32.837052553861689   5.539754936759672 -30.361684068990527   1.021990588748215 -11.784792608231797   6.997269090044031 -29.294722226755393  23.220772072722635   1.897802205078893   60.14204

>> # evaluating formula 1 with 339 points
# r8_339_6dg.txt:3 formula 1   : problem E2, 8_339_6  (d=8 n=339 o=6 plus 0/3432 of order 7) quality N (3 negative weights, stability factor 1.323508)
# evaluating formula 2 with 339 points
# r8_339_6dg.txt:345 formula 2   : problem  G, 8_339_6  (d=8 n=339 o=6 plus 0/3432 of order 7) quality N (3 negative weights, stability factor 1.323508)
E_n^{r^2} 8 dimensions, degree 6, asymmetric 339 point rule with points at 339 distinct radii (3 negative weights, stability factor 1.323508)
#                x1                 x2                 x3                 x4                 x5                 x6                 x7                 x8             Weight     Radius
 -0.186874597997130  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 12.976688472677917    0.18687
 -0.783988461416482 -0.352306842207969  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 -7.116622178374015    0.85951
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G 8 dimensions, degree 6, asymmetric 339 point rule with points at 339 distinct radii (3 negative weights, stability factor 1.323508)
#                x1                 x2                 x3                 x4                 x5                 x6                 x7                 x8             Weight     Radius
 -0.264280590950550  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.133218453585080    0.26428
 -1.108727114879223 -0.498237114367368  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 -0.073059116996481    1.21553
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  0.004760899722562 -0.913677339496828 -0.611216212319811 -0.494282231365424 -1.267069486733181  0.000000000000000  0.000000000000000  0.000000000000000  0.013791726027558    1.74877
  1.299584592723714  0.260052316983883  0.059958754798677  1.706031710949410  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.012080321057119    2.16118
 -0.101500436558662 -0.849299618436668  0.056071048021746 -0.497790720667685  1.325560972360405  1.320580266702479  0.671875027878037 -0.033418526476600  0.009923363432329    2.22174
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 -1.909193566799607 -0.884836937261067 -0.381850172570738  0.113562014710373 -0.337500501382068  0.694958604356317  0.000000000000000  0.000000000000000  0.017075119921124    2.27674
 -0.342967594004871  0.718765549717682 -0.893775382109249 -0.977367029565091  0.729264072158780  1.226324520456668 -0.836559975825961 -0.597393894915238  0.012552811243088    2.34110
 -0.104919372516412  0.302670662719206 -0.579926733474648 -0.593551808610373  0.522241506797645 -0.488327280518989  1.731349400527896  1.110355982998579  0.008279429427342    2.35221
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  2.272130864236668 -0.459607422324968 -2.664561199991620  1.826590257829057  0.993199081657296 -1.055118311284257 -1.321688669723211  0.811648804563545  0.001319756436120    4.50727
 -2.509073439768246  0.118194494936931  0.542062421411999  2.255264634404147  2.870259698912929  0.451542205597704 -0.369125680887859 -0.669945512154834  0.000384561065207    4.55157
  0.376149157053144  2.038563839559492 -2.086136638454173  1.861309754054041 -2.494712328080668 -1.211268543010681 -0.796447716092778  0.671613141321078  0.000372028076723    4.57054
  2.891170745996916  2.054010712148102 -0.023212473016280  1.977207754236675 -0.847567619214196  1.557438695419819  0.170212542663611 -1.236351537355548  0.000298810189679    4.60318
  0.054824127972421 -2.553975536857602 -1.776381009767926  3.142999766497498  1.027725380445369  0.181983393499862  0.833910304115588  0.053578586333301  0.000375920535324    4.62032
  2.204136864710783 -2.493353253211809  0.308224928619824 -1.932993583226202  0.573246577626176 -2.304873308054079 -0.324762166175494  0.954705876104698  0.000332587517210    4.64376
 -1.387440341715956  0.614477616885339  3.477401731393489  1.373595702274179  1.224638028998531 -1.122228724054328  0.746388634106419 -1.475444385956443  0.000362816457155    4.66635
 -1.599905485161207  0.146239651089587  3.000422562590007 -0.935737583831615 -2.326612156352789  0.352140596029253  1.769007547547081 -0.849344349455367  0.000570320169961    4.67409
  1.132131356502076  1.562848939961071 -1.267686321384877  3.420643280050280 -0.540652819735541  0.752162412461076  2.157183908840793  0.075986291672844  0.000272776720276    4.74861
 -0.091888461581643 -2.206713221845277  0.137805999375198 -1.730415864911918 -3.309131277252441  0.693823518969418  0.803358532366306 -1.643643823873395  0.000312489109482    4.76131
 -1.004996039727763 -2.504590662657969 -2.672723654355116  0.673910625976405 -2.330421554536883 -1.751841385593093 -0.077039814125075 -0.326361833302792  0.000221659693860    4.84694
 -3.088221270177451 -1.719321027765589 -0.434775260317957  2.009099279310546  0.275751265758827 -2.265473845219870 -1.255532218660955 -0.037896843507908  0.000299108010129    4.84818
  0.362213028446509  1.745026309062580  0.513600941738497 -0.789277819096333  2.582519948417683 -2.168991950169021  1.195373768157588  2.667451660116944  0.000222708329264    4.89706
  2.080493808690474 -1.783053123614038  0.353239947017336  2.043654890965946 -0.227974249000180 -0.047621975840562 -2.308570286873420 -2.613526131156445  0.000193648742885    4.90136
 -1.849542950657337 -1.285544864123253  1.114015429446113  2.920011377072101 -0.936288183622553  2.874507651834698  0.451555982941060  0.354226470794709  0.000182059278153    4.93049
  1.846875741643154 -0.545841779779960 -2.972455837487295  1.556831740190656  1.886847026044232 -0.935360524142795 -1.535049504135582  1.602190262414486 -0.001709207389727    4.93220
  2.790362428184646 -3.059115736331093  0.131558776435808  1.416886692748777 -1.160684454608245 -0.570318686267964  1.793708843153530 -0.683245877486583  0.000231880694203    4.95236
 -0.196635065243270  0.552820893499455 -0.342533765023155  4.421835255289298  0.003619071739723 -0.412273897016522 -1.567857033439099 -1.407894058561203  0.000214741676969    4.96231
 -0.650815597034599  0.041521408788682 -0.814949058871286 -3.376224929255957  2.028390810144197  1.826094304200002  1.763835421849103 -1.288322690263814  0.000186328440477    4.97073
  2.150913140470869 -0.538211981958318  1.686617191108011  0.629285806232357  2.146276885339625 -1.496963164287893  3.078550176960586 -0.550854575521891  0.000193149713614    4.97846
 -0.121233335941241 -2.796573964637909 -0.368444164566109  1.105741833923507 -2.594992379238977  1.514207829968586 -2.395459315607386  0.928263180660424  0.000238119847057    4.98203
 -0.055850783097182 -3.658000274975611  0.217964286260871 -0.377628186324309  0.316134457241776  3.214084230954591  0.362162775008569  0.868220336255066  0.000223921205269    4.98893
 -3.070102208067166 -1.972838849451805  2.261172882257967  0.887870611702885  1.298567233042251  0.736395547735779  1.881301797031359  0.228029852642512  0.000204224487528    5.00387
 -1.224607936384045  0.422774330218974 -3.119523347449648  1.901742861116691  1.080137470587546  0.599452527786969  1.535037088027601 -2.635218651815200  0.001327268586118    5.08461
  1.224454080319808 -0.249785850155744  1.284951971290736 -0.931658544903943  2.430434012758035  0.341146187873805 -0.285700331537622  4.007074043031443  0.000153111836432    5.12274
  3.479003849253806  1.391954631604243  1.610290542018676  1.439938174712114 -0.915207152579055  1.102358027489633  1.780310845350001  1.521807516627946  0.000152518335276    5.12305
 -1.207338521038830 -2.875768555000732 -1.270251971774933 -2.387918077163616 -2.325266918687323 -0.107016242780339  0.077654007137700  1.989788531041599  0.000189703518321    5.14072
  0.770652970116325  1.095091272591445  0.129585994421566 -1.235046482401237 -3.077002689129404 -3.027575284140116  1.305492379484654 -1.805838727437407  0.000156130551840    5.18987
  2.210037599631693  1.649498727512692  1.835909215676717 -2.656632145121512 -0.345264812845884 -1.709118032941650  2.200598135436004  1.148563484191799  0.000179714191909    5.21876
 -0.217113348625476  1.087069877535142 -0.048773585069645 -3.325924410977991  0.192849534573482  3.299891241877925  0.529069676280082  2.052568964392496  0.000139350664538    5.26426
 -0.673581723835011 -0.392611137602563 -2.405453784819944  1.695658131600085  0.559443697124861  3.708760420467960  1.890276223355891  0.974629539116656  0.000143059061349    5.27828
  0.573968140861983 -2.079186809314266 -2.263893790998147  0.561594119580151  2.181325981800225 -2.749234641989330 -2.365054503679225  0.003756729210541  0.000181868310370    5.29179
  3.286000000529373  0.748647868901424  0.247157935219748  0.386180823442691  2.318020162662009 -2.919269341850335 -0.697950767910927 -1.736927316035781  0.000136508642032    5.38218
  1.582701068375536  1.847943841121416 -1.642804967026383 -1.760049503840668 -1.343015457468417  2.790601999524863 -0.479003806277846 -2.762555654791524  0.000140756390201    5.40081
 -2.910838498313450 -1.806785359748871 -3.863217980088248 -0.549673723855810 -0.764512054083549  0.326396396977698 -0.630131198924460  1.067347615104161  0.000131184330473    5.40290
 -3.802655971946357  0.097688761919500  0.272421625000943 -1.138527044941598 -2.013829213298354  1.726283817748129 -0.899527422785756 -2.384280272834735  0.000129745504202    5.41938
 -1.211395164183285  0.612495386901701 -2.951917252376679  2.054286930043936  2.129195830925626  0.219279367876261  2.034158535109178 -2.449568627758693 -0.086985487543987    5.43105
 -1.209622929278163  0.612039791800233 -2.949947567039170  2.054823503637627  2.140706279010490  0.210895223243509  2.032386630838432 -2.449271063344310  0.085506389631152    5.43313
  0.143694605643305  1.923283568588427 -2.803100015427570  0.549553470775192  1.875426652143141  1.264967555001915  2.344842588268563 -2.694513856424198  0.000166493942230    5.45482
 -1.886142607696386 -2.214851451826373  3.343458753761071 -0.274574493475024 -1.212149378320729 -0.578553032248996 -2.938565687262456 -0.545148966462729  0.000104162487941    5.51848
  1.321255379934430 -0.966312178568384 -3.524172207782535  2.128539500858526  0.875696925328316 -0.212252146143988 -2.150960146902973  2.668518576463916  0.000188251114434    5.67358
  3.351678189374600  4.381033604171347 -0.454770326626269 -0.410996493970604  0.987632222123099 -0.948396770940698  0.020547079827753  0.883348088319412  0.000085562577038    5.78434
 -1.936757299073131  1.455096478695416 -3.535433800949018 -0.716654642768276 -3.467100324929867 -0.357560169208230  1.304908325631909  1.340098504991353  0.000054206544574    5.87610
 -3.385711790279559  0.417796957151475  0.458424666126740 -2.328789311844475 -2.322048909558637 -2.587680117170707 -2.532530686041220 -0.084015138720549  0.000047786338418    5.98162
  1.449825628920297 -1.371659265077274 -3.715504491557347  0.943298356549131  2.618989107543342 -1.567604983312450 -0.595451127755934  2.818558717370180  0.000161617848247    6.02441
 -1.241886386121320  0.535574776406091 -3.693551976400610 -2.085860668144992  0.876209226867620  0.309855958268764 -3.515597403861753 -1.864099953901410  0.000047123310345    6.04320
  4.443238186725406  0.199710371825113  1.737967257190187 -2.956474960936233 -1.014726503328991 -1.422700684762301 -0.817286384061245 -1.963076841836090  0.000047146900050    6.25451
 -1.319672453905400 -1.424726643856351  1.044662703727858  1.142112215522426  2.355844175202043  2.931552950732686  2.900568744180290 -3.251799349697788  0.000052186908887    6.26886
 -1.448654427907292 -0.793044145574973 -2.824350516397740 -1.608870327487973  0.686761284327362 -3.758307818251411  3.538340974938999 -0.166388135353875  0.000054900746421    6.35901
 -1.618827368639209  4.005034421956762  3.565011522033066 -1.144368325408803  1.297977429195340 -0.059312604511287  0.638244608186900  2.597940497930172  0.000034214230943    6.44397
 -3.851366017017114 -0.969601777135640 -1.370153905917143  3.634018701767577 -1.325060298575501  0.887937145187024  3.068472952500457 -0.780206801753462  0.000034133511695    6.58977
 -1.151474560903220 -2.341763103810848 -1.012459836281967 -0.154123942455527  1.762518159399042 -2.954093368563722  0.663733983369393 -5.015392613262021  0.000037288070414    6.72952
  3.493524681492030  2.133828351467394  0.217952209092897  2.171212820591232 -1.508907188805263 -4.225623196838622  2.037818743261365 -0.789050210754619  0.000028308607113    6.81378
 -1.865284225307427 -3.489310720903119 -3.750057876220411  0.186611237259353  3.388427167594060  1.916530310229025  1.607817892719793 -1.767645031238526  0.000025439594473    7.11453
 -1.958686339786745 -1.916602840761241  1.184087640933726 -1.603766345418772  5.022633028561741 -1.996886335325436  3.272974964582494  0.828366221387327  0.000021709260647    7.21782
 -2.311064603464622  2.900882747004874 -0.546904904568274  0.723627211331101 -0.100066687095559 -0.135550481540988  4.996182040713206 -3.901325542737920  0.000019224266200    7.40199
  1.545343799293776  4.559982635109307 -4.110447502300002 -0.072414094895093  1.841540725085873  1.655069217104434 -2.792766393411292  2.635896319344566  0.000013498042239    7.80773
 -1.513734163969439  6.153855538724471  0.945080697798759 -2.207017951785255  1.665811352626406  5.293738725972069 -0.895931262022215 -2.099380900980448  0.000005457057578    9.05175
  4.352461398317779 -2.260666756168979 -0.668709304061167  5.627965985843645 -1.754748364385101  3.997614351579817 -0.299593465681099  3.212735335323477  0.000004592459378    9.25458
 -2.769044910664628  0.821467279115854  0.045000537196185 -0.143817625316480  2.388081824491923 -3.291377440373640 -8.141292551287517  1.764546549488057  0.000003311088414    9.71059
 -4.775234751635493  3.229162730763504 -1.211731894387031  5.694180784740338  1.151951059662155  0.281722386689199 -1.437077126330735  8.207979181927318  0.000000976363448   11.74584
 -13.705745176263784  4.428509542469171  3.537326105644638  0.433055017594639 -4.067393892959475 -2.785269099603624  1.542571016346064 -0.533802935894259  0.000000198137570   15.72022
 -6.316737301533665  5.550370373304403 -8.979857290567248  6.416887978917561  3.672767398858289 -3.290286475099713  4.604442491872860 -4.229438003683246  0.000000277696189   15.99770
 -0.573163363911028  1.558854294646537  3.048688662845871 -0.707441158674505  4.154812794252094  3.837474654238473 -13.393703946654947 -14.010687229900793  0.000000045296139   20.49958
  3.073585023877961  0.927428043384252  4.236972868199413 10.254135992530816 -3.715760107577578  8.960915938398140  2.867854502119228 -14.110903781574924  0.000000032409690   20.85314

>> # evaluating formula 1 with 325 points
# r8_325_6Sbdas2.txt:4 formula 1   : problem  S, 8_325_6  (d=8 n=325 o=6 plus 64/3432 of order 7) quality NO (19 negative weights, stability factor 4.109882)
S 8 dimensions, degree 6, asymmetric 325 point rule with points at 258 distinct radii: 1+1+1+1+1+1+2+1+1+1+1+1+1+1+2+1+2+1+1+1+1+1+1+1+1+1+1+1+1+2+1+1+1+1+2+1+2+1+1+2+1+1+2+1+2+1+1+1+1+2+1+2+2+2+1+1+2+1+1+1+1+1+2+2+1+2+1+1+2+1+1+2+1+2+1+1+2+1+1+2+2+1+1+1+2+1+1+1+1+2+1+2+1+2+1+2+1+1+1+1+1+1+1+2+1+1+1+1+1+1+2+1+1+1+2+1+2+2+1+1+2+1+2+2+1+1+1+1+1+2+1+1+1+2+1+1+1+1+2+2+1+1+1+2+1+1+1+1+2+2+1+1+2+1+1+1+1+1+1+1+1+1+1+1+1+2+2+2+2+2+2+1+1+1+1+1+1+1+2+1+1+1+2+1+2+1+1+2+1+1+1+1+1+1+1+1+1+1+1+1+1+1+2+1+2+1+2+1+1+2+1+1+1+1+2+1+1+1+2+2+1+1+1+1+1+2+1+1+1+2+1+1+2+1+2+1+1+1+1+1+1+1+2+1+1+1+1+1+1+1+1+2+1+1+1+1+1+1=325
 (19 negative weights, stability factor 4.109882)
#                 x1                  x2                  x3                  x4                  x5                  x6                  x7                  x8              Weight     Radius
  -0.010225356691716  -0.055419820358665   0.034185328433662  -0.104494641562390   0.041250155177003   0.054878393538205  -0.052611210972142   0.131675899670453   0.065160145053656    0.20021
  -0.053595851966295   0.059161069114037   0.199490697725634   0.467579176951920   0.355199189837459  -0.131063803341372   0.288061394452161  -0.102736412662402   0.083303197798465    0.70829
  -0.190328834543250  -0.497711298979509   0.123392970936888   0.167740548920355   0.272556282479236  -0.087823117692359   0.325228490112255   0.125468842162790   0.026035309770613    0.72857
  -0.014801895819887   0.199408482210143   0.200617923836237   0.474886278178172   0.385880339935768  -0.226831622792108   0.021732055076355   0.186339704899805   0.723345877638206    0.73573
  -0.032458234283638   0.156823250815528   0.179632100598201   0.530968400412760   0.354794335867184  -0.227747581267568   0.075525237375043   0.139419747166188  -0.856852842882557    0.73670
  -0.089313099817879   0.063058413137547  -0.446767687528215  -0.187553346996807   0.518297630058802  -0.122041709320190  -0.119499031012405   0.062336032156279  -0.651802533245139    0.74056
  -0.285027901199219   0.112680370075289  -0.423242306785751  -0.234513722691266   0.418784994073103  -0.225209894787339  -0.013248412681233  -0.002683612889035   0.081542755510275    0.74455
   0.130237508780135  -0.006492670609491  -0.485737905682580  -0.186201332992746   0.475070842236456  -0.202240860926798  -0.000403715408649   0.011897478133917   0.081542755510273    0.74455
  -0.096834425141300  -0.012219978749477  -0.345018200809803  -0.115220303921012   0.544168307412606  -0.160937421920775  -0.316680598140904  -0.007172772694887   0.101081370194765    0.75113
   0.171313655820865   0.408058347217477   0.031907135319569  -0.376815890823444  -0.086653231079394  -0.164632424879502   0.437246187452731   0.050089093097655   0.027273124304999    0.75311
  -0.146084747435606  -0.002784724279084  -0.461513258241694  -0.003275924002270   0.573293250529659  -0.057812362750966  -0.015850236544076   0.062477319016734   0.111047366425966    0.75532
  -0.075277999837076   0.105257797212213  -0.453078714179094  -0.226093662110901   0.515128229716172  -0.095971597682099  -0.138136521416748   0.095754706462415   0.383350366141781    0.75892
  -0.003781714017134   0.185001862534386  -0.054104444290539   0.222403465579310   0.141552296172485   0.484713022428663  -0.345597536455440  -0.354580337524532   0.029867287502261    0.76602
   0.193436537851139   0.623680769158708  -0.021582723678138  -0.071469482105195  -0.105176543403240  -0.065071547224990  -0.128644790734513   0.354531195155815   0.016920130804978    0.76779
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  -0.617521595905393  -0.186832451503993   0.048273413918628   0.405726008841003   0.536428662572605   0.287879279688231  -0.228145438901235   0.044778762723068   0.010656258575349    1.00393
   0.136828829970142   0.116618004254620   0.269173268772086  -0.251573179433228  -0.420273091595911   0.362365641128499  -0.497686560775291   0.533469001033687   0.007252339109035    1.00413
  -0.160486811414914  -0.115936207953015   0.003933587003305   0.471069519060412   0.658515520599854  -0.225621246554376  -0.433256850234049   0.274172853678674   0.294774668147566    1.00427
  -0.558934013816825  -0.229022328243139   0.194791344982752  -0.320595807763630   0.105674168256504  -0.422376259201891  -0.558045236427178   0.142914020882260   0.007243854982457    1.01341
   0.458617833493961  -0.521039782103483   0.041654313633515  -0.202212816538397   0.243595043435881  -0.366093741385393  -0.526571039145701   0.178643016723616   0.007243854982457    1.01341
  -0.269299268570927  -0.553853239364759  -0.413553357194345   0.223698070268346   0.403516828511118  -0.188920347484811  -0.257814484493101  -0.403795340470399   0.006285061163037    1.01409
  -0.067300781208188  -0.084413474271919   0.334461377588587   0.372972589089309   0.654359292052582  -0.263654171040152  -0.280704590168169  -0.438833936016449   0.006569435431907    1.01573
  -0.041248523135387  -0.541335313578648   0.191151654582698  -0.583556800034274   0.109548568767297  -0.235937788223296  -0.008376510830429  -0.540666477827568   0.007219523921966    1.01582
  -0.012499239265232   0.003026605818520  -0.145758641374996  -0.811754903768837   0.430903787111046   0.329335299784420   0.248303490380649   0.044719235785829   0.007021371916595    1.01890
   0.192576836619189  -0.272313512829042  -0.336020178069005   0.056255446881761   0.217188950434050   0.083674852913454  -0.132397636425253   0.863434877980553   0.013045503794398    1.02203
  -0.487061177490291  -0.077270711863705  -0.233737677036871  -0.022814313812294   0.125069546436228   0.046082922105231  -0.153419720943706   0.839570950217146   0.013045503794398    1.02203
  -0.159524157636080  -0.430430016736873   0.501124508123703   0.650514175185264   0.272174659733565   0.118162209359070  -0.303231492337727   0.048052378860949   0.012464234434745    1.03311
  -0.015471330856602   0.559728761623387  -0.431642750686866   0.178716595656844   0.538583471157675   0.399241816846651   0.147817560500548  -0.265015086787742   0.005560058123768    1.03602
   0.253880176324207   0.606059732381976   0.101422031649422  -0.068852853011262  -0.071170153438789  -0.566512025641480   0.131666049629429  -0.563051288315943   0.005340906982964    1.05221
  -0.421151583132123   0.738566966008012   0.114511778547741   0.200141889210508  -0.575916606958426   0.000000000000000   0.000000000000000   0.000000000000000   0.006138450980265    1.05247
   0.813550907611288   0.384231529858203  -0.071305459690935   0.343788401684291  -0.408562728569289   0.068293488058616   0.038190948088097   0.043353741898922   0.006138450980265    1.05247
   0.473526899144989  -0.010003477113394   0.042885696789022   0.281719490080826  -0.064078575523078   0.612244959058944   0.372124599256100   0.539725666229160   0.005592404749760    1.05559
  -0.504196684746826   0.270584045086930   0.190028751477615   0.167970158527389  -0.196601053596565   0.558165410016378   0.341882341775567   0.505395148373792   0.005592404749760    1.05559
   0.035820346975427   0.121473797281753  -0.642897023962033  -0.417969210779990  -0.120336361039576  -0.586715285346265   0.299160331516502  -0.272736719185536   0.008646454061263    1.06144
  -0.072199511617513  -0.118274312361840   0.391318054650463   0.657465668200372  -0.121491945433968   0.221660742975843   0.689137637590821   0.101086311621376   0.004297575443006    1.07406
   0.021299645102916   0.199581381172939  -0.528702988958282   0.246894685487373  -0.444417731928590   0.318524471770306  -0.198699993441506  -0.670697213859753   0.005855001457664    1.08123
  -0.001051073914488  -0.566294340784026   0.481417363641879  -0.018528381566228  -0.571716430298062   0.219097405472476  -0.140267643147275  -0.488313469491626   0.006377250231720    1.08894
  -0.086995849558214  -0.262403810506735  -0.001766643171618   0.746455845414064  -0.470571109134278  -0.333841165960197   0.439580204334233  -0.192738497756545   0.004495047495315    1.09402
   0.642072842064645   0.149877665181594  -0.382731294231495  -0.552893724642475   0.084526756185523   0.179406902003524   0.522957354606155   0.038812449772780   0.004894232852583    1.09600
  -0.463294914149679   0.467096565232825  -0.216378358817750  -0.681493305814099  -0.065296851068547   0.118267137383830   0.488766897461762   0.000000000000000   0.004894232852583    1.09600
   0.195739165978282   0.437150696050674   0.206456975323676   0.167058440570719  -0.513675691585285  -0.310168816843618   0.717501739220992   0.169081306361398   0.004178005639416    1.09700
  -0.060165836400933   0.095972050525761  -0.888374019646671  -0.075042137839380  -0.077155097449317  -0.370487192675146   0.274883970879392  -0.421796832708818  -0.095330733631729    1.09743
  -0.210878420904100  -0.398184417664665   0.132066619514366   0.622184154694916   0.325640070163210  -0.013387918640516  -0.519640354989723   0.477690475429404   0.006757625992301    1.10091
   0.512671170946585   0.121254208361446  -0.386523485550847   0.257587290617555   0.481073378280590  -0.564314435141605  -0.404094038285820   0.108403796309671   0.004163211458173    1.10373
  -0.522752763090832   0.418400601130286  -0.230696784567022   0.137125043095232   0.340730087133781  -0.621585488375017  -0.436121042370170   0.072047263194397   0.004163211458173    1.10373
   0.279944281978768   0.273687903726081   0.481042702503811  -0.646269879602044  -0.477422736797843   0.048546527323719   0.412604006123727  -0.129740633663458   0.002900271718444    1.10440
  -0.068840273314171   0.099352212551043  -0.912969078781553  -0.058635911607430  -0.060353266674996  -0.357497955724025   0.285552863553740  -0.401618875815431   0.084313148630152    1.10718
   0.479967926467603   0.072166041347824  -0.464414004770615   0.133318243127875   0.521870272771853   0.378439795322353  -0.503776280923139  -0.312230398950306   0.003938187113434    1.11170
  -0.587799580363686   0.378594406137030  -0.303719739805686   0.009093112265142   0.377143073445868   0.319379764242919  -0.536803713627999  -0.349722602332313   0.003938187113434    1.11170
  -0.217082589177494  -0.481345087822768   0.204511941063628   0.634227496590468   0.366580730545146   0.143433001399218  -0.617174581438710  -0.073850524295268   0.227885347895730    1.12437
   0.273698263603615  -0.378667872369591   0.482164674902556   0.148359476635596   0.348067416384816  -0.086343543540740   0.611388212714236   0.544694354269442   0.007364380504942    1.12778
  -0.439867075255141  -0.173888593586679   0.589553087547412   0.065342577327715   0.251349439513995  -0.125812052200708   0.589316712074914   0.519639146427205   0.007364380504941    1.12778
   0.107079128031090   0.266515935945536  -0.201431026364670   0.017876129569794  -0.061433972947437  -0.094802374922503  -0.869522529934099  -0.641433399953478   0.005488257029870    1.14178
  -0.230593030846197  -0.508173655940123   0.189803827511704   0.679374274875775   0.342397124530530   0.164414522652444  -0.596347439964802  -0.079022488144030  -0.397322292770753    1.14679
  -0.176604153169577  -0.219621030502146   0.076759863650201   0.236645946735628   0.359287003925298   0.016491409799226   0.659057061133047   0.786083741182262   0.004506825562321    1.15020
   0.094420971626998   0.149207146546570   0.350041036406345   0.315760212368418  -0.212448167587852   0.010116068868339   0.653792812129538  -0.787300629815282   0.003371426348216    1.16014
  -0.109518445486076   0.402816739856965  -0.818244023819255   0.309468494741220   0.315545524023985   0.122893413231822  -0.083854731432350   0.541105138633097   0.003295916528474    1.16364
  -0.242617593805910  -0.533066710278158   0.168536099195991   0.718106323439409   0.311011523580726   0.187542021524396  -0.574217493732242  -0.094280382576600   0.176911729580665    1.16517
  -0.225828750883005  -0.385426910458187  -0.366937653729879   0.825743341247768  -0.335471292958996  -0.154728946288025   0.055338880541256   0.462667636126816   0.012417596062290    1.17032
  -0.667374875942135  -0.126503103211591  -0.209988093727759   0.637849357637993  -0.630023613391138  -0.211560463047633   0.177866955762243   0.114916112330381   0.004034700989714    1.18274
   0.405712918585917  -0.434458286384660  -0.371483038349422   0.762693456048560  -0.484575292348080  -0.152206157835757   0.211058951860117   0.152595125394364   0.004034700989714    1.18274
   0.144307657412390  -0.256302877421110   0.843884927229970   0.179500302885512  -0.765665358928797  -0.083560486093015  -0.123659291721391   0.013745715190741   0.004576382875937    1.19983
  -0.155538457669723  -0.679034528171947  -0.075741358338603   0.272902978977448  -0.209690461992229  -0.477125988892710  -0.784894204062963  -0.096529658670966   0.001752966211886    1.20933
  -0.051351775203312  -0.285711828645855   0.540245706653141  -0.047228535339531   0.041553054217750   0.030868321195291   0.698015766796019   0.775422452793086   0.062768698234456    1.21225
  -0.050863259356424  -0.344553586215236   0.624217472114472  -0.217371242979156   0.163700221585815   0.139325332020406   0.843315643311207   0.433884846087148   0.006268846715092    1.22632
  -0.247554737529670  -0.502925786360149  -0.371126202778136   0.836019691480371  -0.383682569705350  -0.266385412558445   0.158581409278398   0.340128537242246  -0.011942623205053    1.22878
  -0.033116924014481  -0.219625485788697   0.497863837303785  -0.182924899324415   0.132523986642025  -0.056294759982701   0.761730992135022   0.794201272089038   0.032278941349216    1.24995
  -0.072084480232432  -0.349925267740898   0.545129527648845  -0.116457900575993   0.110824217793573   0.012471109615477   0.727209668712607   0.827236888428084  -0.328767632893111    1.28995
  -0.078203863492272  -0.372387718735073   0.545942708739354  -0.124058400373484   0.113618425106819   0.014613428312602   0.719822805107538   0.838941696158875   0.242899409427946    1.30128
   0.146765680592237  -0.222266056224457   1.076427274903669   0.008099160228675  -0.515004087219415  -0.257182207331752  -0.190073996426510  -0.346444136708929   0.207464769221592    1.31043
   0.238831727868098  -0.248687208899412   1.062571743900373   0.018810215489005  -0.502525283462984  -0.252089878169560  -0.187226274275996  -0.343211448930967   0.207464769221779    1.31043
   0.199677322895120  -0.231243579414239   1.084152198543109   0.004072325508100  -0.525866395608975  -0.243749990248476  -0.196351993741311  -0.356589838391712  -0.613837338194026    1.33057
  -0.277857917945063  -0.800208284206579  -0.266247598776764   0.368209953144928  -0.216467963942998  -0.633456704640565   0.513774639600684   0.392824764730816   0.001531895987560    1.33806
   0.211041378759973  -0.221119591731594   1.106837905976037  -0.009950493363487  -0.549389024502811  -0.228061105986383  -0.208486463283666  -0.377017937123340   0.204374092293331    1.36311
  -0.032451010669139  -0.073176832804989  -0.807947563033025  -0.097676340872497  -0.206153511796863  -0.542637057360355  -0.343632692733777  -0.859872602743855   0.001356194346774    1.36497
  -0.222940981583542  -0.314918986795368  -0.663028736965815   0.019151382468053   0.017231787894242  -0.119664762062629  -0.259533291718027   1.220793598239801  -0.024428549527491    1.47009
  -0.223004250960984  -0.320449308402696  -0.677596268622913   0.015208246140727  -0.004786980005052  -0.129845620121950  -0.265898879288013   1.234664824389604   0.021079685436425    1.49123

>> # evaluating formula 1 with 76 points
# r9_76_4cg.txt:4 formula 1   : problem  G, 9_76_4  (d=9 n=76 o=4 plus 9/1287 of order 5) quality P
# evaluating formula 2 with 76 points
# r9_76_4cg.txt:84 formula 2   : problem E2, 9_76_4  (d=9 n=76 o=4 plus 9/1287 of order 5) quality P
G 9 dimensions, degree 4, asymmetric 76 point rule with points at 76 distinct radii: 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=76

#                x1                 x2                 x3                 x4                 x5                 x6                 x7                 x8                 x9             Weight     Radius
  2.448294535989363  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.004535631535480    2.44829
 -0.477266852151157 -0.905986306461603 -0.151644922116048  0.035183921545496 -1.773342783983723  0.773427537092579 -0.457480316395058  0.625924818257346 -0.312973871711875  0.041488092888760    2.34836
 -0.655498319646276  0.822414546312349 -0.792068954190945  0.452665532887662 -1.031363501987024  0.109958220882648  1.208269697483547  1.206230220919794  0.325203846264243  0.032014058205066    2.45658
 -0.726522123342718  0.112877908390534 -1.313565963122787 -0.222353435752430  1.688247994598761  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.038088595688248    2.27281
  0.399843896601147 -0.550636631805533 -0.210818910226789  0.489140137865917 -0.482543057261262  0.322970265665324 -0.649241619927443 -2.103956947005547 -0.287889496331313  0.031765340108406    2.45254
 -0.546071847874995  0.294719483749790  0.942610923680929  0.938502628367600  1.060227417662086 -0.776910749098928 -0.126466376326157  1.229447913848288  0.822829929221695  0.032380973099453    2.46711
  0.406518375001464 -1.299601956617671 -0.390489547024639  0.209935677003168  0.425939810575383 -0.688700181833992  0.930898940952200 -0.662519085412792 -1.494025599252077  0.028796397299192    2.49883
  0.721823522395937  0.532475780223076  1.451082452252336  1.116094146043367  0.188016884239429 -0.402390752823128  1.390399839053992 -0.603115138402591 -0.046008982223380  0.029980978132600    2.57919
  0.678444768741327  0.790802737875792  0.591001182984399 -0.394705230670552  0.380295491052013  1.523545319672760  0.346641039656617  0.996940243462785  0.901404898335198  0.033477816441818    2.44604
  0.253342663108967  1.220867390156902 -2.172838686194396 -1.107417146954202  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.018812878812858    2.73903
  0.547723639016729  0.750948701837041 -0.025789181256368 -0.570351396261315  0.486772787547566 -1.380362003666977 -1.065142251017075 -0.955884677878307 -0.754477238790271  0.027618367043279    2.43920
  0.766775783127446  0.053817245350534 -0.830562336098056 -0.295958891284224 -0.139046800416070  0.437726583345810 -0.683463778807926  0.612726895791906 -2.132322562127225  0.024214047978290    2.63980
  1.504913621252881 -0.219610118423401 -0.262974397374370  0.182676573979757  0.556361585982595 -0.661044970229245  0.079571262741507 -0.742887009541801  1.678518323015113  0.031817387547017    2.55689
 -1.851628254110893 -0.492658481951667  0.008477494584238  1.206697238327264  0.082403301744689  0.543958188693993 -0.024429516226782 -0.808463550674768  1.029534269951444  0.024189701324316    2.67288
  0.515532751710002  0.717709855543618 -1.087139221856469  2.140744169884476  0.270531566611721  0.513854722835011  0.379835110499371 -0.303251688338348 -0.590497263437021  0.025467003404490    2.73271
 -0.523219839937880 -0.012502358358875  1.512860548623564  0.809517170339732  0.492756301121115  1.546501380793333 -0.368238567127958 -0.136866720063542 -1.098261224184620  0.026602669073835    2.68570
 -0.567242898618567  1.242023686739201  0.241359156342466 -0.400717987064555  1.124315404498758  1.254759930643458 -0.483883410440587 -1.252891323944896  1.610913163398768  0.013099908675914    3.05297
 -1.064049374086761 -0.574919476509802 -0.503851816826174 -1.556038293930400 -0.900992725942271 -0.853962210433234  0.231071522331624 -1.478093986657173  0.313326754072209  0.020493901700930    2.83112
  1.111904490724672 -0.663094261917869  1.271212279785082 -0.897893101718205 -0.781404205450114 -0.811009242071982  0.484817313528567  1.292482807476743  0.275660317383697  0.024886214851314    2.71074
 -0.775314358583990 -0.466722056656250  1.346047908010646 -1.304829241520742  1.598294111570194  0.125481309399845  0.769572943856183 -0.832637112733607  0.379287477224380  0.018359441233650    2.88670
  0.500530016189596  0.872163980681748 -0.293106331069524  0.459433982913252 -0.300221762326215 -2.349094821650305  0.509858255687119  0.347761363451818 -1.055539532509444  0.014676893740164    2.90028
  0.310459813044498  0.710429970402701  0.148674082703593 -1.128847780030529 -1.656992520685252 -0.363144892767874 -1.184375058838721  0.053085358109816  1.598193331650339  0.016987520200771    2.95547
 -0.489634473819983 -1.265308557409346  0.611061730552700 -0.289755349205166  0.366402374261692  0.480800339036485 -2.158732545210808  0.350284156562371  1.118714888321429  0.018600615431150    2.94922
 -2.417341703411775  1.024324220271696 -0.060014142116532 -0.928712390508244 -0.178465947080098 -0.108920440420610 -0.872371112170296  0.368613371200766  0.000000000000000  0.017057433516551    2.94949
 -0.034047903083698  0.658038030053431  1.048452641661266 -1.530210945030917 -1.075451467324238 -0.081161526335159  0.734634907427123 -0.415254945164767 -1.694543696168905  0.019614222800717    2.93628
  1.022890561217640 -0.475063334964094 -1.017272751785320 -1.279650477414343 -0.105803981799307 -0.146066231535718  2.123103544166194  0.236237728215712  0.040193204838905  0.018200047082619    2.92265
  1.037823076497670 -1.429771717714575 -0.755926906674399  0.305509633738945  1.554391151118849  1.549026043783542 -0.715611139034106  0.000000000000000  0.000000000000000  0.016245053706743    3.01891
 -0.119078561503024  0.955275881736202  1.013866237018271 -1.279254503173353  0.843458459130519 -0.236239315918803 -1.708818611492337  1.526981241108547 -0.583412662547624  0.011919379168614    3.15444
 -0.051302431619299 -1.402079668204694 -0.237894402432071 -0.823587767642148  1.654055089313879 -2.286450468331272 -0.459206576291592  0.217366460803423  0.609078159012439  0.010077877669689    3.36098
 -1.889270704719809 -0.369265668792883  0.532294379682113  0.056520637062828  0.182484654611397 -0.910909554932733  1.882334926945009  0.468467166934805 -0.625235159110887  0.015695481448488    3.00148
 -0.632397208158500  2.142880945235456  0.057765287788489  0.019507428183118 -0.819132538482833  0.830821533947047  0.350317366668513 -1.249177356661332 -0.210547578888227  0.016673809778566    2.84329
  0.147824694409910  1.749500747146377  1.253556193207796  0.910362072756721 -1.318509184246260 -0.266456116871936 -0.889930912194142  1.372943876364563 -0.615703869996873  0.012143118545084    3.21687
 -0.515976217879293 -0.118881136458136 -1.630258014093357  0.899531031233939 -0.316299679662114 -1.198919606698859 -2.233013654629246 -0.400903361337548  0.386527972679916  0.012513728103253    3.25287
  1.318216469884562  0.005241477740847 -1.221175798263514  0.186994728472658 -0.045211593535833  0.003662089721203 -1.003779997325310  2.136207733390355  0.681664337776661  0.016402841184922    3.04986
  0.184541688675840 -2.062871298229656  0.827036590855794  1.422485680868825  0.398322331492937  0.752586327722934  0.882317216209580  1.565914658574433  0.333710823537373  0.009932181825297    3.32625
 -1.545254713530985  0.592040172874311  0.450482245321829  1.716922496744132 -1.682379866121640 -0.801113363130357 -0.652068471314344 -0.873876287385456 -1.106315473170944  0.008141159458920    3.43133
 -0.740422387203054 -0.918350796542166  0.907237898637799  0.689691680624264 -1.430187761318356 -2.226252464928984  0.198253013331923 -0.081540931109023  1.234683202318750  0.009983079072899    3.35595
  0.447832995485338 -1.554397844109692 -1.442469321141439  1.646583225726501 -0.843707309134715 -1.025360937030429  0.876550891504289  0.503765504418816  0.693552284266646  0.011223799622083    3.26726
 -0.948700906466611 -1.696814209643177  1.544356234050095 -0.473979957818909 -0.281888866876416 -0.943301174579177 -0.971051673432504 -0.067654269428047 -1.334585677124893  0.012464601935192    3.17598
 -0.384607728838569  1.954285142551656 -0.084977653954607 -0.403461138203123  1.334503894051063  0.761803016532896  1.163384719076094  1.083950442002238 -1.484658785758225  0.010207819970843    3.35127
  0.403263353200791 -2.337328423025824  1.065495829635358 -0.523189427879030 -0.270951234791824  0.740004494740525  0.837051703085385 -1.028050203185846  1.104691133195843  0.012197468700231    3.26093
 -1.245270636461014 -0.717638229296194 -0.441031763415258  1.752229034566873  0.717595009247211 -0.535751750372472 -0.903132269229754  1.463275548990815 -1.571147109062401  0.009946045789872    3.39968
 -1.190242827139320 -2.159540921736308 -2.205387688162687  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.007777457697257    3.30818
 -0.594075455645910 -0.252617806496474 -0.325933049893247 -2.361948552526723 -0.480037741312657  2.121036697986710  0.000000000000000  0.000000000000000  0.000000000000000  0.009978018908178    3.29105
 -1.352972274478081 -0.642307048446288 -0.548151481535077  0.240544923436575  0.028416626721204  2.256443711956248  1.826183087506627 -0.807243010469526 -1.008007059075681  0.008545785488107    3.56321
 -0.132317655194301  0.533650113876335  0.641497374734766 -0.078290462859957 -1.673348608448942  0.677892542750327  1.964446515334088 -0.916121720169373  1.497496286031629  0.010234486316884    3.30460
 -0.769878263050426 -1.451856838709899 -0.091807751649408 -1.596632447935949  0.878717644473487  0.716113263484738  0.552819890687200  2.240088437071083 -0.875825981848051  0.008771637169678    3.55442
  1.894148086629538 -0.998128504224064  0.960576174451656  1.549792007827960 -0.378608786454109 -0.909887594197963 -1.621174530482160  0.265199956557605 -0.693580904343768  0.010535767872352    3.47267
  1.859446350154638 -0.098046566051159  2.049317227498642 -1.004054775627341 -0.944517663651204  1.476053069018644 -1.043530493873442 -1.131962769098209 -0.223694120869369  0.006593714383695    3.76380
 -0.352417223367841  0.812044509264786  2.451587399881256 -0.088346335720900 -0.108335704040704 -1.075562325615212 -1.110973120289682 -1.590743523626790  0.843593500212495  0.009023865522024    3.52798
  1.396394187534666 -0.113895805088405 -0.324528268312121 -2.730013627047094  0.828735127143386  0.080959317196378 -1.095930189293644 -0.386116106538980  0.220006756955958  0.008478567154489    3.40780
 -1.726898946669297  1.686887927682500  0.493512456138270  0.805570602262153  1.873482751111046 -1.288882342510861 -0.031597498097184 -1.344921083464849 -2.038871531803328  0.003915451616831    4.22590
  0.952113697982703  1.570520529912798  0.322153719914644  1.421238473860593  2.479834244632846  0.378146995500777 -2.068449440904807 -0.498195888614024  0.156383026067156  0.005141592802108    4.04233
 -0.566220301308096  2.351722006516289 -0.939039069671605  1.291034704077165  0.033543751107522 -1.300449802613859 -0.476563964024650  0.288787828562877  1.989207773231932  0.006362795631658    3.78940
  0.113084115392382  1.440946950867003 -0.790491108318575  0.052903069096969 -0.826489434749692  1.717422368665110 -2.483509658294537 -0.409264390705428 -0.680582665989711  0.007361683420350    3.62601
  2.340328245295713 -0.339456466386983 -0.359567714997948  0.422578906631997 -1.142184407454945  2.177547703478615  1.148630462111393  0.340947036191119 -0.827146777186560  0.006491599588337    3.75051
 -1.262964788851538 -0.975813119476841 -0.869530380551806 -1.228826034068291  0.137742878252868 -0.077005572406299  0.594612124309563  1.430547479145999  3.132896762395133  0.005616569473315    4.12957
  0.498893347872388 -0.300681078139441 -2.616710617430824  0.048406587414274 -0.893564781188063  2.000766367785790 -0.111543806901696 -1.128430529908670  1.799408761262703  0.005299639626596    4.06374
  1.819690572877530  0.634344781839823 -1.002753446044850  0.130154009322461 -2.842607365343323 -1.067945288840313  0.336457846774346 -0.930945566069631 -0.241338944788340  0.006521313281618    3.87236
  1.840820286461248 -0.504039879430927  1.680366385884008 -0.476732854854208  2.375150103673187 -0.090995921423023  0.299461422784089  0.416710981470150 -1.424910626230843  0.006417455732238    3.82582
  0.728938341828272  0.078965346345755  0.931420041145729  2.574388539831720 -1.411664310178685  1.353113078896851 -0.860407179133847  0.107641211750772  2.072124223303800  0.005768773302537    4.11119
  2.963155664008340  2.919905601707797  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.004066366428775    4.16006
 -0.012281007311860  2.212640158295599  0.822764860120688 -2.118052975442554  0.735185879383416 -1.688023365411417  1.463868009148799  0.459574300599777  1.254247974082779  0.005384861222429    4.16848
 -0.965030843751043  0.860879026187288 -1.529451065508467  0.574198581958702  0.506251501249767 -1.929100026785859  1.941125090494842 -2.395960428658601  0.921745718412625  0.004270392043172    4.32172
 -0.987454442489602 -0.034607615668307 -1.281771133110787 -1.541361028200748 -1.108906466350552 -2.361304228703702 -0.492961625880958  2.096091547538951 -0.807224741583910  0.004739143770106    4.13384
  1.562751303439698  0.974268914199023 -0.534792059892809 -1.050672203181733  1.591002437692414  1.133669898651421  1.499816916116342 -2.962106021574949 -1.041387631082695  0.003526915578753    4.55036
 -2.113824916637962 -1.145179208486071 -0.645554280069519 -1.520786619949339  1.543492100917833  1.243265250834767 -2.330100457606738 -2.232838998427747 -2.539388137290622  0.001749310661053    5.41301
  0.080016109869152 -0.078992909362739 -0.615317469610546  1.449636930053209  2.692863640952351  1.304260755880736  3.212842819946297  0.365455059660579  1.944100852776518  0.002203332143995    5.06762
  2.336169405364385  0.546081078629349 -1.547634862238291  0.851707827654073  2.867890583806552 -2.103863499895056  1.666669099069480  2.664462710410031 -0.596131853936164  0.001352831103235    5.63560
  2.365901693601150 -3.467631658729383 -1.856758668580226 -2.258022845158288 -1.460411360801983 -0.900208240188288 -1.671873844308223 -0.226023214395570 -0.750498239572183  0.001352437283232    5.70271
 -2.932193673074545  1.249501339963886 -2.196966451994156  1.965598828100920  0.622175731770697  4.139252499659571 -1.618830942377366  3.455975595199020  0.533155160471302  0.000638702819677    7.15670
 -3.032251290220358  0.305290637992693  4.420934779798426 -0.892120328346640 -1.821463368826064  1.648853403036361  0.926738022594253  1.932516664624932  1.375096783303190  0.000930260412436    6.49223
 -0.740830476087887 -2.992824515859127  1.083365546205418  3.693437269391761  3.588862596687262 -1.708018751894340 -0.485945899930843 -3.222032986902062  0.416924892052395  0.000619304056770    7.13510
 -0.013002324634129 -2.587275699288773  2.231053230426889  2.626572538521841 -3.974077920349163  0.088940505024476  2.627414812677688 -2.221475236599392 -2.687744644966024  0.000420741002384    7.30986
 -2.783361429417360  0.790781074466581 -4.690365398277254  0.292716048872878 -2.647753557956638 -0.124684309473480  1.137485102432874 -1.360329759403817 -4.347721397877297  0.000417246787031    7.71562
  1.007509429795681  0.304600409089493  1.690425870615736  2.097864073469903 -1.667588815512372  0.590431711737715  2.975325724414448  4.173073503783183 -3.626514931412113  0.000498395901120    7.13545

# E_n^{r^2} 9 dimensions, degree 4, asymmetric 76 point rule with points at 76 distinct radii: 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=76

#                x1                 x2                 x3                 x4                 x5                 x6                 x7                 x8                 x9             Weight     Radius
  1.731205668740099  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.783090929041941    1.73121
 -0.337478627591647 -0.640629060961149 -0.107229152760761  0.024878789513551 -1.253942707923120  0.546895856234574 -0.323487433982311  0.442595683502727 -0.221305947021678  7.163048618543437    1.66054
 -0.463507306878266  0.581534902643921 -0.560077328675759  0.320082867914280 -0.729284126123334  0.077752203633319  0.854375696592834  0.852933568884537  0.229953844961400  5.527326985470975    1.73706
 -0.513728720097678  0.079816734469103 -0.928831400059963 -0.157227622240668  1.193771605305373  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  6.576114825487202    1.60712
  0.282732330702720 -0.389358896319413 -0.149071481023718  0.345874308435517 -0.341209468003927  0.228374464973577 -0.459083152079231 -1.487722224552167 -0.203568615088252  5.484385030451097    1.73421
 -0.386131106647474  0.208398145507280  0.666526576155294  0.663621572680128  0.749693996628761 -0.549358859064580 -0.089425232292319  0.869350956997781  0.581828622715906  5.590675986216912    1.74451
  0.287451899640467 -0.918957356367664 -0.276117806683583  0.148446940821931  0.301184928435167 -0.486984568779214  0.658244953746685 -0.468471737960897 -1.056435632497438  4.971787795743438    1.76694
  0.510406307506122  0.376517235013338  1.026070242048430  0.789197739109876  0.132948013823262 -0.284533230007995  0.983161154755764 -0.426466804200735 -0.032533263325638  5.176309370766033    1.82376
  0.479732896637528  0.559181978532861  0.417900944177542 -0.279098745176945  0.268909520577545  1.077309226985632  0.245112229778745  0.704943206590303  0.637389516207592  5.780049409800328    1.72961
  0.179140315048224  0.863283610509459 -1.536428969432526 -0.783062174213582  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  3.248102195311468    1.93679
  0.387299099364912  0.531000919392198 -0.018235704947630 -0.403299339955591  0.344200338971967 -0.976063333285167 -0.753169308622477 -0.675912537760074 -0.533495971799508  4.768397198353290    1.72478
  0.542192355899041  0.038054539132140 -0.587296260053071 -0.209274538979525 -0.098320935476493  0.309519435389448 -0.483281872690456  0.433263343029837 -1.507779743357234  4.180630895358042    1.86662
  1.064134626687918 -0.155287803954377 -0.185950979661859  0.129171844225018  0.393407050239994 -0.467429381118352  0.056265379472093 -0.525300442102402  1.186891688549857  5.493371183038146    1.80799
 -1.309298894718425 -0.348362153397084  0.005994493907983  0.853263800060289  0.058267933455829  0.384636523907466 -0.017274276585070 -0.571670059024278  0.727990663746614  4.176427369623939    1.89001
  0.364536704657900  0.507497505779312 -0.768723515868577  1.513734719310878  0.191294705276160  0.363350159061370  0.268583982366852 -0.214431325230312 -0.417544619248413  4.396957557053579    1.93232
 -0.369972296871428 -0.008840502376371  1.069753952921322  0.572415080634174  0.348431321995140  1.093541613473323 -0.260383987910592 -0.096779385875690 -0.776587959135182  4.593033776458015    1.89907
 -0.401101300193100  0.878243371287612  0.170666696151221 -0.283350405996770  0.795011046713568  0.887249255719143 -0.342157240826220 -0.885927951251226  1.139087621741942  2.261740085176858    2.15878
 -0.752396527934047 -0.406529460476304 -0.356277036390950 -1.100285229424134 -0.637098066313528 -0.603842469874395  0.163392240379785 -1.045170281196349  0.221555472531631  3.538336039234558    2.00190
  0.786235205423189 -0.468878449168019  0.898882823363648 -0.634906301005566 -0.552536212521457 -0.573470134674054  0.342817610032694  0.913923357733830  0.194921279726044  4.296682602149122    1.91678
 -0.548230040506044 -0.330022331190963  0.951799603556294 -0.922653604969809  1.130164604621816  0.088728684788795  0.544170247218398 -0.588763348681523  0.268196747164502  3.169814783208602    2.04121
  0.353928168635087  0.616713065046706 -0.207257474307972  0.324868884825501 -0.212288844000640 -1.661060878039135  0.360524230040309  0.245904418331457 -0.746379161247907  2.534011474373433    2.05081
  0.219528239089681  0.502349849629898  0.105128452066402 -0.798215920186972 -1.171670647751927 -0.256782216229429 -0.837479635573085  0.037537016701169  1.130093342457068  2.932948338523835    2.08983
 -0.346223856740821 -0.894708261237515  0.432085893397402 -0.204887972308042  0.259085603483297  0.339977180129491 -1.526454421486660  0.247688302447464  0.791050883746423  3.211454260512716    2.08541
 -1.709318710927494  0.724306602287743 -0.042436406857704 -0.656698829100353 -0.126194481391214 -0.077018382031252 -0.616859529126872  0.260649014412097  0.000000000000000  2.945019090519108    2.08561
 -0.024075503155666  0.465303153329420  0.741367972671631 -1.082022535877239 -0.760459025381986 -0.057389865643042  0.519465324738073 -0.293629587647260 -1.198223338577945  3.386456733819698    2.07627
  0.723292852248707 -0.335920505646216 -0.719320461103693 -0.904849530128284 -0.074814713006827 -0.103284422821263  1.501260913241108  0.167045299593431  0.028420887699216  3.142294885959942    2.06662
  0.733851735063379 -1.011001277144717 -0.534521041790834  0.216027933734636  1.099120523572501  1.095326819793927 -0.506013489103638  0.000000000000000  0.000000000000000  2.804759182935887    2.13469
 -0.084201258332720  0.675482053879629  0.716911691411706 -0.904569534057309  0.596415196100357 -0.167046422269057 -1.208317228004015  1.079738790332504 -0.412535049917533  2.057917984240842    2.23052
 -0.036276297289355 -0.991420041151331 -0.168216745166041 -0.582364495402049  1.169593570109966 -1.616764631004192 -0.324708084061243  0.153701298436621  0.430683296510308  1.739977007698865    2.37657
 -1.335916126804467 -0.261110258462824  0.376388965460702  0.039966125744105  0.129036136738204 -0.644110323340561  1.331011791307095  0.331256310502849 -0.442108020843552  2.709873818698211    2.12236
 -0.447172354292317  1.515245647651436  0.040846226712426  0.013793834751789 -0.579214172651767  0.587479540609757  0.247711785538714 -0.883301779799910 -0.148879620794271  2.878785255819064    2.01051
  0.104527843844078  1.237083841998135  0.886398084815621  0.643723194981314 -0.932326785237276 -0.188412927128790 -0.629276182800007  0.970817925165929 -0.435368381677596  2.096547285323426    2.27467
 -0.364850282593422 -0.084061657744716 -1.152766496849131  0.636064492073246 -0.223657648376216 -0.847764183994274 -1.578979097670497 -0.283481485402257  0.273316550600246  2.160534181293184    2.30013
  0.932119804927172  0.003706284453981 -0.863501687973022  0.132225240549152 -0.031969424377438  0.002589488475181 -0.709779642928140  1.510526974303466  0.482009475734906  2.832001683106417    2.15658
  0.130490679474286 -1.458670283693279  0.584803181683542  1.005849271083116  0.281656421696688  0.532158895761172  0.623892486739435  1.107268873837400  0.235969186278624  1.714822165809623    2.35201
 -1.092660086598235  0.418635620974281  0.318539050471195  1.214047540219505 -1.189622211866325 -0.566472691568646 -0.461082037864319 -0.617923848728379 -0.782283173210776  1.405596568922051    2.42632
 -0.523557690933608 -0.649372075743041  0.641514070276217  0.487685664297359 -1.011295464398219 -1.574198214584557  0.140186050117666 -0.057658145331450  0.873052864976709  1.723609734331983    2.37301
  0.316665747946768 -1.099125256231719 -1.019979838632665  1.164310164699226 -0.596591159625816 -0.725039671738000  0.619815079437796  0.356216004302409  0.490415523312364  1.937824006356081    2.31030
 -0.670832844280371 -1.199828834052378  1.092024765664543 -0.335154442320264 -0.199325529309300 -0.667014657246170 -0.686637223166666 -0.047838792688794 -0.943694582369457  2.152052395176806    2.24575
 -0.271958733158507  1.381888276670401 -0.060088275360630 -0.285290106768675  0.943636753003358  0.538676078918775  0.822637223987522  0.766468708009941 -1.049812295157817  1.762411951220218    2.36971
  0.285150251652290 -1.652740777781618  0.753419326461158 -0.369950792298365 -0.191591455492168  0.523262196339557  0.591884935455422 -0.726941270072920  0.781134591399435  2.105931009101370    2.30582
 -0.880539311454074 -0.507446858374042 -0.311856550629595  1.239013032534193  0.507416297184325 -0.378833695720939 -0.638610951880747  1.034692063435877 -1.110968775059671  1.717215822528563    2.40394
 -0.841628774328869 -1.527026030009591 -1.559444589445159  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  1.342802325560902    2.33923
 -0.420074783223718 -0.178627764022124 -0.230469469792322 -1.670149838305399 -0.339437942107645  1.499799432291925  0.000000000000000  0.000000000000000  0.000000000000000  1.722736081112834    2.32712
 -0.956695870040856 -0.454179669560273 -0.387601629710907  0.170090946542002  0.020093589453008  1.595546650090007  1.291306444864128 -0.570807006768445 -0.712768626956309  1.475456514694120    2.51957
 -0.093562711258601  0.377347614302936  0.453607143788322 -0.055359717190514 -1.183236148323321  0.479342413894541  1.389073452271008 -0.647795880724046  1.058889778654643  1.767015979023679    2.33671
 -0.544386140491082 -1.026617815963833 -0.064917883756782 -1.128989630997985  0.621347205155480  0.506368544707691  0.390902693479729  1.583981724310538 -0.619302490904123  1.514450511839454    2.51335
  1.339364956627265 -0.705783433832429  0.679229926801003  1.095868438163868 -0.267716840318510 -0.643387687974880 -1.146343503990843  0.187524687652260 -0.490435760762988  1.819033179126685    2.45555
  1.314827123446907 -0.069329391726827  1.449086108366712 -0.709973940528822 -0.667874844918237  1.043727134494304 -0.737887488592854 -0.800418550080048 -0.158175629778297  1.138425350951598    2.66141
 -0.249196608450332  0.574202179126434  1.733534075127524 -0.062470293081226 -0.076604910971798 -0.760537414031300 -0.785576627072816 -1.124825532685083  0.596510684565146  1.557998523450281    2.49466
  0.987399799215251 -0.080536496126730 -0.229476139210222 -1.930411148416677  0.586004228210592  0.057246882189804 -0.774939668556593 -0.273025317259067  0.155568269750414  1.463851059773459    2.40968
 -1.221101955613758  1.192809892766034  0.348966004335388  0.569624435584100  1.324752357746651 -0.911377444541039 -0.022342805173044 -0.951002818278752 -1.441699886106339  0.676014932045972    2.98816
  0.673246052304175  1.110525716694028  0.227797079936110  1.004967362550058  1.753507610598501  0.267390304803919 -1.462614626205311 -0.352277691198232  0.110579498194556  0.887712031425512    2.85836
 -0.400378214700429  1.662918578273300 -0.664000893963912  0.912899394000122  0.023719013874556 -0.919556874020981 -0.336981610630981  0.204203831900953  1.406582305641294  1.098556508288471    2.67951
  0.079962544838442  1.018903360288139 -0.558961623159738  0.037408118904045 -0.584416283890546  1.214401003044564 -1.756106520522358 -0.289393625965989 -0.481244618279350  1.271017600054122    2.56397
  1.654861972451004 -0.240031969299859 -0.254252769570791  0.298808410465883 -0.807646339876936  1.539758747486937  0.812204388836413  0.241085961316192 -0.584881095185209  1.120794913086369    2.65201
 -0.893050966596756 -0.690004073952876 -0.614850828535900 -0.868911221588266  0.097398923272760 -0.054451162437649  0.420454265275017  1.011549823313459  2.215292545446979  0.969718234932034    2.92005
  0.352770869369418 -0.212613629326880 -1.850293821988166  0.034228626214730 -0.631845716207558  1.414755466231309 -0.078873382259560 -0.797920879796347  1.272374137215345  0.914999308545042    2.87350
  1.286715543742939  0.448549496849226 -0.709053761556485  0.092032782590523 -2.010026944285089 -0.755151355675206  0.237911625037565 -0.658277922683386 -0.170652404424242  1.125925074893892    2.73817
  1.301656507502499 -0.356410016734055  1.188198466336510 -0.337101034481818  1.679484744643240 -0.064343833098523  0.211751202754411  0.294659160792437 -1.007563966392594  1.107993745111984    2.70526
  0.515437244573640  0.055836931879834  0.658613427227200  1.820367593923946 -0.998197406486389  0.956795433800166 -0.608399750947139  0.076113830764114  1.465213089759024  0.995996700697343    2.90705
  2.095267463731618  2.064685051392153  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.702070844958477    2.94161
 -0.008683983550001  1.564572860256485  0.581782611913335 -1.497689621847780  0.519854920744614 -1.193612768483759  1.035110996031158  0.324968104413164  0.886887247763426  0.929713082830525    2.94756
 -0.682379853670529  0.608733397198301 -1.081485219914037  0.406019711050695  0.357973869519578 -1.364079710527440  1.372582714620248 -1.694199866559124  0.651772648019241  0.737296503541299    3.05592
 -0.698235732397162 -0.024471279719767 -0.906349060151805 -1.089906835297434 -0.784115282058084 -1.669694232560860 -0.348576508525172  1.482160547252597 -0.570794088715552  0.818227951006411    2.92307
  1.105032043970322  0.688912155929387 -0.378155092074923 -0.742937439674004  1.125008612576630  0.801625672963494  1.060530711924169 -2.094525254449155 -0.736372255782357  0.608932973415928    3.21759
 -1.494699932795798 -0.809763983994335 -0.456475809061160 -1.075358531703934  1.091413731266874  0.879121289678861 -1.647629834419591 -1.578855597086041 -1.795618571942876  0.302023940884835    3.82758
  0.056579933892636 -0.055856421876039 -0.435095155344166  1.025048103499077  1.904142141328098  0.922251624918757  2.271822944870536  0.258415750904934  1.374686896308845  0.380412165788263    3.58335
  1.651921228533727  0.386137633776465 -1.094343105889413  0.602248380523866  2.027904879510670 -1.487656147466657  1.178513021946123  1.884059650749633 -0.421528876399576  0.233570508799452    3.98497
  1.672945131166109 -2.451985860544728 -1.312926645579969 -1.596663265885560 -1.032666776544953 -0.636543351117119 -1.182193332598761 -0.159822547604694 -0.530682394470073  0.233502514547820    4.03242
 -2.073374029983306  0.883530870590165 -1.553489876244425  1.389888260442483  0.439944679024751  2.926893511552631 -1.144686336949646  2.443743778980447  0.376997629393859  0.110274033622522    5.06055
 -2.144125449576491  0.215873080357426  3.126072961978918 -0.630824333808286 -1.287969099779797  1.165915422469499  0.655302740159794  1.366495638312303  0.972340260261499  0.160612361239475    4.59070
 -0.523846253351419 -2.116246510065324  0.766055124225712  2.611654539074050  2.537709078864317 -1.207751641858271 -0.343615641130893 -2.278321374245185  0.294810418415709  0.106924776711256    5.04528
 -0.009194031920019 -1.829480191766240  1.577592868423017  1.857267253267155 -2.810097446442632  0.062890434224965  1.857862831034383 -1.570820204037419 -1.900522464553302  0.072642246149257    5.16885
 -1.968133741234090  0.559166660189313 -3.316589179364609  0.206981503120129 -1.872244495741958 -0.088165120736265  0.804323429428974 -0.961898397524306 -3.074303283148896  0.072038958971820    5.45577
  0.712416749917908  0.215385014819387  1.195311596205565  1.483413912358192 -1.179163359679652  0.417498267197324  2.103872995972262  2.950808572914995 -2.564333300075774  0.086049606584159    5.04552

>> # evaluating formula 1 with 78 points
# r9_78_4E1ac.txt:4 formula 1   : problem E1, 9_78_4  (d=9 n=78 o=4 plus 2/1287 of order 5) quality P
E1 9 dimensions, degree 4, asymmetric 78 point rule with points at 78 distinct radii: 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=78

#                x1                 x2                 x3                 x4                 x5                 x6                 x7                 x8                 x9             Weight     Radius
 -0.134285186745821  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 162077.947470555431210    0.13429
 -3.614512316515201  6.095658118768336  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 43735.284242061497935    7.08673
  2.305419616197757 -3.625791925643375 -6.193185162220566  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 43211.840345718592289    7.53770
  1.668858597466241  0.452711020819216 -2.783817729522865 -7.107742439855887  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 29247.012638060517929    7.82686
 -1.703013931378291 -2.721332370533582  1.677626463884699 -0.297044079189350 -7.106609067906727  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000 38888.708458113076631    7.98201
  7.051002457657674 -0.599006180944208  1.529350070769312  0.601392472026271  0.625541691252372 -3.806817814557241  0.000000000000000  0.000000000000000  0.000000000000000 29859.460936621686415    8.22552
 -1.972194822221168 -1.121948470666713  0.102230522289676  0.320703855339714 -0.473550225255916  4.611345671403209 -6.522712125543772  0.000000000000000  0.000000000000000 25911.647810115558968    8.32443
  0.636267167085596  0.792195530607357 -0.123540790231340  3.153538488611288 -3.064361311719394  2.389473866862765  6.253287622623374  2.979761950282843  0.000000000000000 29860.709163399718818    8.60668
 -0.961271541466734 -3.491449584550750  7.012326139804786  1.092147137272900  0.355135364950954  0.110815074757625 -2.419817562106818  2.120415922024672 -0.774695647633796 29080.382641787175089    8.63539
 -1.373101365459314  1.208208953668762 -0.776697104434163  1.321945762047771  1.655084423339910  5.948181712739156  2.717749848975864 -1.832623127992824  4.777724278335488 31405.083503589474276    8.79701
  1.875823054792456 -4.294766355032088  0.310544676458379 -1.744512062846568 -0.639072220158318  0.730971199469445  2.967759339014791  6.548077315264186  1.281787827347275 25125.279490755277948    8.90922
  2.162328022857746  5.684766120569818  2.542218483917948 -3.083582272100612 -0.657485736626697  1.019888955048850  2.310314217793993 -4.152560646329766 -1.793548689829860 25307.405062126523262    8.95735
 -2.341244369145274 -0.239965814413435 -0.658701999345656 -3.165622339507644  6.876969024091298 -1.034137041315778  4.423025071947021  0.171088957275232 -0.334820531739565 24396.211006646939495    9.16846
 -3.230863601183165 -5.767991559886213 -0.202106527564606 -1.966499640305303  0.851739496521770  2.317999079600256 -2.252704990035268 -4.939745271234364  1.409473360980656 21976.030837217967928    9.22915
 -2.649516719776655  2.345983997382322  4.365844420864899  0.399611887368200  2.280467154771941 -6.496057341529623 -1.937268910840487 -1.391993735676237 -1.547462256811964 22606.402786592941993    9.33962
  0.438631211419179 -0.472951960944464  4.762639543200323 -5.067549217271349 -1.125475594078589  5.898736724023629 -0.336750793874333 -0.297466816610497  2.253828350045333 18499.699918370064552    9.49328
  2.414513055261840  4.621408911666302 -2.494485274903815 -0.127110664149022 -2.806161003474825 -3.462052472962449  1.341325591928067 -0.526496326461456  5.979060829620634 20435.684870621200389    9.54525
 -1.977879535288575  2.069419123215818 -1.584856061955039  2.419592284972252  5.149728193826322  2.679551954337325 -2.912749934197289 -3.081272861704095 -4.839859085956153 22375.290611806940433    9.57408
  2.161425420638602  5.755684844598064  1.660557522414349 -1.490738389218144  3.706157011897525  1.925954981835498 -4.539511205130298  2.623033383184992  2.350291851861790 20490.280073951213126    9.65586
  0.126062803378543 -5.405268310422995 -0.950926312716657  4.505248476166886  0.625537543042262 -3.344561550156961  4.444069999470392 -1.440171586146423  3.263382525087755 20826.801044733263552    9.72035
  2.189176089159639 -0.964518927447246 -0.291739455503456 -3.344750608149712  5.548491346968538 -1.944239121495269 -3.019806850094032  2.393641011480752 -5.344949558899549 18474.118794789388630    9.74568
  1.757042516776538  1.276616140077124  4.704415419396185  7.271527942961347 -0.311689642273147  1.326285863140666 -1.347205247171872 -2.907758706042940  1.914196037762163 20364.833062262776366    9.77312
  2.071266984352115 -2.141074739328547  1.166519117383854 -6.124913247360889 -3.020009014982604 -4.840394922302870 -1.204946055777806 -3.138725634699047  1.550109225271376 19743.909796212039510    9.69566
  5.977213900815521 -1.342857325704720  3.176993828095224 -0.836598604319551 -1.712281536229586  4.072593455051297 -0.943030505859602  2.332770736767988 -5.058015099554422 18110.095938120099163    9.98780
 -4.891290415829102  0.604026413171561 -4.446577036658717 -2.969261651788943 -1.951931032987770 -2.685516528949809 -6.057924286210263  0.770335173394469  0.044806182139252 17872.161683115780761   10.05952
  1.155908289738311  2.832247805183656 -1.316761000944404  5.316448990225757 -5.257546466947318 -4.626252599301703  0.623491166101565 -2.134086815430912 -2.656752372850694 17506.446880574283568   10.02006
 -8.368975096796682 -2.805248570965409  0.956771460352556  3.144359987833045  3.477454515835772  0.151137615493286  0.901570893967604  0.817739280649911  0.964644086373248 17780.193777245916863   10.16067
  3.663267682253971  0.043337282232518 -3.048179464782310  1.609136182207203 -3.485848966144797 -2.740400741395474 -5.303283539164581  5.547854837141556 -0.456965508501731 16832.900489200394077   10.20173
 -2.897816699341102  1.294046205912816 -2.347751810130798 -0.677134961196227 -0.852060313498599 -7.009418829740178  3.249915456924072  4.832794349277949  2.178478889804729 16289.864987007649688   10.22565
 -1.772078016045233 -2.514095204649885  3.699714353581219  4.417076414412452  0.453529607876404  1.995039713803669  4.555884313613055 -2.791262536732064 -5.787915954035164 14538.367045718792724   10.43515
  5.592775323279861  4.294985161183359 -2.543029933741360  4.666326098429976 -0.208523362078360  4.996866579698104 -0.985833039393134  1.461007074752848 -1.770419116504176 16016.391813386500871   10.45087
 -2.826425107420525 -0.043864504747539  2.208222713338988 -5.575660730731215  3.490037011871138 -1.290828284919753 -1.272170718987875  3.328043565892056  6.250390502922037 12065.010794292405990   10.46724
  0.441309712049931  1.308713069932412 -1.540805772986333 -2.910544375317809 -4.524146458524918  0.970348943539210 -2.117279547091704 -2.674984122092406 -8.004890446985392 14612.726603529679778   10.48232
  0.838620019784811  0.107512360887130 -1.113256112290755 -0.427140056353481  5.136312512416996 -3.341921882050083 -1.640305643500068 -5.684990700641564  6.026371965966190 15205.823889262053854   10.53630
 -0.480413354581942 -3.488279650860656 -2.705172521068398 -3.152333406415088  0.453040967179667  6.384885961154089  4.330879908374444 -2.185497660266988 -4.431023394794330 14346.630518678241060   10.66738
 -0.285594751806740 -1.644607341295143 -2.213746111945305  6.400472317717330  3.254411886912081 -2.688776419364214  1.175246287928418  5.036162917503502 -5.249357594403072 12599.170307058775506   10.98971
  5.069565889309225  1.407447705491841 -3.674859375663412  2.493852546874483  4.026018539142267 -0.727941586884720  5.313135163144913 -4.839088598705468 -2.273726838730612 12886.536649935716923   10.99818
 -4.656729833193748 -0.771359651673980 -3.615604126267994  5.859315051730364 -4.803059060192989 -0.671321171168480 -1.317891959908914 -2.009863876937146  4.640946144970876 8567.863417364487759   10.97812
  3.549462398138273  3.001418377101858  3.209818040666939  3.994331079441831  5.664678247408421 -3.880921159562829  1.649253478366229  4.795776658135509  2.003543358425223 11285.959808303057798   11.16909
 -7.598688604435686  1.136344503202252  2.340687426836920 -4.885704501301303 -3.172320206680248  0.978208554410389  4.378136845837555  2.053369425165561 -1.284488407813449 11509.228534820698769   11.15505
  5.021759244041465 -3.261073356612827  0.756920520210802  0.808736819731647 -2.155867671853169  1.574772994375027 -3.657321399950042  1.274594406180539  8.088369029701040 13218.071204783336725   11.16376
  2.304577394976945  2.535081413816051 -5.086367202004483  0.838913578489733 -3.375163756475626  2.855236006037318 -2.999767027611087 -7.475616323678260  1.473659071556487 12043.479609368345336   11.17640
 -3.421740624575856  3.723220371188048  2.904536235499941  3.586861669530782 -2.995979477910847 -0.823812212175423 -3.658765900944136  4.471063705132091 -6.175883861134340 11028.078984735322592   11.31573
  1.820528878155319 -0.192138500158296  4.001312606209473 -1.807789667129306 -1.150204981470609 -5.581540046998854  6.357562286783905  0.275824786152269 -5.895201664996619 11258.824538139582728   11.41729
  3.650301176536312 -0.052419266454167  5.820714216497215 -1.763638184692529  6.158470304859156  1.821981932578658 -0.728389957352695 -6.535111389104584 -0.351235550251985 9577.248084222888792   11.61579
 -5.182844727746606 -0.017621563825879  2.878438481957971  0.961521609090497 -2.419278490466303 -1.508111957894306  1.560341694670573 -9.519566260517559 -0.778422997916099 9249.450308087711164   11.74147
 -1.248958323518299  0.883203518998279 -3.293789501985290  7.617896089312157  3.737361160845342 -3.006862469785279 -6.468736632536972 -1.166342503094584  2.355705404535648 8778.578342589498789   11.95762
 -3.849411205191646 -1.333401456396306 -5.431850135043982 -1.416972773529641  1.732846633711269 -7.233825089832830  1.263459573184556 -5.061365046438687 -3.604747305092825 8915.828022262801824   11.98531
 -0.874498134338539 -0.329691283734409  8.202079424014769 -0.585122063753447  0.256282539841257 -1.966067591509910  6.302828508393006 -1.229396857286927  6.430132716177358 8713.482622972927857   12.45009
 -3.627483098163266  1.756118726701177  1.895023917892334  5.422983813660982 -1.778854428891353  1.778610074339799 -1.232583836574379  8.290968441660668  5.443145053414620 8617.946856459784613   12.46826
  1.129417013507220  6.459860632398050 -5.076497255353189 -2.834274508345442  0.375851180317259 -0.640175404310330  4.073688002601224  5.214776395669404 -5.808166304006345 8127.582260640106142   12.44524
 -4.053961994197349 -0.939190781615929 -2.799001544859036 -2.655289670991728  2.266230029074856  7.059088000509862 -2.157807294995366  7.690862736224444 -2.529776215374055 8435.080910529930406   12.54486
 -0.849489302378061 -6.217764324358118  0.041488526341984 -1.261936694374841  5.616952197146489 -3.848359931309299 -6.887492452487984  3.747562926423578  2.859172399866204 6862.886761629448301   12.52969
  3.469082427765338 -6.685093260392703  0.042431616984083  3.367165108855666 -0.102719873929218 -2.868790487367060 -5.063574348473965 -5.234344383446146 -5.390210439867631 8744.760710455286244   12.58561
 -0.764158388812790  2.499051491491091 -8.973420053532191  1.435049485148906  5.425944354776822  0.995811716346838  0.195972691818966  4.122855284449500  4.411225192961354 8376.005755202506407   12.50354
 -6.732731220908557  1.712244295519920 -8.540754117442150  3.883403443248739 -3.120248866088451  2.609980493691603  3.101104587706925 -0.972514492156842 -3.622905948467602 6407.121530825660557   13.28619
 -5.265386676817191 -7.866321291412409 -1.881878248794227 -1.988416032377538 -2.143182065911435 -3.262805117218016  0.270101550011034  4.310876415997122 -6.843723438926430 6200.900537761363012   13.33532
  3.950401913753577 -6.321337997751426  0.968809663597658  4.502617639021135  8.637659357582306  6.110392271571246  0.311878409662722  2.047378943829969  1.850726259458596 6039.461333126243517   14.01561
  0.833381008339089  4.617073857901987 -4.524590653145466 -4.353223629513286 -8.780323012199641  6.333541138127810 -1.255914306605896  3.530855636414116  2.694550851577119 5672.703237578729386   14.14026
 -2.672355018507516  0.692861504525055 -4.243985413831885 -4.854064767206539 -4.106517805156604 -1.576361515518972  9.993320993647277 -5.664715077140980  3.365925563269351 4383.145705317840111   14.55432
 -1.359956811318270  4.743497939480374  7.579323115708139  0.048793711954884  5.894430297780046  5.630129318319447  5.018807991191604  5.369127440491297 -4.108040350311802 4385.279583016627839   14.80316
  3.708339302546165  3.640755650443039  5.061958056886559 -1.454505252305170 -4.105856511388787 -1.573291059885266 -11.517387623364705 -4.707270885469051 -0.095828738400339 3997.454175888904047   15.12934
  8.268182586214330 -5.117501958529207  1.890203636581358  0.828201412861352 -6.946569002055709  4.684978905745480  4.452708142397984 -7.578844371835545  2.355063017725227 3592.627691224760383   15.86903
  2.624850199096458 -11.928623712450579  4.495172312073834 -6.473960515099594  3.642675078015166 -1.787802849184972  5.695557539274088 -1.784859810978660 -1.142780930803594 2688.793449591160879   16.26951
  1.648588452116625  3.864379044437940  5.746249938912501 -8.642202282741236 -3.734430016079513 -4.716162602240302 -2.555095267181702  9.729789787241499 -1.319473126558851 2987.891100729586014   16.26299
 -7.762931188581598  4.773732627968678  4.910354589395488 -1.294295071766655 -4.614576821441514 -1.244867730461310 -5.220329013072047 -3.571638312988458  9.574573400512774 2680.068585238760534   16.22847
  9.860797117910620  2.924329798883648 -0.996039871510473 -5.983650731981145  3.459066642987800  2.853863843398455  8.205998652302592  3.543683731727247  5.583795059692310 2867.674310219204926   16.54593
  5.051357356170600  7.975445920220154  9.129438132990868  1.104285506132122 -9.177578808039470 -1.051966956718797  2.189788861334937  2.814461462310685  2.299954630405197 2538.630957643961210   16.64424
 -0.332013532705947 -8.947883410740999 -3.770415505483520  9.532871901503906 -5.550508421402446  7.926131187972540 -3.359304123361614  2.287136678826809 -2.340009456613428 2374.420869055203184   17.34618
 -2.356630137974475 -7.482195101718333  4.225720551637662  3.994250675540497 -5.674255857058031 -12.485240788120716 -3.868105621678237  1.786814608364392  4.584346445244942 1695.027003169816453   17.96099
 10.820646108148557 -2.248010709180505 -6.952826589417585 -8.105320810445335  6.606689674232797  7.452998354426472 -8.637812664988699 -3.436690758663951  1.356129564189282 1119.259999042498293   20.58240
 -7.726308294916496 -9.881877304767521 -8.626119790484559 -6.767659468595659 -4.342474177663094  2.746934750432948  2.776299327788049  2.976837027020240 12.982606900030950 925.396862977845672   22.11512
 -9.478530681965955 -0.556504690205494  9.112413353626144 -12.955626529927180  3.619564937407738  0.924616801475154 -6.010343230913106 -3.896417114598464 -9.416616229806767 878.534279951128951   22.24796
  7.495822867943749 12.689811961714032 -8.893174534478117 -2.625012426277504  4.258772863158551 -11.487373949264599 -7.174909662407560 -3.187011931946348 -4.672648357324993 748.136928751610526   23.16819
 -11.744978500272435 10.959327195760915 -10.453565477533269 -14.740573465773959  8.314942123917385  6.651254627709823 -3.571394371128803 -11.198247657705688  3.560053050862317 294.801232177173119   29.13451
 -10.304941223474531  8.579928058690603  9.913749726298546  6.547649179842062 -10.347721077993743 19.841147565560856 -2.708658986644307 -6.521085183795847 -5.380692370458059 272.388375696823402   30.00868
 -6.888891059191201 18.043419588349440 -0.104976768527315 15.222748337735881  9.724671897601104 -5.239804417099711 14.699913103884722 -6.317521724381701  3.473976357894544 234.010767756993715   31.54135
 15.832745076609193 -6.964697081493116 -16.324793435657028 -5.495500086484768 -21.492705789096238 -9.399889277534978 12.348548718970930  4.295657137940823 -9.254106325644546 106.479433276272189   37.45336

>> # evaluating formula 1 with 78 points
# r9_78_4Sac.txt:4 formula 1   : problem  S, 9_78_4  (d=9 n=78 o=4 plus 11/1287 of order 5) quality NO (4 negative weights, stability factor 2.139121)
S 9 dimensions, degree 4, asymmetric 78 point rule with points at 78 distinct radii: 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=78
 (4 negative weights, stability factor 2.139121)
#                x1                 x2                 x3                 x4                 x5                 x6                 x7                 x8                 x9             Weight     Radius
 -0.949452103015056  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.010656804339141    0.94945
  0.278369698432801  0.627275481318494  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.140339398247582    0.68627
 -0.110066521648215 -0.321216064954329  0.615614400921775  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.108460673138076    0.70305
  0.258969280078805 -0.013790710073993  0.225063340140917  0.634000848130134  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.107941659033617    0.72102
 -0.008682401650060 -0.127646970156121  0.114992898944726  0.297245741263812 -0.538514427463363  0.000000000000000  0.000000000000000  0.000000000000000  0.000000000000000  0.130382221353748    0.63871
 -0.297278238624269 -0.023005434468942 -0.108866421955489  0.205679426288526  0.384074204900978  0.439026903080338  0.000000000000000  0.000000000000000  0.000000000000000  0.102798114455148    0.69521
 -0.152945774724073 -0.225830672081197 -0.367090279095108 -0.293326559604543  0.221276959562156 -0.335935009249309 -0.357841579738346  0.000000000000000  0.000000000000000  0.090829753970299    0.76489
  0.125845435279491 -0.072072296619863  0.148281696026006 -0.594720638414012 -0.301534927227349 -0.131231757152438 -0.233174138034491  0.025731489040307  0.000000000000000  0.095905771823358    0.74826
 -0.235956294874018  0.232000738914848 -0.054825284105115 -0.275287171650801 -0.385350273845533  0.183713321872465  0.383073079169659  0.088525025045692 -0.012087093648067  0.099070723265283    0.72475
 -0.254305380013898  0.202368600899810  0.153795317470946  0.016621432580906  0.561977753802537 -0.241737969996126 -0.418681329809783  0.347141341286589 -0.048431936352004  0.033930614565675    0.89552
 -0.132248047700514  0.122796465946834  0.182108778847029 -0.471475884022047  0.112652818364529  0.505005440198394  0.142377789964460 -0.241252541978164  0.163259377934336  0.073262476310937    0.81294
  0.011002921870181  0.167298545682485 -0.527563051242592  0.509964742424005  0.017618394109243  0.029536118524137 -0.367685722374173  0.149369922943973  0.043637311680084  0.056171702099663    0.85269
 -0.207519514269560 -0.376541330122980 -0.546975425162232  0.293102369660301 -0.207824023768022 -0.058728118743596  0.069815964510937 -0.021013698697091  0.039245175804741  0.075679460142549    0.78958
 -0.142283848834448 -0.241430918282018 -0.013291533081964 -0.186552989352302 -0.245558910669614 -0.355999709946344  0.334020728467171 -0.267839591351591  0.194722804390065  0.102787414065581    0.72234
  0.066885463956962  0.269792934989567 -0.288783164657427  0.314738055355934 -0.132515086045485  0.413764160705636  0.243513289493328 -0.196635061073749  0.169740678001192  0.103299918116558    0.75846
 -0.423143637679483 -0.313493250249668  0.244959224029204  0.332911286344798 -0.190739847525721  0.407340419841252  0.442107636543922 -0.115755058015721  0.094473862501879  0.046227199804760    0.93180
 -0.022409848513745 -0.121817230639687  0.313124898560601 -0.256591505514906  0.462017308080205  0.067122503808696 -0.225005130802691 -0.025959219202127 -0.272979745102437  0.099853232780738    0.72320
 -0.046385112251223 -0.647842748973784  0.152970768767918  0.081817799505171 -0.362778831318623 -0.581740036236410 -0.480412434041672  0.109360986150658  0.180309251749417  0.022848942942288    1.09419
  0.504887295672895  0.084810396924808  0.329456024725825 -0.090235397725270  0.073756766528788 -0.201717545776692 -0.461122670399361 -0.061176541323295  0.018422122899878  0.070379240604201    0.80102
  0.296782472766583  0.177243085428761  0.448223098201147 -0.058058507409313 -0.381764208314688  0.063094325672718  0.281017265306728 -0.193233155073183  0.174250704110146  0.078389047087350    0.78751
 -0.143368739954675  0.132555011276135  0.249136983256014  0.230640744015966  0.096691530119151 -0.472222765410040 -0.264373541377153  0.145111475638578  0.201847848534158  0.090103873411247    0.71932
  0.231762663548995  0.250608844730262 -0.219037917857093  0.241158968530657  0.602631387252055 -0.086101335743782 -0.042299520621274 -0.060424394937346 -0.332596482027644  0.065129958870236    0.84220
 -0.372284437052632  0.260243757093354 -0.449277561671021 -0.120658644006132  0.287580384030382 -0.027569505331967  0.226291426116034 -0.030974494744767  0.028095141282666  0.107217055176872    0.74776
 -0.213788158375743  0.334932664034672  0.403595151084661  0.081667149067491  0.277099447655970  0.047730243618881  0.392810139207981  0.029557036157513 -0.103220778128299  0.102199102693566    0.75653
  0.067191879542349 -0.635618190333793  0.210698008579658  0.396193482892665  0.202606469758559 -0.015938685704407 -0.293857481197565  0.062401060427422 -0.419940700646777  0.027209925441401    0.95801
 -0.500546047515775 -0.107908888868172  0.154315374630147 -0.286837232562276 -0.097103796057171 -0.483477689974808  0.459454314890771  0.384329456285738 -0.592076467585695  0.026442340421465    1.14927
 -0.046751160788730  0.307258745759493 -0.386445793862652 -0.232687068023214 -0.395491382793265 -0.263347860800245 -0.201756415430461  0.060765978621832  0.456395411336950  0.052787673196662    0.88235
  0.698537251573911 -0.099550357657683  0.146983223814757  0.049671168366912  0.724327862718584  0.402349950695324  0.371510634525038  0.744741191726459  0.670332033806732  0.016855763406993    1.53313
  0.613379839358123  0.035763416290235  0.476821277365803 -0.000508067639864  0.229678350071427  0.534955965998487 -0.058882113918009 -0.506621486785713 -0.128486353491380  0.019041603430636    1.10474
  0.276199701535092  0.096714231332539 -0.404342530595100 -0.337543673494799  0.155572056878488  0.256129098843107 -0.251758079372893 -0.172104057983551  0.053364672767733  0.104571318431900    0.74076
  0.282957476305660  0.007847837801334 -0.153019712683675  0.224122761522559 -0.070469294286631  0.018121750575861 -0.774447418992270  0.190150500565934 -0.154664234488519  0.035744164898536    0.90494
  0.461494157296201  0.087502646112969 -0.013988271235317 -0.527799552685412  0.024257718524061  0.283094598036353  0.244534877573665  0.013514937278389 -0.930325374275708  0.022277460755133    1.22704
 -0.351521525962909 -0.292818973886951 -0.041480909000800  0.408292822337825  0.273755731063122 -0.234567583386136  0.081320980209393  0.021149677050249 -0.097672619591226  0.103314847590640    0.72408
  0.037307461089619  0.270165572486454 -0.204268258246449 -0.021697523296355 -0.173738718088172 -0.612059046968594  0.017817369962557  0.331631629842959 -0.302584797987713  0.067844107463209    0.85043
  0.542150045181845  0.037121041173002 -0.183000541806364  0.094941539501639 -0.610933633143375 -0.063372369655531 -0.162648004565712  0.050202011895895 -0.016024750878371  0.046410691932376    0.86273
 -0.260872006077204  0.320657208547752  0.701107417323796 -0.304378694514896 -0.338552723361464 -0.132556341431024 -0.186855859244826  0.220502258254872  0.255243464365271  0.023817464539928    1.01782
 -0.076428689256967  0.450557639158651  0.099350802448255 -0.666311885387503  0.294432172180391 -0.309170262664759  0.071434327757503  0.046932497256596 -0.058188079559143  0.042145812618141    0.92502
  0.310545014009705 -0.690027924166955  0.014719867562731 -0.329317090903134 -0.232264326140955  0.220870747619428  0.097218571714567 -0.272910137506279 -0.472996191884045  0.046650414541949    1.04481
 -0.259671679472743 -0.330761245948054 -0.523341516242516 -0.360794618460232 -0.395413521183084  0.327357964829650  0.071152968271668 -0.203539310174344  0.301490291472976  0.024862643771972    0.99086
  0.822998492642846 -0.582883142107535 -0.128594606937350 -0.127642345997056  0.275583629800377  0.335855175063299  0.659126156841762  1.294227136655948  0.797588130171076  0.064168387694735    1.99606
  0.376563112416696 -0.428479978617845 -0.253357758975456 -0.060545018442546  0.141601659330397 -0.316827134588725 -0.089897673385727  0.021495422701278 -0.666386201367356  0.033020924222037    0.98300
  0.529088695498126 -0.493172500954710 -0.338083755489565  0.077446818475965  0.044871697821393  0.617611375946799  0.084643536256451 -0.299777665123460 -0.841649986958836  0.027087346349722    1.35363
  0.439778489969866 -0.493430492828493 -0.211389390997945 -0.249320729647837  0.474035145188944  0.164588566579459  0.608303584563593  1.146607713932273  0.571549853728303  0.055281541728813    1.67539
 -0.624358878428660  0.409405295283646  0.063103173438555  0.106439758212913 -0.335740584945193 -0.109600274762882 -0.521961588841369 -1.079277484059948 -0.588965178659123  0.035345280072736    1.57532
  0.664785740611990 -0.854456824570238 -0.321153797830149 -0.398999445136944  0.217362231402838  0.659911448565423  0.518954856303851 -0.453039249241817 -1.568206572179738 -0.016214208199439    2.20248
 -0.053706387361203  0.356590866997669 -0.201867893542751  0.532521551083370 -0.197794016883940 -0.392449045506758  0.761985398875385  0.144257487088349 -0.341611789913817  0.025256894634132    1.16861
  0.066379290942791 -0.829136779867573 -0.444896042627430 -0.547696283036833  0.454807571843746  0.559090717301573  0.451722954501993 -0.401766760203810 -1.223204544885243  0.010210743934394    1.88969
  0.192832524547279  0.120319200926375 -0.845731807860411 -0.290641617204373 -0.381162282302710 -0.052441159664172  0.268780743538044  0.083943475100199 -0.637356599811696  0.014936047351985    1.21858
  0.484895043489012 -0.139233067207059 -0.293081645349564  0.233753441001766  0.000291727610630 -0.467607280083154  0.046527877710733 -0.541506635982495  0.240459071483219  0.050924302725169    0.98332
  0.403417963564894 -0.399600349163605 -0.064688836052632 -0.076363425581290  0.112583651167473  0.379117395969421  0.599981019808601 -0.291454080459866 -0.952383914899045  0.038208093246810    1.35676
  0.411477401234328  0.326633110959788 -0.246524955716049 -0.261168100968041 -1.022074665009272  0.781107511111906 -0.210254249454404 -0.183439050844244  0.122086190846517  0.003665721341995    1.46714
 -0.144105850187949  0.431591116313020  0.149091228132837 -0.138558019607151  0.366024720831031  0.155471195106396 -0.510798321767023 -0.230127543255171  0.856160466427256  0.021646494661251    1.20561
 -0.648447163258316 -0.385292629585499  0.138693664362673 -0.434791694606948  0.173732425211603 -0.020828957628386 -0.016600903948944 -0.015716522428308  0.262996842485034  0.041163720609988    0.93676
 -0.388182678841429 -0.171241003358026 -0.088646974181830 -0.085244572185773 -0.303356440579583  0.286718346914790 -0.373932338644806  0.439087135586594 -0.189186715055573  0.089326165948050    0.85894
  0.875489949186839 -0.758305819796550  0.003972419462012  0.015515266294244  0.754222942595585  0.310442569920741  1.019325804307596  1.967735959639539  1.060270489575886  0.009096456428782    2.83587
 -0.079578961912687  0.419277102230537  0.515519011443652  0.667742085391882  0.404582861756328  0.318919181506954 -0.197277670082161 -0.413549847102163  0.088270006982275  0.012361852542168    1.17341
 -0.657131090537196  0.520117118297280  0.129364039463266  0.423865949839631 -0.234972439818822 -0.270048900893386 -0.072623478447801  0.373888379067221  1.018365156704424  0.019367009355060    1.48627
 -0.160762471482999 -0.747110644895575  0.148656673415799  0.184616260147175 -1.183214466673483 -0.655379920140045  0.598419607830000  0.952207836616303  0.056343320180900  0.001345584961730    1.93331
  0.936692001264761 -0.577629232809919 -0.126823432434136 -0.283932290363843  0.542572348727439  0.242535858439585  0.707005388572123  1.647799273486495  0.954656374981495  0.551703858724830    2.40571
 -0.031946293178099  0.302852980780638  0.372566160886761  0.127783694613589 -0.281466558036272  0.768293706467487 -0.469772450523366  0.584886115020216 -0.297850823619194  0.031631746353360    1.25254
  0.930951661152329 -0.602497339202085 -0.181787511131454 -0.201969671951853  0.549123667945892  0.215489090412882  0.646581273728239  1.614685981463244  0.912992537286370  0.547384977163777    2.34741
  0.941822891717382 -0.591330781501211 -0.161696051000529 -0.239962346248198  0.549870970930259  0.238901351711599  0.700217877204769  1.641435171081156  0.936897264444536 -1.224403692265116    2.39630
  1.002134751601636 -0.474729086182232 -0.273764147119337 -0.219249971544277  0.558320297955586  0.262029825765538  0.808689619211828  1.685095120714710  0.907162679447832  0.080244668662224    2.45957
  0.461299430444348  0.038822197348126  0.507854140205504  0.053778550604123 -0.047473732965349 -0.464669873188028  0.325220708781134  0.522695601059455 -0.450122914399782  0.024522705519227    1.12910
  0.576198284520219 -0.468622991121668  0.011067716442936 -0.050465901487661  0.807373707654717 -1.193806540995725  1.199180392506154 -1.824569379617748  1.136163867937309  0.478512906760943    2.94776
  0.944497757480799 -0.647637910343904 -0.186384182476503 -0.200103191580717  0.561393933659897 -0.397411267696571  0.951997606569417  0.677219518807429  1.079221190657802  0.006043800994347    2.09500
  0.971466440305722  0.130567226308036 -0.493927538744188 -0.798617037778645  0.060883187275827 -0.682096016536048  1.147063921428193 -1.303744938024967  0.275179464813983  0.002143798299695    2.32438
 -0.731427643173054  0.744115142793275 -0.067045271975823  0.703526653308663 -0.497454714250300  0.676722224661645 -0.189441795401515  1.809958407445103 -1.646544332433512  0.001579140937005    2.88383
  1.850766943018943 -1.411065457035187 -0.206316271877579 -0.723395499318855  1.248150567450839  0.756491648745252  1.135967167660330  2.216801841596788  0.759356502624199  0.001020953647671    3.85924
  0.066810222838749 -0.737690375936148 -0.016712444809426  0.143514580031997  0.443841992704219  0.784505974053119 -0.974142186654040 -0.844640487211100  1.259826971632915  0.073727662512116    2.15209
 -0.900837402684535  1.253685328197460 -0.502842113654001 -0.645982186290934 -0.083572642152455  1.277163406443945 -1.343046381946210  1.706951960200328 -0.777001455910095  0.000902872386821    3.16428
  0.410391790250504  1.366237748083300 -1.917395187022893  1.298116397300806  1.945589552864907 -2.709051554445487 -0.447711738526372 -0.725863927941834  2.153165163450435  0.000048529801031    4.88715
  0.099924218106294 -0.616975340215337  0.069256465732740  0.085582162151238  0.181138293671416  0.750662311803613 -0.854893659288584 -0.758217005025336  1.207999529408095  0.124752168956701    1.94012
 -0.407349631346608  0.754980868217144  1.036325716462100  0.438865119503228 -0.859134293533712 -1.123761570218998 -0.427248299502851 -1.279595597952564 -2.054180083923591  0.000696128022973    3.16907
  0.534889799265325 -0.407991855508753  0.180158681681315 -0.173017780489883  0.736085986304838 -1.180943897202869  0.867990043668117 -1.414705544761618  0.761367278405635  0.024326862779091    2.40539
  0.584245141664091 -0.471445984952216  0.015561310589407 -0.054799018299745  0.810945167736567 -1.211763226893127  1.204882126204670 -1.835321540851318  1.142731600256770 -0.480287128929958    2.96965
  0.620807573247821 -0.091370765477604  0.228621030111422  0.004356185281978  0.552834600350081 -1.828534340803206  1.424667242895834 -2.025516956317658  1.727165780165015  0.001713354774871    3.63465
  0.091776953755547 -0.698898931257033  0.032516628761025  0.110475903839316  0.320398211914378  0.809442467951724 -0.956218707340748 -0.844738300976353  1.306675277488878 -0.157795362712431    2.14554
>> # evaluating formula 1 with 96 points
# r10_96_4Sa.txt:3 formula 1   : problem  S, 10_96_4  (d=10 n=96 o=4 plus 2/2002 of order 5) quality NO (2 negative weights, stability factor 1.372597)
S 10 dimensions, degree 4, asymmetric 96 point rule with points at 96 distinct radii (2 negative weights, stability factor 1.372597)
#                 x1                  x2                  x3                  x4                  x5                  x6                  x7                  x8                  x9                  x10              Weight     Radius
  -2.474071604289242   0.000000000000000  -0.000000000000000  -0.000000000000000  -0.000000000000000  -0.000000000000000  -0.000000000000001  -0.000000000000000   0.000000000000001  -0.000000000000000  -0.011258190935092    2.47407
  -0.244913135138374   1.491053361992398  -0.000000000000000   0.000000000000000  -0.000000000000000  -0.000000000000000   0.000000000000000  -0.000000000000000  -0.000000000000000   0.000000000000000   0.009053156810479    1.51103
  -2.251075815131959   1.356599578301674  -1.355152384308668   0.000000000000000  -0.000000000000000  -0.000000000000000   0.000000000000000  -0.000000000000000  -0.000000000000000   0.000000000000000   0.000715639202984    2.95705
   1.160031162319238  -0.550498209020169  -0.234546945814660  -0.930083680425474   0.000000000000000   0.000000000000000  -0.000000000000000  -0.000000000000000   0.000000000000000  -0.000000000000000   0.003724506734404    1.60274
   0.295117852857137  -1.560156583492331   0.613957312341779  -0.114159538513604   0.800353086864456   0.000000000000000  -0.000000000000000   0.000000000000000   0.000000000000000  -0.000000000000000   0.010059775757221    1.88460
   0.043197538323974   0.964488321589365  -0.729852147276318  -0.243896043301002  -0.282129569527651  -0.579226026623510  -0.000000000000000   0.000000000000000   0.000000000000000  -0.000000000000000   0.010936008101944    1.39261
  -0.367661113320314   0.057645685261011  -0.186769367262709   0.056910201659732  -0.328205448469197   0.012620807040815   0.527991322572694  -0.000000000000000   0.000000000000000  -0.000000000000000   0.039480644280892    0.75051
   0.102035265711125  -0.111322857910637   0.001274403867456  -0.109491404763653  -0.327470820975489  -0.137259942566995   0.365397480311033  -0.589481946005498   0.000000000000000  -0.000000000000000   0.037564662505430    0.80117
   0.952499524559120   0.234583708042424   0.170516441497264  -0.078734807041510   0.045467751189185   0.154637343900610   0.150725753186825  -0.238933929444493  -0.395152713539503   0.000000000000000   0.022907832582871    1.12227
  -1.060722884111918  -0.208825694213196  -0.232765662726963  -0.022664195953343  -0.202897729926618   0.080523012293583  -0.043036913645360  -0.547010053167494   0.154976983860881  -0.291443079797291   0.010140645018725    1.29658
  -0.348290949976191   0.258720136871493   0.142199279523541  -0.026209515413791   0.241077815866373   0.108643462613221   0.314437385993308   0.054934133609238  -0.461476058569164   0.451580936958880   0.025915114742592    0.89322
  -0.010295713920031   0.672511595501438  -0.544209447925868   0.336453536998832  -0.157418889096941   0.005091728946979  -0.603524458761208  -0.332518254421248  -0.870273323959570  -0.026328169347227   0.004320170630721    1.45583
  -1.267258161560182  -0.276980413876196  -0.175965375037317   0.295197551043663  -0.205880583618483   0.339536002781508   0.053213097500941   0.151537088922213  -0.124608092381660   0.179800365464463   0.013268686679462    1.42551
   0.039384718917716   0.681014470640060  -0.340049241647138   0.589577924124369  -0.182149216259141  -0.128839428703431   0.514459846334816  -0.001611441199295  -0.156771040151556  -0.016675190851392   0.015832557380051    1.12600
  -0.015334332854141  -0.233797798915823  -0.353527331881210  -0.207109528846893  -0.393374335723132  -0.159609376062561  -0.149328030057960   0.036839073064468   0.524207453924948   0.485697049137951   0.023565187250535    0.96816
   0.120328616188976   0.063283632072121   0.404026220483908   0.109896761349728  -0.415561266283077  -0.649018998760921  -0.003547904744681  -0.092179136276297  -0.301364896496714   0.198405553399389   0.024828337744853    0.96250
  -0.166315486578712   0.007539502363949   0.712080895306437  -0.347645430115690  -0.123215192608403   0.027451219117764   0.382908331473249  -0.123853267246678  -0.050728043543455  -0.089384735323337   0.027582123546744    0.91874
  -2.007706376769214   0.010667351328546   0.112036584578176  -0.062835022522455  -0.096300682421701  -0.232202333887085  -0.034156185519564  -0.081775851022427  -0.027917861948277   0.057439862792415   0.013867965815695    2.03042
   0.033389453290279  -0.667400686493742   0.331121246707593  -0.373505360291380  -0.183610921282358   0.306991920173611   0.109798701778051   0.262842632414592  -0.036341328690840   0.094547788986699   0.029751054694111    0.95658
  -0.242183401870936   0.716227134491370  -0.352377302624646   0.444200988273638  -0.534905839044421  -0.142800315890437  -0.415606927327176   0.019826922720370   0.458337333069570  -0.384703697878805   0.010009638019780    1.31561
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  -0.116697530573291  -0.417582276138564   0.289030239517643   0.235776691737583  -0.293163072339695  -0.154382616331377   0.009598215264163  -0.071456659097555   0.520827292239712  -0.168900734551302   0.032965410992447    0.86133
  -0.044808542381702  -0.134532419223514   0.300094879464668  -0.128227425190965   0.184018865613020   0.223627219659097  -0.464910475593483   0.370450222481198   0.617437167847231  -0.447386073697018   0.013563411916237    1.07016
  -0.003004821570124   0.217066261098650   0.053032007694979  -0.140135794281428   0.083442759465243  -0.321777524073342  -0.349498855350716  -0.151509909543214  -0.127522492439357  -0.463979117962329   0.051342458036943    0.74614
   0.202533177642998   0.265141169034018  -0.127926935117690   0.270434492715001   0.689531501771790  -0.006886240959815   0.244369241807329   0.438922568671569   0.075636167209580  -0.075301916110458   0.020737908075828    0.96958
   0.049667669439184   0.275674334469669  -0.080132365341599  -0.695590509889847   0.143649587494170  -0.013045985195244   0.292772872118823  -0.525337733300360   0.080021946266942   0.181694734366854   0.019099562997389    0.99531
   0.009847271183193   0.033305745886395   0.299109462619743  -0.436618760917346   0.042133255317517  -0.454669606198576  -0.236593064133283   0.191502811505045   0.077002228701213   0.319998069723944   0.041592705166294    0.83114
  -0.319912394908240   2.094218046315111  -0.952778322747459   0.371546585374925  -0.696082604265772   0.058448662251713  -0.168309913149782   0.038330643511740   0.160179773625494   0.223138472579959   0.401068879928751    2.47530
  -0.353407566398426   2.040444678242922  -0.889112485994542   0.398307821394904  -0.718423740140032  -0.033910627845492  -0.203025179939351   0.168986191417597   0.086312154780162   0.254853437182240   0.064832667890558    2.42836
  -0.330721044712508   2.106132880951462  -0.950088833617040   0.377426638050921  -0.708161071434033   0.041472058552787  -0.173809918041482   0.048667908125274   0.150573274130507   0.232403645412673  -0.463833611460594    2.49054

>> # evaluating formula 1 with 96 points
# r10_96_4E2ag.txt:3 formula 1   : problem E2, 10_96_4  (d=10 n=96 o=4 plus 0/2002 of order 5) quality P
# evaluating formula 2 with 96 points
# r10_96_4E2ag.txt:102 formula 2   : problem  G, 10_96_4  (d=10 n=96 o=4 plus 0/2002 of order 5) quality P
E2 10 dimensions, degree 4, asymmetric 96 point rule with points at 96 distinct radii
#                 x1                  x2                  x3                  x4                  x5                  x6                  x7                  x8                  x9                  x10              Weight     Radius
  -1.064039763119015   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000  16.482739297156982    1.06404
   0.481290502434513  -1.546555080735425  -0.000000000000000  -0.000000000000000   0.000000000000000  -0.000000000000000  -0.000000000000000   0.000000000000000  -0.000000000000000  -0.000000000000000  10.362398811648553    1.61971
   0.038121167737312  -0.473079883426187   1.672496824634022   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000001  -0.000000000000000   0.000000000000000   0.000000000000000   8.979786648562458    1.73853
   0.637310139510987   0.245845560147705  -0.848295958395840   1.394229950060948  -0.000000000000000   0.000000000000000   0.000000000000000  -0.000000000000000   0.000000000000000  -0.000000000000000   7.463285969983167    1.76921
   0.588526587331599   0.150426840688415  -0.061996131598909  -0.661070384880104   1.570549213904574   0.000000000000000   0.000000000000000   0.000000000000000  -0.000000000000000   0.000000000000000   6.556832472791879    1.81010
  -0.349437562671753  -0.439611449682297  -0.589557848096876   0.217997175745575   0.172587570011079  -1.616582223029459   0.000000000000000  -0.000000000000000   0.000000000000000   0.000000000000000   6.911591698139998    1.83128
  -0.490885992735187   0.416658584006407   0.531751656270270   0.533698726388042  -0.337874711575387   0.627062760233795  -1.366897002133831   0.000000000000000   0.000000000000000   0.000000000000000   7.015835409324611    1.83247
  -0.012313431698968   0.605840722251870  -0.758452831656091  -1.065756009728143   0.265171190765119   0.827633808835633   0.146772636903308   0.796369160809532  -0.000000000000000   0.000000000000000   5.846539309369049    1.86797
   0.243423561528618   1.087810342796267   0.244163107123329   0.088747926729941  -0.625781053133631  -1.022862419839925   0.674072592092577   0.702222706508452  -0.384858688758601   0.000000000000000   5.917278091017409    1.96049
   1.399086503308206   0.144558658748712   0.493735795230337  -0.349932778113803  -0.474626162423738  -0.336402088354941  -0.113347397354096  -0.496037368396553  -0.115235951532930   0.995562413370237   5.892228633257950    1.98654
  -0.503060760934478   1.048947187476385  -0.673191491287202   0.127166628687989  -0.122497519984228  -0.647163731034475   0.763642581775872  -1.057237868057467  -0.153414679934835   0.056555223955416   4.822954885923378    1.99604
   0.668670073877720   0.068695679066274   0.296223379123361  -0.661419260442233  -0.078015446774846  -0.071563725735107   0.949162211633239  -0.837988812592935  -0.422910543558415  -1.108848774404342   6.269863202577839    1.99995
  -0.234789391066492   0.481089704858354   0.440730833708462  -0.349084781719889   0.712136025591673  -1.049994875386891  -0.673463224490087  -0.759070684123845   0.278070228086039  -0.829219463189554   5.561095496490129    2.00174
   0.508943999259812  -0.151642843828141   0.050121618421068   0.998376621298537  -0.631117620293353  -0.334513034116710  -0.286131765311638  -0.273568829125595  -1.445577020979008  -0.315253526483606   5.364480451886298    2.03403
   0.857858888187507   0.819137040120359  -0.923141923434540  -0.335322718810957  -0.562874333127317  -0.316686470856382  -0.922172522796328  -0.308944461596827   0.060998149779482  -0.727239123238836   5.153155728202016    2.06570
  -0.348640616065764   0.046751885827911  -0.216611546358586   0.958872697785367  -1.193120867540881  -0.294356604415747  -0.361233126750066  -0.661183521319933   0.575170819414084   0.952879385007950   4.960203912990991    2.09922
  -0.447868267365849  -0.055485230330898  -0.308001777402784   0.050409774005278   0.139130339045456   0.031068586878986   1.847699852404414   0.786920132680600   0.012992282896015  -0.287768931733302   4.679276448619807    2.10656
   0.753945784689135  -0.039303888586772   0.491012684717545  -0.418127519606451   0.004831917546584  -0.451276208171511   0.498527742164853   1.122291326022631   1.022919617800444  -0.836112989692796   4.832220138465215    2.10786
   0.421663766372007  -0.543184505635180  -1.196283580104273   0.205903350056625   0.839528350947286   0.569907980273283  -0.556641038582059   0.660159442463087   0.824714571163775   0.314764725126334   4.557745739224606    2.12152
   0.445080121998888  -0.603303112248679  -0.558308619573187  -1.031274656825559  -0.883937930070172  -0.845053140314106  -0.029406696567604   0.712575053776127  -0.731773259033129  -0.239444714497663   4.627273842558250    2.12937
  -0.531248280387387  -0.519003428072006   0.451302676343577  -0.149765078603653  -0.684600282491560   0.024335111721612   0.068311574014043   0.053177544117421  -1.125263602504966   1.429369090142550   4.517205194980041    2.13630
   0.341685269232404   0.547208088075360  -0.647043627004142   0.164977122668019   0.689436146569448  -0.627647872354085  -1.168655633830133  -0.242244954588739  -0.980199107455541   0.672575663861611   4.722984096276903    2.13750
  -0.072616130268679   0.261681176625337   0.619780164532632  -0.185158512553283   0.671266520587693   0.441893584367573  -0.772575705997747  -0.608679906186401   1.158655795082819   1.115242260641404   4.441726456220892    2.16602
  -0.516362896490288   0.990248238373252  -0.796850611920468  -0.002430215434821  -0.898109434453240   0.228989110874359  -0.329037502301353   0.970451923064905   0.871125308559907  -0.457500183893259   4.229519181686468    2.18161
  -0.086159561114867  -0.749644632546481  -0.199706190653093   0.016092243156291  -0.962573227524834   0.059927776498911  -0.357787705169578  -1.101613362587142   0.153921112624673  -1.381101007127580   3.546258446209667    2.19371
  -0.238079961366058   0.747244001326729   0.065622489631601  -1.114543331784379  -0.958951281930830   0.846781925538687  -0.238956978056472  -1.048815320472544  -0.240035830888381   0.382032970975036   4.511129137617266    2.20429
  -0.133001690947087  -0.200121961122286   0.548894083656037   1.440954842566304   0.138280720251353   0.968742567406013   0.322190016980324   0.947902746734255   0.749708810796885   0.038512412457686   3.930361400209747    2.22684
   0.084928472174212   0.957703406298956   0.641797901818515   0.824067264937653  -0.377157785509087  -0.487516168405539   0.132743124034352  -0.726832248286030   1.290245261692121  -0.628316549776367   3.444065632613767    2.23623
  -1.252159609674184   0.886738469069563  -0.234393837006149   0.041476148531746   0.987383230054162   0.554129642822254  -0.010402921085348   0.115409828590416  -0.922388909406964   0.670083313354017   3.609152475721553    2.23743
   1.409616474843895   1.244776198917224  -0.073227988722714   0.184907318146952   0.383080362980360   0.365232812878141   0.765019174381889  -0.335219882121892   0.698310201456149   0.119754359463433   3.679319295113269    2.24851
   0.932556638800338   0.411527204038142   0.007675313975094  -0.458879225585456  -0.187750293837628   0.643723845848255  -0.660406520932585   1.336656662163313  -0.672830648019731   0.833230736676582   3.318676329300485    2.25145
  -0.015087552286049  -0.726563241626451   0.242421544779146   0.479760012796196   0.854502371101830   0.266864772008811   0.618946419693252   1.115602172539511  -1.380934142975072  -0.062178547822339   3.474481052022977    2.27089
  -0.091912036260564   0.066794032996556   0.558653249405015  -0.431101591327080  -0.598436404481706   0.458931514698488   0.286065319597261   1.139694032916200   0.970354992255374   1.335765410038728   3.603830324913226    2.27732
  -0.671662604447238  -0.308126141788102   0.831974921337456   0.796053533169576  -0.421040950928041   1.049945141765920   0.567442479669506  -1.309226372425997   0.052023895963713  -0.353625935353875   3.058211405655527    2.30552
  -0.754689420496244  -0.868084526127985  -0.022419097258770  -0.477076138929206  -0.399519022228038   0.063823795341350  -0.919303155361911  -0.038379111424501   1.565955966609703  -0.553108525643963   3.461934214588307    2.30644
   1.069621278077490  -0.131615282386242  -0.275805486446007   0.106367026759982  -0.213490389231849   1.152673869119926   0.333338330583376   0.810784296708726  -0.342565451096522  -1.374164039736611   3.353164149806900    2.32319
   0.598230076943904  -0.734601231902066  -0.730428420279826  -0.049605762630062   0.131911592937279  -0.156720141825760  -0.237397551154925  -1.903781229016710   0.122057213692122   0.497719158007267   3.663781293586753    2.32784
  -0.815393084139381   0.730529365810754  -0.222014761925463   0.611916626359502   1.343978384406174  -0.469593240658222  -0.031970138220509   0.759222249023749   1.106848633389016  -0.037941034784595   3.466194416259452    2.33518
   0.111957757548044   0.606933385196555  -0.636495355849268  -0.203469444266203   0.849948640251987   1.299001462904733  -0.874024881904883  -0.950645629734074   0.175060433676023  -0.733146781359409   3.204928099458759    2.33945
  -0.174437276965594  -0.408207096253848  -0.279478605435877   0.133204004869064   0.428670397879139  -0.246673711045867  -1.346025812816895   1.097628100436036  -0.272753813401504  -1.366895850797611   3.737477082114491    2.34454
  -0.585148866376819   0.345586520637350  -0.761521303053562   0.015122273770289   0.038870108859070   0.951202827645073   1.056815832554442  -0.746179854933799   1.380385088748510  -0.077613693456599   3.083576534529264    2.35232
   0.767189190437354   1.021944137579413   1.029440294457774   0.619485618418741   0.892307532717885   0.059670962141485  -0.640558134875654   1.103849017865811  -0.186955923003990  -0.122922983162254   3.031408069562009    2.35692
  -0.087185668301108   1.013704212944058   0.383481281635093   0.572817864464135  -1.232977363808094   1.015586976209674   0.943176740373717   0.353559081880323  -0.646456041325499   0.361383997892734   3.089423873772167    2.37173
   0.990922161012009  -0.136864152702431   0.793841552927795   0.290606377359113   0.608214381043853   1.505499192809639  -0.103650620877805  -0.509457579079931  -0.991356254097815   0.173301284705626   3.037310339097390    2.37379
  -0.203349567079126   0.978259869530526   0.563901654226913  -1.121614263529208   0.060146506582924  -0.106403253739404  -0.105107770413073   0.426677365719242  -1.599377617014197  -0.549940284297154   2.831391272066886    2.37546
  -0.402053047247066  -0.916675344024727  -1.511022230157524  -0.447155517440331   0.952914084400098  -0.151826357702880   0.083061954957471  -0.156842526182136  -0.934740290552287  -0.622377325926426   2.762703346416042    2.38930
  -0.066143894816894  -0.453571267864835  -0.373812945371860   0.798918765429517   0.596854357650478   1.122359859112731   0.476507363368143  -0.472356883008105  -0.112109196741532   1.632660705993004   2.873099663022050    2.39424
  -0.305112884802249   0.520664963290948  -1.244087329141215  -0.353593072892358   0.147388757484809  -0.601925187029906   0.722526473876141   0.072730609845129   0.397294783048721   1.634894420712596   2.799807993876574    2.40397
  -0.881626486174684  -0.690195312272676   0.533991625688092  -0.618452551914778  -1.273756504385559   0.842064059477859   0.188403882122393   0.765986604531875  -0.558047537124605  -0.783458176247168   3.178379518355820    2.40837
  -0.407211316854068  -0.001846749274915   0.712979851891870  -1.127751302113427  -1.312533808019179  -0.817996399804320   0.838638509220567  -0.405375805020513   0.806037954026473   0.123139272291636   3.145642521973285    2.42288
  -0.879679381391864  -0.527520521391088  -1.389523003862712   0.584283958948547  -0.487420123526532   1.378651170731331   0.127688587122323  -0.230822952913786  -0.517270519569628  -0.369038911119017   2.659505825433608    2.43637
  -0.539213005936716   1.227705398218883  -0.027440843552218   1.006803369505086   0.402456745021701   0.509053468388460   0.164918711710107  -0.092786824790788  -0.704906860988328  -1.473877260723640   2.954141576370441    2.43691
  -0.736195543261196  -0.508941069634337  -1.153106059377689  -1.204818598632029  -0.330684418133604  -0.078355156917582  -1.178158552194186  -0.076445204403960   0.049071052879213   0.945348259472858   2.890443846101472    2.44698
  -0.146767531869172   0.932983171079497   1.269250203155981  -0.559005329107411   0.798322972888124   0.593021815430117   1.375418047990545   0.003087302862999  -0.022777082417853   0.562765241031972   2.665088010804535    2.45224
   1.102806627176388  -0.327281091974176   0.166420792899362  -0.105239061907823  -0.927867023964928   1.403959790981404  -0.077689599692996  -0.177653138795108   1.337366199385454  -0.049412783515475   2.684762220761276    2.45412
   0.107799398507197  -0.811393403500788   0.664029499839740   0.285989792705829   0.607436221767775  -0.994405861372889   1.008705905709763  -0.583810950478746   1.382269539286830   0.603943642915558   2.714672527998709    2.48682
  -1.091733707844049   0.653949363592295   0.929224732578037  -0.336830670792194  -0.553234762928902  -1.027325039333714  -1.236033034584672   0.812421802899987  -0.204282530023591   0.432328332494140   2.226408981242221    2.52475
   0.127858023671492  -0.058200009392209  -0.173641164361539   1.083658065877268   1.704907258154687  -0.180531170807775   1.056173931721749  -0.972448694008069  -0.432216093564153  -0.151550368829035   2.274590554775639    2.53662
   0.896513576634360  -0.444146405091778   0.815955304047731  -1.773988482501318   0.153047987071640   0.200406405023809  -1.229860786458240   0.148198797274765   0.257965666986354  -0.317316382943734   2.504404611428968    2.56499
   1.493270708952994  -0.506598761004537  -0.640612987160433   0.296850617625834   0.454788035982429  -0.386781857028994   1.017940354699958   1.089252375236273  -0.128030806077599   1.022556533524702   2.083795579498678    2.57413
   0.193110550001636  -1.181379975850657  -0.071164077103572  -1.493130582569284   0.106108826494541   1.200324417527054   1.112861139614300  -0.193652451273447   0.048348926838875   0.524029269635180   2.528898985905707    2.58310
  -1.552476337057190  -0.585843083890886   0.458735423608639  -1.069176578753061   0.911274771853943  -0.037534716784689   0.106038133291120  -1.323581554439756   0.139598045220720   0.389517505944342   2.063183777753424    2.62166
  -0.165021759319171   0.529740018810095   0.953920957298520   1.496715046940785   0.405492757354827  -1.103556347504849   0.446058993537512   0.307273824338754  -0.226476065607097   1.301040096344758   2.140940443342885    2.62252
   0.590599687521435  -0.368329265318883  -1.384997054095641  -0.137495774693930  -1.928283538748136  -0.046266826491799   0.787501946353452   0.149132869301445   0.364429933848607   0.273201630981569   2.032132593475224    2.64421
   0.986048650732083   0.008903011443164  -0.268119092251545   0.411528642507169  -0.353383487712185  -1.358570058645759  -1.224957240603595   0.700204959922521   1.310007341659787   0.645806985985849   2.026055872245626    2.70337
  -0.370035916991648  -1.092095367175353   0.484749033691895   0.036953777102523   1.494160831269177   0.804731537762880   0.506470818322978  -0.110356781319063   0.828173496297395  -1.439292628094765   1.906339898186527    2.73353
  -0.841025373744767  -0.667837361355918   0.492684028873573  -1.268218724248052   0.943843458690826  -0.944216680936182   0.154110760885516   1.708109631192032   0.235129462246844   0.363592671666995   1.730542453334802    2.81349
   0.863109281311006   0.526679550342116  -1.536299148519813  -0.439793953946544  -0.216216068668457   0.657478618736021   0.881771171750108  -0.585493000205033  -1.620962636296004   0.364663875540461   1.668842122736711    2.81706
  -0.381600393424879  -0.902421750083543   0.484377172351190  -0.838597875639669   0.487071410048817   0.486712628540860  -1.169469080626992  -0.931896219313716  -1.747779996200002  -0.626272740108799   1.583194186402574    2.83814
  -0.751427239070526  -0.273429219474040   0.384255495230895   1.371975859362998  -1.146786264744684  -0.997717863919747   0.503436635092382   0.554658862229238   0.434461513717202  -1.549935589387689   1.408355715711149    2.85168
  -1.292494784646643  -1.122655423233180   0.113435591661632   1.785186343997027   0.748382218167931  -0.242378435456123  -1.007046272971559  -0.621468444568098  -0.269912880836566  -0.053405645894102   1.621881276101417    2.86802
   0.373927410426947  -0.712458013983301  -1.617376614092203   0.969153156157966   0.011496341052503  -0.659727366576085   0.830493579026508  -0.136330105685734   0.862712766128297  -1.488004921178099   1.313064883249107    2.88179
   0.396148120591945  -1.260844456890424   0.766832064031085   1.095732203568046  -1.318888935282198  -0.448330591995646  -0.631859593554325   1.565825871122992   0.090658948129070   0.145678345918099   1.300361288900271    2.89072
   1.615660286331453  -0.410252679317069   0.692639967936340   0.399713628000642   0.806250200222099  -1.667061411924802   0.163826034662105   0.073667157532672  -0.727578485701078  -0.995138049488626   1.331492869338862    2.89815
  -1.320159688046230  -0.285195664899462   1.535201180690697   0.384397728297313   0.515860676728795  -0.997008759311736   0.585021694063857   0.324632747907871  -0.910117537235115  -1.240409086251862   1.206463508326265    2.89887
   0.352583734639928  -0.067938940957347   0.418146687915708  -1.478444522217066   0.846029935380348  -1.336669426246667   0.865614932763703  -0.401084848617243  -1.130529698007894   1.113694511469892   1.364902774021572    2.90183
   0.594422558708682  -1.031720263885267  -0.707945646958749   0.398299687948123  -1.100819037175454   1.316436026720503  -1.666933335422718   0.115678554910070  -0.603862589085137   0.626240630403114   1.323881663204194    2.92768
  -0.954829524309404  -1.003605231488875  -0.075105098715185   0.256304081506511  -0.587436478962594  -0.761473346335454   1.593525808040944  -1.028783889607330  -1.431056446676800   0.237580033355900   1.277092653034933    2.93552
  -1.457558845947289   0.311332522853192  -0.884039645894416  -1.621281049612656   0.147365107089345  -0.420439056157260   0.601722764128560   0.030498492115336   0.177323711823873  -1.553059984656775   1.322839573551111    2.93878
  -1.543875366474265  -1.798662018119288  -0.604491506832789   0.504355430204059  -0.465972295442381  -0.168304846200260   0.662816153505313   0.656580770227263   0.908219087027345   0.722306651455643   1.257075526694155    2.94974
   0.940596538083672  -0.207964874770003  -1.252290267261182  -1.589637516691917   0.454306556978252  -0.817523053233543   0.438732578451598  -0.578639833862500   1.599687249541514  -0.233749087424251   1.249054818686892    3.00647
   1.499279792363121  -0.607862210637759   0.669301330391160   1.443919308553367   0.759217460585910   0.060501602445298  -1.278835982090376  -0.851580120383019   0.896157484702287  -0.832125888113285   1.216304341247231    3.09619
   0.045612574193791  -1.405796299664528   0.672196000434031   0.199780028443101   1.524960303402302  -0.555183298200510  -1.368855580086112   0.461600251963358  -0.274578768142352   1.527305806330204   1.104267068092351    3.09818
  -0.121087550777240   2.147164922773494   0.125923337530310  -1.550345905872241   0.197111289306914  -0.971097623581980  -0.564622765933440  -0.002428410061325   0.844476674027835   0.834636748110599   0.982040179728510    3.12328
   1.269000563985481  -0.894540220498349   0.724929245158538   1.261168701265921  -1.167436980441637   0.001486517625081   1.928020627289328  -0.581736972793342   0.043527940238572   0.234993695611444   0.986595825516845    3.16265
  -0.998154912209719   0.159121283625018  -1.436264675095717   1.079206352226228  -0.424891477598246  -0.357718022286595  -0.255144056298029   2.033243859892377  -1.043735614143661   0.563570969744077   1.119833042864878    3.18808
   1.169098406861780   0.964576871407323   1.423846381006114   0.151580112283481  -2.028801948532445   0.075910615955846  -0.907107204657693   0.007374924863764  -0.241078032020276  -0.968821519326245   0.927996401091501    3.20764
  -0.038126834981785   1.439684329963046   1.470434698013179   0.682718401053196   0.278445216698312  -0.445644028578662  -0.362346874873962  -2.145791871055413  -0.992001788472750   0.609252625309195   0.884896349544344    3.32709
  -0.623938809629234   1.538532118173488   1.577556177956103  -1.086125843348121   0.159420979138566   1.247350989129256  -0.026063602095279   0.287832472738543   1.094848555879812  -1.510050092076961   0.814625450324082    3.40125
  -0.120984388639277  -1.217697012018590   1.119131628644113  -0.503409145150690  -1.381512142580385  -2.126903650768848  -1.468110163910303  -1.368952854955855  -0.275167546489779   0.123246817334355   0.540249567056094    3.68183
  -1.673379635855015  -0.783721156483262   0.727341313969274  -0.589442147196620   1.136490382731701   2.641962582600381  -0.974778608650669   1.527693019548999   0.003223730839388   0.255215782874065   0.433684104444119    3.98894
  -2.085081851174209   1.055784245132493  -1.322435132652821   0.094526971912360  -2.027226347629931  -1.076091550330471  -0.953615864817949  -0.929077243294305  -1.660135043358673  -0.843938186401660   0.333472147582003    4.21052
   0.337871530557270   3.296026469795223  -0.959717339146781   1.534944913684706  -0.266643808371328   1.649270398216641  -1.086742436016721   0.062690669183125   0.199378027611055   1.961966442890251   0.208012341153754    4.70322
   1.214144945217617   3.287361433855106  -3.053690144252095  -0.075000173515161   2.450436269699139  -2.260734956702307   1.196452704485166   2.160754118758176  -1.173779000135877  -2.163708050229265   0.053857565403476    6.69976
  -3.228772751154547   1.369522919422421  -4.227932747211863   2.107597005619273   1.542783091434428  -0.812398666145836  -3.096145857678958  -2.940453405521338   2.669281262669844  -0.211689289303595   0.026970944637336    7.94106
  -8.232760072245810   3.186682796893730   3.409454180041581   1.741604088429609  -1.954119550518665  -0.152378189108158   2.350599251991209   0.231945640060186   2.512773872734346   1.823378034140441   0.008539832757489   10.56648

# G_n 10 dimensions, degree 4, asymmetric 96 point rule with points at 96 distinct radii
#                 x1                  x2                  x3                  x4                  x5                  x6                  x7                  x8                  x9                  x10              Weight     Radius
  -1.504779463907167   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.053861696213177    1.50478
   0.680647555984249  -2.187159170133055   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.033861870091525    2.29062
   0.053911472427606  -0.669035987227196   2.365267692423370   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.029343820332549    2.45866
   0.901292642734327   0.347678125410095  -1.199671649269680   1.971738904442956   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.024388254550421    2.50203
   0.832302281621501   0.212735678246493  -0.087675770121844  -0.934894703980645   2.221091998678252   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.021426178768181    2.55987
  -0.494179340332992  -0.621704474315202  -0.833760704582099   0.308294562498423   0.244075682206684  -2.286192504499509   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.022585448066811    2.58982
  -0.694217628505082   0.589244220381030   0.752010404111772   0.754763977079217  -0.477826999492810   0.886800659981741  -1.933084278784789   0.000000000000000   0.000000000000000   0.000000000000000   0.022926091876238    2.59150
  -0.017413822108035   0.856788166046506  -1.072614280948322  -1.507206603138172   0.375008694330655   1.170450957133854   0.207567853693920   1.126236067872521   0.000000000000000   0.000000000000000   0.019105108592839    2.64171
   0.344252902114933   1.538396140072207   0.345298777524967   0.125508521613976  -0.884988052417699  -1.446545906579385   0.953282601761310   0.993092875350594  -0.544272377239539   0.000000000000000   0.019336266211663    2.77256
   1.978607107911615   0.204436815760893   0.698247857843808  -0.494879680727435  -0.671222755956746  -0.475744395762190  -0.160297426597855  -0.701502773830265  -0.162968245530838   1.407937867177079   0.019254410504318    2.80939
  -0.711435350811268   1.483435338742217  -0.952036537052530   0.179840770971818  -0.173237654118764  -0.915227725504928   1.079953695953044  -1.495160131661287  -0.216961121030971   0.079981164740797   0.015760276628307    2.82283
   0.945642287230891   0.097150361011954   0.418923120248244  -0.935388088532188  -0.110330502903584  -0.101206391508537   1.342318072583769  -1.185095143885855  -0.598085826370888  -1.568148975383405   0.020488431020302    2.82836
  -0.332042341147553   0.680363585328754   0.623287522386508  -0.493680432726319   1.007112425646218  -1.484916993194389  -0.952420825833397  -1.073488056287765   0.393250687851456  -1.172693411026405   0.018172345678978    2.83089
   0.719755506241629  -0.214455366378582   0.070882672539164   1.411917758196618  -0.892535098071493  -0.473072869638425  -0.404651423129474  -0.386884748391944  -2.044354628523410  -0.445835812739061   0.017529854184545    2.87656
   1.213195674277077   1.158434711580366  -1.305519828116312  -0.474217936714275  -0.796024515820363  -0.447862302105167  -1.304148888586379  -0.436913447610287   0.086264410697809  -1.028471431172681   0.016839294935611    2.92134
  -0.493052287634315   0.066117151004350  -0.306334986626921   1.356050773797344  -1.687327712426667  -0.416283102138842  -0.510860787028383  -0.935054703068250   0.813414373496644   1.347574949583977   0.016208774009003    2.96875
  -0.633381377865323  -0.078467965245351  -0.435580290838036   0.071290186074427   0.196760012415651   0.043937616928029   2.613042190465088   1.112873124141340   0.018373862677732  -0.406966726086853   0.015290769454596    2.97913
   1.066240354001400  -0.055584092293414   0.694396798024777  -0.591321609028865   0.006833363326648  -0.638200933972455   0.705024694188773   1.587159614194890   1.446626796710891  -1.182442329699868   0.015790553283707    2.98097
   0.596322617164613  -0.768178894740196  -1.691800463427704   0.291191310188134   1.187272379906371   0.805971595007135  -0.787209306136193   0.933606436859959   1.166322531626522   0.445144543230301   0.014893635820920    3.00028
   0.629438344873499  -0.853199443563980  -0.789567621790202  -1.458442606214365  -1.250077009001238  -1.195085611958183  -0.041587349110496   1.007733305258936  -1.034883667506611  -0.338625962681149   0.015120837229164    3.01139
  -0.751298523111227  -0.733981686897560   0.638238365620362  -0.211799805331159  -0.968171004304016   0.034415045038568   0.096607154437713   0.075204404104550  -1.591363047907331   2.021433152916485   0.014761158904368    3.02118
   0.483215941811568   0.773869099596425  -0.915057872756336   0.233312884358402   0.975009948868758  -0.887628133477764  -1.652728647106300  -0.342586100195849  -1.386210871589629   0.951165625555178   0.015433595716533    3.02289
  -0.102694716273017   0.370073069001301   0.876501514371877  -0.261853679641682   0.949314217382114   0.624931900138281  -1.092587041381983  -0.860803378472792   1.638586739528304   1.577190730330704   0.014514512226027    3.06321
  -0.730247411322820   1.400422488823519  -1.126916942563226  -0.003436843627412  -1.270118542699002   0.323839506234275  -0.465329298283942   1.372426271229440   1.231957225891868  -0.647002964850032   0.013821069009512    3.08527
  -0.121848019856758  -1.060157606307429  -0.282427203311471   0.022757868520632  -1.361284113142863   0.084750674287624  -0.505988225101164  -1.557916557862166   0.217677325009369  -1.953171775286964   0.011588334419395    3.10238
  -0.336695910293142   1.056762601078199   0.092804214833698  -1.576202295661965  -1.356161908561645   1.197530483469216  -0.337936199191153  -1.483248850636956  -0.339461927497843   0.540276208826583   0.014741303785024    3.11733
  -0.188092795155925  -0.283015191547838   0.776253457412720   2.037817881124455   0.195558469994183   1.370008877273716   0.455645491674792   1.340536920242293   1.060248368059560   0.054464776017366   0.012843492087666    3.14923
   0.120106997180397   1.354397145918894   0.907639297054340   1.165407102382531  -0.533381655421554  -0.689451977235279   0.187727126321155  -1.027896023096232   1.824682347872621  -0.888573786157208   0.011254392458545    3.16251
  -1.770821102257032   1.254037569236131  -0.331482943230765   0.058656131768596   1.396370755202350   0.783657656192191  -0.014711952087196   0.163214144823720  -1.304454905465857   0.947640909665151   0.011793857242399    3.16420
   1.993498736468789   1.760379382627968  -0.103560014796966   0.261498437105456   0.541757444805633   0.516517197395942   1.081900491886335  -0.474072503673890   0.987559757642774   0.169358239306490   0.012023145823756    3.17987
   1.318834246272506   0.581987353236220   0.010854533119050  -0.648953224314215  -0.265519011884707   0.910362993221570  -0.933955858582493   1.890317979867709  -0.951526227609782   1.178366208394147   0.010844649851950    3.18403
  -0.021337021065944  -1.027515590229887   0.342835836438105   0.678483116780670   1.208448842292176   0.377403779894464   0.875322421112467   1.577699722618266  -1.952935793739414  -0.087933745619016   0.011353782860279    3.21153
  -0.129983248225017   0.094461027349326   0.790055001972372  -0.609669717215380  -0.846316879435820   0.649027172287029   0.404557454699040   1.611770758305779   1.372289190363990   1.889057559025628   0.011776465711485    3.22062
  -0.949874364548120  -0.435756168638429   1.176590217309719   1.125789702983435  -0.595441823116900   1.484846659233106   0.802484850615235  -1.851525692101374   0.073572899239370  -0.500102593784321   0.009993512044172    3.26050
  -1.067292013845280  -1.227656910136418  -0.031705391399514  -0.674687545958274  -0.565005219660929   0.090260476973862  -1.300090990245195  -0.054276259888358   2.214596166058512  -0.782213578429879   0.011312782761074    3.26180
   1.512672918060030  -0.186132117366188  -0.390047859508852   0.150425691833268  -0.301921003887992   1.630127018702469   0.471411587969817   1.146622148564612  -0.484460706941159  -1.943361421920916   0.010957347897929    3.28548
   0.846025088233569  -1.038883025091885  -1.032981778302485  -0.070153142283294   0.186551163766139  -0.221635750067025  -0.335730836517456  -2.692353233866751   0.172614966988870   0.703881183506795   0.011972371307282    3.29206
  -1.153139958255139   1.033124536841384  -0.313976287362024   0.865380792039197   1.900672458763492  -0.664105129737590  -0.045212603062386   1.073702401424789   1.565320348832872  -0.053656725962844   0.011326704093207    3.30244
   0.158332179137323   0.858333424801982  -0.900140364629524  -0.287749247609781   1.202008894364931   1.837065486382365  -1.236057841841429  -1.344415942580639   0.247572839539547  -1.036826121408658   0.010472947522012    3.30849
  -0.246691562868175  -0.577292011779131  -0.395242434200536   0.188378910248242   0.606231490468549  -0.348849307641967  -1.903567959789922   1.552280546078460  -0.385732142101387  -1.933082650549492   0.012213191725679    3.31569
  -0.827525462837339   0.488733144458670  -1.076953754814379   0.021386124659862   0.054970635119415   1.345203939423300   1.494563283329106  -1.055257670816967   1.952159313805732  -0.109762337912190   0.010076399290107    3.32668
   1.084969358022541   1.445247259352482   1.455848426075537   0.876084963262868   1.261913414577307   0.084387483940340  -0.905886001829564   1.561078251878051  -0.264395601878223  -0.173839349915419   0.009905925076973    3.33319
  -0.123299154555989   1.433594246180231   0.542324429404565   0.810086792694773  -1.743693309996432   1.436256875525203   1.333853337951358   0.500008048695332  -0.914226901120543   0.511074151044514   0.010095507012694    3.35414
   1.401375559359239  -0.193555140954480   1.122661490525807   0.410979480173371   0.860145026502574   2.129097376613139  -0.146584113793784  -0.720481817788602  -1.401989459688518   0.245085027207377   0.009925212298773    3.35704
  -0.287579715665997   1.383468375015404   0.797477367252324  -1.586202103234117   0.085060005338934  -0.150476924518891  -0.148644834428965   0.603412917357777  -2.261861517337439  -0.777733008548351   0.009252317458119    3.35941
  -0.568588872210231  -1.296374703812792  -2.136908130936011  -0.632373397254075   1.347624021934959  -0.214714894189122   0.117467343218079  -0.221808827683634  -1.321922396195612  -0.880174455238652   0.009027861551960    3.37898
  -0.093541593118231  -0.641446638517210  -0.528651337135517   1.129841753304792   0.844079527350788   1.587256534620381   0.673883175845872  -0.668013510230343  -0.158546346498628   2.308930913168939   0.009388610621692    3.38596
  -0.431494779742120   0.736331452538548  -1.759405173648027  -0.500056119245551   0.208439179776336  -0.851250763031655   1.021806738529248   0.102856614842648   0.561859670447578   2.312089862819858   0.009149110769920    3.39972
  -1.246808133695574  -0.976083571302352   0.755178199241757  -0.874623986602130  -1.801363723663002   1.190858413300533   0.266443325301230   1.083268644725094  -0.789198395450520  -1.107977178400836   0.010386193033909    3.40595
  -0.575883767046831  -0.002611697870887   1.008305776244243  -1.594881186432726  -1.856203112373927  -1.156821602575634   1.186013953668080  -0.573287961317921   1.139909806371699   0.174145228935585   0.010279216267347    3.42647
  -1.244054511704349  -0.746026675781403  -1.965082277292050   0.826302299022080  -0.689316149264791   1.949707183429794   0.180578931668648  -0.326432950517683  -0.731530984191145  -0.521899833147913   0.008690636444841    3.44554
  -0.762562346003668   1.736237624759806  -0.038807213114505   1.423834979797023   0.569159787078220   0.719910318968024   0.233230278789532  -0.131220386028669  -0.996888843019540  -2.084377211388678   0.009653436439696    3.44631
  -1.041137721838612  -0.719751363125549  -1.630738228026523  -1.703870802384762  -0.467658388989998  -0.110810925594717  -1.666167803138868  -0.108109844846464   0.069396948501710   1.336924329712316   0.009445287312578    3.46056
  -0.207560634085408   1.319437454006482   1.794990851347994  -0.790552917862536   1.128999175412394   0.838659494164386   1.945134857400957   0.004366105580006  -0.032211658866617   0.795870236299579   0.008708877707245    3.46799
   1.559604088827778  -0.462845358978156   0.235354542379162  -0.148830508641465  -1.312202129369963   1.985498977432398  -0.109869685541172  -0.251239478282192   1.891321417030270  -0.069880228602190   0.008773168375247    3.47065
   0.152451371384540  -1.147483555650880   0.939079524489183   0.404450643544853   0.859044543100659  -1.406302255656840   1.426525572300583  -0.825633364028970   1.954824329314645   0.854105290720196   0.008870908189790    3.51689
  -1.543944616132920   0.924824059097478   1.314122219304372  -0.476350502857548  -0.782392104910317  -1.452857003591212  -1.748014681050816   1.148937932028763  -0.288899124515251   0.611404591211358   0.007275378323471    3.57053
   0.180818551134444  -0.082307242612703  -0.245565689626344   1.532523933738630   2.411102967070686  -0.255309630187449   1.493655498465813  -1.375250131778215  -0.611245861394344  -0.214324586980666   0.007432824317728    3.58732
   1.267861658927923  -0.628117869760047   1.153935057274564  -2.508798571447030   0.216442539010615   0.283417455971106  -1.739285804040084   0.209584749033354   0.364818544878723  -0.448753132322203   0.008183802336723    3.62744
   2.111803688895811  -0.716438838494023  -0.905963574674626   0.419810169445284   0.643167408491374  -0.546992147890255   1.439585055303560   1.540435481906245  -0.181062902356500   1.446113318003852   0.006809351434241    3.64036
   0.273099558849641  -1.670723584163999  -0.100641202993636  -2.111605520263522   0.150060541516073   1.697515070514345   1.573823316680522  -0.273865922977704   0.068375708061722   0.741089300198539   0.008263844163097    3.65305
  -2.195533091129583  -0.828507234660970   0.648749857608304  -1.512044018244245   1.288737141404294  -0.053082105536740   0.149960566229028  -1.871826985195566   0.197421448831915   0.550860939688231   0.006741996937880    3.70759
  -0.233376010115840   0.749165519133015   1.349047955243493   2.116674718391542   0.573453356895259  -1.560664353484274   0.630822678279242   0.434550809742114  -0.320285523534455   1.839948549441955   0.006996087342698    3.70881
   0.835234088026125  -0.520896242432882  -1.958681617748839  -0.194448389341151  -2.727004732598400  -0.065431173512665   1.113695932928261   0.210905726361718   0.515381754983430   0.386365451796584   0.006640529006822    3.73948
   1.394483375025003   0.012590759528885  -0.379177656593298   0.581989387538627  -0.499759721041278  -1.921308202370844  -1.732351142988727   0.990239350763339   1.852630149383596   0.913308998256479   0.006620671718119    3.82314
  -0.523309812374753  -1.544456079664210   0.685538657794330   0.052260532759300   2.113062511947528   1.138062254773621   0.716257900218555  -0.156068056841261   1.171214190461720  -2.035467154875232   0.006229468210596    3.86579
  -1.189389489849751  -0.944464653889001   0.696760435597625  -1.793532119887100   1.334796220037696  -1.335324035998858   0.217945528151934   2.415631806451878   0.332523274422979   0.514197687450932   0.005655003711768    3.97887
   1.220620851440120   0.744837363118384  -2.172655091698958  -0.621962574320891  -0.305775696713924   0.929815179586810   1.247012749998619  -0.828012141564471  -2.292387344349855   0.515712598496854   0.005453381614675    3.98393
  -0.539664451788373  -1.276217077948610   0.685012766442983  -1.185956489106886   0.688822993935224   0.688315600260743  -1.653879034598687  -1.317900272077670  -2.471734174670440  -0.885683402806424   0.005173504402220    4.01373
  -1.062678592630108  -0.386687310529277   0.543419332771922   1.940266867559634  -1.621800688745115  -1.410986134577220   0.711966917143122   0.784406085455018   0.614421365028012  -2.191939931316806   0.004602173604287    4.03289
  -1.827863653743776  -1.587674525408070   0.160422152183696   2.524634739043837   1.058372282771949  -0.342774870648821  -1.424178497173657  -0.878889102895116  -0.381714456738265  -0.075526988730734   0.005299924667393    4.05600
   0.528813215168839  -1.007567785996585  -2.287315943114269   1.370589537455286   0.016258281434116  -0.932995389280586   1.174495282923059  -0.192799884420522   1.220060094291046  -2.104356740407976   0.004290785686452    4.07546
   0.560238044849741  -1.783103330977377   1.084464305015314   1.549599343014888  -1.865190619539896  -0.634035203627001  -0.893584406720078   2.214412183256802   0.128211113994610   0.206020292541455   0.004249273342702    4.08810
   2.284888689117539  -0.580184903090099   0.979540836497238   0.565280433783862   1.140209967820116  -2.357580858052896   0.231685000088954   0.104181093284180  -1.028951362169344  -1.407337726020323   0.004351003989410    4.09860
  -1.866987735333213  -0.403327577230832   2.171102330703973   0.543620480703468   0.729537165324825  -1.409983309223430   0.827345614027590   0.459100034881757  -1.287100564511500  -1.754203352668201   0.003942437589179    4.09963
   0.498628699399943  -0.096080171715145   0.591348717111784  -2.090836294535585   1.196467008788521  -1.890336031007500   1.224164377707104  -0.567219632576865  -1.598810431588323   1.575001882461200   0.004460179661250    4.10380
   0.840640444306335  -1.459072789761693  -1.001186335352058   0.563280820585207  -1.556793212092020   1.861721682984686  -2.357399730526628   0.163594181229542  -0.853990663293932   0.885637992825161   0.004326132366724    4.14036
  -1.350332863032610  -1.419312129640157  -0.106214649206385   0.362468708158087  -0.830760635581598  -1.076885933773224   2.253585809723048  -1.454920129433631  -2.023819435411781   0.335988905320966   0.004173236940398    4.15145
  -2.061299487895533   0.440290676226816  -1.250220856899392  -2.292837648780705   0.208405733066315  -0.594590615368941   0.850964493819236   0.043131381181437   0.250773598191660  -2.196358493480562   0.004322727064043    4.15606
  -2.183369481881638  -2.543692220149659  -0.854880087302279   0.713266289651097  -0.658984339904738  -0.238018996109526   0.937363593647181   0.928545430048768   1.284415750480182   1.021495862680867   0.004107825702703    4.17157
   1.330204380879110  -0.294106746396961  -1.771005879988591  -2.248086935362796   0.642486494353669  -1.156152189435538   0.620461562701168  -0.818320300777662   2.262299403856923  -0.330571129627710   0.004081615924686    4.25178
   2.120301816151843  -0.859646982338010   0.946535018753534   2.042010269128554   1.073695629551055   0.085562186723446  -1.808547189922926  -1.204316155692978   1.267358068888134  -1.176803716571564   0.003974595105216    4.37868
   0.064505921039608  -1.988096192919487   0.950628700386758   0.282531625715516   2.156619543152126  -0.785147749918188  -1.935854126287870   0.652801336721419  -0.388313017846612   2.159936585203350   0.003608483777333    4.38149
  -0.171243656543714   3.036549754438055   0.178082491754649  -2.192520206454125   0.278757458634685  -1.373339429657919  -0.798497173207680  -0.003434290443729   1.194270365517887   1.180354608832986   0.003209075195334    4.41698
   1.794637808247374  -1.265070911916984   1.025204770264095   1.783561881770728  -1.651005210956457   0.002102253386096   2.726632919647650  -0.822700316658213   0.061557803427554   0.332331271405879   0.003223961969012    4.47266
  -1.411604214196311   0.225031477364716  -2.031184982677750   1.526228259917527  -0.600887290156184  -0.505889678622984  -0.360828184775557   2.875441042271621  -1.476065061053777   0.797009708771831   0.003659349703764    4.50862
   1.653354822732708   1.364117693495645   2.013622862754695   0.214366650577335  -2.869159230983546   0.107353822612853  -1.282843311353256   0.010429718763818  -0.340935822473290  -1.370120532150084   0.003032472900371    4.53629
  -0.053919487121601   2.036021104969762   2.079508692514224   0.965509622051104   0.393781001832668  -0.630235829206527  -0.512435864730264  -3.034607966076505  -1.402902383156529   0.861613325623677   0.002891632118912    4.70522
  -0.882382726668587   2.175812987667552   2.231001342270985  -1.536013898106828   0.225455310824558   1.764020685866089  -0.036859499567439   0.407056586638232   1.548349676469828  -2.135533320077979   0.002662003429275    4.81009
  -0.171097763249083  -1.722083629257884   1.582691127309195  -0.711928040494752  -1.953753208620294  -3.007895988778154  -2.076221304859738  -1.935991693727939  -0.389145676170775   0.174297320593564   0.001765407893401    5.20690
  -2.366516176025113  -1.108349088617356   1.028615950689615  -0.833597078799778   1.607240112765761   3.736299315595708  -1.378545128664952   2.160484187388900   0.004559043874503   0.360929621472170   0.001417177149073    5.64121
  -2.948751032588566   1.493104398406212  -1.870205699956283   0.133681325688520  -2.866930994818323  -1.521823264832442  -1.348616489319692  -1.313913637959014  -2.347785493688682  -1.193508829013781   0.001089708159839    5.95458
   0.477822500853847   4.661285335525119  -1.357245277065997   2.170739914428511  -0.377091290121545   2.332420565178449  -1.536885891821222   0.088657994593020   0.281963110686751   2.774639552456291   0.000679735165729    6.65135
   1.717060248213492   4.649031124180155  -4.318570017286366  -0.106066262565476   3.465440206339458  -3.197162036699355   1.692039641420891   3.055767779701338  -1.659974181220888  -3.059945269650073   0.000175993794129    9.47490
  -4.566174214503452   1.936797886627983  -5.979199831908356   2.980592269363701   2.181824771706459  -1.148905211717254  -4.378611463014861  -4.158429085614431   3.774933763456073  -0.299373863942266   0.000088134672305   11.23035
 -11.642880949933728   4.506650030348140   4.821696341704444   2.463000122141584  -2.763542370841913  -0.215495301646609   3.324249341870021   0.328020669906423   3.553598889997678   2.578645945214604   0.000027906155003   14.94326

>> # evaluating formula 1 with 107 points
# r10_107_4E1a.txt:3 formula 1   : problem E1, 10_107_4  (d=10 n=107 o=4 plus 0/2002 of order 5) quality P
E1 10 dimensions, degree 4, asymmetric 107 point rule with points at 107 distinct radii
#                 x1                  x2                  x3                  x4                  x5                  x6                  x7                  x8                  x9                  x10              Weight     Radius
  -0.434383071450982   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000 742880.954487320268527    0.43438
  -1.270605573096530  -3.042412591537708   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000 326133.739455784554593    3.29708
   1.553140672433129   0.809919991523982  -3.525517654025670  -0.000000000000001   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000 440371.676971009757835    3.93669
   1.828514750989025  -1.422062670362334   1.449157585547727   3.353581337058738   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000 229816.966722451325040    4.32577
  -1.236392149409277   3.202726094880199  -0.188334647541426  -1.498650602089990   6.148173354146525   0.000000000000000  -0.000000000000001   0.000000000000000  -0.000000000000000   0.000000000000000 343615.839785523305181    7.20191
  -3.610461932555011   1.863895550133837   1.654459998350492   2.173637776531523  -0.063613918247853  -6.278524900180521  -0.000000000000001  -0.000000000000000   0.000000000000000   0.000000000000000 225636.831872185808606    7.96212
   1.310198500930178   1.129693963051351   2.208029193060769   1.839022111920580  -4.180489397738389   4.287428025176706   5.318956638136453   0.000000000000000   0.000000000000001   0.000000000000000 210295.774718123837374    8.68332
   4.177014720728277  -1.272783028363006   3.368882720306617  -0.894831839334352   1.268183991128138   2.173769856747501  -0.978384915022978   6.278582357845393   0.000000000000000  -0.000000000000002 163534.536990139022237    8.82774
  -1.819951079396106   2.879562965973435   1.931891205533983  -0.123055081306244  -2.901665549158240  -0.432589495861447  -4.301175900662388   3.668465239591264  -5.033238634223320   0.000000000000001 229567.242460501089226    9.01385
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   0.371613624151364   0.563438218891618  -0.482718090269040   5.667786989274640   0.338277197012773   1.400102279089270   0.503690483002804  -2.014228280137978  -2.558591753905084   6.027378503201946 171418.394295689184219    9.05945
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   1.176049670428268  -3.621879281309127  -5.677937333364775  -2.610236635076028   2.455936946058645  -3.116999222754511   1.555401668923081  -1.192313924603165  -2.533551276075936  -2.151945776265450 126750.466306457718019    9.17558
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   2.081745027740839   0.932755794933883   0.398491485988512  -4.282421402967389  -3.218859138936994  -4.207396118119999   4.562920574490938  -1.081746764073296  -1.857445403405015   2.953407884768448 168221.195326523971744    9.26974
   4.058200067681616  -2.101385891909769   0.245107988985656  -0.034223444116874  -0.430158301418989   5.380072935349913  -0.391252615271187   0.142745899260142   4.613333326951100  -4.111684927195979 132565.804934042273089    9.40418
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   1.059826416389687   1.596712804583674   5.471717974200718   2.584361411054203  -1.309819526536598  -3.546011530643219  -3.477771547298075   1.534773332383458   4.741185833455635  -0.344653113486635 99758.184472306384123    9.57232
   3.443486161686500   3.030764438171038  -0.094278098730747  -0.489409363113496  -2.395652031712883   1.945560314283309  -1.664561803947177  -4.411447584447274  -4.780752885282589  -4.247882833070324 162289.377008256094996    9.69266
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   0.843816489892316  -5.775945994149068   4.004194125090324  -3.864573271243534  -0.741014547502853  -1.547912562129691   0.265788221733473   0.592195180891953   6.822275015629333  -0.212954261539334 118413.289594277201104   10.72368
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   2.323333548788061  -4.770948065549189  -1.824025119077345  -1.386162170588206   3.111475826634173   0.582215460948313  -2.385012263383437  -0.472774556269583  -8.473634394693361  -1.180011237341661 82469.232345832089777   11.06957
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   1.075461667178072   3.577661259798901  -5.747232340496669   1.619857202929725  -0.811741062904981  -3.663484403282058   3.183028934269112  -3.239793159270785   0.968492432779483  -6.552246978838135 93537.574345187560539   11.32205
   0.481471289052642  -1.377735249959689   1.309796380606257   3.531539790583313   3.744481870910714  -4.905731424205903   1.817145022350925  -8.548363427620981   1.589979894242584   1.231485389012123 92933.401299759891117   11.61145
   3.623119179727845  -3.399590864367917   1.959405401279332   4.360414498607985   2.388532396139443  -3.606967579083955  -2.775194134959070   2.227692693220624  -1.626548890155204  -7.542687703898269 86066.063297940054326   11.76665
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   0.228772793040454   2.149509106993925   0.221861527030582   6.969277798905643   1.730161561151494   0.383447575669248   3.799849835258338   8.419290415910806  -0.754976384302518  -0.332768342965496 68958.315783130499767   11.93471
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   1.217794043828520   5.859325480420487   4.242108166781643   8.392625776398823  -0.430890900518312   1.094293385148723  -4.103376126138805  -0.538338788022940   1.917330359867604   0.848545497652274 70170.040175401372835   12.13067
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   4.558595198453884  -5.795701974497010  -2.593182221692711  -1.590585858813945  -2.412754522898939   5.357154256376656   0.294833726286948   3.065218766153012  -0.083197613817887   6.670531531783801 76649.893844014339265   12.33416
   6.076792556403350   6.659113451713632   2.637553882738620   0.597344931618052   0.950142327177963  -6.482678455193590  -0.109732703192670  -2.239224224893795  -3.982239709161106  -0.501278226552368 58907.535244934522780   12.35509
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   1.780051087582495   1.236706291744922  -0.192110356650313  -0.125264115688315  -6.600311029498519  -5.450274036242795  -4.653550704162665  -2.998993167013956   3.774675258028648  -5.833798023080089 62523.729565390625794   12.52801
  -0.971206152912854  -2.980978359144070   2.966346231436574  -1.674319291256935   5.743074046987954  -6.116295153566559   0.294198225708457  -1.793692147809018  -3.308646850065782   7.201176760915150 48679.532771886770206   12.56710
   2.840698502514378   9.150451224772006  -1.751557859304340  -1.179294777879080  -2.943399414291185  -1.679567072706066  -0.254408490989971   5.694252808671266   4.371425718143561  -0.782245248128980 71542.641515021925443   12.64730
   1.953690913304557   6.895587201849000   5.285261250900843  -1.601750780874436   2.968588915810844   4.102212120438741   2.931272076542956   1.268838581113219  -4.188092949035744   5.001890901832945 69366.423198694887105   12.65969
   0.747818868873630   0.317835558727549  -5.039862014955856   8.327745231387631  -5.981852935030745   2.705610676912214  -2.385832543068903   2.584137420015705  -1.806240247032369  -2.620071793243310 65867.690175506446394   12.68905
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  -5.742870752482609   1.205222248802501   0.442785641851464   2.672257798243781   1.593629027544591   0.241463149505570  -4.411464232512951   4.301825336427729   4.490707910625841  -7.668137333348854 63219.352837526435906   12.70046
   8.078269999807308  -1.184485207723983  -0.543972707533933   4.052434762012830  -4.331183361529422  -3.061792196410697   5.181913983492745   0.281906934708119   4.670819524412028  -1.399933623962879 68902.900678467340185   12.73662
  -0.936072394537454   2.164963580545125  -8.335895182200774   1.759047610785539   2.920207854120703  -1.396894634757945   6.702823588147305   0.464579942382641   0.031988339636714   5.561735455863529 69350.643088302575052   12.83360
   3.443838154520668  -0.275540944737460  -7.068861601861684  -3.563147359650412  -0.095479815509367   1.341060072594289  -8.076078209742340   2.531561887572796   0.236934169953541  -4.082343055244738 63564.862442049685342   12.83596
  -5.560845768482634   9.384383748787823  -1.746916750099941   1.583844872087974  -2.583898025016140   4.404603172795508   1.419391756113578  -1.276844828009040  -0.592054300725986  -3.229430564726266 54287.401794805780810   12.84725
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  -6.100060687741783  -2.772846050958345   0.699324761622014   1.360542606733164  -1.690993010322609   0.983192277692416   3.766538433142068   2.928366141835531  -8.663623114109754   4.274693841124309 61315.447487591081881   12.92901
  -2.025328625899150  -0.042472647071361  -0.298522262000226   2.330178515450929  -8.287257480855329  -3.239882093902157   2.599613998328170   3.254937321998711   3.486333101134052   7.093374479150899 56968.578488525687135   12.98542
  -5.841184643464207  -2.051967748083242  -6.887887120850708   4.901101973283029   3.562425944654263  -1.964624062256286  -4.554903622238403  -3.143610450214871  -3.207616113911176  -1.729313291008589 64099.985329391245614   13.04811
   4.065329852852186  -4.007880120170248   9.146032724888700   2.614457663813559  -3.158382453333883  -0.803454780387712  -0.056651624696920  -0.285842474326291  -4.984434021611120   3.571907679733861 61812.924801571389253   13.09138
   2.176737012185177   2.521480016972892  -3.429286126896265  -2.018434027001600   1.596519149872893   4.270529743413281  -2.780575279229266  -6.310462646234589  -6.979918266719826   5.236223728020466 49185.298653468897101   13.09226
   0.842079982399423  -3.790575217470066  -1.251724367083095  -3.133996915948955   4.680089723495498  -4.442590037452153   1.988813191897004   8.039233842647429  -4.414578658816914   4.129284985398216 45039.329312531473988   13.16170
   6.831599126470112  -5.146062949594011  -0.737812906060336   3.997773586760789  -0.186384588805002   2.352812122983071  -6.032834070568905  -6.099774770942584   2.115825244171480   0.396158390370488 52693.183469123723626   13.17140
   6.944846070640626  -1.207716548912467  -3.476030641550031   4.949375699750874  -1.870279244166067  -6.414116039523449  -2.472866534189798   1.568731272387391  -4.795795395867769   3.467776733682953 54065.423111105184944   13.21017
   8.376066148282279  -3.367129512924723   1.334642759104199  -0.795496385968433   7.008701459857978   2.395348559586751   5.273795731920437  -2.321129733999609  -2.134232547561884  -0.219192231692498 59392.487528364363243   13.28809
  -4.382803957067503  -3.135621527342940   4.744462655310839   7.614189338901177  -5.303545351701064  -0.756836594788918   1.452115975310203  -4.218051267480760   2.506323749193246  -4.233608765529375 49074.704622307050158   13.50307
  -2.297575938026265   1.854734693845385   2.898211569946673  -3.844644092352406  -8.588020722647478   2.865439320497258   1.943204097468318   2.772483942262665   5.769365006074525  -5.793998302295130 33634.983057139623270   13.86302
  -8.305710489268590  -5.066932863078950  -1.332831192633235  -6.086809225375750   2.267971953291618  -1.428849183026711  -3.728794745179646   6.364884336110162   0.222097057615056  -1.545882492608659 41150.361058432943537   14.05434
   3.754285623507714  -6.043040962429232   5.506259338337655  -3.548889823907397  -4.932189816553399  -1.126270667266199   2.623549645659732  -7.667287970775485  -2.906824068722744  -2.171349496816417 37392.511145795542689   14.06969
   1.180196896315307 -10.835928933067756  -1.884081174081649   1.729308026790648  -5.251313223176526   1.630639754113942   1.403538101615803   2.733562812236270  -4.168480306566830  -4.181693462316543 36875.358268627634970   14.13828
  -0.860789418832004  -5.794484764282810   1.404667144709512  -3.659612927409242   1.201087206936787   2.564946713624893  11.222746763053431  -0.607694038744784   1.820254655599167   3.691492576882538 38040.414204573346069   14.17618
   1.722154955437430   0.296805110861870   1.037918076936121   7.668293078078168   3.511041239762197  -1.211788636343223   8.025792959038300  -1.662833484883844  -7.109552704480276  -2.776431215136562 39560.917542039533146   14.21838
   2.709457841724709   5.162996555982811  -3.615127777506930   6.668275660315970   6.599059040239748   4.293802359790168  -1.868586062387398  -4.426685123791426   2.252714950336467  -4.910055537926626 36257.184018403873779   14.34530
  -2.768229425975453  -0.794026082918571  -2.697884195987438   2.598567797828582  -9.069429699930785  -4.820892681550764  -1.623316938918757  -5.902940135370574  -6.408182590856841   1.803196555453635 36300.276601299192407   14.47814
  -5.979159237127800   1.048126667334470   5.320369622547753   5.728682161987528   2.246028532561780   1.360928491573046  -2.412725774255234  -4.756905284720726  -7.745302083539815  -4.591145517594711 34464.496498456494010   14.64198
  -6.483932821338270   1.145324145641205  -5.925930725856634   3.231032469139071  -3.870979923573551  -6.001600767559896   2.539569812704487   6.787469982891920  -1.837633435896729  -4.525063316356958 29473.772021383269021   14.70664
  -5.322800966513714   2.879617754102692   0.721968097335871  -5.534266598489928   4.241044178999856  -0.960132368777302   6.413884419733414  -7.464836828786880  -5.906193405385035  -0.304818373909692 38517.065684872279235   14.78242
   1.286102382731838  -4.442202469396008  -7.325827295889656  -0.890760785616710   0.386779779291424   2.359387513021382   4.401154158719294   7.469956783304998   6.312101350194350  -4.686117355141852 33721.897867829116876   14.78301
   5.979944771988383   0.406949996914355   3.969899988063672   3.306451895939308   4.559075602846887  -1.864179763538143   1.620259062504490   2.972654182907196   6.156923341234899   9.101732405740623 35657.881160904471471   14.80167
   0.572769687378755  -2.697889797202445   4.071417817072209 -11.405898370253059  -0.253079025250859   6.648532231124443  -1.127159037200707   0.768619727627195  -4.610576432253270  -0.378997435871202 37503.292912973731291   14.89319
  -5.353066644659878   2.368958555239414  -1.919418894681487  -6.726394208222348   1.177722089122505  -8.337752787334500   1.584800224363670  -1.364218007494818   8.123708280834640   0.301570381379893 38073.909977788222022   14.98530
   5.516841659278877   0.585882059129105  -1.159455933563418  -6.713960416735869   4.931507594359188  -4.810918720900047   6.728473597213799   4.651575427434850   1.409129744690505  -5.998907673319735 29172.721845974294411   15.15081
  -0.962838054254637   7.052950201732952   1.477080487333032  -8.069075170895545   4.258230143773426  -0.271452140598733  -4.098629653453669   3.294258327886574  -0.894125014319353  -8.066941383536278 26670.420010311259830   15.15569
   6.790968428571642   3.973512277791083   5.907540319899869   1.541041813191494  -0.099692552922908   6.129427982458697  -0.707198320507474   4.456417789838192  -2.080903229552506  -8.439822913564017 25152.728147600551893   15.25386
  10.066895773707465   5.483325800528243  -6.450736989413219   2.424952297022902   4.623082732207321   4.522821356094359  -1.190510139899958   2.731141460214352   0.313958211558964   1.904262916338275 27807.191352299643768   15.27520
   6.344224725985742   3.163028179146405  -4.788097118483623  -2.753172968816754  -5.370027551202972   2.127968873240346   5.287003982439777   5.459128218008506  -8.053612928848807   0.423480392847671 33017.181144830756239   15.39220
  -0.060844399442487   7.423930026324769  -5.804749935017316   2.128934228651483   0.259690861203549  -5.578040453537747  -7.912253773287634  -4.469565119906214   1.787552968645920   5.454866546854441 26790.107574884426867   15.49386
  -3.025245902251534  -2.306620613723664   6.906619191007992  -0.426577187323565   0.199950589644975   2.364284693113043   1.738368757258161  -5.126806132643926   6.973408894998657   9.774181461971827 20507.568640992729343   15.53882
   0.304328350713913   2.940672612694978   9.214114575727093   0.287249247198622   0.159331502245371  -8.207757419171161   6.831944554943491   6.207824551329936   0.061239688442847   0.774426872873018 22593.124014858101873   15.71405
   6.908357990796286   3.255399472679880   2.806176203062837  -1.032867668812524 -10.128097659041586   4.788517413107630  -5.964983382909036  -1.172251653018963   1.291324971977682   4.595149082687279 31279.031992308926419   15.89059
   0.083368632383591   3.686845313353708   0.591302696101212  -6.503950968174850  -0.908897376923738  -3.713017296468914  -6.127580386208317   2.384997462020520  -1.275798439689992  12.174296678699111 21689.060905235197424   16.24623
  -0.537619547786334   7.559725738363687  -2.373383626350440   2.743608857537188   8.163215093308121  -5.988011991351434  -1.366048405950877   5.084712006359015  -7.756631937838454  -1.822125946730723 20625.036305466554040   16.25728
 -11.469983023701710   3.713313048256603   2.440185554854023   4.827694127704197   5.340395395675642  -0.768953860798998  -1.504667221674273   1.752249102507709   1.763938844818222   7.333640784792058 25792.065674418026902   16.30796
  -1.569027791828467  -4.403817236741700  -6.015373157540523  -5.705451102492832  10.100719272183802   4.057366239475426  -2.148606125053904  -2.290135585923962   4.745347535888921   5.130714705771999 27592.851089268904616   16.36407
   3.697151391844078   5.763302917893991  10.811705153454641  -2.041358706839010   2.235308560206347  -0.446518723386596   2.873003045286144  -5.983686263255477   4.709300853241128  -6.175975994727330 24208.553849171217735   16.65892
   4.333146325581641  -4.244801812274105   2.568403766282641  -4.260079871485230  -8.310158893048095  -5.955888058045376  -3.001377168281257   9.500074483023900  -1.290448599154792  -3.304771652553458 20667.144092130183708   16.67085
  -5.267467958775557   6.304736772376354  -9.079874025233416  -8.639686949417076  -1.079738090752049  -3.506663330907498  -1.407986703882273   0.687710045822541  -6.686014467986892   1.716515757700219 19590.029535059897171   16.97502
   2.845737658245445   4.284955627837327  -4.983258339645477 -10.364779155814098  -0.908952818327903   8.073918648686011   4.608903539853338  -4.705208294561293   3.957394724187143  -2.989368606344241 20702.931545253533841   17.10886
  -6.112527855507540  -4.357979508649085   6.740215521614382   4.945108437584263  -5.945765963140766   5.725873520210460   0.590611738900455   9.793870955305142   2.877595472917445   2.206022277925241 19007.829038323088753   17.42966
   4.372218648905076  -1.193047070176406  -2.605753574643976   2.722398070589902  10.336455294164249  -8.585264693935418  -3.756332384995951   2.182364825306689   7.981344956386000  -2.498061475350452 19818.027665329605952   17.43861
   1.093774585157087  -0.709977575474973   0.452358278984354   3.951770084458327   7.007925949817449   5.534476669585562 -10.655976505668381   6.846693053847034  -5.421813917023773   4.221945742483272 18423.605499527635402   17.46170
   1.214077877094235  -4.442639265078800  -8.506952784302150   3.766621933963396  -3.735340164357826   6.837354449848082   6.958909484913574  -9.172044220651285  -2.496807124171197  -1.127959148785103 19714.808222577918059   17.56497
   6.751314714138507  -7.562696440513560  -9.740442094031735  -3.593200959857239  -2.231641718136922  -6.593748055444901  -1.479799580484389  -6.835758551772916   3.745945283484591   5.050731960913208 12895.283749603881006   18.64079
  -3.946941522035835  13.119995976937293  -0.151905165423270   5.322405310493402  -6.418769427420301  -3.855682749180512   8.076575662793005  -4.338246115223764  -2.034986342989008   4.481741853047984 10233.536689870505143   19.50408
  -3.571810151493566  -4.302184673561839   2.714969424831731  -7.214514788816565   0.347188146036387 -13.531526956116728  -6.757570867753943  -3.827553834261646  -7.157391143868824  -5.729980234449129 10760.348192457149707   20.45203

>> # evaluating formula 1 with 119 points
# r11_119_4E2as2g.txt:3 formula 1   : problem E2, 11_119_4  (d=11 n=119 o=4 plus 0/3003 of order 5) quality N (1 negative weight, stability factor 1.002626)
# evaluating formula 2 with 119 points
# r11_119_4E2as2g.txt:125 formula 2   : problem  G, 11_119_4  (d=11 n=119 o=4 plus 0/3003 of order 5) quality N (1 negative weight, stability factor 1.002626)
E2 11 dimensions, degree 4, asymmetric 119 point rule with points at 119 distinct radii (1 negative weight, stability factor 1.002626)
#                 x1                  x2                  x3                  x4                  x5                  x6                  x7                  x8                  x9                 x10                 x11              Weight     Radius
   0.199667187070785  -0.382843528154354   0.325104559446135   0.164430451578807   1.036855807001472  -0.409116748950432   0.729271152078995  -0.071032142825921  -0.763262256310202   0.259013177247411   0.633564711915987  12.730213506998068    1.77470
   0.508745460537098   0.553694675542131  -0.039461400297019  -0.448964734581484   0.991161144712047  -0.694034526229489  -0.384277484549402   0.298942546579214   0.762849951549829  -0.166375961885240   0.508327281824217  13.278017869347249    1.82693
  -0.978107261819643   0.357084449021409   0.900213163241611   0.102933611168725  -1.237594580363286   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000  12.638991023975972    1.85387
   0.417591333337138  -0.009187560125169   0.331192077221201  -0.286328018728485  -0.581894777084917   0.597451529870779   1.215157254147294  -0.410067602263837   0.092943148409510  -0.877510868271001  -0.352093144394197  14.023887216156261    1.89976
  -0.558782069862474   0.360488975180330   0.322184208183410  -1.752735563537461   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000  11.005518007334464    1.90212
  -0.412144918718328  -0.414340317320278   0.700424546808003   0.186629546287269   0.261231576690567   0.368813534137293  -0.641723169287440  -0.328028158498069   1.411813540048440  -0.211924889299486   0.075140669165182  12.138122096190028    1.90642
   0.246159075191238  -0.425717847792092   0.142625039911257   0.330292405952746  -0.497661131867976  -0.024762643432780  -0.163029748993458   0.221323214665924  -0.966810166996079   1.021080538071768  -0.996946450736747  10.422810251277841    1.91477
   1.932368183508450   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   9.352715245620738    1.93237
   0.372183421487582  -0.245724666935487   0.123829139877588  -0.874216458084825  -0.346581247257998  -1.202686675936744   0.980322436564104   0.466024705848802  -0.003031691054288   0.136110530293291  -0.215281119991800   9.836057617369907    1.94632
   0.216048410484435  -0.192806301612184  -0.206907584681053   0.749410429529731  -0.160967291257562   1.104398234678535  -0.085068999542095  -0.434034180015842  -0.981377645622675  -0.477937272674965   0.719030757458145  11.400786119904266    1.95909
  -0.441087490470728   1.057004250897912   0.109805809493346   0.900858479554711  -0.099223719658914  -0.465244580045127   0.432420751611811   0.443194537549098   0.674624091479505   0.667648418461188   0.461124181549375   7.303095320415088    1.96434
   0.754639207066189   0.579645719626296   1.744579808065736   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   9.050412073704390    1.98722
   0.285860248865554  -2.007078303636149   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000  10.885168234268594    2.02733
  -0.138839087700140  -0.077946163211035  -0.945449759604835   1.124819256389139  -0.174437573781870   0.565872578955410  -0.053321946925412   0.683594569585445   0.742559076314812  -0.258867901596997  -0.708888262263880   7.190851518135505    2.03130
  -0.000382337638614  -0.439757825930726   0.380683065808958  -0.380591189973358  -0.158134635506156  -0.312171153713483  -0.774972419679938   0.985821256797628  -0.031312890912616  -1.055288365209190  -0.917990425807980   8.972686687483700    2.03356
  -1.261337347204293   0.014172453489711  -0.503511028245336  -0.405556685566901   0.077122536391072  -0.460000457633203  -0.114472537325788  -0.157366012083873   0.659006412798540  -1.009330516430878  -0.647711135012891   9.891511225208511    2.03400
  -0.482666634560818   0.482354791180675  -0.361657676800475   0.560150337208865  -0.783101917336855  -0.469216487360624  -0.875339884595477  -1.145901685495258  -0.381980656998619  -0.214179099837720  -0.350636799115965   8.073684502785309    2.03412
  -0.193493315969480   0.722400878262174  -0.730752533660714  -0.447243922753615   0.426016686357960  -0.766124205540462   0.029511214667788  -0.760793148144397   0.394117799904817   1.219987776958916   0.000000000000000   8.123381490038781    2.07006
   0.502078315894090  -0.322495952215687  -0.628473664908349  -0.467224640992206  -0.141671094499759   0.504670964870851  -1.756319956568782   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   8.561132977999709    2.08057
   0.707782799247334   0.342413820511478   0.305285231168894  -0.454785302579887  -0.929133022425466   0.128099239040361   0.148224864272230   0.961947847915050   1.047651729910965   0.749755637207747   0.153366727708286   8.614638471994999    2.10439
  -0.947068824311242  -0.304359002401421   0.660487738941190  -0.078124362159750   0.690412713529071   0.378927898107439  -1.048578057183980  -0.661121050180350  -0.700628049096112   0.467904619137229  -0.390256647098872   8.526456258696639    2.10971
  -0.032752049411241  -0.376561560735586  -0.634731134968300  -0.351484242273437  -0.890993984514647   0.216320300786885   0.663223973814561   1.232544313740410  -0.955508642096256  -0.274368262899278   0.028423465593174   6.257554114296552    2.11142
  -0.679776993687516  -0.489198328283220   0.150017214853374   1.536964875930338   0.536476496634961  -1.060657556716144   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   7.101508329216620    2.12108
  -0.101576146070380   0.339860458730284  -0.916717915280279   0.166008400144332   0.371099929716685  -0.841438392767940   1.076773607065068  -0.068762793373379  -0.328096585661283  -0.858028377838347   0.821692024609200   8.500945396014421    2.12666
   0.665752640316054  -0.015234634271439   0.518265586727745   0.759635804413770  -0.524891478406864  -0.495441471249681  -0.397339594087694   1.018288695768271  -0.907818594810012  -0.374128126093290   0.752197630883383   7.646676445022838    2.12950
   0.664553852730268   0.660559138228865   0.313357912725528   0.289707057386998  -0.390464105980904  -0.740174492894534   0.848367095249997  -1.073107445167870  -0.784415889532069   0.564206463207198  -0.324425987485575   7.469331850331303    2.16115
  -1.004428379855876  -0.557616389923565   0.148620615247254  -0.548860375370361  -0.199924733929010   0.112038090813304  -1.113309367174801   0.036362460647578  -0.655215081401637  -0.855237876434765   0.781659335517961   5.498384859616098    2.16983
  -1.061869713202850  -0.574473114484503  -0.769449193570389   0.863278569042369   0.098657065985701   0.116300055189732   0.924619138806291  -0.716476102912139  -0.267490879089664   0.466607068122622  -0.571470364665592   7.327840371937301    2.19141
   0.551777683109925  -0.016873669396984   0.156329314340552   1.115944573288109  -0.976200874060345   0.524056769910444  -0.285830405397569  -1.003761629087292   0.614438487769795   0.757307888501766  -0.048604895111082   7.777537338531625    2.20108
  -0.404108142987139  -0.160777565334881   1.073845472820243   0.229211251498478  -0.093944560446747   1.356651872881918  -0.220862709080437   1.254869729624525   0.000000000000000   0.000000000000000   0.000000000000000   6.401993052127263    2.20627
  -0.584767555530705   0.641628457655975  -0.661898248453467  -0.115912474375085  -0.700801469972780  -0.364010936734315  -0.957957977943906   0.833421103742833   0.415593231987364  -0.253606436212823   1.091251120155935   6.579951675031932    2.20657
  -0.949273651391961   0.062318757299953   0.729635203218030   0.156640684541243   0.400929837383519  -0.843001745439541   0.256077479847968   1.208761028757097  -0.207532720891670   0.613264413357755  -0.791890295058872   6.356841130307921    2.21500
   0.347101527380014  -0.111541193594207  -0.059036164639306  -0.978533863641635   0.290548546686185   1.007347595437313   0.001662110083740   0.665508161890285  -0.075296980069007  -0.552776239563914   1.400199751228121   6.956598313056720    2.21535
  -0.642740723652789  -0.741344252077512  -0.474904124054488  -0.520870204737243   1.113353928052873   0.387842689785418  -0.322081764685018   0.690326361347357   0.478679998858456   0.952009135136040  -0.586762814945432   6.771966962266142    2.21575
   0.621071713172146  -0.139053654503397   0.454326707797885  -0.761374884513519   1.044098672356067   0.678130773780002   0.014785009743219  -1.324084954458238   0.243557163353306   0.310904100464035   0.564496271423000   7.182302048321511    2.22918
  -0.663838435255205  -0.353719286506829  -0.849366635595220  -0.465612646025253  -0.894214379573321  -0.331294832119243  -0.613378649182631   0.318249971747192   0.703539070685879   1.029826208092315  -0.743127986632882   6.592240658116810    2.23577
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   1.231326107047468   1.279970251610503  -1.257520570353186   0.811979545651826   0.025530847438385  -0.127053122165471  -0.445296311518519   0.324511668217971  -0.876697737268674  -1.036609587214252  -0.221911017419495   2.368239838127653    2.75825
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   1.268965462911777   0.815478978658095  -0.575365025490580  -0.825303134991316  -1.297041555538498  -0.423598718310315  -0.175686561678239  -0.468205340632331  -0.748043614786868   0.332153301398558   1.461939755652159   2.476281402079010    2.86469
   0.394834517058792   1.120075852066993   0.873662123813669  -1.102243524150123   0.191947601086424  -1.334545384855426  -1.264004615438356  -0.389552906316945  -0.758125306832564   0.571380557968629  -0.690451828253619   2.365807277828980    2.88686
   0.967289478345942  -0.278291089312955   0.715514288050916  -0.963205535645054   1.059475613528098   0.483710537254885  -0.015998908726598   0.228084584990213  -1.939992160118667  -0.224768561073121  -0.826072338269094   2.430983820794725    2.89103
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   1.059054739298986   0.528993140097650   0.019943751635772  -0.669505839397905  -0.599233145201924  -0.559516326392135  -1.027067059696109  -0.951908671068332   1.582953593794656  -0.207980174923448  -1.310510741154674   1.911994376857142    2.95798
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   0.411915976876961   1.811096395364729  -0.600205436013803   0.573466657010084   0.902021236748688   1.396237126581958  -0.249893694709724   0.383954844444678   0.837342112770063  -0.770527273080959  -0.659382125986326   3.705028592759012    2.97346
   1.546273543238766  -0.737259771207179  -0.427509620877231   1.143053997757642   0.266356945165391  -0.524343715916181  -0.223601609462691  -0.457882343557541   1.086835709810136  -1.296889225362447   1.048237006646410   1.656926127175807    2.99855
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   0.804683371717888  -0.998298645519385   1.535259926940896  -0.640653685779386  -1.457842645609225   1.022189611982324  -0.715504552151368  -0.669518579513944  -0.914010888246018   0.096330010384063   0.292694013458074   1.965311010602242    3.07771
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   1.255125127367042  -0.253496094241850   0.995219118782857   0.620394577663227   1.207727889457155  -0.569973559416739  -0.074726169022796   0.157018450753077   0.878416043013068   1.819975706436007  -1.010154222564522   2.018932051974658    3.15167
   1.006475426678222  -0.588331053458266  -0.332557850090781   0.936810581724995   0.869188407487420  -0.613996501671585  -0.847795233881462  -1.091980751572183  -1.678988131230501   1.193325450305216   0.675946815066211   1.637586931059039    3.17662
   0.560798051884813  -0.481481666679045  -2.214658004936316  -1.834814183285964  -0.085432378612330  -0.052516624993436   0.426585740938604   0.567571254666246   0.946729046047814  -1.034010621286678  -0.164951693058300   1.460782179064493    3.36518
   0.692829771314419   0.026605544493803   0.509346207283382   2.063350351467962  -1.225508367788511  -0.090641692963844   1.836400920655361   0.912719922001135  -0.602505627339783   0.508439532346112   0.019569453198771   1.401096977142291    3.36675
  -0.064765271967815   2.059334704216690  -1.657261671275852   0.607014127825776  -1.081210754996759   1.415896948243824   0.931561067389210  -0.080729777113839   0.011964868854854   0.016523262659820   0.065669350257856   1.917642567941564    3.37829
   1.122584208963015   1.050809433703096   1.053089391551373   0.681388890419062  -0.063493183782438   0.938235764740446   1.197257793037271  -0.182269279421036   1.045280355649896  -0.111228158450436   2.030518292082937   1.158255996513432    3.39362
  -0.691478422366089   0.175807818969747  -0.616153779682162  -0.342897772120215  -0.549649047909243   2.085706472524078  -0.562204895632712  -0.077221310707058  -0.875119320274670  -1.159237328397442  -1.952566376761077   1.283532075866624    3.45004
  -0.742028067354959   2.237729365545229   0.319777553186676   0.236816022915035   0.170750174405314   1.744078146490904   0.257591171781053  -0.531796255222131   0.494380182859741   0.872817072566441  -1.759749219374420   1.614601100909794    3.63860
   0.503674312302423   2.203489814130148  -1.106065418619115  -0.567850752740133   0.113041264023515   0.062926917015474   0.651307971942729   1.239263398915865   0.206113232555197   0.368870558021756  -2.192209250575077   1.229281601647331    3.68998
  -0.439464235045514  -0.918833338005973   1.151045728081622   0.903625601673544  -1.496304329517762   0.189516889556268   0.973682614708785   0.797237887227814   1.395736540343192   0.072672093161094  -2.224699611164596   0.920259259609854    3.73363
  -2.224391329105290   1.347040226052942  -0.264551254344634   0.949274665672080   1.100538633668687   1.879905095375841   0.269892061528283  -1.123124783918064   0.385796010275525   0.226311289039382   1.165863579464909   0.633733257118891    3.92075
   0.104122887153178   1.958261739494251   0.881169578605788  -0.898629044078387  -0.287882547967157  -0.342518802509427   0.791081740256768   1.907194900370176  -0.354782558937686  -2.307764999188573   0.251549390239177   0.778275001457110    3.92530
   0.070127633557183   2.267537343811417  -0.834251377702031   1.815196954762500   2.075788114369109   0.907430571572931  -0.052546712605852   0.470528539689694  -0.887602056296898   1.145812621194491  -0.445360506306462   0.917975779354397    4.09794
  -0.863179908294258  -0.377919605492064   1.416405040330453   0.872594097990128  -0.726726394805462  -1.158383922842899   0.718674631539489  -0.302269487711110  -2.966427992762402  -1.287612239430497  -0.709911914134655   0.643052244284244    4.13461
   0.159836464535023   1.444080482866430   1.341774047694526  -0.672427095836319  -0.803508812077847   1.382968939436633  -1.734215138701674  -1.398303084672367   0.648158265198734  -2.192339466665796   0.326768997880713   0.604596336349101    4.14942
   1.871800291291122  -1.604463861176348  -0.978892425895898   0.424616524392174  -1.091555619982149   2.325034754290009  -0.021962073484084   1.546298829406244  -0.279348751452515   0.987595964495239  -0.810224296915185   0.507263598710669    4.23263
   0.660399245143474   2.346752022739473   0.474049397420881  -0.314874104340802   0.538945404074141  -1.215615267036022   1.291821263217988   1.854078254752105  -0.981355275309417   1.620110967651014   1.416067441786634   0.417465066667628    4.32838
   1.212111138435121   1.161499907271210  -0.060791366634306   2.275371482614189   1.541343148348755  -0.529823572842127   1.324977550940394  -2.414207227549395   0.819897610389838  -0.539098688716525   0.349586468177260   0.424184837422856    4.39600
   0.648518773401863   3.164177427375591  -0.327132787651011   0.317290729448839   0.548871576091184   2.598173587841707  -0.208499707495043   0.653053421723470  -1.330674513951346   0.299354838191919  -0.904546999546359   1.481456322567017    4.56514
   0.034478396645228  -0.794777886661475  -0.758349529825847   0.374758516706799   1.216146985951660  -2.023039658641132  -0.605304020330676   2.908601175167982   2.318317348460706  -1.025707101661996   0.003558783308043   0.302073646736538    4.70884
  -0.457092635726668   3.680341244465366  -1.669890067652103  -0.133280251991809   1.582835315374541   2.038284901325393   0.095703548523514  -0.640945141741024  -1.262444004592894  -0.731226921753427  -1.360882369767271   1.090191357824420    5.25553
  -0.081121301224234  -2.528262264556004   3.004282063870473  -1.074783854387563  -0.227203189357605  -1.954303533309361   0.907069865984519   0.278592527098189   1.282133406259091  -1.466300556541710   2.230301902942271   0.348685012347374    5.48808
  -0.477058589158498  -1.339402764020960  -0.783808538446896  -2.687854149578258   3.640631050864692  -1.824445354029617   2.318899017129778  -1.046970986834884  -0.445612336320889   0.352218928908895  -1.426033869902474   0.126296157085880    5.93910
  -1.413903987749312   4.257399800759125  -2.022899714620057   0.302483360046745   1.236730792332955   3.155347694444353  -0.540703769630716   1.496244364941804  -1.066626370096001  -0.140022984949967  -1.427425553139582   0.892309120568204    6.44359
  -1.174271763848623   4.658750422649154  -1.145300572220240   1.867407233172026   0.920438734786574   2.684085071481592   0.222571675458883   0.858053069047864  -1.841893082844858  -0.845374329957629  -2.451771156082472   0.703098444626512    6.84379
  -3.856162526392540  -2.904103062166723  -0.057503048107337   3.310625468237189  -1.969186067923478   1.118557117377461  -3.201649963956901   1.067833668857230  -0.451599244615200   0.289522080307826  -0.324267890438454   0.071176994636943    7.15402
  -3.403010001091590   2.901448822070696   3.213049789318764  -2.385328996155109  -0.048307589806399  -0.852559440614071  -4.023299438330313   2.678940163871384   3.347752011646363   1.151721164463975   0.368610601711034   0.033059745184117    8.53083
  -1.069818904637261   6.781451991265411  -2.505479006386894   1.328803253651025   2.024701073436689   4.907599306107302   0.403915376551676   1.263934841565325  -1.982650530364804  -0.555473979438386  -2.926331440973529  -0.712175037782697    9.89562
  -5.016592591835167   2.740593499397233  -1.240183007243041   3.876873506183251   1.617353285382470  -1.980033186156067  -5.132043976365063  -1.753613831141353   5.234334348553792   2.132368192554906  -3.106226877084363   0.008644727639552   11.26004
  -5.700523871490173   2.648760202417537  -2.942045404632263  -1.777755105834298  -5.183227249363630  -3.658030729166145   6.439579128505549  -1.239306735591548  -0.009627293948506   1.360912403259047  -2.224184656608347   0.009808635612752   11.89026
   1.146908657751917  -9.369214907173790   3.525642990930376  -2.098803954775761  -3.189698457966994  -7.970783312124218  -1.768166869471645  -1.983698747560771   2.497826602701537   1.134872895562093   4.093973107656122   0.056398786160998   14.52548

# G_n 11 dimensions, degree 4, asymmetric 119 point rule with points at 119 distinct radii (1 negative weight, stability factor 1.002626)
#                 x1                  x2                  x3                  x4                  x5                  x6                  x7                  x8                  x9                 x10                 x11              Weight     Radius
   0.282372043916378  -0.541422509782615   0.459767277157975   0.232539774689854   1.466335544486776  -0.578578454959686   1.031345153917550  -0.100454619748842  -1.079415834521315   0.366299948096615   0.895995808232627   0.023469908029044    2.50980
   0.719474730087314   0.783042519565486  -0.055806847490305  -0.634932016672384   1.401713533348986  -0.981513039748935  -0.543450430364372   0.422768603742728   1.078832747537466  -0.235291141750993   0.718883336080076   0.024479861082475    2.58367
  -1.383252555120978   0.504993670718586   1.273093664483128   0.145570108938859  -1.750223040269204   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.023301726773831    2.62176
   0.590563327134849  -0.012993172134150   0.468376327356742  -0.404928967373238  -0.822923485627591   0.844924056403757   1.718491869231172  -0.579923164611357   0.131441461010356  -1.240987771038622  -0.497934900020884   0.025854974309105    2.68667
  -0.790237181610420   0.509808397785988   0.455637276795452  -2.478742405208339   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.020290193507133    2.69001
  -0.582860933714571  -0.585965696192315   0.990549893514883   0.263934035498996   0.369437238675894   0.521581101963729  -0.907533609295262  -0.463901870588185   1.996605855878497  -0.299707052651766   0.106264953419184   0.022378305680913    2.69608
   0.348121502636647  -0.602055954091856   0.201702265776521   0.467104000047234  -0.703799122153587  -0.035019666182842  -0.230558882096906   0.312998291848554  -1.367276050406102   1.444025945216342  -1.409895191591581   0.019215891223441    2.70789
   2.732781292615837   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.017243023183853    2.73278
   0.526346842358122  -0.347507156589734   0.175120849031836  -1.236328771473271  -0.490139900336395  -1.700855808395133   1.386385285287546   0.659058459412303  -0.004287458605992   0.192489357922556  -0.304453479615349   0.018134131648394    2.75251
   0.305538592236229  -0.272669286650951  -0.292611512413819   1.059826393224794  -0.227642126394914   1.561854961743330  -0.120305732889894  -0.613817023911925  -1.387877576249303  -0.675905372980563   1.016863048960750   0.021018924902229    2.77057
  -0.623791911216798   1.494829747105808   0.155288865012797   1.274006279565058  -0.140323530050769  -0.657955194920390   0.611535291580950   0.626771725771715   0.954062539673940   0.944197448284704   0.652128071485255   0.013464265576006    2.77800
   1.067221001331510   0.819742838066992   2.467208425208852   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.016685685505432    2.81035
   0.404267440889024  -2.838437357747069   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.020068312067075    2.86708
  -0.196348120812987  -0.110232521148024  -1.337067872575553   1.590734647603889  -0.246691982629846   0.800264675733760  -0.075408620514069   0.966748711472348   1.050137116587581  -0.366094497301550  -1.002519394700677   0.013257328613411    2.87269
  -0.000540707073932  -0.621911481590925   0.538367154632833  -0.538237222580047  -0.223636146213715  -0.441476679363206  -1.095976506376446   1.394161791438817  -0.044283115005817  -1.492403118293360  -1.298234510306282   0.016542388013595    2.87589
  -1.783800383144015   0.020042875937289  -0.712072124948964  -0.573543765039801   0.109067736928850  -0.650538885882701  -0.161888614805394  -0.222549148545574   0.931975806670513  -1.427408905253596  -0.916001871635353   0.018236368038625    2.87651
  -0.682593700700893   0.682152687563371  -0.511461191467554   0.792172203848611  -1.107473352218136  -0.663572320114402  -1.237917536481010  -1.620549704773596  -0.540202225691661  -0.302894987767298  -0.495875316776882   0.014884953235994    2.87668
  -0.273640871672567   1.021629119508655  -1.033440143841546  -0.632498421247148   0.602478575644717  -1.083463241937631   0.041735160025317  -1.075923988266314   0.557366737798024   1.725323260104753   0.000000000000000   0.014976576500560    2.92750
   0.710045963710899  -0.456078149433887  -0.888795980507711  -0.660755423966123  -0.200353183237796   0.713712523056342  -2.483811502446071   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.015783631869772    2.94238
   1.000956033909996   0.484246268911267   0.431738514311273  -0.643163542876436  -1.313992521562826   0.181159681180480   0.209621613334671   1.360399692817105   1.481603285083643   1.060314590604875   0.216893306341824   0.015882276642889    2.97606
  -1.339357575841727  -0.430428629026407   0.934070718191777  -0.110484532518063   0.976391023107704   0.535884972665139  -1.482913309676432  -0.934966355535423  -0.990837689210647   0.661717058280851  -0.551906243133363   0.015719700545105    2.98358
  -0.046318392472930  -0.532538466260645  -0.897645379532624  -0.497073782383496  -1.260055776893504   0.305923103189387   0.937940338659488   1.743080884717451  -1.351293280617331  -0.388015318476927   0.040196850531474   0.011536665859419    2.98599
  -0.961349843862148  -0.691830910548356   0.212156379835062   2.173596572431785   0.758692337435599  -1.499996301741481   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.013092612096613    2.99966
  -0.143650363386354   0.480635270050762  -1.296434908659810   0.234771330952015   0.524814553601002  -1.189973586953882   1.522787838716811  -0.097245274975270  -0.463998641210510  -1.213435368840037   1.162048005296111   0.015672667743921    3.00756
   0.941516413120624  -0.021545026404485   0.732938221661629   1.074287257066138  -0.742308647537036  -0.700660048003348  -0.561923042826664   1.440077683966623  -1.283849368954788  -0.529097069986332   1.063768091180213   0.014097704865193    3.01157
   0.939821071458425   0.934171692032722   0.443155010053398   0.409707649671914  -0.552199634298048  -1.046764806374088   1.199772251973611  -1.517603102839944  -1.109331589517245   0.797908432246231  -0.458807631488360   0.013770745594275    3.05633
  -1.420476237224633  -0.788588661231437   0.210181289730949  -0.776205786697913  -0.282736270176179   0.158445787530583  -1.574457206175625   0.051424285009026  -0.926614054389502  -1.209489003909256   1.105433233445100   0.010137032414463    3.06861
  -1.501710549884640  -0.812427669722635  -1.088165485104282   1.220860260445718   0.139522160740946   0.164473115354080   1.307608926129537  -1.013250221854504  -0.378289229019681   0.659882044038150  -0.808181140204370   0.013509886498475    3.09912
   0.780331482868861  -0.023862972108225   0.221083036536873   1.578183950400695  -1.380556515696607   0.741128191460773  -0.404225235851818  -1.419533309244913   0.868947242648082   1.070995086811368  -0.068737701863793   0.014338965008516    3.11280
  -0.571495216477760  -0.227373813421982   1.518646831555335   0.324153660517643  -0.132857671494997   1.918595478048531  -0.312347038603947   1.774653790646441   0.000000000000000   0.000000000000000   0.000000000000000   0.011802959004057    3.12014
  -0.826986207867260   0.907399666821610  -0.936065479873876  -0.163924993309479  -0.991082943366529  -0.514789203581775  -1.354757164591818   1.178635428081005   0.587737585106924  -0.358653661597284   1.543262134079280   0.012131050320850    3.12056
  -1.342475672201944   0.088132031763844   1.031859999975847   0.221523380497662   0.567000413587852  -1.192184501504788   0.362148245019244   1.709446240536366  -0.293495588521270   0.867286850691291  -1.119901995183869   0.011719715195786    3.13249
   0.490875687541196  -0.157743068744228  -0.083489744703402  -1.383855861203345   0.410897695251311   1.424604631491323   0.002350578622648   0.941170668415212  -0.106486010419283  -0.781743654948921   1.980181478218219   0.012825450453969    3.13298
  -0.908972648479192  -1.048419095675286  -0.671615853064757  -0.736621707775443   1.574520224773680   0.548492391961764  -0.455492399810593   0.976268902681087   0.676955746422323   1.346344230412374  -0.829807930792026   0.012485057041091    3.13355
   0.878328039974375  -0.196651564096247   0.642514991916077  -1.076746687729305   1.476578502901688   0.959021737342253   0.020909161298753  -1.872538900328976   0.344441843627484   0.439684795473669   0.798318282955507   0.013241566484194    3.15253
  -0.938809318362484  -0.500234612250873  -1.201185815485965  -0.658475718821361  -1.264610103261631  -0.468521644727175  -0.867448404544218   0.450073426269786   0.994954495423306   1.456394190371437  -1.050941677275281   0.012153706759612    3.16185
  -0.625430051642343   0.815605170194092   1.611476365849843  -0.085806943794396   1.434087469859695  -0.839053866488215   0.974786388085872  -0.737246485362297   0.406800322014716  -0.755491414529283  -1.260214761742785   0.011293404921723    3.19990
   0.225029798999901  -0.739624090852163  -0.018745762109659   1.530530607787177   0.774079869787099   0.702185412335689  -0.726896804930021   1.033650738328009   0.896647121236685   1.195551872607811   1.546462804196804   0.011727690741908    3.20227
   0.046205947075824   1.271758123471701   0.931421869311278   0.985598761623176   0.294027865464466  -0.737712756861531  -1.431591752257945  -0.961467228690449  -0.251594024092772  -0.121046552706545   1.771558301019493   0.011321805260779    3.20615
  -1.437983921148729  -0.691498659917157  -0.781756561774913  -0.023607512218213  -0.450861480142174  -0.050309621087422   1.239946618810067   2.052132605158615   0.694120479870220   0.042793756199180   0.844697353920556   0.010097300572194    3.21082
   0.257470680534025  -0.697914870419116  -0.635492815538878   0.371101096148173   0.328751065862758  -0.321085526094723   1.722045099586294  -0.648679947502550   2.320554368518700   0.302431840285974  -0.554172014308122   0.012011500914687    3.23665
   0.962314743070242  -0.015091872996615   0.027901333637589  -1.059909776271623   0.352155455805592  -0.958366664096409  -0.514764248986507  -1.034994801886863  -1.043775386530474  -2.225838927447899   0.251860152201601   0.012065617647773    3.24598
   1.536625198211817  -0.447099181530184  -1.311228608874135  -0.984381198299658  -0.441923042907377   0.607411018508816   0.041643808904808  -1.793041749655059   0.232950935495521   0.221725644400674  -1.189857577182902   0.008763772116312    3.24802
   1.156182454337988  -0.371746554824496  -1.777784343709943  -0.092231695972908   0.729751175745799   0.831297152385336   1.303998281644080   0.136121711012224   0.233010996788662   1.238070282972122   1.175826576770916   0.010451660206352    3.24903
   0.569566842487466   0.379793148760835   0.687003784387043   1.312442713739195  -0.341141049496973  -0.607647656837593  -2.267578260020262   1.094084010000522   0.127356971424104   0.503736132922152  -0.963491517441795   0.010167182012847    3.26894
  -0.153236419002350   1.295248129937649  -0.488330449358639  -1.264233995304072  -0.950916218520040  -0.411268674629660   0.386781757795496  -1.434157051131238   1.578572317269363  -0.548383557298964   1.078959235854479   0.010016718449225    3.28245
   0.313680075322258  -0.543290700172634  -0.912869759346501   0.265293971624473   1.885807141607223  -1.311460003012318  -1.338619890211737  -1.054311019092974   0.252227909877673  -0.297019848322652  -1.085870277710802   0.009690475596742    3.28754
   0.817954964745658  -0.589416315952236  -1.070786207620484   0.312356310066423   0.419895445872221  -1.259582046357497   0.773042275502474   0.002998588721378  -0.666089243577573  -0.529241188550233  -2.362503583270170   0.009148577085246    3.30549
  -0.457388394485615  -0.772034420242449  -1.698582049328271  -1.595030017289072  -0.303362018862238   0.037376988603884   0.073505171969117  -1.104519049647896  -1.818091497837354   0.432538400480645   0.103963936651973   0.011140093572658    3.32516
  -1.457159047247371   0.151649468003009   0.562256119539076   1.721441601502607  -0.240636102554127   0.284592019790264   0.636271655068589   0.243721030456740   0.479546424258465  -2.119333426239823   1.000476348428052   0.009075772335246    3.42804
   0.783417667993256  -0.802407076066806   1.347692140663311   1.839723721993427   0.303147212474366   0.313727945890434  -0.636038007649859  -0.932936958190380  -0.310247817753725  -1.445124108706036  -1.355402602233653   0.009398864367965    3.45622
  -1.213394548798334   1.389739249217587   1.121312367666487  -0.802769556315586  -0.149681075595946   0.238242511486345   1.128579837017019  -0.547468565146544  -1.642357578494740  -0.007728072624903   1.556384163709719   0.008392898638651    3.47531
  -1.495861863696086   0.708255717779405  -0.805049269604766  -0.287072884757637   0.059282326126680  -2.334136701618926  -0.686210534971337   0.545160700705673  -1.603063844932174   0.000000000000000   0.000000000000000   0.008425704800189    3.50134
   0.434874190605149   0.765698808261379   0.377109548907440  -0.858660240263364  -0.233258037855238   1.043851016191611  -1.578454414093484  -0.595163593047034   0.297907378356716   2.324873749431439   1.070542343207770   0.007556925984796    3.50493
  -1.271666332363469   0.074251617917525  -0.699915531764889   0.705101030321638  -1.057656011268623   0.468098501199925  -0.363849032706945   0.469684376393649  -1.599574861567614   2.066009440511599   1.085742399874294   0.008127518780004    3.50804
  -1.520765928161916  -0.050619997198751   1.427669575030547   0.294329474992412  -0.066500189598882  -1.047306719236597   0.442957633329557  -1.121666756647431   0.824412257424732   2.111585122653270   0.512571127152890   0.006533256869582    3.52093
   1.157114893617663  -0.196332706867924  -1.134816098369348  -1.436952295064619   1.102223993260523  -0.687047998259224  -0.979726595790923   1.806069198690593  -1.041019908989060   0.869978907356126   0.275244055172873   0.007234414849355    3.54332
   0.034174939802093  -1.126212052379294  -1.421351156715976   0.816262292423839  -2.382505115421084  -0.622303473632481   0.050342356966579  -0.433010654795045  -0.296772313954230  -1.463939867566394  -0.433098430494080   0.007803179712562    3.55365
   1.463488776255537  -0.640421493090105   0.469729668321945   0.978151023622513   1.443818839687516   0.045318459887970   1.579697795477307   1.937822331005116   0.230993552963985  -0.906636215784302  -0.460197694116222   0.007837903675034    3.62681
  -0.400097468260987  -0.378891736716483  -2.375874943591720   0.756912691759596   0.456069834256685   0.218325925933249  -1.226947099888409  -1.408186333772408   0.930849502028273  -0.333696600312828   1.394872038043862   0.007300621423577    3.63165
   0.540091140457666   1.026951950180865   0.058499010580093  -1.397607263424103  -2.715560617583881  -0.025420638606646  -0.617154269992354   0.484672307797750  -1.099262925304260  -0.171182421311584  -0.939348436684051   0.006209219942917    3.66249
   0.353368384682509  -0.395632654088701   0.515472094996315  -1.360087876492800  -0.430469405312415   0.963606229125670   2.083778931204861  -0.096251425829527  -0.363641829004751   2.390508351629774  -0.275615183769755   0.007043881761630    3.71280
  -1.128549992448696  -0.566435654953419   0.319103914780837  -0.177261769076148   0.098648036117125  -0.133833774103801   0.663445999096428  -3.263836941729063  -0.220095550097889  -0.919744679408621   0.370900765117028   0.005781763645456    3.72560
   1.169453128811341  -0.103280592642653  -2.202776302825149   1.248185343601504  -0.752023822716939  -1.808285360090036  -0.190464871993594   0.610541592791093   0.266794586929375   1.339946407587262   0.123815330198351   0.006948803346173    3.73027
  -1.387129542153515  -0.901904236747596  -0.632729166013572  -1.039480627579102  -1.367172594211852   2.394434912870906   0.114007745318574  -0.653207065391036   1.130879607947263   0.421355656764821   0.473460408452771   0.007850615646858    3.73379
   0.501046523070693   1.454664817494018   0.526829695095873   0.999672094734265  -1.210856245969563  -2.295482096014322   0.302617225111500   0.044137487919772   1.297946611965609  -1.146063500390867  -0.694289609557669   0.007216460863859    3.73538
   0.632312149004684  -0.501187579753135  -0.847887033058003   1.044202539651494   1.610108129846710   2.243979457986987  -0.353454039021966  -0.870689767421938   0.037632855356025   0.569928009118302  -1.722433658144706   0.004807952151993    3.77680
   1.240040530202735  -0.568893764397531  -0.241174351390116   0.205216369061769  -1.704435301025255   0.914578299372900  -0.615925511861276   0.993790082653665   1.754631358786157  -1.914647181795821   0.711391855340593   0.005502559781235    3.78429
  -0.905974840467122   0.417680640807064   1.286493106553076   0.327052254428894   2.615220758869172   0.025420156256591  -1.116345613054064   0.938628359769488  -0.587082241884877  -1.337392460486558   0.689251247940555   0.005900138303379    3.78588
  -0.212143733111333  -1.340184856019638  -0.176724491992725   0.383965932111997  -1.841200975800984  -0.442431602873871   1.364475464498436  -0.817205758938582   0.231809463349943   0.477340700218507   2.470002292504991   0.006416128188129    3.81020
   1.741358080290633   1.810151289261649  -1.778402645556596   1.148312485830326   0.036106070706118  -0.179680248508231  -0.629744083024250   0.458928802342133  -1.239837830147243  -1.465987337124359  -0.313829570474707   0.004366177453427    3.90076
   1.145784460256673  -0.794163085992192   1.169814200481197  -2.181089701211298   0.851758680660346   1.222425507860111  -0.199365802191087   0.860840325788691   1.315181111635178  -0.178801708148786  -1.577963687720511   0.005518854932776    3.91425
  -2.158950160626985  -1.887562874111668   0.751226551945193  -0.951520007079889   0.220529134370703   0.598479355175213   1.593008369894022   0.574272468542357  -1.286273294057614  -0.917788878062821  -0.701138855756022   0.004823137114167    3.99455
  -0.458490795318831  -1.256293358442447   2.022190393334207   1.417125022394651   0.848185907704344   1.893586529717410   1.585259117921576  -0.458197311549609  -0.246829368226037   0.983822782620437   0.259236065696273   0.004800592111829    4.00126
  -0.118395871754522  -0.699324138034570   1.778123036779547  -1.091983276465607   0.392242421232794  -0.055618794112319  -0.668960007603156   1.830507063570666  -1.260267879272125   1.900691164174717   1.440807739265694   0.004036708966806    4.01114
   1.794588167832950   1.153261431448409  -0.813689022363916  -1.167154886573784  -1.834293758804082  -0.599059052438366  -0.248458318252052  -0.662142342697858  -1.057893425278232   0.469735703624866   2.067495029815772   0.004565367008878    4.05128
   0.558380328917612   1.584026460879715   1.235544824428972  -1.558807740890981   0.271454900721463  -1.887332182864916  -1.787572470055183  -0.550911003375301  -1.072151090900819   0.808054134355566  -0.976446339681476   0.004361692692315    4.08264
   1.367953899017598  -0.393563032794006   1.011890010233362  -1.362178331862049   1.498324781655010   0.684070002048684  -0.022625873704310   0.322560313461286  -2.743563223737295  -0.317870747464634  -1.168242704281340   0.004481854657251    4.08853
  -2.456377242483713  -0.650054109076900  -0.937077252765566  -0.835418512571119   1.773415672882418  -0.549644860068497  -0.099940616578107  -0.148189093517633   0.258463327911586   0.786199419912064   2.223799082437493   0.004152120850361    4.14025
  -0.581629191541820   2.027392083885413  -1.158977198773034   0.095433434574426   1.338007306869600   1.892890928113547   1.466106446207462   0.863738204134131  -1.201068540006335   0.068710390852161  -1.281690622179512   0.009435463379483    4.14244
  -0.229567950093616  -1.523719672360148  -0.787016688375380  -0.444776666060492   2.169947343224472   1.570918085917926   0.653932373475057  -0.463029178435075   0.555970420868129  -2.430472457782567   0.187582093473429   0.004407726426071    4.15471
   1.497729575612070   0.748109273128281   0.028204724047880  -0.946824238164503  -0.847443640968032  -0.791275577152874  -1.452492165288877  -1.346202152765388   2.238634440951576  -0.294128384081374  -1.853342063776589   0.003525025888389    4.18321
  -0.729838130322898  -1.050573257938774   1.349869644539751  -1.381687057318873  -0.745491986306529  -0.327885044669245  -0.108318004924237  -1.927994343106389   0.181439460937318   0.680072230982256  -2.699301999836562   0.003935297612979    4.18824
   0.582537161057641   2.561277085089742  -0.848818667820749   0.811004323912359   1.275650666558417   1.974577480701067  -0.353403052209958   0.542994148352569   1.184180572225570  -1.089690119769487  -0.932507145356235   0.006830732278703    4.20511
   2.186761015986981  -1.042642767433309  -0.604589903889609   1.616522466153624   0.376685604285073  -0.741533994393763  -0.316220428670538  -0.647543420230187   1.537017800884890  -1.834078331403120   1.482430991380713   0.003054772317397    4.24059
  -1.330242376471856   0.913328803195718   0.906396523850297  -0.975259908551689   1.385229749365390   0.632805424919845   2.307128454887405   0.884421014696539   2.155876775392944   0.228300660388159   0.774473628498713   0.003629385574033    4.25447
   1.137994137699490  -1.411807483792219   2.171185410447728  -0.906021131213475  -2.061700841226378   1.445594412582278  -1.011876241592129  -0.946842255409505  -1.292606594314153   0.136231207148714   0.413931843457907   0.003623322471532    4.35254
  -0.574067334187789  -1.511402678690493  -2.191827598812707   1.262577219221131   1.399542613566677   0.099365859687869  -1.003040654268474   1.645819138793529  -1.847688928830063  -1.122297304306171   0.114512021241433   0.003577574200023    4.40251
   1.775014977597750  -0.358497614485414   1.407452375315673   0.877370425754097   1.707985160926591  -0.806064337921222  -0.105678761696232   0.222057622597896   1.242267881435152   2.573834327231331  -1.428573801639141   0.003722180272207    4.45713
   1.423371198603506  -0.832025754965917  -0.470307821872009   1.324850230050126   1.229218034126267  -0.868322179913479  -1.198963517870451  -1.544293988723718  -2.374447786249513   1.687617036146573   0.955933153309609   0.003019117836507    4.49242
   0.793088210727930  -0.680917903051485  -3.131999386599093  -2.594819102437528  -0.120819628499417  -0.074269723315843   0.603283340350371   0.802666965962127   1.338877056813249  -1.462311844261446  -0.233276921459540   0.002693153840213    4.75908
   0.979809259008698   0.037625921857405   0.720324314283482   2.918018050973379  -1.733130554528300  -0.128186711505978   2.597063087945284   1.290780892342137  -0.852071629590139   0.719042082290533   0.027675386121916   0.002583115921443    4.76130
  -0.091591925987643   2.912339068168809  -2.343721931919367   0.858447612123217  -1.529062913500239   2.002380667129027   1.317426295680608  -0.114169145681699   0.016920879806521   0.023367422148240   0.092870485766882   0.003535439109283    4.77763
   1.587573813221356   1.486068952612505   1.489293299923148   0.963629410080974  -0.089792921623481   1.326865743199372   1.693178208570315  -0.257767686961105   1.478249655442315  -0.157300370198379   2.871586507310310   0.002135405010868    4.79930
  -0.977898162998411   0.248629801958200  -0.871373031733874  -0.484930679839984  -0.777321138098720   2.949634380572869  -0.795077788236339  -0.109207424906243  -1.237605611427180  -1.639409151828779  -2.761345851449110   0.002366368777425    4.87909
  -1.049386156514731   3.164627217674568   0.452233752659062   0.334908431393668   0.241477212421574   2.466498968605976   0.364288928680331  -0.752073476554265   0.699159159568682   1.234349741494221  -2.488661212414645   0.002976740281781    5.14576
   0.712303043477083   3.116205179693909  -1.564212715882961  -0.803062235928877   0.159864488689801   0.088992099481623   0.921088567202982   1.752583106099423   0.291488128863991   0.521661745914518  -3.100252053723079   0.002266350530303    5.21842
  -0.621496281379232  -1.299426568168523   1.627824479564598   1.277919581194235  -2.116093876241523   0.268017355509189   1.376995159168023   1.127464632555234   1.973869544852887   0.102773859754506  -3.146200362315162   0.001696625133117    5.28015
  -3.145764385645894   1.905002556746295  -0.374131971837036   1.342477106610617   1.556396661649801   2.658587281854957   0.381685013790335  -1.588338301654221   0.545597950041270   0.320052494277613   1.648780085956219   0.001168374847079    5.54478
   0.147251999165516   2.769400310669276   1.246161968814997  -1.270853381678068  -0.407127403705788  -0.484394735876643   1.118758526016850   2.697180894192436  -0.501738306543225  -3.263672560622590   0.355744559282916   0.001434857529723    5.55121
   0.099175450473741   3.206782064805650  -1.179809612774694   2.567076151803422   2.935607703953495   1.283300621230556  -0.074312273625327   0.665427842312870  -1.255258866005243   1.620423748831404  -0.629834868163877   0.001692415221669    5.79536
  -1.220720733077725  -0.534459031573578   2.003099217848986   1.234034407824391  -1.027746323668269  -1.638202254119381   1.016359410856500  -0.427473609012778  -4.195162699167811  -1.820958692080210  -1.003967057059389   0.001185555687886    5.84722
   0.226042895907293   2.042238204027922   1.897555055889760  -0.950955518638827  -1.136333059526816   1.955813430491889  -2.452550569224535  -1.977499186651853   0.916634209208357  -3.100436207084415   0.462121148565966   0.001114656906658    5.86816
   2.647125357997691  -2.269054552812991  -1.384362944806233   0.600498447603061  -1.543692761863246   3.288095682505524  -0.031059062178937   2.186796776027783  -0.395058792936195   1.396671607134029  -1.145830189261593   0.000935210552571    5.98584
   0.933945569062829   3.318808538084713   0.670407087067498  -0.445299228798846   0.762183899820245  -1.719139597270186   1.826911150604886   2.622062613571515  -1.387845939849059   2.291182903001534   2.002621781409762   0.000769654547792    6.12126
   1.714184011078473   1.642608921558114  -0.085971975169534   3.217861210149880   2.179788384665544  -0.749283682378324   1.873801222379812  -3.414204603579378   1.159510320370685  -0.762400677040383   0.494389924518382   0.000782043373912    6.21688
   0.917144044798471   4.474822631549495  -0.462635624992937   0.448716852801736   0.776221626909218   3.674372325325417  -0.294863114090292   0.923557005955521  -1.881857944734273   0.423351672133018  -1.279222634562247   0.002731269481111    6.45608
   0.048759816144626  -1.123985666390882  -1.072468190098993   0.529988576941606   1.719891561371923  -2.861010122469050  -0.856029154910769   4.113383229457011   3.278595836077935  -1.450568894193042   0.005032879619591   0.000556914517027    6.65930
  -0.646426604705418   5.204788502083979  -2.361581181345640  -0.188486739963399   2.238467170005721   2.882570151434741   0.135345256289214  -0.906433312187297  -1.785365433031832  -1.034111029915981  -1.924578304119148   0.002009918442305    7.43243
  -0.114722844388687  -3.575502783771034   4.248696439919724  -1.519973903494397  -0.321313831803861  -2.763802561799829   1.282790506495332   0.393989330198058   1.813210451903255  -2.073662133576548   3.154123199327299   0.000642849011637    7.76132
  -0.674662726834530  -1.894201554358418  -1.108472665375470  -3.801199792014486   5.148629807729677  -2.580155363477444   3.279418439798631  -1.480640568993087  -0.630191009585773   0.498112786187503  -2.016716439219524   0.000232844420842    8.39916
  -1.999562195368479   6.020872538678254  -2.860812211736278   0.427776070170247   1.749001459521644   4.462335503486164  -0.764670604237977   2.116009073525134  -1.508437478574629  -0.198022404360232  -2.018684576527904   0.001645095188835    9.11261
  -1.660671054346374   6.588468031421607  -1.619699602227261   2.640912635625367   1.301696942068567   3.795869510652419   0.314763882034071   1.213470287483264  -2.604830178200391  -1.195539842708079  -3.467328020766809   0.001296259157136    9.67859
  -5.453437343539029  -4.107021937045102  -0.081321590511198   4.681931437118489  -2.784849644093299   1.581878645684242  -4.527816800998878   1.510144856856259  -0.638657776492145   0.409446052577832  -0.458584048500179   0.000131224626908   10.11731
  -4.812582896435020   4.103268274703840   4.543938588634746  -3.373364617084289  -0.068317248669757  -1.205701123645386  -5.689804631174832   3.788593512533049   4.734436298332340   1.628779690856907   0.521294112174177   0.000060950209398   12.06441
  -1.512952404220967   9.590421378629628  -3.543282391073185   1.879211583038642   2.863359717805388   6.940393497389947   0.571222603570512   1.787473794897627  -2.803891269488173  -0.785558835267037  -4.138457611823416  -0.001312993111086   13.99452
  -7.094533280272884   3.875784495798980  -1.753883628667876   5.482727092048854   2.287282951336544  -2.800189785810294  -7.257806194069796  -2.479984463165137   7.402466625719576   3.015624017883879  -4.392868177380266   0.000015937750182   15.92410
  -8.061758171693157   3.745912601732902  -4.160680512348273  -2.514125381248621  -7.330190272911705  -5.173236668764540   9.106940139506982  -1.752644393413875  -0.013615049671240   1.924620777890990  -3.145472106598044   0.000018083575393   16.81536
   1.621973778595545 -13.250070790513210   4.986012133859002  -2.968157017606011  -4.510914819137068 -11.272389862743225  -2.500565567345697  -2.805373672462949   3.532460257996821   1.604952640473404   5.789752292837764   0.000103978957102   20.54213

>> # evaluating formula 1 with 123 points
# r11_123_4Sa.txt:3 formula 1   : problem  S, 11_123_4  (d=11 n=123 o=4 plus 0/3003 of order 5) quality NO (6 negative weights, stability factor 6.057536)
S 11 dimensions, degree 4, asymmetric 123 point rule with points at 123 distinct radii (6 negative weights, stability factor 6.057536)
#                 x1                  x2                  x3                  x4                  x5                  x6                  x7                  x8                  x9                  x10                  x11              Weight     Radius
  -0.032293843320796   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000  -1.831127715431129    0.03229
   0.046556732471094   0.402215888425812  -0.000000000000000   0.000000000000000   0.000000000000000  -0.000000000000000   0.000000000000000  -0.000000000000000  -0.000000000000000   0.000000000000000  -0.000000000000000   0.212229366176981    0.40490
   0.120805401179242   0.069426993347232  -0.419850028065087   0.000000000000000  -0.000000000000000  -0.000000000000000   0.000000000000000  -0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.198256742893402    0.44237
  -0.157204844235702   0.044143341351749   0.105907914751639  -0.422835013144298   0.000000000000000  -0.000000000000000  -0.000000000000000  -0.000000000000000   0.000000000000000   0.000000000000000  -0.000000000000000   0.326278435008882    0.46548
  -0.131945257286318  -0.291951844946472   0.149932543521737   0.035964161337208  -0.316494158740413   0.000000000000000  -0.000000000000000  -0.000000000000000   0.000000000000000  -0.000000000000000  -0.000000000000000   0.134711576677736    0.47601
   0.052821644998747  -0.262846093560140   0.064321178083906  -0.057777164698373   0.044324005730958  -0.407086531135417   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000  -0.000000000000000   0.141165497545257    0.49703
  -0.310821455961586   0.085711006171066   0.106220821418915   0.071517934138053   0.010865707179201  -0.101432346713871   0.372466680771507   0.000000000000000  -0.000000000000000  -0.000000000000000   0.000000000000000   0.113043834482842    0.51913
   0.035068022144493  -0.069435114161195  -0.115255305487718  -0.200247878408121  -0.109635567601254  -0.028686354784969  -0.290060670594380   0.340280660612353  -0.000000000000000  -0.000000000000000   0.000000000000000   0.117997983853311    0.52173
  -0.237919882608357   0.110210628704133   0.110560725891666   0.161307963391233  -0.044961133430982   0.266913182443172  -0.085596635628579  -0.124388180688117   0.266849691217024  -0.000000000000000  -0.000000000000000   0.121076769804106    0.52371
  -0.144879775618961   0.050405871648633   0.132192507483075   0.325794810400899   0.062934212575829  -0.234164509750172  -0.130538491353089  -0.060582882306537  -0.110868501046577  -0.221798976305335  -0.000000000000000   0.119338773886741    0.53679
  -0.183176871389208  -0.096895989545120   0.177468630317000   0.003028986005753   0.073071272548212   0.062130204697734   0.018575256469800   0.400481716885654  -0.009605276660880  -0.037320693371002   0.216372369706728   0.109229532532936    0.54100
   0.402840138978131  -0.025756443213507   0.191936805239631   0.121765475427244  -0.051601243729533   0.011884928123272  -0.191967836774104   0.054177796463941   0.072505212805583  -0.158007159100488   0.157349795258227   0.110108733319975    0.55873
   0.059735585977529  -0.124128873585855   0.182332343939932  -0.097022163682730   0.294906170142205   0.188363236602922   0.139972577666333  -0.247882249996663  -0.094697841843668   0.043621413729610  -0.204026555754402   1.426345203881872    0.56358
   0.049927716788877  -0.034192738647611  -0.114297539475484   0.033802460697298  -0.196168576405972  -0.081536863608352   0.313546220352926  -0.245954383102404   0.114026404831662  -0.241795202362423   0.176861860179675   0.106241228720265    0.56969
  -0.145177734765589  -0.119057499470195  -0.140126969417728   0.270071458674058  -0.181427085083208   0.194825116614098  -0.206949712732510  -0.050848112305954  -0.126745021074983   0.278911758592171  -0.004331508379030   0.072658054074785    0.58137
  -0.094031545208179  -0.102385266865362  -0.176059812016563  -0.058150140608555   0.085985396664940   0.324498000985841  -0.014294175270463   0.223839272975625   0.185999952550821   0.284186906539131  -0.090221494600077   0.075080687896467    0.58327
   0.124592669752468  -0.191451453776833   0.036276740163334  -0.241120978852623   0.176357565430364   0.227665524629620   0.048717642636523  -0.367649272112684   0.059980832455670   0.074387142577536   0.036596099701325   0.132121907926892    0.58530
  -0.284145215110192  -0.218062260727258  -0.256699069159373  -0.130778106628261   0.332433380950863  -0.000733260461455   0.076613987631531  -0.047640684125750  -0.106618162395265  -0.065651536043554  -0.015157984805168   0.090100638761537    0.58809
   0.004838827791179   0.177287424379080   0.135997114991060   0.266246901141816  -0.225211250753685  -0.160109481331778   0.009693750487373  -0.323143723687672   0.075538270245006   0.220408823586000   0.126375474264877   0.064773950913089    0.60989
  -0.071159024200126   0.145656060166627   0.023656398960825  -0.070230864954837   0.279030491148722  -0.250065581884840  -0.036012654440075   0.016800887972331   0.336656174595689  -0.133712535841210   0.258926828640542   0.064328872672123    0.60992
  -0.025553143656185   0.106317072999554  -0.042739596282159  -0.003028272947873  -0.102440899448332   0.186740968803968  -0.010465315564381  -0.217035523678877  -0.481510688995185   0.091536962720927  -0.159374747960863   0.065308575870963    0.60992
   0.068431095149985  -0.136350977659868   0.191694939986153  -0.164247803442294   0.296896556947640   0.197298679084943   0.175176796716991  -0.255814204750152  -0.102661461922890   0.091712803207799  -0.230408927797251  -1.916982802081930    0.61826
  -0.144907439202542   0.154529695119877   0.100467017096745  -0.479003518149743  -0.079175967875539  -0.044306091445131   0.019349825408180   0.157914914559716   0.076371167796610   0.212363441589749   0.136415541214218  -0.599364084331396    0.62249
  -0.059242989683752   0.038960212955029   0.404327881672416  -0.223487702235566   0.228572709176676   0.046228119114626  -0.168605880346201  -0.032073255941933  -0.052292103611646   0.290573917321461   0.146080466142115   0.070711648568082    0.64094
  -0.166027519048472   0.161580201933488   0.177752194004907  -0.429025910807323  -0.174564253577456  -0.079455371011307   0.012290163317633   0.168405443893380   0.119223655441719   0.228350051432173   0.116066738314801   0.311719799203713    0.64379
  -0.139292606207370   0.029428246954937  -0.218434326067069   0.037670521347507  -0.145182337941543  -0.147976520782043   0.161684076239491   0.273381999324873  -0.449027641261337  -0.037458908967042   0.056005574680314   0.062144223830887    0.64763
  -0.206242176945509  -0.088622054979241  -0.159696020084736   0.171228812508763  -0.200584009269477  -0.072517471923562   0.219340916157789   0.092508805938532   0.050112259680408   0.092147826631467  -0.462339254620185   0.058213492131867    0.65737
  -0.174699803981216  -0.143181071985326  -0.045541906667940  -0.129171376010550   0.009758519747362  -0.079886835209956  -0.303976269228265  -0.286102048135565   0.072782945700371   0.133496325104786  -0.405335010619597   0.058827704626933    0.66176
   0.035291192401323  -0.007908876946670  -0.110523652831726   0.256904181126477  -0.203919357777523   0.348606744770930  -0.007869240637604  -0.002654835546635  -0.202783242354009  -0.295781365850322   0.271678831476873   0.055000842534350    0.66717
   0.168161221069911   0.188414386036757  -0.030831008956964  -0.197478292274148   0.051243816104216  -0.072309464943575   0.039513995742294  -0.037476153511124  -0.211311722076034  -0.462429507481515  -0.274794686747994   0.047235536534523    0.66974
   0.204756949655869  -0.067051073641189   0.068638434021746  -0.216166216829601   0.097214463563850   0.340257658369697   0.303706048303368   0.190345991657839  -0.281120190953323   0.131440928419355  -0.069414357863053   0.077633188110203    0.67281
   0.210053103597812   0.104510654666971  -0.088261024289833  -0.113390247550163  -0.181166107373431  -0.158669586508007   0.124921547856585  -0.128826342486660   0.461105877243816  -0.005607414050078  -0.274816247360730   0.051805876333567    0.67384
   0.167421978965736  -0.332534359075233   0.143894379497036  -0.069376030653803   0.223558592309768   0.105881847532344   0.213695077492880  -0.156207813453370  -0.235470238636853   0.321757255576875  -0.181969458790407   0.117494430328471    0.69819
  -0.103122224024548   0.189571721243752  -0.039920515231422  -0.531178259159051  -0.010908441899082  -0.160038955270393   0.060303735120032   0.167323502302612  -0.004927619921247   0.309515171837809   0.150695095321021   0.143238162543645    0.71149
   0.065897843049709  -0.110433147578594   0.213801479237357  -0.247824924367447   0.292867879959914   0.216953387843453   0.254246483580368  -0.269864406529648  -0.099962130360204   0.148653152937815  -0.289477401287191   0.506446310371869    0.71405
  -0.090287126753874  -0.341006231531691  -0.126637067961493   0.396555651001547   0.156709088974052  -0.127557349313242   0.097417190521161   0.126320556871705  -0.052069542284765   0.154249960443822   0.353250918554905   0.046314996437412    0.71784
   0.149499459634000  -0.257992709696412  -0.125584805145047  -0.019067479431216  -0.117410578623151  -0.112411432186439  -0.314228770164184  -0.092602111759184   0.399677842631652   0.268643209079362   0.254835135025871   0.042759785532920    0.73187
  -0.337541117178863  -0.173720770267211   0.084753615411796   0.006949836399479   0.073687573081035   0.315590900974117  -0.040976616682269   0.121481394539314  -0.045265412041475  -0.394579603581746  -0.357225334161671   0.028380127317576    0.74710
   0.102168431928465  -0.177624321770128   0.368731947585213  -0.060932980274041   0.204426445191930   0.009740324266843  -0.123329126780334   0.302980810798915   0.332046041895602  -0.013342065860711  -0.343463444426572   0.035321911999301    0.74763
  -0.012115780184636   0.072143906948540   0.101992473254365   0.149271555478813  -0.447568262724817   0.066546819019885  -0.084738347996286   0.227842642506211   0.044886152521579  -0.416553093144695  -0.285794209879155   0.033819811693070    0.74772
  -0.306900851504044   0.106863454702383  -0.074456378522009  -0.269364716403471  -0.069743714479726   0.132395615541142  -0.060212980853218  -0.044534844507177  -0.080643228185833   0.257473016349765   0.544094257209021   0.044547882943864    0.76194
   0.098259258417187   0.097654750919279   0.018992695765590  -0.547025872413575  -0.166692369766304   0.063630662393064   0.082058223987708   0.248574128551974   0.167702781313297  -0.183055560031593   0.316184761309305   0.043648688214737    0.76207
  -0.240245146636909   0.267006107258442   0.059496794238818   0.184783231865655   0.329870036984409  -0.204779883379638  -0.237626979414823   0.123958096000239  -0.059965302093663   0.452687833284916  -0.153922929955487   0.054854343146781    0.78835
  -0.279218571620691   0.280227067856915  -0.003732698724497  -0.014997407562244   0.108680770219748   0.094496256404996  -0.641093205718711   0.101000472939993  -0.227539290902119  -0.160064422730035   0.068423180932084   0.030069539675729    0.82507
  -0.259446355778610  -0.113791036576784  -0.030226154738140  -0.321069262895128   0.073163886609171   0.007188414046837   0.314841759761313   0.133166766491184   0.506293918599571   0.315074233395012   0.163862084233403   0.027537387703453    0.83005
   0.226044211141947   0.336733823392734   0.174371521211636   0.155784440806845  -0.072317554455739   0.053084812037824  -0.201797740689194   0.227800635885014  -0.066899607797596   0.196986971660325  -0.578771983765886   0.023229605740583    0.83551
   0.291308415248667   0.169272318605346  -0.000518918586480   0.310815845390614   0.375164559731749  -0.047375420458014   0.262375660288344  -0.131470414165383   0.351276375365537   0.358532213374057  -0.089684248489950   0.021627448914109    0.83620
   0.221604121457584   0.251130462411088   0.429324934695653   0.061638282786150  -0.004277803675806  -0.356701233096380   0.372415698324197   0.354396819981846  -0.038842268426968  -0.146600722081464  -0.062468101702962   0.025703918493932    0.84779
   0.450662167499119  -0.033245297401796  -0.156366694331779  -0.079493012526509   0.347391110334205  -0.097558878693641   0.436843236258398   0.184990597102077   0.088770442710372   0.112017219219727   0.379904941381889   0.020248946913419    0.86890
   0.365845555481742   0.239922947511586   0.001643234057624  -0.100395308062863   0.270231233838809  -0.195365002361597  -0.483782524181495  -0.182192981096945  -0.319204445575675   0.263016754610090  -0.141701308987865   0.026424887198155    0.87811
  -0.197887748340710   0.437359690446196  -0.064082689237410   0.047981177226669   0.304853681412576   0.323954005381047   0.331496172291374   0.049779155901695  -0.037067434314232  -0.337097648602851   0.345675355877908   0.019506348154763    0.88408
   0.129150819397055  -0.309864628293017   0.280172788237362  -0.183323408641870   0.269539870697508   0.051736186025453  -0.033919051985419  -0.023108608318224  -0.530293945579018  -0.384317969573103   0.261266591304611   0.018974690987884    0.89386
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   2.018943999615359  -0.511023917714303  -0.600551269856409  -0.211319204222178  -0.472446871778472  -0.072889904328778   0.444329144190679  -0.839463325096282  -0.350998922500413   0.429178866925155  -0.053260901504096   0.000138574871005    2.48666
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   0.124336090983530  -1.490813631360413  -0.822721514846702  -0.060920558310606  -0.401635226015091   0.773667207749876  -0.150117021739344   0.824149069312026   1.633444800833254  -1.611715916431872  -1.331832824173774   0.000241640932776    3.37931
   1.496347236234276   0.021695529059022  -1.013819729999175  -0.006234059071917  -0.107761784202197   1.788219062649993   1.331091070231347  -0.307199416297377  -0.979728591838530   1.595663008337049  -0.362598412000501   0.000191632803417    3.46127
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   1.748192602542578  -1.203757722721756  -1.144468190189472  -0.080823319534198   0.055881179793236   0.883829076766743  -0.616545864055572   0.604199684881335  -1.362097172562746   1.041381479036109   1.454727643797276   0.000102375654522    3.52236
  -0.422158464267091  -1.709201096435976   0.928877568577054   1.106031935306762   0.949087264275296   0.158842270541387  -2.434742055768017  -0.409006639399804  -0.082174532970458   0.348210655163347   0.539338876518281   0.000091764923463    3.55329
  -1.164573286073129   1.765357494644823  -1.582536071793751   1.959151918488661   0.539259361074708   0.183136489423353  -0.088284622554773  -0.125930624779440  -0.878791580192236  -0.453045998321941  -1.121878617092925   0.000076986528876    3.66054
  -1.411693876053140   0.816410043812225  -0.856322185413415  -0.130965427751807  -0.493086315551452   0.664401652415871   0.379516806344001  -2.287993791150243  -0.537944007976845  -2.024108099825507  -0.704446062823511   0.000060247263847    3.78893
  -0.167225080999762   2.526568255881455   0.939602346618406   0.650081551756090   1.970087697264641  -0.062869427363504  -1.970132030921085  -0.268853093708489  -0.482469126996854   1.262396722416316  -0.809907928362392   0.000549715154596    4.24715
  -1.650806919290113  -2.729638988177406   1.598979147195874  -0.642357114032977   1.599512208139563   1.131010819666187   0.303593971299872  -0.113141138934508   0.600294643114971   0.686855993962120  -0.870718148241511   0.000036872407746    4.32184
   0.404576736537439   1.790922168926290   0.544497982580209   1.526252330567041  -2.102575865860564   1.599929137348346   1.684230528018364  -1.298172001519536  -0.078417106220419   0.012665319523107  -1.600341278895200   0.000032377579911    4.47961
   2.971811779065988   1.822084703407727   0.220143338880064  -0.358969871604020   0.844240954994619   1.367251481508870   0.805235961343631  -1.695368394717651  -0.154430377406637  -1.391180561800680   0.399266795561076   0.000033142680774    4.53348
   2.864521993510598   1.563412640614529   1.878465424945681  -1.351551450871842  -0.114628185223139  -2.617810200290905   0.178407471683921  -1.280314358230707   1.718321145787254   0.796211122079258   0.090809884481793   0.000014941823664    5.30443
  -1.978622265296752   0.256800622695245  -1.097272257555023  -0.680682264790316  -0.398302505773937  -1.807492271840941   0.914134602317576   1.688436187660558  -0.734232424791899  -3.764970379857112   1.014904320612589   0.000016101513954    5.33896

>> # evaluating formula 1 with 133 points
# r11_133_4E1a.txt:3 formula 1   : problem E1, 11_133_4  (d=11 n=133 o=4 plus 0/3003 of order 5) quality P
E1 11 dimensions, degree 4, asymmetric 133 point rule with points at 133 distinct radii
#                 x1                  x2                  x3                  x4                  x5                  x6                  x7                  x8                  x9                 x10                 x11              Weight     Radius
   1.722942255566033   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000 7316836.492310459725559    1.72294
   2.115448277179939  -1.396673450040125   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000 3085623.353724393993616    2.53492
  -0.057119163913140   2.847933324461065   6.643195378776335   0.000000000000000   0.000000000000002  -0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000 1927826.164050484076142    7.22814
  -1.113965953267885   0.221045221360292  -5.552968413993880   5.421860571011547   0.000000000000001  -0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000  -0.000000000000000   0.000000000000000 2015741.421354060526937    7.84358
  -6.707199140281200   4.004337404563726   0.180532111022548  -1.878005033865100   1.564781893243744   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000  -0.000000000000000  -0.000000000000000 1533029.944920830661431    8.18714
  -0.875239543250916  -3.271516570217243   0.317509790166590  -1.536709952234636   2.086719413116059   7.608180716230504   0.000000000000000   0.000000000000000  -0.000000000000000  -0.000000000000001   0.000000000000001 1669067.432778242975473    8.72754
   3.218379445681005   0.550687238869838  -1.706530246754301   0.635122232667684  -0.435394963931777  -2.166829060762491  -7.992601185636129   0.000000000000000  -0.000000000000000  -0.000000000000000   0.000000000000001 1701552.766078474232927    9.09633
   1.831135100985377   0.223969806907753  -3.517461665041413  -0.236224494913633  -4.901774826033368  -4.020329624148096   4.158556697376286   3.827715824473835  -0.000000000000000   0.000000000000001  -0.000000000000001 1391115.079475451959297    9.37907
  -2.809892704390007  -0.081475241026576  -0.197741032972343   3.386004173473649  -3.385016212072488   4.069670151017867   2.398505023735145  -1.957904300991859   5.816474509705715   0.000000000000000   0.000000000000000 1369641.939713490428403    9.53123
  -2.520899055818466  -0.940070272717522   3.580494652284166   3.582578173727404   0.634848130160293  -3.287789241335826  -2.752934675398722  -4.771282908362432   0.676006831430696  -4.309328652130765   0.000000000000000 1223939.916866469662637    9.66836
  -2.224481794207820  -3.797814344374002  -2.532775007280253  -0.020065817768395  -2.895747915462374   2.049334465849515   0.506726177733085   3.196292701980309  -6.093918407385696   3.808965426696372  -0.270351281043431 1304962.782043464714661   10.02808
   1.611153213680787  -0.393203058609536  -3.196084193428125   3.346168512142125   4.582821953958746  -4.301581897081123   4.491440921201139   0.172927579272821   2.724914073658885  -3.183009060006295  -0.804176232119244 1057768.313459776109084   10.10319
   4.328166245796359   2.576297379899769  -2.816554474652406  -2.628029631507428   6.978188021516633   1.851659958320149   1.431677868006207  -0.042379752828723  -2.857996700857711  -1.868005528168151   0.818449064645664 805347.179866142687388   10.33018
  -1.021900585430987  -1.771758984509423   1.380437040579948   2.897789062541598   3.471377519216105  -5.451489536782256   2.130295049576327  -3.958957030710187  -3.523623372620017   3.997373919602560  -1.986111875997591 1257368.358063774649054   10.43103
  -0.023795057943367   2.719873460604078   0.980798842105444  -5.962016449635615   2.621841319329289   1.469276702390676  -0.804755678011571   3.870758262056417  -2.191343767091464   4.386187202325850  -4.262252930278967 822645.781493467278779   10.52504
  -3.260998960038042  -1.946162751215790  -0.239144057226013  -5.294851919176280  -0.593368640782914  -4.474095139564984  -3.143722760799352   0.861237841692568   0.328329709431661   5.613079479554530   2.459565382567913 835552.853325494332239   10.54384
   0.412044660782635   3.480285221491609  -0.792420779405400  -2.148846988609304   0.452370869246391  -1.402004461624264  -0.042580469550437   1.668818822233590   2.230155305926643  -2.916666164570664   8.720036807460165 1063061.802141316467896   10.58321
   1.046052072264337  -6.891819812270388  -1.096897742818733  -3.838688315599445   3.379624555358767  -0.336016865775583   3.481555673495484  -1.169551998212664  -1.357241706940726  -0.144597825086630   4.714382980129909 1148485.827040102100000   10.66032
   4.376229257677135  -0.645127554171347   0.711072711836830   3.479779922278229   3.615669178031792  -0.136783031543797  -1.180475388789822   1.914163070785581  -4.946176286583229  -1.620062523731543  -6.020957333105468 1019104.262552955187857   10.66173
  -2.820245279205543  -1.636981468628188  -5.167412679952243  -4.569413576603223  -0.986661084374948  -2.295081127038622  -2.656424204721623   1.408528528257752  -0.701096507327607  -4.303165120057135  -4.888288964088595 764578.957363415509462   10.78892
  -1.338175888330483   1.389654029753517  -1.060936588682839   1.665877017598292   3.511488911795588  -0.800017048372467  -3.245846870729218  -0.137255269024811   3.871816323125084   6.892065375993196   4.800615854991104 913687.988395834225230   10.80208
   3.198119032401748   3.805024406022214  -4.556051023592225  -1.203659302474248  -0.486049718800399   1.987234748186125   2.430785692048469  -5.207927211462930  -1.626375966925158  -5.654305025094216  -0.972269322270515 912163.532039472134784   10.94033
   6.254348979068340  -1.081957991343926  -0.859223600647167  -5.412493807869565  -0.726943941769879   2.704264610219679  -0.653826275414383  -1.840698573187633   5.507257710541246  -3.213270238008604  -0.489649767324719 748604.074039999162778   11.08480
  -3.776186930132287  -0.198022001325343  -3.627252982453892   0.679323074291191   1.318743836273818   3.193676414786420   0.194262952280830   5.988589551154480  -1.372871664046035  -6.735188786827322   1.519278865808888 823799.503469528397545   11.19431
  -2.787255050622650   6.672805156973554  -2.389762224508689  -2.211526235722320  -7.125596606662281  -1.591504672723643  -2.050338816275096  -0.086807757705067   1.638191774953217  -1.595574372707184   0.238887004241019 862435.974074834259227   11.21169
  -0.401730258441944   1.468554261401620   3.841986003921804  -3.786107047798494  -2.848104915409650  -1.022708633921348  -2.069193492872631   7.912814700235115   4.149307006498892  -0.251087609511798  -1.007704176111638 837123.967511278926395   11.21430
  -0.437563199873252  -0.484028173709682   5.931657298524758   1.862947092884712  -5.815556740662243  -0.888382630735177   1.105726046030636  -1.852804903175129  -1.267931673690499   4.953229227135355   5.030323924396040 779298.611088475794531   11.39266
   1.318141940106603   5.911628434288383   2.111753496013131   1.496174422167689  -3.048494999523888   5.461398303742423   1.078192597706763   3.398556706563706  -5.407250921264798   0.797221500935010   3.181815473349545 618499.244993428816088   11.62814
   0.028371491718851  -5.384711487992522  -0.647916991214824  -0.475381760380451  -5.886847624865016  -2.445730461830091   0.920288050141355  -0.487987507329499   5.044389457751026  -5.503520726347735  -3.129310499648984 705323.429522427730262   11.70002
  -2.782692058938548  -1.941315513500303  -6.162882503143593  -5.711152208491171  -1.926068489141181   0.622594849077442  -0.911497580643880   0.906525696801787   6.379394862328037   2.990052673755562  -1.417746952990606 649645.158163359272294   11.81133
   2.970480560858956   2.486140506731499   2.905531853054091  -4.326056680735631  -1.497710866705769   2.420144819933127   7.058129084894927  -1.009869027156947  -3.977593878344018   2.937207858901314  -3.739876050341011 605082.734374019782990   11.81245
  -2.233911651759441   2.574021181331893   1.485138707261688  -5.008461850814647   0.829184997732360  -4.240612628835365  -1.024374349797587  -1.586367194804504  -7.909967375082808  -3.784577803284455   1.492970594657335 877273.185533684678376   11.84323
  -0.622106075754521  -2.652277077427335   4.495213950377953  -0.423406240339304   0.659704662593700  -2.561144049935285   4.114562180438210   7.152931351614672  -4.441440493599611  -3.462270415422632  -2.751738433643298 735108.939869846450165   11.92402
  -4.242765818692169   2.480068118419149   1.635765236127372   1.295159396467568   6.210098186768461   2.290914767749055  -0.880600297387802   0.070085806474959   5.579480064761377   0.943240708769790  -6.153976950426639 684672.646964712534100   11.95787
  -0.267256188256661  -3.312565124405290  -3.339315409579577  -4.723961318428517  -3.989756315290000  -1.813285386647700   3.172769821863983  -7.565345623684141  -2.565748177606695   2.311005934326432  -1.119766559594817 695203.619200341752730   12.00817
  -0.843863602937185  -3.702602833582832   3.025010675103636   3.078073260280058   2.884434712484822  -2.002954538457749  -3.467592195346509   3.434168955581329  -6.161465287324468  -0.019689131317373   6.098278563292309 678343.846429944853298   12.01454
  -5.714479961213328   4.055418391082098   0.350833460562194  -0.022414648357201  -0.452028254518629   1.747587009027972  -4.738715673868905  -3.246520705853913  -4.695693724982569   6.296237721916019  -0.964192290933517 570856.497520399629138   12.16967
  -1.457607745633205  -1.850357722782973   2.480668187145081  -1.030837851545729  -4.450782583358525   4.174264017058644   3.407379083488997  -1.427926061771136  -1.822827433524001  -7.650829424021212   4.812109511241283 713191.343331486452371   12.19271
  -3.662575742873419   0.745239855730192   0.947882292036018   1.910500741198877  -3.294062457622567  -2.629213885158090   4.411629976584218   0.496053091141932   3.135070692294570   6.432835789807445  -6.511937156552090 683991.444070602767169   12.23135
 -10.854153232861565  -5.640895541955059  -0.135706935457717  -0.219652815840445   1.685873793047124  -0.631558640742564   0.827764392806134   0.360259731929358   0.051203390952150  -0.212530426430157   0.197043034560463 664682.342631735606119   12.40329
  -2.127342439247689   1.704137046291231   3.588049587803343  -0.843166428337117  -2.969538568422476  -4.547052780597196   8.258690083234466  -5.387833855856100   2.375070698007285  -0.661277295384817   0.701601303404312 433407.527601044450421   12.42231
  -0.369734609109131  -2.082354619212768  -3.314542240910931   2.471899146069153   0.783920054309930  -0.005603266788158  -3.696475632032326  -7.820496322825571   2.545548386471996   2.255396342369973  -6.763347236086827 551758.471487220260315   12.42246
   4.838377323750754   5.355780347076715   1.995945325322259   1.682802668124457  -0.666743234215719   3.753363091353319   8.375547264927889   3.210212344132464   1.420619280926422  -1.110938350330618   0.217570715295391 519750.055941340455320   12.53783
   1.124475808435680  -5.466255643442989   2.928300310779613   6.114141061271589   0.682214831264056   1.905094334047269  -1.699337757734063   4.055469369380933   3.970096949652270  -5.992724080481389  -2.544891448177857 511159.193366849212907   12.59692
  -1.072103438435271  -3.345339285432556   3.887233585081930   2.296966833692736   3.979041872467648  -4.268223832827835   2.309022383494236   2.673912045847313   8.351300377206112   0.898636702645437   3.126471686282591 563131.406309725134633   12.63273
  -2.010653339179155   0.319854574959623  -2.846897639941020   3.192065658625391   7.269097330734546   0.122645804857201  -0.419132993265651   8.871382625611751  -1.200130149379589   2.142965740901294   1.170772095703199 458091.931506547611207   12.71119
  -3.472205841030412   2.378665607664605   0.268757812592503   1.646621254595464   0.788640954909052   0.336413583268392   4.749770311786152  -5.224917679807093  -2.139196904090869   3.492961538713462   8.700197876581086 464394.151485885027796   12.78919
  -1.266158707451138  -3.111407842600618  -0.119050189779759  -3.894438158429479  -7.879860909518609   0.676553779572763  -6.431330088099699   2.015855244070019  -4.335002778412736  -1.576940265621050   3.020505621767218 480905.660609542625025   12.83912
   1.752535057456484   4.822772096068636   0.779734809258279   7.596807298096323   2.141928042719634   6.648350059827830  -2.527937948465155   0.360974249134858  -1.233107745417291   3.835815506488099  -3.254950564065613 546367.039176259539090   12.91464
   3.876910201239501  -6.137603869366325   7.067202165741101  -2.743662372657318   2.792893637320462   0.154740331843203  -1.323363011922415  -1.453716122961392   4.458538881547328   3.135226511443901  -4.043667292804379 449251.255288743413985   12.95847
  -3.886223083890715  -1.630674515658293   2.840930503987895   2.868669481303447  -0.461912255411169   6.087338826740480   2.670330679524563  -5.935701007440099  -7.154994888341276  -0.879213298763723  -1.540313408490110 497752.233130107400939   12.96278
  -2.378618557748616  -1.406974308404053  -1.428523986321767  -0.774315518086994  -2.847577529506466   6.390770369689853  -6.598985189425405  -3.764565085570990  -0.195459648463509  -3.993926296666374  -6.145447899765430 431449.883371091913432   13.06534
  -0.936371581099747  -8.809060644595565   0.753343539967963   3.917940256911767  -0.276096033656274   2.389991469584428  -3.907433509368877  -5.076068984197402   2.492402146776798   3.530047059711296   3.714589226284420 557013.302643922623247   13.17909
  -5.232650324023374  -4.128423038793107   7.475079901156432  -4.830456108717971  -3.085964068604187  -1.318860937404351  -0.293665194334739  -3.032302255628375  -1.025314121069876  -1.097393832757483  -5.253382424457377 500318.053304658678826   13.19211
  -0.937205759624571  -3.798428482284376   1.748347118851046  -4.716240950899532   5.844754463721530  -2.296492740834430  -6.370247980585756   2.287478823419748   3.424863128055065  -5.777689620740275   1.809519509374865 547854.888933514361270   13.19998
  -0.393294934663596   1.952943970526342   5.411276948631748  -2.464955575375842   4.663927575948727   3.527639658922912   3.143380826957380  -7.083736029883758   5.401252332340067   3.105193340570505   1.528845425197807 466948.497471334994771   13.21879
   0.568102668749155   1.055967613578120  -2.482975106994064  -7.457467950417859   7.325223522107967  -3.263753991778694  -1.501686032789594  -5.549631905499403   1.140713805377802   2.892639626421039  -2.530051268028636 478912.458125770615879   13.29101
   2.016106368970291  10.492282822507503  -2.294886500600942   2.460476526213803   0.382284925959932  -2.245932304842192   1.471309577941159  -5.311147604482779   0.765130992605761   4.057961874760645  -0.515890805741187 502354.111322487064172   13.35497
  -3.570593629229852   0.323748459355670   1.566374620364938  -5.936496608773838   3.887571966735527  -5.128458311436601   7.533775472914032   3.607828231693744   0.879659497003879   4.164614866481354   1.130994381557035 382288.258736718329601   13.45864
   7.685004395403769  -3.026889831854969   2.258277160247026   2.043713252029131  -2.352597975351622   1.761556550208824  -0.535614853483233   7.392422071305560   0.532207862498235   2.462134634292868   5.852987707232577 453801.417803675343748   13.47863
   0.180744540832988   8.228368353221081  -6.719756340370499  -2.865937572072803   3.580125129400665   0.054382388187298   1.948490010492739   4.399501463882803   4.592703833252274   1.577397164782076  -1.230930326840068 395851.825574565562420   13.49727
   3.197707532637717   5.320537080606037   3.369242465297293  -3.565184342185499  -3.270657371239752  -0.576074228200643  -4.008677914071475  -3.859720987937634   0.305122119072762  -0.721121657406202  -8.836875270225171 360339.502499293826986   13.53866
   1.829621318083171   2.465002546591223  -1.489326789078653   7.858709625536639  -4.251380518401806  -3.020955894682602  -2.923662411754608   6.649781146531264   4.096649454725998   3.481532794541435   1.554497997048796 371546.583601004211232   13.59003
   6.272244118984809  -2.616091435580895  -0.652104393222187   0.405523628899269  -2.321342670860274  -6.144747850507174  -2.035619345456842  -6.541959129927445   1.242406679477841  -3.744926947583668   5.703402952320261 389421.943123357021250   13.59997
  -0.211065272672505  -4.457443355539200  -1.317500356213672  -1.411177913462037   2.160049097646967   4.940253655477440  -6.194601176574391   7.370556962095426   3.171162441615227   4.582574070115514  -2.989930465192806 358493.458297382341698   13.61641
  -3.120965981625565   0.633448710379859  -7.767292665688748  -3.064409969315149   3.896022895832537   5.670749107144495  -5.645728663731880  -2.821344943046470  -2.771335186137694  -1.256188339273972   3.043794038973754 428209.480095542734489   13.62192
   2.838833001755714   2.308597809753886   3.173999169620713   3.838461987196647  -8.247404298833796  -3.443663028410392  -0.520630138263249  -1.788595873598669  -6.893165296069059  -1.900059588607184  -4.175425943685054 452553.205279586254619   13.78787
  -1.288823923062534  -4.440294921289957   4.148420363846443   0.070412573465459   7.944942444861258  -0.093761787921611   2.722598905696381  -4.559990594404125  -1.185601717414631  -7.288630395878524  -2.833832868414402 277262.923653708829079   13.87404
  -3.448230785736981   8.233723625581423   5.086832497593075   6.215808818046915   1.955636658977035  -4.098371187773640   2.850294102721796   3.271254632581859   0.425641647192129  -2.902905560076530   1.746874759506129 390092.315932450932451   13.97507
  -5.152642945855623   2.508334457041250  -0.940091920647132   1.886481227146552   1.983994537477156  -7.745797619726041  -5.724576467421258   4.472676932940450  -0.303236747412073  -1.979634134542152  -6.226498294166104 389522.111667170829605   14.02760
   2.747904102628542   0.124667393425318   1.081650042738318  -1.410167001097766  -6.668344800177965   4.488536034263313  -3.488796282548288  -1.457595660596172   2.204772874923602   9.729579578972455  -2.968380120691219 388205.729016963567119   14.07026
   3.919041405025575   1.784986397361570  -4.749418822530783   3.326630645042560  -8.089548635172076   5.466398369006953  -1.334601107826988  -4.801283700943472  -0.375739700767572  -0.021683172016875   5.081328047616532 383549.914445329864975   14.08140
  -4.143522072408738   2.288667259065929  -1.743690617231372   9.305405087397684  -1.362885619449819   1.153582247055200  -3.929976961861698  -0.659586789517088  -6.245200040479613  -4.471331082869035   3.339476096050392 310518.469670853286516   14.18637
  -1.044123666059357   7.100109283342678   1.860357245637722   1.123290371309708   2.869577116292167  -0.642123763718894  -5.636274418705058  -9.094688505599617  -0.904538923815256  -4.037214558329441   3.124541720156660 276634.034093573864084   14.36079
   6.244443611356489  -7.652089390113930   0.628021802619772   2.604593369867553  -6.938318285583517   3.174774805500491   3.937092469293684  -1.427303106545068  -1.584908381271259   1.188873547044492  -4.761476189122987 320123.327534893236589   14.39028
  -4.943009695906137  -3.168387458605552   3.017666806941712   2.715745122468112  -5.020710043396927  -8.385139482503256   0.863579942782201   3.401670413595313   0.507274553197203  -3.432647884036227   6.051803496009552 347747.652564640040509   14.40325
   6.224197304678859  -1.781675242608538   1.065934596927958   0.730992250213842   5.087809177258454   1.533428392790324   4.622801331264734   2.557925612130803  -1.113159155357456  10.717145266128227   0.316366199182031 328796.832203573721927   14.69464
   7.294032430374580   2.810810762316322   1.713122303691349   1.466468095431808   0.503305521729564  -2.102295892041624   1.628628525136698   4.894948435354519   6.222757590334886   1.494482118513619  -8.910991857363708 296790.929484850668814   14.75929
  -4.111595334636830  -5.298413402368832   0.630897486176062   7.430620786827838  -5.662393555814345  -0.737955711801039  -6.196457546353011   3.463151019594415  -0.763225164007472   2.142600944695751  -5.520064078519052 273332.151181928871665   14.80647
   4.302878378995850   3.522550540863879   7.813972322006226   3.535369796549868  -6.845463804106045   2.253214789292378  -1.720843615666070  -1.881898565093168   6.795861092766669  -3.451359121697619   0.101135887850432 280147.583068111154716   14.86695
   7.100715184317611  -0.427440430480363  -4.145580546287325  -1.212738411241575  -2.117700569960558  -2.376340180200098   6.053028415552788  -3.004568664568622   7.810213249683553   4.821757983086079   3.739687678906663 318934.211313555657398   14.94295
  -5.436875395745858   2.049627480918363   3.906839906259950  -0.050861220768577  -7.049418309541315   5.214143874639070   0.314788373799234   7.423691108270129  -1.990874067462741  -1.781734465262753  -5.957023479853148 241311.588944683287991   14.95803
   3.340420819363552   0.424632492831689   1.332307829896029   7.441875219981782   6.589950517839397   4.966398253187022   0.338873252785894  -2.365555524555249   2.066239945365501  -3.774872045944553   8.003058658760162 338163.910398559295572   14.99555
  -8.036042679480952   2.151094572194574   3.327566350178287   2.439756435606372  -2.299263701738879   4.948126650903726  -7.581826260005577   2.347112836583610   4.669174672045571  -1.252746888624713   4.987436038847295 315679.479811003955547   15.07445
   0.172357204762995   6.152095975405643   4.407525468826561  -2.071924544521655   4.976310812019246   5.847198048779705  -2.494364117481418   0.815501772163451  -1.225401984174187  -8.794241192786608  -4.737733544456768 288606.055881104490254   15.12362
  -0.904943649718472  -5.556239289704831  -2.608832392794406  -4.163983604712913   3.434789503274294   3.252982130382391   7.744280819139597   0.931636703620429   1.605690753309812  -2.189426708347468  -9.138022499229168 320993.352046147803776   15.16352
  -7.032687463012116   2.879629942060620  -3.073732592854583   3.327644723548323  -2.868773935569270   3.159848373465081   5.245717046633058   6.143856136066185   1.489987490376011   6.222863796927179   5.264851694197914 265087.774798827653285   15.17939
   5.582525211766205   5.677587257781039   0.682204571906672  -2.734242518941715   1.704341875662913   7.950831083670115  -5.474591730940644   0.596440124775309   6.423234300181184   2.575747468647863   3.879016802489299 264450.504766094905790   15.18972
  -5.553476303380449   4.133861536652365  -0.671403619099846   6.438162009170419  -2.972503889967999  -0.141420390521019   6.328910997540678  -1.679505491709570  -0.307654884111803  -6.563973733717637  -6.962395823354398 276291.469362245697994   15.27146
   0.223323699950211  -1.125891285719564  -0.305279316799703  -0.272406684585218   3.505970373658618   7.198458442242540   7.495110431747815   6.942270550188342   7.192713015287231  -2.667916297286754   2.540173681928173 223114.434678498655558   15.33857
   5.002715517255521  -3.517442741077510   7.964425520704079   1.393536781640536  -1.440800954679041   5.760555026933451  -7.803034835979743   1.447355511468678  -3.227260962201003  -4.720712777925060   1.271520786340480 225860.846723757800646   15.34056
  -4.962817662696126   0.817269950130581  -6.251387457883272  -5.221974117262180  -4.267700560876705  -1.413139706225375   9.006238178810760   2.228445434648257  -5.222408657261889  -3.052784751507507   2.072251782347206 211424.528057055198587   15.45387
   7.102328337733907   5.406982781438114   5.560513730899182  -0.032611117550344   8.621574186380093  -6.163166231804215  -2.701731317249412   1.991883791869625   0.766073870742523   0.837874790497935   1.888848367961356 292577.304006642603781   15.46088
   1.285393181696412   2.456403097022198  -6.100852237324689  -8.116412720921431  -1.793420851478657   5.625731349448809   1.933250806368449   1.670232280346683  -2.660049700967406   4.534727449777870   7.856841601875463 217091.587828228890430   15.54171
  -2.818727007145747   4.178548721209809   2.985384744503311  -8.601453710618744   0.903428799962479  -1.328027220166781   4.497476093764425   0.868731109493467   6.885661412308228  -7.954033677474376   0.254648705582333 246719.769689788110554   15.57590
  -3.922450884832908   4.318993384663503  -7.322952295923608   0.705656256643435   1.777399602258329  -0.123917924369348   2.642896755299877  -0.001702005823329  -8.098070792111448   1.190373078728334  -8.854776155760785 234714.301516504812753   15.61170
   2.978247376205538  -1.283136295641231  -8.053342017080830   0.929469320932912   1.449989960625781  -2.525078998052984  -4.678276170521285  -1.358323777965197  -6.391731502717453   6.768990068565898   7.077352696794729 168515.985303851892240   15.65914
   5.348875742369735  -8.380963415742904   3.098006276020738  -2.473354798647484  -2.585538751596930  -9.835663124536534  -2.600466229878314   1.853931105134044  -1.620907883388105   3.097340053329986  -2.225585887968033 274965.331411438470241   15.66413
   7.698104230733270  -0.286317051119016   3.474752769257696  -1.682509366806215   1.986634141767164   3.655223275133596  -3.741676354736180  -7.934104795196173  -7.594166149987117   3.827899479540437   2.373098834921700 306680.087766680750065   15.69907
  -6.785085797182206  -1.092624370312784  -6.557040846636214  -0.613608224272727   3.349412525978104  -0.600940231625155   3.197748359052175  -7.642604120491317   6.176294942657863  -5.103052902811447   3.858785752551735 252823.673009840567829   15.80807
  -0.479476321580768  -1.561209278282937  -8.805396802532908   2.742596874579229   3.825604670805367   6.634165368238648   6.392576026243828  -3.901536470553812   0.440950288197822   6.934744438620784  -1.058988928454085 244973.148631296207896   15.87026
  -3.338387345145343  -3.758788103947117   9.148609228780620   7.845495464603337   2.743067580970333   4.164338076493646   4.535204201132939   3.422650712149653  -0.949848532141269   4.516257896335918  -2.149596160056841 249299.018778416735586   15.92452
  -4.899218600197136   6.068690064209160  -0.157993538262080  -7.722311568316670  -4.348761518844381   8.543336235951422   3.565573590224403  -4.542330639727981   1.206499217164208   1.773208537073384  -2.195570193330049 213911.540243537077913   15.97364
   6.142286199782891   5.937771670485488   4.424081272249143  -8.343663737882803  -4.603605753821213  -6.144926396949516  -0.110988562473205  -0.497354895496416  -0.337791700187802   3.930084316728657   4.646341815675769 237147.796207414503442   16.07903
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   8.181836965482640   1.528802272462151  -9.533273335446967  -2.283386375102391  -2.925851399916680  -3.186246001647016  -2.951064018442448   0.057887390760537  -3.244198939291047   5.938051075308544  -5.273739402242260 216501.431342454481637   16.32174
   6.802876726997061   3.368862908262390  -3.535024595125636   3.887565743083814   0.579952361584493  -4.061930319409611   5.899791783015370   0.146603063872243 -10.032607364397995  -0.173921872171692   5.540143246446792 199981.121282412525034   16.37923
   3.086352794448036   3.084439276743856   0.280289825274830  -4.400250590345506   1.272166715004088 -11.400874854392487   3.441232664938862  -2.749917810437430   1.707891082589602  -5.116156697492483  -7.173702734037696 200578.883229172555730   16.43279
  -3.293116968307451   1.938881931168266  -8.881352607668660   0.679053997905662   3.447428347338450 -11.661558404404634  -1.481829784602817  -0.577924859549808  -1.012343667006378  -0.793137654445949   5.238526718329538 197652.879744384379592   16.53620
  -1.492027045304663 -10.144741683972804  -6.893047502414305   3.311592819036695   3.313487449463395  -5.352374981173964   0.716263448795600   4.415455452219941   3.268136917715659   4.809488148551472  -4.868381608755465 179591.667355263460195   16.75626
   0.144240792488468  -7.209687238548254  -1.306908729259987   9.719249661384065  -2.266698515136868  -0.644903072763894  10.770581580396069   0.384143298601687  -2.457950473214469  -1.270197392039104   3.438109973340628 182905.723952922853641   17.01042
  -5.489249901585558   4.618371467074653   0.257372325364682   1.112032039367322  10.636801123830198   2.082678385657362   8.904792649716562  -0.655200057333877  -6.327372069763937  -0.960408617218463   1.614608713693966 158976.718063685955713   17.13280
   2.305076443869016   9.744254617276093  -2.881024957275341  -1.688749852734314   0.388509593925962   2.057514661967825  -8.605005306651048   7.785615357702367  -6.563916152637769  -1.151701566147372   1.437067808157267 159974.041043309785891   17.23191
  -1.917467260615698   2.043133072507081   1.278109050801206  -0.181725959296450  -3.295424219410648  -8.957622707954274  -5.276295319339636  -4.682351451698297  11.773793815153885   3.062401782401816  -0.853180765197306 170222.653665142948739   17.29476
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  -3.753665132063792   0.410030893345742   9.280066993844516  -7.000785985631509   6.285879250454704   5.746324004385172  -0.865565773311600   4.198783284404006  -3.564284721469082   2.504382954821511   7.051078135751329 177408.104100585245760   17.57823
   8.321211476140787  -2.137704011712235   0.768881862607008 -11.870583468355209  -4.299055651754241   3.665291999810925  -0.665012165617964   3.607335188694458  -5.083550346717272  -4.681310961514901  -1.936801213076373 165861.829547065717634   17.66901
   8.059385198380326   0.354919411954541   2.521753109352155  13.122968253136609  -1.497196724610666  -5.849814197224736  -0.269634915023643  -4.351658277669261   1.792828152105032   4.088492265524332   0.476439394006375 143534.588964403141290   17.86840
  -8.024964584385376  -0.241607494236321  -6.233647375365880   3.822734990623160  -9.780043666635368  -6.061896854976051  -1.913816957345228  -7.500852601953669  -2.050283932121896   2.659381626307225   1.859294163115635 134408.464928230736405   18.02732
   3.920824000108972   2.708883025012270  -8.496595793060767   1.814452566665337  -6.844193963396020   9.011123944471162   0.639032001797923   6.971050646916888   1.559521892620778  -2.026824998548626  -7.787084933122948 138301.996053797338391   18.50463
  -0.717231616269278   7.026222842215915   1.187824593916305   1.679708134509132  -2.084588684990708  -9.061305549958185   0.787897044865464   7.744500002357864  -7.471288074827099   9.465445378214977  -0.624654996843299 118339.022423856440582   18.62714
   0.657640408443168   6.178292860835809  -6.616474058844786   5.150810404920336   2.691822787329444   1.204354252131003  -6.309111136057560  -0.197775090897457  11.405958552888839  -7.528883123165367  -2.221330324820661 124989.482707496528747   18.68601
   1.459883996058007 -10.154331963132005  -7.056258726017477   2.039924564468758   0.657137716439207  -2.869508994336103  -2.648798406093454  -4.611659191687596  -8.267523441103663  -9.095668066131902  -1.550728196969668 148924.802572563698050   18.69843
  -3.129432844453707   1.996545681949845  12.602810796334490   2.642186951654841   1.755111858824058  -3.526064408869366 -10.996996952870942   0.819718528685508  -1.748784732555743   7.009907209406840  -2.817425604767979 93009.309833871302544   19.41252
   0.101119952356980  -8.270431587739923 -10.324985668860073   0.842603971000946  -5.484565324499131   1.391785080362920  -4.177823841458470   4.658256764258867   6.305875401743601  -3.120829689672134   9.040982953621686 117912.148504885670263   19.44581
   8.874701642674069   4.970806553002160  -1.388627417992115   3.917783796861768  -3.581920637142765  -4.736457654767232  -2.182890435507857   5.659799282071067  -0.537803754329463 -13.594287186346298   1.443218860025126 122567.327476525271777   19.49323
  -4.801242343845924  -3.020660821259133  -1.289602657821983   5.537426716825585  15.530123821952561   0.685289810500530  -7.665419802918840  -2.904738079433847  -2.930310755301059   1.363720591854677   0.021741601126322 89709.832746407249942   19.59081
   8.792970732016153  -0.444029930577662   3.315555315531038   6.323831754839726   2.256515631136056   4.367525444912102   6.323072819159250 -12.016476219233315   3.004050486723123  -2.781710446917891  -6.788897317300833 88552.407484978655702   19.99732
   7.480146947324136  -3.972921048623976  -7.547752972806876  -8.391992519032573   5.515701535202851  -5.527037884392564   1.149413719665752  11.847457693100891  -1.726937014292959  -2.683876353963470   2.000071821695875 85067.039053431144566   20.39537
  11.223341294486309  -7.280159964934166  -7.738096722510725   5.156345376704370   0.967541979571764   9.766090795359871   0.503881494004197   3.919416374170609  -5.403197940701737  -3.726108537882254   1.011789612227330 64216.339983046462294   20.52951
   9.784187722596274  -3.999354126622623  11.925684445142455  -2.276485568640464   2.111377031049187  -3.240702898206483   8.565021921400639  -2.232762287422957  -2.524567908541957  -6.670565478769536   4.277730258329324 92365.524274769602926   20.53298
  12.257769709032388  -6.678744564645766  -8.188566657991377   2.688039282401193   9.572918778430111   1.641516346630976  -5.206485718038829  -2.063578679644728   7.414288501434481  -0.156489094081885  -2.276831569626510 69356.979643358034082   21.33115
  -0.822035650305382  -9.231630612202151   2.106408148381611  -7.104617361327613   7.008833259587293   2.399876822845091  -7.820030004387307   0.389974177283274 -10.729474308589616   4.595225047953900  -8.959171532512290 63592.885320816116291   21.76014

