var x1;
var x2;
var x3;
var x4;
var x5;
var x6;
var x7;
var x8;

subject to

cons1:  8*x1^2+ 8*x1*x2+ 8*x1*x3+ 2*x1*x4+ 2*x1*x5+ 2*x1*x6+ 2*x1*x7-8*x2*x3-2*x4*x7
-2*x5*x6-x1 = 0;
cons2:  8*x1*x2-8*x1*x3+ 8*x2^2+ 8*x2*x3+ 2*x2*x4+ 2*x2*x5+ 2*x2*x6+ 2*x2*x7-2*x4*x6
-2*x5*x7-x2 = 0;
cons3: -8*x1*x2+ 8*x1*x3+ 8*x2*x3+ 8*x3^2+ 2*x3*x4+ 2*x3*x5+ 2*x3*x6+ 2*x3*x7-2*x4*
x5-2*x6*x7-x3 = 0;
cons4:  2*x1*x4-2*x1*x7+ 2*x2*x4-2*x2*x6+ 2*x3*x4-2*x3*x5+ 8*x4^2+ 8*x4*x5+ 2*x4*x6+
 2*x4*x7+ 6*x4*x8-6*x5*x8-x4 = 0;
cons5:  2*x1*x5-2*x1*x6+ 2*x2*x5-2*x2*x7-2*x3*x4+ 2*x3*x5+ 8*x4*x5-6*x4*x8+ 8*x5^2+
 2*x5*x6+ 2*x5*x7+ 6*x5*x8-x5 = 0;
cons6: -2*x1*x5+ 2*x1*x6-2*x2*x4+ 2*x2*x6+ 2*x3*x6-2*x3*x7+ 2*x4*x6+ 2*x5*x6+ 8*x6^2
+ 8*x6*x7+ 6*x6*x8-6*x7*x8-x6 = 0;
cons7: -2*x1*x4+ 2*x1*x7-2*x2*x5+ 2*x2*x7-2*x3*x6+ 2*x3*x7+ 2*x4*x7+ 2*x5*x7+ 8*x6*
x7-6*x6*x8+ 8*x7^2+ 6*x7*x8-x7 = 0;
cons8: -6*x4*x5+ 6*x4*x8+ 6*x5*x8-6*x6*x7+ 6*x6*x8+ 6*x7*x8+ 8*x8^2-x8 = 0;

solve;
display x1, x2, x3, x4, x5, x6, x7, x8;

# TITLE : the construction of Virasoro algebras

# ROOT COUNTS :

# total degree : 256
# generalized Bezout number : 256
#   based on the set structure :
#      {x1 x3 x6 x7 }{x1 x2 x3 x4 x5 x6 x7 }
#      {x1 x2 x6 x7 }{x2 x3 x4 x5 x6 x7 }
#      {x1 x3 x5 x7 }{x2 x3 x4 x5 x6 x7 }
#      {x1 x2 x3 x4 x8 }{x4 x5 x6 x7 x8 }
#      {x1 x2 x3 x5 x8 }{x4 x5 x6 x7 x8 }
#      {x1 x2 x3 x6 x8 }{x4 x5 x6 x7 x8 }
#      {x1 x2 x3 x7 x8 }{x4 x5 x6 x7 x8 }
#      {x4 x6 x8 }{x5 x7 x8 }
# mixed volume : 200

# REFERENCES :

# Schrans, S. and Troost, W.:
# `Generalized Virasoro Constructions for SU(3)',
#  Nuclear Phys. B, Vol. 345, No. 2--3, 1990, pp. 584--606.

# SYMMETRY :

# x1 x2 x3 x4 x5 x6 x7 x8
# x2 x1 x3 x4 x5 x7 x6 x8
# x1 x2 x3 x5 x4 x7 x6 x8
# x2 x1 x3 x5 x4 x6 x7 x8
# x1 x2 x3 x6 x7 x4 x5 x8
# x2 x1 x3 x6 x7 x5 x4 x8
# x1 x2 x3 x7 x6 x5 x4 x8
# x2 x1 x3 x7 x6 x4 x5 x8

# SYMMETRIC SET STRUCTURE :

#  { x1 x2 x4 x5 x6 x7 } { x1 x3 x4 x5 x6 x7 }
#  { x2 x1 x4 x5 x6 x7 } { x2 x3 x4 x5 x6 x7 }
#  { x3 x1 x2 x4 x5 x6 x7 } { x3 x1 x2 x4 x5 x6 x7 }
#   { x4 x1 x2 x3 x8 } { x4 x5 x6 x7 }
#   { x5 x1 x2 x3 x8 } { x5 x4 x7 x6 }
#   { x6 x1 x2 x3 x8 } { x6 x7 x4 x5 }
#   { x7 x1 x2 x3 x8 } { x7 x6 x5 x4 } 
#   { x8 x4 x5 x6 x7 } { x8 x4 x5 x6 x7 } 


# ------------------------------------------------
# |    orbit information of list of solutions    |
# ------------------------------------------------
# |       TYPE        | NB <> | NB GEN | NB SOLS |
# ------------------------------------------------
# |  1 2 3 4 5 6 6 7  |   7   |    4   |    32   |
# |  1 2 3 4 4 4 5 6  |   6   |    4   |    32   |
# |  1 2 3 4 4 4 4 5  |   5   |    8   |    16   |
# |  1 1 2 3 4 5 5 6  |   6   |   20   |    80   |
# |  1 1 2 3 3 4 4 5  |   5   |   16   |    48   |
# |  1 1 2 3 3 3 4 5  |   5   |    8   |    32   |
# |  1 1 2 3 3 3 3 4  |   4   |   16   |    16   |
# ------------------------------------------------
# | Total number of generating solutions :   76  |
# | Total number of solutions generated  :  256  |
# ------------------------------------------------

# THE GENERATING SOLUTIONS :

# 76 8
# ===========================================================
# solution 1 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x1 : -1.25000000000000E-02   0.00000000000000E+00
#  x2 : -1.25000000000000E-02   0.00000000000000E+00
#  x3 :  1.12500000000000E-01   0.00000000000000E+00
#  x4 :  5.00000000000000E-02  -2.20561949492296E-55
#  x5 :  5.00000000000000E-02  -5.65137976246300E-55
#  x6 :  5.00000000000000E-02   0.00000000000000E+00
#  x7 :  5.00000000000000E-02   0.00000000000000E+00
#  x8 :  5.00000000000000E-02   1.56607307231965E-53
# == err :  7.589E-18 = rco :  2.635E-01 = res :  7.980E-18 ==
# solution 2 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x1 :  5.00000000000000E-02  -1.42433516186397E-65
#  x2 :  5.00000000000000E-02   4.74778387287990E-66
#  x3 :  5.00000000000000E-02  -4.74778387287990E-66
#  x4 :  5.00000000000000E-02  -1.66172435550796E-65
#  x5 :  5.00000000000000E-02   7.59645419660784E-65
#  x6 :  5.00000000000000E-02  -1.51929083932157E-64
#  x7 :  5.00000000000000E-02   1.13946812949118E-64
#  x8 : -7.50000000000000E-02   0.00000000000000E+00
# == err :  2.689E-17 = rco :  3.082E-01 = res :  1.388E-17 ==
# solution 3 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 :  5.00000000000000E-02  -1.11516433779272E-57
#  x2 :  5.00000000000000E-02   6.37236764452981E-58
#  x3 : -5.09615384615385E-02   3.18618382226490E-57
#  x4 :  5.00000000000000E-02   1.99136488891557E-58
#  x5 :  5.00000000000000E-02   3.61287334976893E-58
#  x6 : -4.40261467514519E-02  -5.62330058276822E-57
#  x7 :  1.90261467514519E-02   5.25720330673709E-57
#  x8 :  8.36538461538462E-02  -1.43378272001921E-57
# == err :  4.549E-17 = rco :  7.693E-02 = res :  6.939E-18 ==
# solution 4 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 : -2.16840434497099E-19   1.63132611699963E-55
#  x2 : -2.16840434497098E-19  -1.63132611699963E-55
#  x3 : -7.21153846153846E-03  -7.56230941304486E-55
#  x4 :  6.25000000000000E-02  -2.07451226879080E-55
#  x5 :  6.25000000000000E-02   2.85482070474935E-55
#  x6 : -3.15261467514519E-02   5.87277402119867E-54
#  x7 :  3.15261467514519E-02  -6.03590663289864E-54
#  x8 :  6.49038461538462E-02   2.12072395209952E-54
# == err :  4.949E-17 = rco :  8.817E-02 = res :  6.939E-18 ==
# solution 5 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 2
# the solution for t :
#  x1 :  9.41662253455395E-35  -6.68191177523049E-52
#  x2 :  8.68173107743309E-34   1.33638235504610E-51
#  x3 :  1.03211738679125E-01  -2.00457353256915E-50
#  x4 : -6.06555085024300E-35   0.00000000000000E+00
#  x5 : -3.56409887169318E-35   6.68191177523049E-52
#  x6 :  6.25000000000000E-02   3.34095588761525E-52
#  x7 :  6.25000000000000E-02   1.50499458581891E-52
#  x8 :  7.19617386791248E-02   2.54543299191604E-52
# == err :  1.713E-16 = rco :  1.967E-01 = res :  3.469E-18 ==
# solution 6 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 2
# the solution for t :
#  x1 :  6.50395100180695E-33  -4.77927573339736E-58
#  x2 :  5.40595342749339E-32   5.57582168896358E-58
#  x3 :  1.03211738679125E-01  -6.96977711120448E-58
#  x4 :  6.25000000000000E-02   1.67274650668907E-57
#  x5 :  6.25000000000000E-02  -1.35412812446258E-57
#  x6 : -4.84003360681272E-33  -3.98272977783113E-59
#  x7 : -5.38632829755259E-33  -1.99136488891557E-59
#  x8 : -4.07117386791248E-02  -1.35128540351057E-58
# == err :  1.685E-16 = rco :  4.551E-02 = res :  6.939E-18 ==
# solution 7 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 : -2.50000000000000E-02   1.46166820083167E-52
#  x2 :  2.17186805708301E-18  -2.29690717273548E-52
#  x3 :  1.00000000000000E-01   7.30834100415835E-53
#  x4 :  1.00000000000000E-01  -1.50343014942686E-51
#  x5 : -2.22072606808498E-17   1.67047794380762E-51
#  x6 :  1.00000000000000E-01   1.33638235504610E-51
#  x7 :  1.74613567881738E-17  -1.50343014942686E-51
#  x8 : -2.50000000000000E-02  -1.67047794380762E-52
# == err :  2.710E-17 = rco :  2.463E-02 = res :  1.128E-17 ==
# solution 8 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 : -1.25000000000000E-02  -8.53150932668468E-51
#  x2 :  1.25000000000000E-02   1.00228676628457E-50
#  x3 :  1.12500000000000E-01  -2.30525956245452E-50
#  x4 :  5.00000000000000E-02   0.00000000000000E+00
#  x5 : -5.00000000000000E-02   6.41463530422127E-50
#  x6 :  5.00000000000000E-02   6.41463530422127E-50
#  x7 : -5.00000000000000E-02  -4.27642353614751E-50
#  x8 :  5.00000000000000E-02   1.10251544291303E-50
# == err :  1.297E-17 = rco :  3.266E-02 = res :  1.388E-17 ==
# solution 9 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 : -1.25000000000000E-02   3.49436893043961E-63
#  x2 : -1.25000000000000E-02  -1.06350358752510E-63
#  x3 :  1.02003143396115E-01  -1.62629691818402E-63
#  x4 :  1.19337524528154E-01  -6.68487969301490E-63
#  x5 : -1.93375245281536E-02  -9.03978049396333E-63
#  x6 :  5.00000000000000E-02  -2.37009370934165E-62
#  x7 :  5.00000000000000E-02   3.09935331221600E-62
#  x8 : -2.98343811320384E-02   8.28013507430255E-63
# == err :  3.746E-16 = rco :  3.893E-02 = res :  2.667E-17 ==
# solution 10 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 : -5.69879941673280E-52  -1.80411617931223E-50
#  x2 :  3.34095588761525E-52   1.80411617931223E-50
#  x3 :  1.14503143396115E-01  -6.68191177523049E-51
#  x4 :  6.93375245281537E-02   1.00228676628457E-51
#  x5 : -6.93375245281537E-02  -3.34095588761525E-52
#  x6 : -7.22742722875516E-51   7.55056030601045E-50
#  x7 :  7.22742722875516E-51  -7.48374118825815E-50
#  x8 :  4.51656188679616E-02   2.67276471009220E-51
# == err :  2.057E-16 = rco :  3.826E-02 = res :  2.082E-17 ==
# solution 11 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x1 :  5.00000000000000E-02   0.00000000000000E+00
#  x2 :  5.00000000000000E-02   0.00000000000000E+00
#  x3 : -7.50000000000000E-02   1.95759134039956E-54
#  x4 :  5.00000000000000E-02  -1.75367557577461E-54
#  x5 :  5.00000000000000E-02  -5.22024357439882E-54
#  x6 :  5.00000000000000E-02  -5.22024357439882E-54
#  x7 :  5.00000000000000E-02   2.61012178719941E-54
#  x8 : -7.50000000000000E-02  -2.61012178719941E-54
# == err :  2.689E-17 = rco :  2.727E-01 = res :  2.082E-17 ==
# solution 12 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x1 :  0.00000000000000E+00   8.79709548981352E-88
#  x2 : -6.28363963558107E-89  -8.79709548981352E-88
#  x3 :  1.25000000000000E-01   0.00000000000000E+00
#  x4 :  0.00000000000000E+00   0.00000000000000E+00
#  x5 :  0.00000000000000E+00   0.00000000000000E+00
#  x6 :  0.00000000000000E+00   0.00000000000000E+00
#  x7 :  0.00000000000000E+00   0.00000000000000E+00
#  x8 :  0.00000000000000E+00   0.00000000000000E+00
# == err :  3.924E-44 = rco :  2.927E-01 = res :  8.820E-88 ==
# solution 13 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x1 : -6.07230601530078E-79   0.00000000000000E+00
#  x2 :  3.37350334183377E-79   1.02608195375848E-116
#  x3 :  1.25000000000000E-01   8.15663058499816E-56
#  x4 :  2.49639247295699E-78   0.00000000000000E+00
#  x5 :  2.42892240612031E-78   0.00000000000000E+00
#  x6 :  1.95663193826359E-78   8.25326788892688E-117
#  x7 : -4.04820401020052E-79   0.00000000000000E+00
#  x8 :  1.25000000000000E-01   8.15663058499816E-56
# == err :  4.592E-40 = rco :  3.889E-01 = res :  8.157E-56 ==
# solution 14 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x1 :  5.00000000000000E-02   5.22024357439882E-54
#  x2 :  5.00000000000000E-02   6.52530446799853E-55
#  x3 : -7.50000000000000E-02  -3.26265223399926E-55
#  x4 :  5.00000000000000E-02   0.00000000000000E+00
#  x5 :  5.00000000000000E-02  -1.04404871487976E-53
#  x6 :  5.00000000000000E-02   0.00000000000000E+00
#  x7 :  5.00000000000000E-02   0.00000000000000E+00
#  x8 :  5.00000000000000E-02   3.91518268079911E-54
# == err :  1.041E-17 = rco :  2.697E-01 = res :  9.714E-18 ==
# solution 15 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 :  6.25000000000000E-02   3.98272977783113E-59
#  x2 :  6.25000000000000E-02  -9.95682444457783E-59
#  x3 :  5.20031433961152E-02   3.98272977783113E-59
#  x4 :  4.31676718270679E-19   7.56718657787915E-58
#  x5 : -4.84036244000490E-18  -7.16891360009604E-58
#  x6 : -6.93375245281536E-02   3.40032587733493E-59
#  x7 :  6.93375245281536E-02  -1.99136488891557E-59
#  x8 :  4.51656188679616E-02   1.65106184451162E-59
# == err :  6.124E-17 = rco :  4.188E-02 = res :  3.469E-18 ==
# solution 16 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 :  5.00000000000000E-02  -2.13821176807376E-50
#  x2 :  5.00000000000000E-02  -3.20731765211064E-50
#  x3 : -4.37500000000000E-02   2.94004118110142E-50
#  x4 : -1.25000000000000E-02   4.00914706513829E-51
#  x5 : -1.25000000000000E-02   0.00000000000000E+00
#  x6 : -1.25000000000000E-02   8.01829413027659E-51
#  x7 :  1.12500000000000E-01   4.00914706513829E-51
#  x8 :  1.87500000000000E-02  -1.40377513982835E-50
# == err :  1.691E-17 = rco :  1.953E-01 = res :  5.638E-18 ==
# solution 17 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 2
# the solution for t :
#  x1 :  1.80555932286300E-35  -2.67276471009220E-51
#  x2 :  1.80555932286300E-35   0.00000000000000E+00
#  x3 : -9.46173867912483E-03   2.67276471009220E-51
#  x4 :  6.25000000000000E-02  -2.67276471009220E-51
#  x5 :  6.25000000000000E-02  -2.67276471009220E-51
#  x6 : -2.69630192214213E-33  -4.16951294774383E-49
#  x7 :  2.58796836277035E-33   4.27642353614751E-49
#  x8 :  7.19617386791248E-02   7.90586005512443E-51
# == err :  4.234E-17 = rco :  5.475E-02 = res :  3.469E-18 ==
# solution 18 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 2
# the solution for t :
#  x1 :  3.36917177326146E-67  -2.24611451550764E-68
#  x2 :  5.93472984109987E-67   1.48368246027497E-67
#  x3 : -9.46173867912483E-03   0.00000000000000E+00
#  x4 :  6.25000000000000E-02   9.50932750040110E-67
#  x5 :  6.25000000000000E-02  -5.93472984109987E-67
#  x6 : -2.37389193643995E-66   5.93472984109987E-67
#  x7 :  0.00000000000000E+00  -3.12614893756093E-67
#  x8 : -4.07117386791248E-02  -7.78934199156135E-67
# == err :  3.318E-17 = rco :  2.431E-01 = res :  3.469E-18 ==
# solution 19 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 :  3.75000000000000E-02   3.18618382226491E-58
#  x2 : -6.25000000000000E-02  -3.18618382226491E-58
#  x3 :  3.75000000000000E-02   1.59309191113245E-58
#  x4 :  1.00000000000000E-01  -1.11516433779272E-57
#  x5 : -4.98322386799634E-18   0.00000000000000E+00
#  x6 :  1.00000000000000E-01   6.37236764452981E-58
#  x7 : -3.92782743314660E-18  -1.59309191113245E-58
#  x8 : -2.50000000000000E-02   1.59309191113245E-58
# == err :  2.194E-17 = rco :  8.968E-02 = res :  6.939E-18 ==
# solution 20 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 :  1.25000000000000E-02   2.65875896881274E-64
#  x2 : -1.25000000000000E-02  -3.79822709830392E-64
#  x3 :  1.25000000000000E-02   5.31751793762549E-64
#  x4 : -5.00000000000000E-02  -2.43086534291451E-63
#  x5 :  5.00000000000000E-02   3.34243984650745E-63
#  x6 : -5.00000000000000E-02   1.82314900718588E-63
#  x7 :  5.00000000000000E-02  -2.43086534291451E-63
#  x8 :  7.50000000000000E-02  -6.07716335728627E-64
# == err :  7.459E-18 = rco :  3.955E-02 = res :  8.240E-18 ==
# solution 21 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 :  5.00000000000000E-02   1.83830061809396E-53
#  x2 :  5.00000000000000E-02   1.69657916167962E-53
#  x3 :  5.72115384615385E-02  -1.09625115062375E-52
#  x4 :  8.15261467514519E-02   1.41990625223648E-51
#  x5 :  1.84738532485481E-02  -1.50343014942686E-51
#  x6 : -1.25000000000000E-02   4.40458051589900E-54
#  x7 : -1.25000000000000E-02   9.78795670199779E-54
#  x8 : -1.49038461538462E-02   4.59381434547096E-52
# == err :  4.958E-17 = rco :  8.817E-02 = res :  1.214E-17 ==
# solution 22 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 : -2.65875896881274E-64   1.89911354915196E-65
#  x2 :  2.65875896881274E-64  -1.89911354915196E-65
#  x3 :  1.04968566038848E-02  -1.36002805471735E-65
#  x4 : -6.93375245281536E-02  -2.08205196015392E-65
#  x5 :  6.93375245281536E-02   2.37389193643995E-65
#  x6 :  1.36736175538941E-63  -3.47679709332055E-65
#  x7 : -1.36736175538941E-63   5.69734064745588E-65
#  x8 :  7.98343811320384E-02  -5.69734064745588E-65
# == err :  5.782E-17 = rco :  6.676E-02 = res :  3.036E-18 ==
# solution 23 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x1 :  4.09091122108145E-92  -1.63636448843258E-91
#  x2 :  4.14536090644533E-75   2.21085915010418E-75
#  x3 :  4.09091122108145E-92  -1.63636448843258E-91
#  x4 : -1.09090965895505E-91   8.70040595733137E-55
#  x5 :  0.00000000000000E+00  -2.61012178719941E-54
#  x6 : -1.09090965895505E-91   8.70040595733137E-55
#  x7 :  0.00000000000000E+00  -2.61012178719941E-54
#  x8 :  1.25000000000000E-01   1.30506089359970E-54
# == err :  4.847E-38 = rco :  3.199E-01 = res :  1.740E-54 ==
# solution 24 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x1 :  0.00000000000000E+00   0.00000000000000E+00
#  x2 :  0.00000000000000E+00   0.00000000000000E+00
#  x3 :  0.00000000000000E+00   0.00000000000000E+00
#  x4 :  0.00000000000000E+00   0.00000000000000E+00
#  x5 :  0.00000000000000E+00   0.00000000000000E+00
#  x6 :  0.00000000000000E+00   0.00000000000000E+00
#  x7 :  0.00000000000000E+00   0.00000000000000E+00
#  x8 :  0.00000000000000E+00   0.00000000000000E+00
# == err :  0.000E+00 = rco :  1.000E+00 = res :  0.000E+00 ==
# solution 25 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 2
# the solution for t :
#  x1 :  5.00000000000000E-02   1.89179664446979E-58
#  x2 : -7.50000000000000E-02   3.98272977783113E-58
#  x3 :  5.00000000000000E-02   1.09525068890356E-58
#  x4 :  5.00000000000000E-02  -3.18618382226490E-57
#  x5 :  5.00000000000000E-02  -2.54894705781192E-57
#  x6 :  5.00000000000000E-02   6.37236764452981E-58
#  x7 :  5.00000000000000E-02   3.18618382226490E-57
#  x8 : -7.50000000000000E-02   2.62860165336855E-57
# == err :  2.689E-17 = rco :  2.576E-01 = res :  1.388E-17 ==
# solution 26 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 2
# the solution for t :
#  x1 : -6.25000000000000E-02  -1.63132611699963E-55
#  x2 :  6.25000000000000E-02  -4.07831529249908E-56
#  x3 :  6.25000000000000E-02   0.00000000000000E+00
#  x4 : -3.72874541028487E-55  -5.47889895680550E-93
#  x5 :  2.61012178719941E-54   0.00000000000000E+00
#  x6 :  0.00000000000000E+00   8.34829626992462E-77
#  x7 :  2.61012178719941E-54  -8.34829626992462E-77
#  x8 :  1.25000000000000E-01   1.63132611699963E-55
# == err :  1.185E-38 = rco :  2.176E-01 = res :  3.639E-54 ==
# solution 27 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 8
# the solution for t :
#  x1 :  5.00000000000000E-02   9.36979021910309E-02
#  x2 :  5.00000000000000E-02  -9.36979021910309E-02
#  x3 :  1.09375000000000E-01  -1.19660096012905E-17
#  x4 :  4.99999999999999E-02  -1.96253980851345E-01
#  x5 :  5.00000000000000E-02   1.96253980851345E-01
#  x6 :  1.90408538509349E-01  -3.84086840852990E-17
#  x7 : -2.15408538509349E-01   3.58516680124820E-17
#  x8 :  2.83766198545515E-17   1.71926826689891E-17
# == err :  2.852E-16 = rco :  8.929E-03 = res :  1.528E-16 ==
# solution 28 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 8
# the solution for t :
#  x1 :  2.46385698621358E-17   9.36979021910309E-02
#  x2 :  1.40125758504151E-18  -9.36979021910309E-02
#  x3 : -5.93750000000000E-02   1.50184827928554E-17
#  x4 : -3.65430975184500E-17  -1.96253980851345E-01
#  x5 :  3.45489973730669E-17   1.96253980851345E-01
#  x6 : -1.40408538509349E-01   2.69178866777704E-17
#  x7 :  2.65408538509349E-01  -3.34280621371992E-17
#  x8 :  5.00000000000000E-02  -2.54215991345194E-18
# == err :  2.472E-16 = rco :  8.929E-03 = res :  6.283E-17 ==
# solution 29 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 : -6.33673867912483E-03  -3.91518268079912E-54
#  x2 :  1.06336738679125E-01  -3.09951962229930E-54
#  x3 :  3.12500000000000E-03   4.40214791914558E-54
#  x4 :  5.00000000000000E-02  -1.63132611699963E-55
#  x5 :  5.00000000000000E-02   3.26265223399926E-55
#  x6 : -1.25000000000000E-02   1.63132611699963E-55
#  x7 : -1.25000000000000E-02   6.03320212957789E-55
#  x8 : -2.19617386791248E-02  -2.44698917549945E-55
# == err :  1.884E-16 = rco :  1.357E-01 = res :  7.264E-18 ==
# solution 30 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 : -5.63367386791248E-02  -8.35238971903811E-53
#  x2 :  5.63367386791248E-02   1.67047794380762E-52
#  x3 :  4.68750000000000E-02  -1.67047794380762E-52
#  x4 :  9.78101081696150E-19  -1.25285845785572E-52
#  x5 : -4.51647637815127E-19   1.01987178685095E-52
#  x6 :  6.25000000000000E-02  -8.35238971903811E-53
#  x7 :  6.25000000000000E-02   1.04404871487976E-53
#  x8 :  7.19617386791248E-02   0.00000000000000E+00
# == err :  4.210E-17 = rco :  1.332E-01 = res :  3.697E-18 ==
# solution 31 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 :  1.00000000000000E-01  -1.67047794380762E-52
#  x2 : -1.25039789028809E-18   0.00000000000000E+00
#  x3 : -2.50000000000000E-02  -1.67047794380762E-52
#  x4 :  1.00000000000000E-01   2.36429632079167E-52
#  x5 :  5.47191045700141E-18   0.00000000000000E+00
#  x6 :  1.00000000000000E-01  -3.34095588761525E-52
#  x7 : -5.75000555115954E-18   7.51715074713430E-52
#  x8 : -2.50000000000000E-02  -3.34095588761525E-52
# == err :  1.489E-17 = rco :  1.277E-01 = res :  5.204E-18 ==
# solution 32 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 : -5.00000000000000E-02  -2.85482070474935E-54
#  x2 :  5.00000000000000E-02   3.58891745739919E-54
#  x3 :  7.50000000000000E-02  -3.91518268079912E-54
#  x4 :  5.00000000000000E-02  -1.82708525103959E-53
#  x5 : -5.00000000000000E-02   1.82708525103959E-53
#  x6 :  5.00000000000000E-02   2.99424810881167E-54
#  x7 : -5.00000000000000E-02   0.00000000000000E+00
#  x8 :  7.50000000000000E-02   9.01307679642296E-54
# == err :  1.353E-17 = rco :  1.277E-01 = res :  1.388E-17 ==
# solution 33 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 :  1.00000000000000E-01   5.72517405563225E-59
#  x2 : -8.55968860983371E-36  -1.99136488891557E-59
#  x3 : -8.55968860983372E-36  -5.47625344451780E-59
#  x4 :  1.00000000000000E-01   9.95682444457783E-60
#  x5 : -2.31111593452025E-34   0.00000000000000E+00
#  x6 :  2.56790659281526E-34   3.98272977783113E-59
#  x7 :  1.00000000000000E-01   0.00000000000000E+00
#  x8 :  7.70371974885035E-35   0.00000000000000E+00
# == err :  6.939E-18 = rco :  1.200E-01 = res :  6.939E-18 ==
# solution 34 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 : -5.00000000000000E-02  -5.09391138584602E-57
#  x2 :  5.00000000000000E-02   1.91171029335894E-57
#  x3 :  5.00000000000000E-02   6.37236764452981E-57
#  x4 :  5.00000000000000E-02  -2.29405235203073E-56
#  x5 : -5.00000000000000E-02   5.09789411562385E-57
#  x6 : -5.00000000000000E-02  -3.11250332137503E-56
#  x7 :  5.00000000000000E-02   2.03915764624954E-56
#  x8 :  5.00000000000000E-02  -5.09789411562385E-57
# == err :  1.457E-17 = rco :  1.012E-01 = res :  1.041E-17 ==
# solution 35 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 8
# the solution for t :
#  x1 : -5.00000000000000E-02   0.00000000000000E+00
#  x2 :  5.00000000000000E-02   0.00000000000000E+00
#  x3 :  4.37500000000000E-02  -5.34552942018439E-51
#  x4 :  1.12500000000000E-01   6.41463530422127E-50
#  x5 :  1.25000000000000E-02   0.00000000000000E+00
#  x6 : -1.25000000000000E-02   2.67276471009220E-51
#  x7 :  1.25000000000000E-02   7.35010295275354E-51
#  x8 : -1.87500000000000E-02  -3.20731765211064E-50
# == err :  1.084E-17 = rco :  1.378E-01 = res :  1.908E-17 ==
# solution 36 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 8
# the solution for t :
#  x1 : -5.00000000000000E-02   0.00000000000000E+00
#  x2 :  5.00000000000000E-02   9.28603632813875E-63
#  x3 :  5.00000000000000E-02   0.00000000000000E+00
#  x4 :  5.00000000000000E-02   0.00000000000000E+00
#  x5 : -5.00000000000000E-02  -2.43086534291451E-63
#  x6 :  7.50000000000000E-02   2.43086534291451E-63
#  x7 :  5.00000000000000E-02  -6.07716335728627E-63
#  x8 :  5.00000000000000E-02   4.86173068582902E-63
# == err :  1.045E-17 = rco :  1.618E-01 = res :  1.214E-17 ==
# solution 37 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 2
# the solution for t :
#  x1 :  1.12500000000000E-01  -5.13772141340216E-56
#  x2 : -1.25000000000000E-02  -1.27447352890596E-56
#  x3 : -1.25000000000000E-02  -6.11747293874862E-56
#  x4 :  5.00000000000000E-02   6.52530446799852E-55
#  x5 :  5.00000000000000E-02   8.15663058499816E-56
#  x6 :  5.00000000000000E-02   1.52936823468715E-55
#  x7 :  5.00000000000000E-02  -1.83524188162459E-55
#  x8 : -7.50000000000000E-02  -4.89397835099889E-55
# == err :  2.689E-17 = rco :  2.176E-01 = res :  1.388E-17 ==
# solution 38 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 2
# the solution for t :
#  x1 : -6.25000000000000E-02  -4.97841222228891E-60
#  x2 :  6.25000000000000E-02   4.97841222228891E-60
#  x3 :  6.25000000000000E-02   1.42240349208255E-60
#  x4 :  1.42240349208255E-60  -1.42240349208255E-60
#  x5 : -4.97841222228891E-60  -9.95682444457783E-60
#  x6 : -4.97841222228891E-60   0.00000000000000E+00
#  x7 :  0.00000000000000E+00   0.00000000000000E+00
#  x8 :  7.23875286018941E-86  -2.41291762006314E-86
# == err :  1.268E-43 = rco :  3.274E-01 = res :  9.575E-60 ==
# solution 39 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 2
# the solution for t :
#  x1 : -1.25000000000000E-02   0.00000000000000E+00
#  x2 :  1.12500000000000E-01   3.82342058671789E-57
#  x3 : -1.25000000000000E-02  -6.37236764452981E-57
#  x4 :  5.00000000000000E-02  -2.91308235178506E-57
#  x5 :  5.00000000000000E-02   5.09789411562385E-57
#  x6 :  5.00000000000000E-02  -4.16328019442614E-57
#  x7 :  5.00000000000000E-02   5.09789411562385E-57
#  x8 :  5.00000000000000E-02   9.55855146679472E-58
# == err :  7.806E-18 = rco :  3.274E-01 = res :  7.980E-18 ==
# solution 40 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 2
# the solution for t :
#  x1 : -7.50000000000000E-02   0.00000000000000E+00
#  x2 :  5.00000000000000E-02  -2.61012178719941E-54
#  x3 :  5.00000000000000E-02   1.95759134039956E-54
#  x4 :  5.00000000000000E-02  -1.04404871487976E-53
#  x5 :  5.00000000000000E-02   0.00000000000000E+00
#  x6 :  5.00000000000000E-02   2.08809742975953E-53
#  x7 :  5.00000000000000E-02   3.91518268079912E-54
#  x8 :  5.00000000000000E-02   6.26429228927858E-53
# == err :  8.674E-18 = rco :  2.667E-01 = res :  7.980E-18 ==
# solution 41 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 8
# the solution for t :
#  x1 :  6.05688839631642E-18  -4.89397835099889E-55
#  x2 :  1.00000000000000E-01   9.78795670199779E-55
#  x3 :  6.25000000000000E-03  -3.26265223399926E-55
#  x4 :  3.75000000000000E-02  -6.11747293874862E-55
#  x5 :  6.25000000000000E-02   1.63132611699963E-55
#  x6 : -6.25000000000000E-02   0.00000000000000E+00
#  x7 :  3.75000000000000E-02   6.52530446799852E-55
#  x8 :  6.87500000000000E-02  -1.14192828189974E-54
# == err :  2.440E-17 = rco :  1.210E-01 = res :  1.236E-17 ==
# solution 42 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 8
# the solution for t :
#  x1 : -7.03085406470469E-18  -9.36979021910310E-02
#  x2 :  5.52653552517866E-17   9.36979021910310E-02
#  x3 :  1.53125000000000E-01  -4.02221130501150E-17
#  x4 :  6.25000000000001E-02   1.96253980851345E-01
#  x5 :  6.25000000000000E-02  -1.96253980851345E-01
#  x6 :  2.02908538509349E-01  -7.36608760480691E-17
#  x7 : -2.02908538509349E-01   6.81975294348483E-17
#  x8 : -1.87500000000000E-02   3.07570128866565E-17
# == err :  2.418E-16 = rco :  9.096E-03 = res :  1.320E-16 ==
# solution 43 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 : -6.33673867912484E-03   7.08282648174432E-50
#  x2 :  1.06336738679125E-01   1.01565058983503E-49
#  x3 :  3.12500000000000E-03  -5.61280589119361E-50
#  x4 :  5.00000000000000E-02  -3.31502799051724E-50
#  x5 :  5.00000000000000E-02  -1.93775441481684E-50
#  x6 : -1.25000000000000E-02  -2.95337957211306E-50
#  x7 : -1.25000000000000E-02   0.00000000000000E+00
#  x8 :  9.07117386791248E-02   3.34095588761524E-50
# == err :  1.927E-16 = rco :  1.512E-01 = res :  6.939E-18 ==
# solution 44 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 :  5.63367386791248E-02   1.91171029335894E-57
#  x2 : -5.63367386791248E-02  -2.54894705781192E-57
#  x3 :  4.68750000000000E-02   1.27447352890596E-57
#  x4 :  6.25000000000000E-02  -7.96545955566226E-58
#  x5 :  6.25000000000000E-02   7.96545955566226E-58
#  x6 : -4.08689689809300E-21  -3.18618382226491E-58
#  x7 :  2.61695190033332E-18  -1.99136488891557E-58
#  x8 : -4.07117386791248E-02  -1.59309191113245E-58
# == err :  3.655E-17 = rco :  1.346E-01 = res :  6.939E-18 ==
# solution 45 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 :  5.00000000000000E-02  -6.26429228927858E-53
#  x2 :  7.50000000000000E-02   1.25285845785572E-52
#  x3 :  5.00000000000000E-02  -1.67047794380762E-52
#  x4 :  5.00000000000000E-02  -9.18762869094192E-52
#  x5 : -5.00000000000000E-02   1.02316774058217E-51
#  x6 :  5.00000000000000E-02   7.93477023308621E-52
#  x7 : -5.00000000000000E-02  -1.02316774058217E-51
#  x8 :  5.00000000000000E-02   2.08809742975953E-52
# == err :  8.465E-17 = rco :  2.181E-02 = res :  1.388E-17 ==
# solution 46 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 :  1.25000000000000E-02   1.04404871487976E-53
#  x2 :  1.12500000000000E-01   0.00000000000000E+00
#  x3 :  1.25000000000000E-02  -2.08809742975953E-53
#  x4 :  5.00000000000000E-02  -2.08809742975953E-53
#  x5 : -5.00000000000000E-02   6.26429228927858E-53
#  x6 :  5.00000000000000E-02   8.35238971903811E-53
#  x7 : -5.00000000000000E-02  -6.26429228927858E-53
#  x8 :  7.50000000000000E-02  -4.17619485951906E-53
# == err :  1.344E-17 = rco :  9.085E-02 = res :  1.388E-17 ==
# solution 47 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 :  3.75000000000000E-02  -3.11150763893057E-59
#  x2 : -6.25000000000000E-02   1.99136488891557E-59
#  x3 :  6.25000000000000E-02  -5.75628913202156E-60
#  x4 :  1.00000000000000E-01   3.48488855560224E-59
#  x5 :  4.10615870326590E-18  -1.59309191113245E-58
#  x6 : -3.65604400531437E-18   1.59309191113245E-58
#  x7 :  1.00000000000000E-01  -7.96545955566226E-59
#  x8 :  1.35034409385458E-18   5.97409466674670E-59
# == err :  7.373E-18 = rco :  9.325E-02 = res :  6.939E-18 ==
# solution 48 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 :  5.00000000000000E-02   0.00000000000000E+00
#  x2 :  7.50000000000000E-02   4.07831529249908E-56
#  x3 : -5.00000000000000E-02  -8.15663058499816E-56
#  x4 :  5.00000000000000E-02   8.15663058499816E-55
#  x5 : -5.00000000000000E-02  -6.52530446799852E-55
#  x6 : -5.00000000000000E-02   7.34096752649834E-55
#  x7 :  5.00000000000000E-02  -8.15663058499816E-55
#  x8 :  7.50000000000000E-02   4.07831529249908E-56
# == err :  1.804E-17 = rco :  2.628E-02 = res :  2.082E-17 ==
# solution 49 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 8
# the solution for t :
#  x1 :  1.00000000000000E-01  -2.54894705781192E-56
#  x2 : -2.03915764624954E-56  -1.52936823468715E-56
#  x3 :  7.13705176187339E-56   1.78426294046835E-56
#  x4 :  1.00000000000000E-01   2.03915764624954E-56
#  x5 : -1.01957882312477E-56  -7.64684117343577E-57
#  x6 :  1.01957882312477E-56   0.00000000000000E+00
#  x7 : -2.50000000000000E-02  -3.84964015386621E-57
#  x8 : -1.52936823468715E-56  -5.09789411562385E-57
# == err :  5.204E-18 = rco :  1.619E-01 = res :  3.469E-18 ==
# solution 50 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 8
# the solution for t :
#  x1 :  5.00000000000000E-02  -9.36979021910308E-02
#  x2 :  5.00000000000000E-02   9.36979021910308E-02
#  x3 : -1.03125000000000E-01  -3.12839761632453E-17
#  x4 :  2.52908538509349E-01   4.17224368666313E-17
#  x5 : -1.52908538509349E-01  -4.68625397252667E-17
#  x6 : -1.24999999999999E-02  -1.96253980851345E-01
#  x7 : -1.25000000000000E-02   1.96253980851345E-01
#  x8 :  6.87500000000000E-02   1.77229729028103E-17
# == err :  4.137E-16 = rco :  9.156E-03 = res :  1.314E-16 ==
# solution 51 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 2
# the solution for t :
#  x1 :  0.00000000000000E+00   0.00000000000000E+00
#  x2 :  1.25000000000000E-01   0.00000000000000E+00
#  x3 :  0.00000000000000E+00   0.00000000000000E+00
#  x4 :  1.47390610006945E-74   7.36953050034727E-75
#  x5 :  0.00000000000000E+00   2.94781220013891E-75
#  x6 :  0.00000000000000E+00   0.00000000000000E+00
#  x7 :  0.00000000000000E+00   0.00000000000000E+00
#  x8 :  1.25000000000000E-01   0.00000000000000E+00
# == err :  6.650E-38 = rco :  2.333E-01 = res :  1.349E-74 ==
# solution 52 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 2
# the solution for t :
#  x1 :  0.00000000000000E+00  -1.55575381946529E-61
#  x2 :  1.25000000000000E-01  -3.11150763893057E-61
#  x3 :  6.87273085141685E-90  -1.96363738611911E-90
#  x4 :  0.00000000000000E+00  -1.03090962771252E-89
#  x5 : -1.20272789899793E-89  -1.03716921297686E-61
#  x6 :  0.00000000000000E+00   3.48545636036138E-89
#  x7 :  7.14273099200816E-89   3.11150763893057E-61
#  x8 :  1.63344351410361E-132  -2.35636486334291E-89
# == err :  2.803E-45 = rco :  2.667E-01 = res :  4.149E-61 ==
# solution 53 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x1 : -1.25000000000000E-02   1.89911354915196E-65
#  x2 : -1.25000000000000E-02   0.00000000000000E+00
#  x3 : -1.25000000000000E-02   1.89911354915196E-65
#  x4 :  5.00000000000000E-02  -2.27893625898235E-64
#  x5 :  5.00000000000000E-02  -1.51929083932157E-64
#  x6 :  5.00000000000000E-02   7.59645419660784E-65
#  x7 :  5.00000000000000E-02   6.66831856066510E-65
#  x8 :  5.00000000000000E-02   7.59645419660784E-65
# == err :  6.939E-18 = rco :  4.483E-01 = res :  7.980E-18 ==
# solution 54 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x1 :  5.00000000000000E-02   5.87277402119867E-54
#  x2 :  5.00000000000000E-02   1.04404871487976E-53
#  x3 :  5.00000000000000E-02  -3.91518268079911E-54
#  x4 :  5.00000000000000E-02   4.40458051589900E-54
#  x5 :  5.00000000000000E-02  -1.04404871487976E-53
#  x6 :  5.00000000000000E-02  -2.44698917549945E-54
#  x7 :  5.00000000000000E-02  -1.79445872869959E-54
#  x8 :  5.00000000000000E-02  -6.26429228927858E-53
# == err :  6.939E-18 = rco :  1.000E+00 = res :  9.714E-18 ==
# solution 55 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 :  5.00000000000000E-02  -1.87093529706454E-50
#  x2 :  5.00000000000000E-02   1.62036360549339E-50
#  x3 : -6.45031433961153E-02   5.72138695754111E-51
#  x4 :  5.00000000000000E-02  -6.78214045185895E-50
#  x5 :  5.00000000000000E-02   7.21646471724893E-50
#  x6 :  1.19337524528154E-01  -3.34095588761525E-52
#  x7 : -1.93375245281536E-02  -4.00914706513829E-51
#  x8 :  4.83438113203841E-03  -5.34552942018439E-51
# == err :  3.562E-16 = rco :  3.868E-02 = res :  2.168E-17 ==
# solution 56 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 :  5.00000000000000E-02  -7.93477023308621E-52
#  x2 :  5.00000000000000E-02  -3.63328952778158E-51
#  x3 :  3.95031433961152E-02   7.09953126118240E-52
#  x4 :  5.00000000000000E-02  -1.67047794380762E-51
#  x5 :  5.00000000000000E-02   6.34781618646896E-51
#  x6 :  1.19337524528154E-01  -8.04266690157216E-52
#  x7 : -1.93375245281536E-02   1.15262978122726E-50
#  x8 : -2.98343811320384E-02  -1.20274411954149E-50
# == err :  3.567E-16 = rco :  4.316E-02 = res :  1.214E-17 ==
# solution 57 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 2
# the solution for t :
#  x1 :  5.00000000000000E-02   7.64684117343577E-57
#  x2 :  5.00000000000000E-02   1.52936823468715E-56
#  x3 :  5.94617386791248E-02   0.00000000000000E+00
#  x4 :  5.00000000000000E-02   2.03915764624954E-55
#  x5 :  5.00000000000000E-02  -2.19209446971825E-55
#  x6 : -1.25000000000000E-02   2.54894705781192E-57
#  x7 : -1.25000000000000E-02  -6.37236764452981E-57
#  x8 : -2.19617386791248E-02   5.09789411562385E-57
# == err :  3.524E-17 = rco :  5.475E-02 = res :  3.469E-18 ==
# solution 58 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 2
# the solution for t :
#  x1 :  5.00000000000000E-02  -1.22349458774972E-55
#  x2 :  5.00000000000000E-02   2.03915764624954E-56
#  x3 : -5.32117386791248E-02  -2.03915764624954E-56
#  x4 : -1.25000000000000E-02   2.28385656379948E-54
#  x5 : -1.25000000000000E-02  -2.32463971672447E-54
#  x6 :  5.00000000000000E-02   3.05873646937431E-56
#  x7 :  5.00000000000000E-02   3.05873646937431E-56
#  x8 :  9.07117386791248E-02  -1.01957882312477E-56
# == err :  6.062E-17 = rco :  4.551E-02 = res :  1.388E-17 ==
# solution 59 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 :  2.54894705781192E-57   0.00000000000000E+00
#  x2 : -2.50000000000000E-02   0.00000000000000E+00
#  x3 :  0.00000000000000E+00  -3.82342058671789E-57
#  x4 :  1.00000000000000E-01  -3.78447834000131E-56
#  x5 :  1.01957882312477E-56   1.01957882312477E-56
#  x6 :  1.00000000000000E-01   4.07831529249908E-56
#  x7 : -1.52936823468715E-56  -2.03915764624954E-56
#  x8 : -1.72053926402305E-57   6.88215705609219E-57
# == err :  1.041E-17 = rco :  2.181E-02 = res :  3.469E-18 ==
# solution 60 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 :  3.75000000000000E-02  -8.09137754031817E-53
#  x2 :  6.25000000000000E-02   7.30834100415835E-53
#  x3 :  3.75000000000000E-02  -5.22024357439882E-53
#  x4 :  1.00000000000000E-01  -5.42905331737477E-52
#  x5 : -9.06337504611844E-18   6.68191177523049E-52
#  x6 :  1.00000000000000E-01   6.68191177523049E-52
#  x7 :  1.64269789090424E-18  -7.51715074713430E-52
#  x8 : -2.50000000000000E-02  -2.08809742975953E-53
# == err :  1.440E-17 = rco :  3.605E-02 = res :  1.041E-17 ==
# solution 61 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 : -1.25000000000000E-02   8.21438016677671E-59
#  x2 : -1.25000000000000E-02  -8.83668169456282E-59
#  x3 : -2.00314339611523E-03   4.82283684034239E-60
#  x4 :  1.19337524528154E-01   3.11150763893057E-60
#  x5 : -1.93375245281536E-02  -4.66726145839586E-60
#  x6 :  5.00000000000000E-02   3.28575206671068E-58
#  x7 :  5.00000000000000E-02  -3.33553618893357E-58
#  x8 :  4.83438113203841E-03  -5.28956298618197E-60
# == err :  3.480E-16 = rco :  4.088E-02 = res :  5.204E-18 ==
# solution 62 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 :  8.03579522620406E-33   9.14613085271584E-62
#  x2 :  1.12989946402170E-31  -1.06958075088238E-61
#  x3 :  1.00961538461538E-01   3.26222129019127E-60
#  x4 :  9.40261467514520E-02  -2.27140057641932E-59
#  x5 :  3.09738532485481E-02   2.33363072919793E-59
#  x6 :  1.47846298308834E-34  -8.50802870020078E-63
#  x7 :  6.42361299510939E-36  -1.20023976306404E-62
#  x8 : -3.36538461538462E-02  -1.04235505904174E-59
# == err :  4.533E-16 = rco :  7.848E-02 = res :  1.561E-17 ==
# solution 63 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x1 : -1.25000000000000E-02   1.95759134039956E-54
#  x2 : -1.25000000000000E-02   7.64684117343576E-55
#  x3 : -1.25000000000000E-02   1.30506089359970E-54
#  x4 :  5.00000000000000E-02   2.61012178719941E-54
#  x5 :  5.00000000000000E-02   5.22024357439882E-54
#  x6 :  5.00000000000000E-02  -2.87419270238873E-54
#  x7 :  5.00000000000000E-02  -1.04404871487976E-53
#  x8 : -7.50000000000000E-02  -1.04404871487976E-53
# == err :  2.689E-17 = rco :  2.399E-01 = res :  1.388E-17 ==
# solution 64 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x1 :  6.25000000000000E-02   0.00000000000000E+00
#  x2 :  6.25000000000000E-02   0.00000000000000E+00
#  x3 :  6.25000000000000E-02   0.00000000000000E+00
#  x4 :  3.98272977783113E-60   0.00000000000000E+00
#  x5 :  9.95682444457783E-60   0.00000000000000E+00
#  x6 :  6.40081571437146E-60   0.00000000000000E+00
#  x7 : -2.98704733337335E-59   0.00000000000000E+00
#  x8 : -1.78591779887855E-102   0.00000000000000E+00
# == err :  8.968E-44 = rco :  4.483E-01 = res :  1.613E-59 ==
# solution 65 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x1 : -1.25000000000000E-02   2.98704733337335E-59
#  x2 : -1.25000000000000E-02   6.47193588897559E-59
#  x3 :  1.12500000000000E-01  -1.99136488891557E-59
#  x4 :  5.00000000000000E-02  -1.59309191113245E-58
#  x5 :  5.00000000000000E-02  -1.11516433779272E-57
#  x6 :  5.00000000000000E-02   0.00000000000000E+00
#  x7 :  5.00000000000000E-02   9.55855146679472E-58
#  x8 : -7.50000000000000E-02   2.38963786669868E-58
# == err :  2.689E-17 = rco :  2.121E-01 = res :  1.388E-17 ==
# solution 66 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x1 :  6.25000000000000E-02   6.07716335728627E-63
#  x2 :  6.25000000000000E-02   6.68487969301490E-63
#  x3 : -6.25000000000000E-02  -7.29259602874353E-63
#  x4 :  0.00000000000000E+00  -9.72346137165803E-63
#  x5 :  7.77876909732643E-62  -1.45851920574871E-62
#  x6 :  0.00000000000000E+00   4.86173068582902E-63
#  x7 :  1.94469227433161E-62  -1.94469227433161E-62
#  x8 :  1.25000000000000E-01  -7.29259602874353E-63
# == err :  8.769E-46 = rco :  2.613E-01 = res :  8.153E-62 ==
# solution 67 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 : -7.70371977754894E-34   1.27447352890596E-57
#  x2 : -3.85185988877447E-34  -1.27447352890596E-57
#  x3 :  9.37500000000000E-02  -1.27447352890596E-57
#  x4 :  6.25000000000000E-02  -6.37236764452981E-58
#  x5 :  6.25000000000000E-02   0.00000000000000E+00
#  x6 :  6.25000000000000E-02   2.54894705781192E-57
#  x7 : -6.25000000000000E-02   1.27447352890596E-57
#  x8 :  3.12500000000000E-02  -6.37236764452981E-58
# == err :  3.253E-18 = rco :  1.953E-01 = res :  8.667E-34 ==
# solution 68 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 :  5.00000000000000E-02   1.06910588403688E-50
#  x2 :  5.00000000000000E-02   8.01829413027659E-51
#  x3 :  5.00000000000000E-02  -1.60365882605532E-50
#  x4 :  5.00000000000000E-02  -3.07745787862178E-51
#  x5 :  5.00000000000000E-02   2.67276471009220E-51
#  x6 : -7.50000000000000E-02  -6.68191177523049E-52
#  x7 :  5.00000000000000E-02  -4.00914706513829E-51
#  x8 :  5.00000000000000E-02   4.00914706513829E-51
# == err :  1.140E-17 = rco :  2.410E-01 = res :  6.939E-18 ==
# solution 69 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 2
# the solution for t :
#  x1 :  5.00000000000000E-02   5.34552942018439E-50
#  x2 :  5.00000000000000E-02   6.41463530422127E-50
#  x3 :  5.94617386791248E-02  -6.41463530422127E-50
#  x4 :  5.00000000000000E-02  -2.00457353256915E-50
#  x5 :  5.00000000000000E-02  -2.13821176807376E-50
#  x6 : -1.25000000000000E-02   0.00000000000000E+00
#  x7 : -1.25000000000000E-02  -1.87093529706454E-50
#  x8 :  9.07117386791248E-02   3.74187059412907E-50
# == err :  6.061E-17 = rco :  2.431E-01 = res :  1.214E-17 ==
# solution 70 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 2
# the solution for t :
#  x1 :  5.00000000000000E-02   1.89911354915196E-64
#  x2 :  5.00000000000000E-02  -3.03858167864314E-64
#  x3 : -5.32117386791248E-02   0.00000000000000E+00
#  x4 : -1.25000000000000E-02   0.00000000000000E+00
#  x5 : -1.25000000000000E-02   1.89911354915196E-65
#  x6 :  5.00000000000000E-02  -1.89911354915196E-65
#  x7 :  5.00000000000000E-02  -3.79822709830392E-65
#  x8 : -2.19617386791248E-02   1.41743028561297E-64
# == err :  4.210E-17 = rco :  1.727E-01 = res :  1.388E-17 ==
# solution 71 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 :  6.25000000000000E-02   6.78631664671847E-53
#  x2 :  3.75000000000000E-02  -7.56935318287829E-53
#  x3 : -6.25000000000000E-02   3.91518268079912E-54
#  x4 :  1.00000000000000E-01   1.67047794380762E-52
#  x5 :  2.85788547043062E-17  -1.46166820083167E-52
#  x6 :  1.00000000000000E-01  -4.17619485951906E-53
#  x7 : -2.74404104157819E-17   4.17619485951906E-53
#  x8 :  3.41533286557293E-18  -2.08809742975953E-53
# == err :  2.602E-17 = rco :  3.266E-02 = res :  1.388E-17 ==
# solution 72 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 :  1.12500000000000E-01  -7.13705176187339E-56
#  x2 :  1.25000000000000E-02   2.03915764624954E-56
#  x3 : -1.25000000000000E-02   5.09789411562385E-56
#  x4 :  5.00000000000000E-02   4.07831529249908E-56
#  x5 : -5.00000000000000E-02  -5.09789411562385E-57
#  x6 :  5.00000000000000E-02  -4.07831529249908E-56
#  x7 : -5.00000000000000E-02   2.03915764624954E-56
#  x8 :  5.00000000000000E-02   1.01957882312477E-56
# == err :  1.683E-17 = rco :  9.144E-02 = res :  1.388E-17 ==
# solution 73 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 :  0.00000000000000E+00  -2.54894705781192E-57
#  x2 : -2.03915764624954E-56   0.00000000000000E+00
#  x3 : -6.79719215416513E-57  -1.27447352890596E-57
#  x4 :  1.25000000000000E-01   7.64684117343577E-57
#  x5 :  2.03915764624954E-56   2.54894705781192E-57
#  x6 :  1.01957882312477E-56  -5.09789411562385E-57
#  x7 :  5.09789411562385E-57   5.09789411562385E-57
#  x8 : -1.52936823468715E-56  -2.54894705781192E-57
# == err :  1.616E-40 = rco :  2.446E-01 = res :  1.336E-56 ==
# solution 74 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 4
# the solution for t :
#  x1 :  6.25000000000000E-02   6.26429228927858E-53
#  x2 :  6.25000000000000E-02   1.00228676628457E-51
#  x3 : -5.20031433961152E-02  -4.17619485951906E-52
#  x4 :  6.93375245281536E-02  -2.92333640166334E-51
#  x5 : -6.93375245281536E-02  -1.67047794380762E-51
#  x6 :  1.50259986170648E-18   1.25285845785572E-52
#  x7 :  1.70878377792039E-18   1.33638235504610E-51
#  x8 :  7.98343811320384E-02   2.33866912133067E-51
# == err :  6.665E-17 = rco :  3.893E-02 = res :  1.388E-17 ==
# solution 75 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x1 :  6.25000000000000E-02   1.21543267145725E-63
#  x2 :  6.25000000000000E-02   0.00000000000000E+00
#  x3 :  6.25000000000000E-02   1.21543267145725E-63
#  x4 :  0.00000000000000E+00   0.00000000000000E+00
#  x5 :  9.72346137165803E-63   3.54501195841699E-64
#  x6 :  4.86173068582902E-63  -1.21543267145725E-63
#  x7 :  2.71777592913021E-108  -7.59645419660784E-64
#  x8 :  1.25000000000000E-01  -1.51929083932157E-64
# == err :  6.569E-47 = rco :  2.031E-01 = res :  1.102E-62 ==
# solution 76 :
# t :  1.00000000000000E+00   0.00000000000000E+00
# m : 1
# the solution for t :
#  x1 :  6.25000000000000E-02  -3.11150763893057E-61
#  x2 :  6.25000000000000E-02  -6.22301527786114E-61
#  x3 : -6.25000000000000E-02   6.22301527786114E-61
#  x4 : -2.90755820785393E-104  -4.59317794318322E-61
#  x5 : -3.87568966770518E-104  -7.26018449083800E-61
#  x6 :  0.00000000000000E+00   1.24460305557223E-60
#  x7 : -1.94469227433161E-61   1.24460305557223E-60
#  x8 : -7.54036756269726E-88  -3.77018378134864E-88
# == err :  1.253E-44 = rco :  2.635E-01 = res :  8.035E-61 ==