Starting with polynomial:
P : t^31 - 465*t^29 + 94395*t^27 - 11044215*t^25 + 828316125*t^23 - 41912795925*t^21 + 1466947857375*t^19 - 35835440515875*t^17 + 609202488769875*t^15 - 7107362368981875*t^13 + 55437426478058625*t^11 - 277187132390293125*t^9 + 831561397170879375*t^7 - 1343291487737574375*t^5 + 959493919812553125*t^3 - 191898783962510625*t
Extension levels are: 31
-------------------------------------------------
Ending with final polynomial:
P : t^31 - 465*t^29 + 94395*t^27 - 11044215*t^25 + 828316125*t^23 - 41912795925*t^21 + 1466947857375*t^19 - 35835440515875*t^17 + 609202488769875*t^15 - 7107362368981875*t^13 + 55437426478058625*t^11 - 277187132390293125*t^9 + 831561397170879375*t^7 - 1343291487737574375*t^5 + 959493919812553125*t^3 - 191898783962510625*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 current precision for weights: 53
Linear system for weights solvable: 0
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 0
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   31 out of 31
Indefinite weights: 0 out of 31
Negative weights:   0 out of 31
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-6.5500142687656830651 + 2.067061389396511888e-369j)  +/-  (3.21e-120, 3.21e-120j)
| (-9.8933857089866511454 + 7.6125017994080775805e-375j)  +/-  (6.1e-122, 6.1e-122j)
| (-8.8743014094887900445 + 1.3478950225282818349e-380j)  +/-  (4.71e-121, 4.71e-121j)
| (2.8287927681575078515 - 1.891829847217460707e-387j)  +/-  (1.97e-122, 1.97e-122j)
| (4.0046009014912233904 + 2.83616416080199804e-387j)  +/-  (3.7e-121, 3.7e-121j)
| (-5.8778558859862577222 + 1.4320789365241062666e-383j)  +/-  (2.83e-120, 2.83e-120j)
| (-4.0046009014912233904 + 8.421261134983863367e-387j)  +/-  (3.66e-121, 3.66e-121j)
| (8.8743014094887900445 + 5.9398150705351392096e-391j)  +/-  (4.83e-121, 4.83e-121j)
| (7.2600004888908646829 - 8.4231415889977626813e-402j)  +/-  (3.16e-120, 3.16e-120j)
| (3.4115324158431556302 - 1.7661943698419111432e-412j)  +/-  (9.96e-122, 9.96e-122j)
| (-8.0241932273616464551 - 1.6510878484273737052e-412j)  +/-  (1.51e-120, 1.51e-120j)
| (9.8933857089866511454 + 4.6038754157071853685e-420j)  +/-  (7e-122, 7e-122j)
| (5.8778558859862577222 - 4.3884343837822666118e-422j)  +/-  (3.96e-120, 3.96e-120j)
| (-2.2540950007544107882 - 3.2900209901201856503e-428j)  +/-  (3.32e-123, 3.32e-123j)
| (-1.6854979050690520312 + 6.9411635553201931245e-432j)  +/-  (3.32e-124, 3.32e-124j)
| (2.2540950007544107882 + 1.7676397572966421472e-432j)  +/-  (3.54e-123, 3.54e-123j)
| (-5.233641511712707723 - 9.4553712196987572159e-432j)  +/-  (2.05e-120, 2.05e-120j)
| (-7.2600004888908646829 - 2.2796919546151124807e-441j)  +/-  (3.34e-120, 3.34e-120j)
| (-4.6107897973239905731 - 4.8145524386894884242e-446j)  +/-  (1.01e-120, 1.01e-120j)
| (-2.8287927681575078515 - 1.0816283812101000272e-447j)  +/-  (1.99e-122, 1.99e-122j)
| (1.6854979050690520312 - 6.0282120276534724514e-450j)  +/-  (3.32e-124, 3.32e-124j)
| (0.55994758784100286353 - 1.8797563126651213545e-457j)  +/-  (4.72e-126, 4.72e-126j)
| (-3.4115324158431556302 - 7.3594436686878668348e-448j)  +/-  (9.57e-122, 9.57e-122j)
| (5.233641511712707723 - 1.5145510976767789065e-444j)  +/-  (2.1e-120, 2.1e-120j)
| (-0.55994758784100286353 - 4.0784431743491417929e-463j)  +/-  (4.72e-126, 4.72e-126j)
| (4.6107897973239905731 + 1.886273642047215876e-455j)  +/-  (1.04e-120, 1.04e-120j)
| (1.1212973740470093023 + 1.1332721754275025039e-469j)  +/-  (4.01e-125, 4.01e-125j)
| (6.5500142687656830651 - 5.1641094223992269967e-471j)  +/-  (3.4e-120, 3.4e-120j)
| (6.6100470620129776011e-490 - 1.6514020622644067143e-489j)  +/-  (5.51e-488, 5.51e-488j)
| (-1.1212973740470093023 - 4.8442061015089824046e-486j)  +/-  (4.29e-125, 4.29e-125j)
| (8.0241932273616464551 - 7.7075924535320356137e-487j)  +/-  (1.71e-120, 1.71e-120j)
-------------------------------------------------
The weights are:
| (1.3272514835897104702e-10 + 8.9850157918303898922e-379j)  +/-  (7.9e-31, 4.72e-91j)
| (2.6059738548930083167e-22 - 1.1498213896326812568e-385j)  +/-  (1.45e-36, 8.64e-97j)
| (2.8833523678578342821e-18 + 1.7397588926210662107e-383j)  +/-  (4.59e-35, 2.74e-95j)
| (0.0042217177672707051766 + 1.6497836000509029909e-376j)  +/-  (2.51e-23, 1.5e-83j)
| (7.8716240696022419012e-05 + 2.0017957087448256025e-377j)  +/-  (1.23e-27, 7.32e-88j)
| (8.2439316191197409886e-09 - 3.2168110780628389498e-378j)  +/-  (7.6e-31, 4.54e-91j)
| (7.8716240696022419012e-05 + 8.3004920249406760117e-377j)  +/-  (1.52e-27, 9.05e-88j)
| (2.8833523678578342821e-18 - 2.6216393041302453981e-384j)  +/-  (1.31e-38, 7.85e-99j)
| (1.0496033623113593945e-12 - 1.7666415828814876044e-381j)  +/-  (2.45e-36, 1.46e-96j)
| (0.00069603127137929193123 - 6.3069238311237664292e-377j)  +/-  (6.01e-28, 3.59e-88j)
| (3.3284683241484067845e-15 - 9.3197012438498730959e-382j)  +/-  (3.39e-36, 2.02e-96j)
| (2.6059738548930083167e-22 + 2.3378863258200034193e-386j)  +/-  (2.05e-40, 1.23e-100j)
| (8.2439316191197409886e-09 - 1.7398045723208047635e-379j)  +/-  (2.26e-34, 1.35e-94j)
| (0.017967875843441640652 - 7.4305719262365832586e-376j)  +/-  (1.97e-27, 1.18e-87j)
| (0.054567258894474982276 + 1.1435532303837839906e-375j)  +/-  (1.45e-25, 8.67e-86j)
| (0.017967875843441640652 - 3.6257088744688462729e-376j)  +/-  (1.41e-27, 8.39e-88j)
| (2.8456100881628338026e-07 + 9.6502551192267598314e-378j)  +/-  (2.71e-33, 1.62e-93j)
| (1.0496033623113593945e-12 + 3.4363126550043571037e-380j)  +/-  (4.55e-36, 2.72e-96j)
| (5.9232023176863260452e-06 - 2.9886852839340661625e-377j)  +/-  (9.74e-33, 5.82e-93j)
| (0.0042217177672707051766 + 4.1580438130359463565e-376j)  +/-  (4.37e-31, 2.61e-91j)
| (0.054567258894474982276 + 6.7546902785687826716e-376j)  +/-  (6.63e-31, 3.96e-91j)
| (0.19113200477464314855 + 1.4642978385974240814e-375j)  +/-  (5.49e-30, 3.28e-90j)
| (0.00069603127137929193123 - 2.0018186857263129023e-376j)  +/-  (7.85e-32, 4.69e-92j)
| (2.8456100881628338026e-07 + 1.0780468450749760393e-378j)  +/-  (3.9e-37, 2.33e-97j)
| (0.19113200477464314855 + 1.7380610824068514044e-375j)  +/-  (1.1e-31, 6.54e-92j)
| (5.9232023176863260452e-06 - 5.1929337758595664847e-378j)  +/-  (3.07e-36, 1.83e-96j)
| (0.11968310969585459495 - 1.073932018998234884e-375j)  +/-  (1.79e-32, 1.07e-92j)
| (1.3272514835897104702e-10 + 2.0942781062640523025e-380j)  +/-  (1.8e-39, 1.06e-99j)
| (0.2232941387424068185 - 1.718012819913476683e-375j)  +/-  (2.09e-33, 1.05e-93j)
| (0.11968310969585459495 - 1.5175717136662375107e-375j)  +/-  (5.57e-34, 2.49e-94j)
| (3.3284683241484067845e-15 + 9.4268641899382871893e-383j)  +/-  (6.14e-42, 3.76e-102j)
