Starting with polynomial:
P : t^29 - 406*t^27 + 71253*t^25 - 7125300*t^23 + 450675225*t^21 - 18928359450*t^19 + 539458244325*t^17 - 10480903032600*t^15 + 137561852302875*t^13 - 1192202719958250*t^11 + 6557114959770375*t^9 - 21459648959248500*t^7 + 37554385678684875*t^5 - 28887988983603750*t^3 + 6190283353629375*t
Extension levels are: 29
-------------------------------------------------
Ending with final polynomial:
P : t^29 - 406*t^27 + 71253*t^25 - 7125300*t^23 + 450675225*t^21 - 18928359450*t^19 + 539458244325*t^17 - 10480903032600*t^15 + 137561852302875*t^13 - 1192202719958250*t^11 + 6557114959770375*t^9 - 21459648959248500*t^7 + 37554385678684875*t^5 - 28887988983603750*t^3 + 6190283353629375*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: 1
  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:   29 out of 29
Indefinite weights: 0 out of 29
Negative weights:   0 out of 29
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (5.4422710891785068052 + 8.6917288581679255292e-275j)  +/-  (1.06e-120, 1.06e-120j)
| (6.8467221357079942963 - 4.3529765687911206472e-276j)  +/-  (1.1e-120, 1.1e-120j)
| (-9.5158120069473620141 + 8.1192868600683505182e-288j)  +/-  (3.2e-122, 3.2e-122j)
| (-7.6221027224809872954 + 2.389997228127339442e-311j)  +/-  (5.92e-121, 5.92e-121j)
| (-6.8467221357079942963 - 4.1582435805690674014e-334j)  +/-  (9.28e-121, 9.28e-121j)
| (2.9276781543228852572 + 1.3773046267914485404e-346j)  +/-  (1.56e-122, 1.56e-122j)
| (-8.4838265578465487362 - 2.0206108516052996193e-345j)  +/-  (1.88e-121, 1.88e-121j)
| (7.6221027224809872954 + 1.500058161664269528e-352j)  +/-  (5.78e-121, 5.78e-121j)
| (-6.1256353482437163654 - 3.977267489470573528e-352j)  +/-  (1.18e-120, 1.18e-120j)
| (3.5335337709909930353 + 3.062987712178904244e-359j)  +/-  (7.19e-122, 7.19e-122j)
| (3.8029009936670324561e-365 + 4.9486262799505780194e-365j)  +/-  (1.81e-363, 1.81e-363j)
| (8.4838265578465487362 - 2.2124226078818052058e-358j)  +/-  (1.83e-121, 1.83e-121j)
| (-2.3315048840655651231 + 5.4033516859408595241e-358j)  +/-  (2.64e-123, 2.64e-123j)
| (-3.5335337709909930353 + 6.792353546446618673e-357j)  +/-  (7.08e-122, 7.08e-122j)
| (9.5158120069473620141 + 1.5531283527481863837e-365j)  +/-  (3.41e-122, 3.41e-122j)
| (4.7866110623528069815 + 1.677883916195421614e-363j)  +/-  (5.22e-121, 5.22e-121j)
| (-2.9276781543228852572 - 4.3662423213018246741e-363j)  +/-  (1.37e-122, 1.37e-122j)
| (-4.1519648551009832838 + 3.213113367348461958e-368j)  +/-  (2.08e-121, 2.08e-121j)
| (-1.7426162326106616133 - 1.1298459463473836877e-379j)  +/-  (2.93e-124, 2.93e-124j)
| (6.1256353482437163654 + 5.4665238404576837676e-375j)  +/-  (1.19e-120, 1.19e-120j)
| (2.3315048840655651231 + 2.3253898610530295612e-382j)  +/-  (2.49e-123, 2.49e-123j)
| (1.7426162326106616133 + 1.8873262906699199952e-383j)  +/-  (3.1e-124, 3.1e-124j)
| (-1.158946149400189452 - 4.7675476330867846668e-383j)  +/-  (3.31e-125, 3.31e-125j)
| (-0.57864617803316430756 + 7.9051246143533765669e-385j)  +/-  (3.34e-126, 3.34e-126j)
| (-4.7866110623528069815 - 2.1360323630275969935e-379j)  +/-  (4.72e-121, 4.72e-121j)
| (4.1519648551009832838 - 5.2585349255965080573e-389j)  +/-  (2.34e-121, 2.34e-121j)
| (0.57864617803316430756 + 7.0141420619219474874e-398j)  +/-  (3.34e-126, 3.34e-126j)
| (-5.4422710891785068052 + 1.3528699486857171895e-391j)  +/-  (9.79e-121, 9.79e-121j)
| (1.158946149400189452 - 6.5759417840105239173e-402j)  +/-  (3.02e-125, 3.02e-125j)
-------------------------------------------------
The weights are:
| (9.8689685435606542803e-08 - 2.3337148030297199957e-281j)  +/-  (1.04e-34, 4.28e-95j)
| (1.9657099447347823124e-11 + 8.6490524316081399066e-284j)  +/-  (1.49e-37, 6.13e-98j)
| (1.0293418087219364448e-20 + 1.8508243715431509593e-289j)  +/-  (1.01e-42, 4.15e-103j)
| (7.8428404256585651489e-14 + 5.8494210864308177258e-286j)  +/-  (1.93e-40, 7.95e-101j)
| (1.9657099447347823124e-11 - 9.8448679722137204083e-285j)  +/-  (1.27e-39, 5.24e-100j)
| (0.0032979722108336659672 - 6.2330534843696672494e-280j)  +/-  (2.55e-32, 1.05e-92j)
| (8.6574916679572283533e-17 - 1.8231807410145636692e-287j)  +/-  (8.24e-42, 3.4e-102j)
| (7.8428404256585651489e-14 - 3.500998793582373065e-285j)  +/-  (4.25e-42, 1.75e-102j)
| (1.9861235460670706094e-09 + 1.0512756313072962798e-283j)  +/-  (1.49e-39, 6.14e-100j)
| (0.00047436637388934908609 + 3.1144112277063225925e-280j)  +/-  (1.88e-35, 7.76e-96j)
| (0.23073727670048704578 + 2.4086666318509855653e-279j)  +/-  (7.17e-34, 2.96e-94j)
| (8.6574916679572283533e-17 + 8.3420285500367778239e-287j)  +/-  (6.89e-44, 2.84e-104j)
| (0.015594005777867257963 + 4.3835786795733159279e-280j)  +/-  (2.49e-34, 1.03e-94j)
| (0.00047436637388934908609 + 6.6215564314682797257e-281j)  +/-  (2.14e-37, 8.82e-98j)
| (1.0293418087219364448e-20 - 6.7933037877085472849e-289j)  +/-  (4.79e-46, 1.97e-106j)
| (2.7211278280581157879e-06 + 6.8681553531370493904e-281j)  +/-  (3.19e-39, 1.31e-99j)
| (0.0032979722108336659672 - 1.8723187493254961475e-280j)  +/-  (9.21e-37, 3.8e-97j)
| (4.5083940269809461426e-05 - 1.9097421804300666865e-281j)  +/-  (3.76e-39, 1.55e-99j)
| (0.051210835288719042046 - 8.5950057571074408776e-280j)  +/-  (2.38e-35, 9.81e-96j)
| (1.9861235460670706094e-09 - 1.7819016513380544768e-282j)  +/-  (2.06e-41, 8.48e-102j)
| (0.015594005777867257963 + 1.0955746888450149599e-279j)  +/-  (2.4e-37, 9.9e-98j)
| (0.051210835288719042046 - 1.6693185321085579608e-279j)  +/-  (8.93e-37, 3.69e-97j)
| (0.118560319266903537 + 1.4234247739188201036e-279j)  +/-  (6.3e-36, 2.61e-96j)
| (0.19544595696790116136 - 2.003751046016383905e-279j)  +/-  (8.47e-36, 3.51e-96j)
| (2.7211278280581157879e-06 + 4.4006655071152471304e-282j)  +/-  (7.41e-41, 3.06e-101j)
| (4.5083940269809461426e-05 - 1.4204082417177753141e-280j)  +/-  (3.33e-40, 1.32e-100j)
| (0.19544595696790116136 - 2.4806019073815727667e-279j)  +/-  (8.52e-38, 3.38e-98j)
| (9.8689685435606542803e-08 - 7.8758203238663474078e-283j)  +/-  (9.88e-42, 4.11e-102j)
| (0.118560319266903537 + 2.1938123717239023216e-279j)  +/-  (4.15e-38, 1.59e-98j)
