Starting with polynomial:
P : 536870912*t^29 - 108984795136*t^27 + 9563415773184*t^25 - 478170788659200*t^23 + 15122151191347200*t^21 - 317565175018291200*t^19 + 4525303744010649600*t^17 - 43960093513246310400*t^15 + 288488113680678912000*t^13 - 1250115159282941952000*t^11 + 3437816688028090368000*t^9 - 5625518216773238784000*t^7 + 4922328439676583936000*t^5 - 1893203246029455360000*t^3 + 202843204931727360000*t
Extension levels are: 29
-------------------------------------------------
Ending with final polynomial:
P : 536870912*t^29 - 108984795136*t^27 + 9563415773184*t^25 - 478170788659200*t^23 + 15122151191347200*t^21 - 317565175018291200*t^19 + 4525303744010649600*t^17 - 43960093513246310400*t^15 + 288488113680678912000*t^13 - 1250115159282941952000*t^11 + 3437816688028090368000*t^9 - 5625518216773238784000*t^7 + 4922328439676583936000*t^5 - 1893203246029455360000*t^3 + 202843204931727360000*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:
| (4.3314782938191503922 - 3.8232320002430398433e-342j)  +/-  (8.8e-121, 8.8e-121j)
| (-4.3314782938191503922 - 1.0505716701535634906e-351j)  +/-  (7.73e-121, 7.73e-121j)
| (5.3896405219667516537 + 1.683976450386399906e-363j)  +/-  (4.06e-121, 4.06e-121j)
| (6.7286951986088499628 + 3.3560863057690080024e-366j)  +/-  (2.32e-122, 2.32e-122j)
| (-5.3896405219667516537 - 1.4586108413283897134e-362j)  +/-  (5.3e-121, 5.3e-121j)
| (-3.8482667922136200802 - 1.0061156295626360322e-373j)  +/-  (7.79e-121, 7.79e-121j)
| (-4.8413636510591640675 + 2.1410347795535626073e-386j)  +/-  (6.99e-121, 6.99e-121j)
| (-5.9989712894638202106 - 7.7303498635662952141e-390j)  +/-  (1.62e-121, 1.62e-121j)
| (-6.7286951986088499628 + 3.6836610470561528706e-393j)  +/-  (2.92e-122, 2.92e-122j)
| (5.9989712894638202106 + 1.1343940563513777676e-392j)  +/-  (1.37e-121, 1.37e-121j)
| (2.0701810760534277408 + 3.2975733121487088866e-394j)  +/-  (1.05e-122, 1.05e-122j)
| (3.8482667922136200802 + 1.4107396350015901492e-391j)  +/-  (7.64e-121, 7.64e-121j)
| (-0.40916463639492873678 + 1.108243512806331582e-398j)  +/-  (1.91e-126, 1.91e-126j)
| (-1.2322157550847529038 + 1.9237858266607398341e-394j)  +/-  (2.67e-124, 2.67e-124j)
| (2.4985856910194042426 - 2.8290817444980476387e-393j)  +/-  (5.25e-122, 5.25e-122j)
| (1.6486229138923164114 - 2.3361720447884309513e-394j)  +/-  (1.53e-123, 1.53e-123j)
| (0.40916463639492873678 - 5.551364629101087235e-397j)  +/-  (1.42e-126, 1.42e-126j)
| (3.3846451410922140749 - 1.0013594911676301931e-392j)  +/-  (4.34e-121, 4.34e-121j)
| (5.7293916189492943711e-402 - 6.3374884112332308419e-402j)  +/-  (2.48e-400, 2.48e-400j)
| (-2.4985856910194042426 - 4.3524603406937067734e-391j)  +/-  (5.02e-122, 5.02e-122j)
| (2.9358825042901264849 + 2.095250265511113633e-396j)  +/-  (1.54e-121, 1.54e-121j)
| (0.8194986812709115793 + 2.421898476069692118e-400j)  +/-  (2.63e-125, 2.63e-125j)
| (1.2322157550847529038 - 1.1237003696866896966e-399j)  +/-  (2.09e-124, 2.09e-124j)
| (-2.0701810760534277408 + 3.3891634682398908536e-395j)  +/-  (1.16e-122, 1.16e-122j)
| (-0.8194986812709115793 - 6.3000390241966440905e-400j)  +/-  (2.63e-125, 2.63e-125j)
| (4.8413636510591640675 - 9.4080493868957494114e-397j)  +/-  (7.44e-121, 7.44e-121j)
| (-3.3846451410922140749 + 9.0132205514543936456e-398j)  +/-  (3.27e-121, 3.27e-121j)
| (-2.9358825042901264849 + 2.636849936661394782e-410j)  +/-  (1.69e-121, 1.69e-121j)
| (-1.6486229138923164114 - 9.0096401166951774273e-417j)  +/-  (2.04e-123, 2.04e-123j)
-------------------------------------------------
The weights are:
| (1.9861235460670706094e-09 + 3.2890695345751184179e-350j)  +/-  (6.78e-33, 3.88e-93j)
| (1.9861235460670706094e-09 + 8.7653804363977417364e-352j)  +/-  (1.02e-33, 5.83e-94j)
| (7.8428404256585651489e-14 - 4.509394356355253539e-353j)  +/-  (7.66e-36, 4.38e-96j)
| (1.0293418087219364448e-20 - 7.2111786920153912167e-357j)  +/-  (8.45e-39, 4.83e-99j)
| (7.8428404256585651489e-14 + 4.9085613313062180948e-354j)  +/-  (3.56e-37, 2.04e-97j)
| (9.8689685435606542803e-08 - 6.5437981320895493699e-351j)  +/-  (9.06e-34, 5.19e-94j)
| (1.9657099447347823124e-11 - 8.2354927996473642562e-353j)  +/-  (5.9e-36, 3.37e-96j)
| (8.6574916679572283533e-17 - 1.5346544462004662098e-355j)  +/-  (2.93e-39, 1.67e-99j)
| (1.0293418087219364448e-20 + 1.5629736275547520427e-357j)  +/-  (3.02e-41, 1.73e-101j)
| (8.6574916679572283533e-17 + 9.5074884268526578268e-355j)  +/-  (3.73e-41, 2.13e-101j)
| (0.0032979722108336659672 - 4.3271268835809770355e-348j)  +/-  (1.93e-33, 1.11e-93j)
| (9.8689685435606542803e-08 - 1.1077261341092629665e-349j)  +/-  (8.22e-38, 4.7e-98j)
| (0.19544595696790116136 - 1.5889487250832423625e-347j)  +/-  (3.34e-31, 1.91e-91j)
| (0.051210835288719042046 - 6.9302910239672606257e-348j)  +/-  (3.04e-31, 1.74e-91j)
| (0.00047436637388934908609 + 2.0246675019389342613e-348j)  +/-  (2.33e-35, 1.34e-95j)
| (0.015594005777867257963 + 7.930770188455534624e-348j)  +/-  (1.72e-33, 9.85e-94j)
| (0.19544595696790116136 - 1.9204579742290080923e-347j)  +/-  (1.53e-32, 8.73e-93j)
| (2.7211278280581157879e-06 + 2.9684845876243878437e-349j)  +/-  (1.49e-37, 8.52e-98j)
| (0.23073727670048704578 + 1.8895418768192111245e-347j)  +/-  (1.08e-32, 6.2e-93j)
| (0.00047436637388934908609 + 5.4333284316872643115e-349j)  +/-  (3.35e-38, 1.92e-98j)
| (4.5083940269809461426e-05 - 8.1975686990986013114e-349j)  +/-  (7.79e-37, 4.45e-97j)
| (0.118560319266903537 + 1.6705192190323592812e-347j)  +/-  (1.12e-33, 6.4e-94j)
| (0.051210835288719042046 - 1.2441030231689338615e-347j)  +/-  (3.61e-34, 2.07e-94j)
| (0.0032979722108336659672 - 1.5284974427331424321e-348j)  +/-  (1.4e-37, 8.01e-98j)
| (0.118560319266903537 + 1.1389741143705560245e-347j)  +/-  (8.36e-35, 4.78e-95j)
| (1.9657099447347823124e-11 + 1.4815658528806064282e-351j)  +/-  (6.59e-41, 3.77e-101j)
| (2.7211278280581157879e-06 + 3.6425799022417317123e-350j)  +/-  (4.81e-40, 2.75e-100j)
| (4.5083940269809461426e-05 - 1.5742293059189730762e-349j)  +/-  (1.58e-39, 9.04e-100j)
| (0.015594005777867257963 + 3.5579848430014449744e-348j)  +/-  (4.67e-38, 2.64e-98j)
