Starting with polynomial:
P : 7391536347803839/67108864*t^30 - 54496920530418135/67108864*t^28 + 180700315442965395/67108864*t^26 - 355924863751295475/67108864*t^24 + 463373879223384675/67108864*t^22 - 419762220002360235/67108864*t^20 + 271274904083157975/67108864*t^18 - 126155198555389575/67108864*t^16 + 42051732851796525/67108864*t^14 - 9888133564634325/67108864*t^12 + 1591748329916745/67108864*t^10 - 166966608033225/67108864*t^8 + 10529425731825/67108864*t^6 - 347123925225/67108864*t^4 + 4508102925/67108864*t^2 - 9694845/67108864
Extension levels are: 30
-------------------------------------------------
Ending with final polynomial:
P : 7391536347803839/67108864*t^30 - 54496920530418135/67108864*t^28 + 180700315442965395/67108864*t^26 - 355924863751295475/67108864*t^24 + 463373879223384675/67108864*t^22 - 419762220002360235/67108864*t^20 + 271274904083157975/67108864*t^18 - 126155198555389575/67108864*t^16 + 42051732851796525/67108864*t^14 - 9888133564634325/67108864*t^12 + 1591748329916745/67108864*t^10 - 166966608033225/67108864*t^8 + 10529425731825/67108864*t^6 - 347123925225/67108864*t^4 + 4508102925/67108864*t^2 - 9694845/67108864
-------------------------------------------------
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
-------------------------------------------------
The nodes are:
| (-0.99689348407464954027 + 1.7776115594308808412e-426j)  +/-  (1.59e-118, 1.59e-118j)
| (-0.98366812327974720997 + 3.5211398290015500277e-429j)  +/-  (4.41e-118, 4.41e-118j)
| (-0.88256053579205268154 - 4.1390409453568784141e-430j)  +/-  (1.9e-118, 1.9e-118j)
| (0.99689348407464954027 - 1.1604589143094837183e-430j)  +/-  (1.64e-118, 1.64e-118j)
| (0.92620004742927432588 + 5.2601020729467238732e-444j)  +/-  (2.94e-118, 2.94e-118j)
| (0.76777743210482619492 - 1.7083549310908084891e-453j)  +/-  (2.02e-119, 2.02e-119j)
| (0.44703376953808917678 + 7.8800164377245347145e-459j)  +/-  (1.14e-122, 1.14e-122j)
| (-0.92620004742927432588 - 1.877956386252452141e-454j)  +/-  (3.56e-118, 3.56e-118j)
| (-0.53662414814201989926 + 5.4893276367190947774e-458j)  +/-  (1.25e-121, 1.25e-121j)
| (0.98366812327974720997 - 3.5489531665930591183e-453j)  +/-  (3.98e-118, 3.98e-118j)
| (0.88256053579205268154 + 3.8941739624055645069e-464j)  +/-  (1.63e-118, 1.63e-118j)
| (0.96002186496830751222 + 2.0691205581998716417e-474j)  +/-  (4.97e-118, 4.97e-118j)
| (-0.82956576238276839744 + 4.6709639038656935709e-485j)  +/-  (7.51e-119, 7.51e-119j)
| (-0.76777743210482619492 - 2.2833807609809605708e-485j)  +/-  (2.26e-119, 2.26e-119j)
| (-0.15386991360858354696 + 5.8621555681258677056e-493j)  +/-  (2.13e-126, 2.13e-126j)
| (0.82956576238276839744 + 5.103483803995093141e-486j)  +/-  (8.58e-119, 8.58e-119j)
| (0.35270472553087811347 + 1.856350854747189413e-493j)  +/-  (6.12e-124, 6.12e-124j)
| (-0.051471842555317695833 - 1.1044077808011429858e-497j)  +/-  (1.34e-127, 1.34e-127j)
| (-0.69785049479331579693 - 8.2486940571765090743e-488j)  +/-  (4.89e-120, 4.89e-120j)
| (-0.96002186496830751222 + 7.0744372323238771032e-489j)  +/-  (4.92e-118, 4.92e-118j)
| (0.25463692616788984644 + 1.6502864312608645546e-497j)  +/-  (4.02e-125, 4.02e-125j)
| (0.69785049479331579693 + 1.8368170075123941795e-492j)  +/-  (4.24e-120, 4.24e-120j)
| (0.15386991360858354696 + 1.1970046040704202385e-499j)  +/-  (2.13e-126, 2.13e-126j)
| (-0.44703376953808917678 - 1.1516009340138024995e-496j)  +/-  (7.8e-123, 7.8e-123j)
| (-0.35270472553087811347 + 1.8080652567770928644e-496j)  +/-  (6.01e-124, 6.01e-124j)
| (0.051471842555317695833 + 1.8579876129517818759e-501j)  +/-  (1.21e-127, 1.21e-127j)
| (0.62052618298924286114 - 6.422214022326849134e-495j)  +/-  (8.18e-121, 8.18e-121j)
| (0.53662414814201989926 - 2.017651310893621345e-495j)  +/-  (9.94e-122, 9.94e-122j)
| (-0.25463692616788984644 - 2.6174354739375393085e-498j)  +/-  (3.9e-125, 3.9e-125j)
| (-0.62052618298924286114 - 6.9039047901691476689e-496j)  +/-  (7.27e-121, 7.27e-121j)
-------------------------------------------------
The weights are:
| (0.0079681924961666056155 + 2.2776589259108226541e-426j)  +/-  (7.36e-30, 6.93e-86j)
| (0.018466468311090959142 - 3.7240420194626410686e-426j)  +/-  (5.74e-30, 5.41e-86j)
| (0.048402672830594052903 + 1.8200276578525765386e-426j)  +/-  (8.91e-31, 8.39e-87j)
| (0.0079681924961666056155 - 6.9454867154344195145e-429j)  +/-  (1.98e-31, 1.87e-87j)
| (0.038799192569627049597 + 7.7552765727523310757e-428j)  +/-  (1.2e-31, 1.13e-87j)
| (0.065974229882180495128 - 1.8752136670037227809e-427j)  +/-  (5e-32, 4.71e-88j)
| (0.092122522237786128718 - 3.7820742705957737037e-427j)  +/-  (1.81e-32, 1.7e-88j)
| (0.038799192569627049597 - 2.1133658585806790571e-426j)  +/-  (2.1e-31, 1.98e-87j)
| (0.086899787201082979802 - 1.0871658568496100288e-426j)  +/-  (1.99e-33, 1.87e-89j)
| (0.018466468311090959142 + 2.4601646071928129552e-428j)  +/-  (6.32e-32, 5.95e-88j)
| (0.048402672830594052903 - 1.1061092046921025756e-427j)  +/-  (1.54e-32, 1.45e-88j)
| (0.02878470788332336935 - 4.8654372999840400325e-428j)  +/-  (4.98e-32, 4.69e-88j)
| (0.057493156217619066482 - 1.6093030050676705708e-426j)  +/-  (1.72e-33, 1.62e-89j)
| (0.065974229882180495128 + 1.4447890534451487539e-426j)  +/-  (4.12e-34, 3.88e-90j)
| (0.1017623897484055046 - 7.521452222003938659e-427j)  +/-  (8.63e-36, 8.13e-92j)
| (0.057493156217619066482 + 1.4737397688129485982e-427j)  +/-  (8.92e-34, 8.4e-90j)
| (0.096368737174644259639 + 4.3294682517493892514e-427j)  +/-  (1.13e-35, 1.06e-91j)
| (0.10285265289355884034 + 6.8148128109770141262e-427j)  +/-  (3.23e-36, 3.04e-92j)
| (0.073755974737705206268 - 1.3084450287900917555e-426j)  +/-  (8.64e-36, 8.13e-92j)
| (0.02878470788332336935 + 2.5897499610546051349e-426j)  +/-  (5.2e-35, 4.9e-91j)
| (0.099593420586795267063 - 4.9050784985107292471e-427j)  +/-  (6.53e-37, 6.15e-93j)
| (0.073755974737705206268 + 2.3082028877103302635e-427j)  +/-  (6.62e-37, 6.24e-93j)
| (0.1017623897484055046 + 5.5098762221141770711e-427j)  +/-  (1.88e-37, 1.77e-93j)
| (0.092122522237786128718 + 9.9327841375353833691e-427j)  +/-  (7.65e-38, 7.22e-94j)
| (0.096368737174644259639 - 9.0711081264596704339e-427j)  +/-  (4.07e-38, 3.84e-94j)
| (0.10285265289355884034 - 6.1455730538488260485e-427j)  +/-  (8.35e-38, 7.85e-94j)
| (0.080755895229420215355 - 2.7710264583356816953e-427j)  +/-  (1.47e-38, 1.38e-94j)
| (0.086899787201082979802 + 3.2625368341066088587e-427j)  +/-  (1.35e-38, 1.27e-94j)
| (0.099593420586795267063 + 8.2709742850136219027e-427j)  +/-  (4.65e-39, 4.54e-95j)
| (0.080755895229420215355 + 1.1910656487464599492e-426j)  +/-  (2.25e-39, 1.94e-95j)
