Starting with polynomial:
P : 68719476736*t^37 - 635655159808*t^35 + 2701534429184*t^33 - 6992206757888*t^31 + 12315818721280*t^29 - 15625695002624*t^27 + 14743599316992*t^25 - 10531142369280*t^23 + 5742196162560*t^21 - 2392581734400*t^19 + 757650882560*t^17 - 180140769280*t^15 + 31524634624*t^13 - 3940579328*t^11 + 336540160*t^9 - 18356736*t^7 + 573648*t^5 - 8436*t^3 + 37*t
Extension levels are: 37
-------------------------------------------------
Ending with final polynomial:
P : 68719476736*t^37 - 635655159808*t^35 + 2701534429184*t^33 - 6992206757888*t^31 + 12315818721280*t^29 - 15625695002624*t^27 + 14743599316992*t^25 - 10531142369280*t^23 + 5742196162560*t^21 - 2392581734400*t^19 + 757650882560*t^17 - 180140769280*t^15 + 31524634624*t^13 - 3940579328*t^11 + 336540160*t^9 - 18356736*t^7 + 573648*t^5 - 8436*t^3 + 37*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:   37 out of 37
Indefinite weights: 0 out of 37
Negative weights:   0 out of 37
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-0.99909896620468147236 + 9.9584057355082647644e-427j)  +/-  (1.02e-115, 1.02e-115j)
| (-0.99190043525887688731 - 3.5321855197936947287e-432j)  +/-  (2.79e-115, 2.79e-115j)
| (-0.92788902729650932713 - 1.6250286974524448064e-434j)  +/-  (1.82e-115, 1.82e-115j)
| (0.99909896620468147236 + 3.1025035230168225301e-432j)  +/-  (1.06e-115, 1.06e-115j)
| (0.92788902729650932713 + 3.0663948757187062695e-441j)  +/-  (1.39e-115, 1.39e-115j)
| (0.95616673473925093551 - 7.0463870485186835678e-451j)  +/-  (2.3e-115, 2.3e-115j)
| (-0.084805924475509191089 - 7.3099288298790710939e-471j)  +/-  (5.52e-127, 5.52e-127j)
| (-0.89292585814956848973 + 8.2669930483110161584e-457j)  +/-  (6.54e-116, 6.54e-116j)
| (-0.97755523894768619434 + 1.5574946449000349684e-455j)  +/-  (2.83e-115, 2.83e-115j)
| (0.99190043525887688731 + 1.6928190950489384034e-459j)  +/-  (3e-115, 3e-115j)
| (0.89292585814956848973 - 1.1039787758080510217e-470j)  +/-  (8.03e-116, 8.03e-116j)
| (0.97755523894768619434 - 4.1516797761869546162e-476j)  +/-  (2.89e-115, 2.89e-115j)
| (-0.95616673473925093551 - 6.4120302092983598171e-483j)  +/-  (2.23e-115, 2.23e-115j)
| (-0.85152913773331129989 + 2.6374162997820443597e-486j)  +/-  (2.44e-116, 2.44e-116j)
| (0.48769494381363454535 + 1.0080803942613771621e-491j)  +/-  (6.06e-121, 6.06e-121j)
| (0.75067230525272435529 + 5.0375934216801977296e-487j)  +/-  (1.71e-117, 1.71e-117j)
| (0.80399713036694054483 - 2.8162666080933396118e-486j)  +/-  (8.04e-117, 8.04e-117j)
| (-0.41190124824399267538 + 8.7607954776851333988e-494j)  +/-  (4.52e-122, 4.52e-122j)
| (-0.80399713036694054483 + 5.6797271286583722865e-489j)  +/-  (7.8e-117, 7.8e-117j)
| (-0.75067230525272435529 + 1.7483272006561880779e-490j)  +/-  (2.15e-117, 2.15e-117j)
| (0.85152913773331129989 - 6.8131827537899262164e-490j)  +/-  (2.17e-116, 2.17e-116j)
| (0.69193886897754620001 - 3.985580373584940482e-493j)  +/-  (3.19e-118, 3.19e-118j)
| (0.25197806138512519445 + 3.5190127324997173455e-499j)  +/-  (2.32e-124, 2.32e-124j)
| (-0.69193886897754620001 + 4.548082026555643221e-494j)  +/-  (3.59e-118, 3.59e-118j)
| (-0.55997478613759539038 - 6.1081979006404323406e-496j)  +/-  (6.14e-120, 6.14e-120j)
| (1.6005304020315640067e-514 + 5.9136238372882703309e-515j)  +/-  (6.31e-513, 6.31e-513j)
| (0.62821999729564231679 - 4.8839573359010594269e-497j)  +/-  (4.99e-119, 4.99e-119j)
| (0.41190124824399267538 - 1.5680453301668986906e-499j)  +/-  (5.09e-122, 5.09e-122j)
| (-0.25197806138512519445 + 1.7188660604565415629e-502j)  +/-  (1.94e-124, 1.94e-124j)
| (-0.62821999729564231679 - 1.2215077072896716193e-498j)  +/-  (5.4e-119, 5.4e-119j)
| (-0.16900082032184907409 - 1.4075894280237305184e-506j)  +/-  (8.5e-126, 8.5e-126j)
| (0.3331397947420575668 + 2.627417608969683947e-502j)  +/-  (3.09e-123, 3.09e-123j)
| (0.55997478613759539038 - 3.1261618644001614502e-500j)  +/-  (6.04e-120, 6.04e-120j)
| (0.084805924475509191089 - 5.1769606344473683076e-507j)  +/-  (5.52e-127, 5.52e-127j)
| (-0.48769494381363454535 - 1.7094899352777653124e-501j)  +/-  (6.77e-121, 6.77e-121j)
| (-0.3331397947420575668 + 1.0245005717877191499e-502j)  +/-  (3.3e-123, 3.3e-123j)
| (0.16900082032184907409 - 1.4597957919104531134e-506j)  +/-  (1.04e-125, 1.04e-125j)
-------------------------------------------------
The weights are:
| (0.027027027027027027027 + 7.4643324047785411835e-426j)  +/-  (6.13e-17, 1.1e-71j)
| (0.027027027027027027027 - 1.118977340602490994e-425j)  +/-  (4.37e-17, 7.8e-72j)
| (0.027027027027027027027 + 3.3204887032188332073e-426j)  +/-  (4.62e-18, 8.25e-73j)
| (0.027027027027027027027 + 1.344620260682795551e-428j)  +/-  (5.02e-18, 8.98e-73j)
| (0.027027027027027027027 + 1.2269503521339220547e-427j)  +/-  (2.08e-18, 3.71e-73j)
| (0.027027027027027027027 - 9.4959487069939768275e-428j)  +/-  (1.58e-18, 2.82e-73j)
| (0.027027027027027027027 - 6.9110970465649077548e-427j)  +/-  (3.78e-20, 6.76e-75j)
| (0.027027027027027027027 - 2.6890287853184939584e-426j)  +/-  (7.8e-19, 1.39e-73j)
| (0.027027027027027027027 + 6.2015767998827175599e-426j)  +/-  (1.72e-18, 3.07e-73j)
| (0.027027027027027027027 - 4.0422210405049918288e-428j)  +/-  (8.44e-19, 1.51e-73j)
| (0.027027027027027027027 - 1.5088952175468373853e-427j)  +/-  (3.91e-20, 6.99e-75j)
| (0.027027027027027027027 + 6.7572170011099013112e-428j)  +/-  (7.08e-19, 1.26e-73j)
| (0.027027027027027027027 - 4.3253611925978193082e-426j)  +/-  (2.08e-19, 3.72e-74j)
| (0.027027027027027027027 + 2.2531450716035907922e-426j)  +/-  (7.69e-21, 1.37e-75j)
| (0.027027027027027027027 + 3.7236382166709744101e-427j)  +/-  (2.68e-23, 4.79e-78j)
| (0.027027027027027027027 + 2.3944060483594798384e-427j)  +/-  (8.46e-23, 1.51e-77j)
| (0.027027027027027027027 - 2.0913112773485369639e-427j)  +/-  (2.24e-22, 4e-77j)
| (0.027027027027027027027 - 9.8410920275860283844e-427j)  +/-  (5.04e-25, 9e-80j)
| (0.027027027027027027027 - 1.9328073659544448806e-426j)  +/-  (2.25e-23, 4.02e-78j)
| (0.027027027027027027027 + 1.6865150901741054483e-426j)  +/-  (3.52e-24, 6.3e-79j)
| (0.027027027027027027027 + 1.7965970844136641916e-427j)  +/-  (2.47e-23, 4.42e-78j)
| (0.027027027027027027027 - 2.7073907091262527353e-427j)  +/-  (8.02e-25, 1.43e-79j)
| (0.027027027027027027027 - 4.9053515107240068962e-427j)  +/-  (2.36e-27, 4.22e-82j)
| (0.027027027027027027027 - 1.4905504349748440894e-426j)  +/-  (5.82e-26, 1.04e-80j)
| (0.027027027027027027027 - 1.1964946617521173097e-426j)  +/-  (4.5e-27, 8.04e-82j)
| (0.027027027027027027027 + 6.3473297382801519793e-427j)  +/-  (4.58e-28, 8.19e-83j)
| (0.027027027027027027027 + 3.0319487390747108712e-427j)  +/-  (7.17e-27, 1.28e-81j)
| (0.027027027027027027027 - 4.0954146599188361335e-427j)  +/-  (7.99e-28, 1.43e-82j)
| (0.027027027027027027027 - 8.2141901991280060216e-427j)  +/-  (3.92e-29, 7.01e-84j)
| (0.027027027027027027027 + 1.3303562953918272909e-426j)  +/-  (4.15e-28, 7.41e-83j)
| (0.027027027027027027027 + 7.5297095422798498817e-427j)  +/-  (4.46e-29, 7.95e-84j)
| (0.027027027027027027027 + 4.4881916879875064611e-427j)  +/-  (2.55e-29, 4.55e-84j)
| (0.027027027027027027027 - 3.3699777098330978623e-427j)  +/-  (6.84e-29, 1.22e-83j)
| (0.027027027027027027027 - 5.8296269839424015545e-427j)  +/-  (4.22e-30, 7.64e-85j)
| (0.027027027027027027027 + 1.0825739834766128356e-426j)  +/-  (2.45e-30, 4.52e-85j)
| (0.027027027027027027027 + 8.9785848468266929284e-427j)  +/-  (1.88e-30, 3.5e-85j)
| (0.027027027027027027027 + 5.3508993152265979409e-427j)  +/-  (1.6e-30, 2.68e-85j)
