Starting with polynomial:
P : 34359738368*t^35 - 10222022164480*t^33 + 1349306925711360*t^31 - 104571286742630400*t^29 + 5306992802188492800*t^27 - 186275447356816097280*t^25 + 4656886183920402432000*t^23 - 84156586037990129664000*t^21 + 1104555191748620451840000*t^19 - 10493274321611894292480000*t^17 + 71354265386960881188864000*t^15 - 340554448437767842037760000*t^13 + 1106801957422745486622720000*t^11 - 2341311833009653914009600000*t^9 + 3010258071012412175155200000*t^7 - 2107180649708688522608640000*t^5 + 658493953033965163315200000*t^3 - 58102407620643984998400000*t
Extension levels are: 35
-------------------------------------------------
Ending with final polynomial:
P : 34359738368*t^35 - 10222022164480*t^33 + 1349306925711360*t^31 - 104571286742630400*t^29 + 5306992802188492800*t^27 - 186275447356816097280*t^25 + 4656886183920402432000*t^23 - 84156586037990129664000*t^21 + 1104555191748620451840000*t^19 - 10493274321611894292480000*t^17 + 71354265386960881188864000*t^15 - 340554448437767842037760000*t^13 + 1106801957422745486622720000*t^11 - 2341311833009653914009600000*t^9 + 3010258071012412175155200000*t^7 - 2107180649708688522608640000*t^5 + 658493953033965163315200000*t^3 - 58102407620643984998400000*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:   35 out of 35
Indefinite weights: 0 out of 35
Negative weights:   0 out of 35
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (6.2129737476337168733 + 2.0491018706138983828e-428j)  +/-  (6.39e-120, 6.39e-120j)
| (-4.2948958144927632315 - 1.1707382296264548353e-427j)  +/-  (1.98e-119, 1.98e-119j)
| (5.6864689480904415917 + 2.8482376637059533028e-435j)  +/-  (1.31e-119, 1.31e-119j)
| (-6.2129737476337168733 + 1.8014658648215079273e-435j)  +/-  (6.9e-120, 6.9e-120j)
| (-3.8687007309691543826 + 5.92478537580815525e-438j)  +/-  (1.22e-119, 1.22e-119j)
| (-7.5040211464489360801 + 1.412546066559581756e-444j)  +/-  (2.06e-121, 2.06e-121j)
| (4.2948958144927632315 + 1.179232389175200167e-442j)  +/-  (2e-119, 2e-119j)
| (6.7996094132841301572 + 1.1852777332281917038e-444j)  +/-  (1.92e-120, 1.92e-120j)
| (-3.0505384204304466909 - 9.0014773344339142388e-444j)  +/-  (2e-120, 2e-120j)
| (7.5040211464489360801 + 1.4433538900704046864e-446j)  +/-  (2.04e-121, 2.04e-121j)
| (-6.7996094132841301572 - 1.3041754602218158707e-443j)  +/-  (1.8e-120, 1.8e-120j)
| (4.7365184774132108005 - 4.3980707002765497746e-447j)  +/-  (2.54e-119, 2.54e-119j)
| (-2.2644675010425686494 + 7.6407960538563716601e-449j)  +/-  (1.33e-121, 1.33e-121j)
| (2.2644675010425686494 + 4.5319061841429376243e-451j)  +/-  (1.31e-121, 1.31e-121j)
| (-2.6542927811971720357 + 1.1202602572844503916e-446j)  +/-  (6.13e-121, 6.13e-121j)
| (1.1217809907203026168 - 1.4493438613941357458e-454j)  +/-  (4.15e-124, 4.15e-124j)
| (2.6542927811971720357 + 3.1979053909813038153e-451j)  +/-  (5.43e-121, 5.43e-121j)
| (5.1980993461977526242 + 1.5033849022475783859e-449j)  +/-  (2.52e-119, 2.52e-119j)
| (-1.4992244886117301685 + 2.2897920528295143504e-453j)  +/-  (3.1e-123, 3.1e-123j)
| (-5.6864689480904415917 + 6.5738310355713560033e-449j)  +/-  (1.5e-119, 1.5e-119j)
| (-4.7365184774132108005 + 4.085280251569272603e-463j)  +/-  (2.94e-119, 2.94e-119j)
| (0.74661763987986701712 - 1.5508955194894713734e-478j)  +/-  (2.8e-125, 2.8e-125j)
| (3.8687007309691543826 - 2.7761890320016965811e-471j)  +/-  (1.29e-119, 1.29e-119j)
| (3.4547164957519908273 + 3.0384339382363131841e-473j)  +/-  (4.5e-120, 4.5e-120j)
| (-0.74661763987986701712 - 4.0658327712154777741e-477j)  +/-  (2.21e-125, 2.21e-125j)
| (-5.1980993461977526242 - 1.5933821149036724e-473j)  +/-  (2.29e-119, 2.29e-119j)
| (3.0505384204304466909 + 3.2571377084841743761e-482j)  +/-  (2.41e-120, 2.41e-120j)
| (1.8798039887309170789 + 3.1060898374462375499e-484j)  +/-  (2.42e-122, 2.42e-122j)
| (-3.4547164957519908273 - 4.5121472183022300245e-486j)  +/-  (5.27e-120, 5.27e-120j)
| (-1.1217809907203026168 - 8.9117969486931686363e-500j)  +/-  (3.59e-124, 3.59e-124j)
| (-1.8798039887309170789 - 1.8991679291553710563e-496j)  +/-  (2.51e-122, 2.51e-122j)
| (1.4992244886117301685 - 1.0118540765824512349e-497j)  +/-  (3.24e-123, 3.24e-123j)
| (0.37294171704961686115 + 4.0653103574507089128e-500j)  +/-  (2.22e-126, 2.22e-126j)
| (2.6087171093641809913e-504 + 4.7256580187154988903e-505j)  +/-  (9.28e-503, 9.28e-503j)
| (-0.37294171704961686115 - 4.5178350471536483721e-500j)  +/-  (2.22e-126, 2.22e-126j)
-------------------------------------------------
The weights are:
| (5.3540941980660238582e-18 - 1.2592053084212358987e-441j)  +/-  (1.22e-34, 1.39e-93j)
| (2.3831233337056717398e-09 - 1.1982819902481425489e-435j)  +/-  (5.66e-30, 6.48e-89j)
| (2.5785970044203139112e-15 + 2.9080586935431083329e-440j)  +/-  (1.59e-33, 1.82e-92j)
| (5.3540941980660238582e-18 + 6.8946029129253224025e-441j)  +/-  (9.67e-36, 1.11e-94j)
| (7.4864601785189610172e-08 + 3.6691294650670927146e-435j)  +/-  (4.05e-29, 4.64e-88j)
| (1.6046191917901400567e-25 + 7.1339741148783744366e-445j)  +/-  (9.22e-39, 1.06e-97j)
| (2.3831233337056717398e-09 - 3.2481780350542774705e-437j)  +/-  (5.76e-32, 6.6e-91j)
| (2.9595426287091171414e-21 + 2.8020073882243911561e-443j)  +/-  (1.17e-37, 1.34e-96j)
| (2.050985370117567337e-05 + 2.0800304479858348465e-434j)  +/-  (7.33e-29, 8.4e-88j)
| (1.6046191917901400567e-25 - 1.9401887303051939233e-445j)  +/-  (1.13e-39, 1.29e-98j)
| (2.9595426287091171414e-21 - 1.2413281166720222101e-442j)  +/-  (2.04e-38, 2.34e-97j)
| (4.592895709255708504e-11 + 4.2888674602822032789e-438j)  +/-  (7.79e-34, 8.93e-93j)
| (0.0012948310774983528932 + 1.0128679268317904945e-433j)  +/-  (1.56e-27, 1.79e-86j)
| (0.0012948310774983528932 + 3.135334747730185257e-434j)  +/-  (9.44e-29, 1.08e-87j)
| (0.00019314471461398673192 - 4.8414074076272758669e-434j)  +/-  (7.95e-29, 9.1e-88j)
| (0.060296580867740502845 - 2.5908979810611843159e-433j)  +/-  (1.35e-23, 1.54e-82j)
| (0.00019314471461398673192 - 1.1430031076231333091e-434j)  +/-  (2.85e-30, 3.27e-89j)
| (4.9211583184976970368e-13 - 4.2237399235725884583e-439j)  +/-  (4.07e-35, 4.66e-94j)
| (0.022581561213936442563 + 3.0720284679855282771e-433j)  +/-  (5.57e-27, 6.37e-86j)
| (2.5785970044203139112e-15 - 2.0855391161772429498e-439j)  +/-  (1.54e-37, 1.76e-96j)
| (4.592895709255708504e-11 - 8.7705101247771593514e-437j)  +/-  (1.78e-35, 2.04e-94j)
| (0.12093245219703023979 + 3.9422746901821245897e-433j)  +/-  (1.84e-27, 2.11e-86j)
| (7.4864601785189610172e-08 + 1.9155889911087502987e-436j)  +/-  (3.79e-34, 4.34e-93j)
| (1.5119240781611664958e-06 - 9.0683484105940032705e-436j)  +/-  (7.5e-34, 8.6e-93j)
| (0.12093245219703023979 + 5.6012978433665277382e-433j)  +/-  (1.5e-30, 1.71e-89j)
| (4.9211583184976970368e-13 + 4.4389557516786703865e-438j)  +/-  (1.65e-37, 1.89e-96j)
| (2.050985370117567337e-05 + 3.5237511836709176752e-435j)  +/-  (2.14e-33, 2.46e-92j)
| (0.0063001959597203624085 - 7.3468195763165510282e-434j)  +/-  (2.69e-32, 3.08e-91j)
| (1.5119240781611664958e-06 - 8.3642379180160101593e-435j)  +/-  (1.49e-34, 1.7e-93j)
| (0.060296580867740502845 - 4.4227783349828914081e-433j)  +/-  (1.83e-32, 2.1e-91j)
| (0.0063001959597203624085 - 1.8783543109744443775e-433j)  +/-  (5.1e-33, 5.85e-92j)
| (0.022581561213936442563 + 1.4822687832452469574e-433j)  +/-  (5.67e-33, 6.5e-92j)
| (0.18320856219115164582 - 5.2407457538110470769e-433j)  +/-  (9.66e-33, 1.11e-91j)
| (0.21034114541276070868 + 6.1030233911424513437e-433j)  +/-  (4.03e-33, 4.69e-92j)
| (0.18320856219115164582 - 6.2374285266652700582e-433j)  +/-  (2.88e-33, 3.16e-92j)
