Starting with polynomial:
P : t^35 - 595*t^33 + 157080*t^31 - 24347400*t^29 + 2471261100*t^27 - 173482529220*t^25 + 8674126461000*t^23 - 313507713519000*t^21 + 8229577479873750*t^19 - 156361972117601250*t^17 + 2126522820799377000*t^15 - 20298626925812235000*t^13 + 131941075017779527500*t^11 - 558212240459836462500*t^9 + 1435402904039579475000*t^7 - 2009564065655411265000*t^5 + 1255977541034632040625*t^3 - 221643095476699771875*t
Extension levels are: 35
-------------------------------------------------
Ending with final polynomial:
P : t^35 - 595*t^33 + 157080*t^31 - 24347400*t^29 + 2471261100*t^27 - 173482529220*t^25 + 8674126461000*t^23 - 313507713519000*t^21 + 8229577479873750*t^19 - 156361972117601250*t^17 + 2126522820799377000*t^15 - 20298626925812235000*t^13 + 131941075017779527500*t^11 - 558212240459836462500*t^9 + 1435402904039579475000*t^7 - 2009564065655411265000*t^5 + 1255977541034632040625*t^3 - 221643095476699771875*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
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (10.612288477642586681 + 3.8529989315296564939e-731j)  +/-  (6.33e-249, 6.33e-249j)
| (8.7864717365715975543 - 6.9956610567931546248e-730j)  +/-  (2.37e-247, 2.37e-247j)
| (2.6584442954663036626 - 1.0262362305462858037e-731j)  +/-  (7.54e-250, 7.54e-250j)
| (-4.3141128067129363688 + 5.5665030210158604747e-727j)  +/-  (6.56e-248, 6.56e-248j)
| (-4.885706922446518436 - 3.8175262647549162368e-730j)  +/-  (1.92e-247, 1.92e-247j)
| (5.4711690424992846196 - 7.4176539427548740779e-736j)  +/-  (3.89e-247, 3.89e-247j)
| (6.6984486691885249844 + 1.7886528021155651414e-735j)  +/-  (9.34e-247, 9.34e-247j)
| (8.0418815084029699112 + 1.2544909651352647513e-735j)  +/-  (5.33e-247, 5.33e-247j)
| (-3.7537368496780427836 + 1.433066459540298651e-734j)  +/-  (1.75e-248, 1.75e-248j)
| (9.6160998511061804336 - 9.0216931456489158556e-739j)  +/-  (5.93e-248, 5.93e-248j)
| (1.5864378910889790429 - 8.2902265081749771631e-742j)  +/-  (8.33e-252, 8.33e-252j)
| (-3.2024406515275113362 + 1.1253378614181504663e-736j)  +/-  (4.81e-249, 4.81e-249j)
| (-2.6584442954663036626 - 1.6900414283046879773e-739j)  +/-  (8.39e-250, 8.39e-250j)
| (3.2024406515275113362 - 2.3563082408262786083e-743j)  +/-  (3.89e-249, 3.89e-249j)
| (-5.4711690424992846196 + 8.6250970232022732694e-740j)  +/-  (3.66e-247, 3.66e-247j)
| (2.1202236048365765903 + 1.0551903496454338566e-757j)  +/-  (1.03e-250, 1.03e-250j)
| (7.3512225939555800243 - 3.2365353715423720007e-752j)  +/-  (7.24e-247, 7.24e-247j)
| (-2.1202236048365765903 + 3.9486024852078780114e-756j)  +/-  (9.08e-251, 9.08e-251j)
| (-6.0738999098351062764 + 2.3351501520435558744e-759j)  +/-  (7.64e-247, 7.64e-247j)
| (4.3141128067129363688 + 1.7095324638592154487e-771j)  +/-  (7.59e-248, 7.59e-248j)
| (6.0738999098351062764 - 1.3009114998646649137e-770j)  +/-  (6.57e-247, 6.57e-247j)
| (4.885706922446518436 + 5.3359515744107033646e-771j)  +/-  (1.58e-247, 1.58e-247j)
| (-1.5864378910889790429 + 6.9786182651386642773e-775j)  +/-  (1.01e-251, 1.01e-251j)
| (-0.52741923422627750006 + 8.5563012926514622957e-779j)  +/-  (6.32e-254, 6.32e-254j)
| (3.7537368496780427836 - 5.1262480095464837291e-778j)  +/-  (2.12e-248, 2.12e-248j)
| (-1.3248770469812357667e-779 - 9.6597852686453369392e-780j)  +/-  (5.74e-778, 5.74e-778j)
| (0.52741923422627750006 - 1.5603460890008077873e-780j)  +/-  (6.32e-254, 6.32e-254j)
| (1.0558767922250993312 - 3.8881299431274942938e-778j)  +/-  (7.88e-253, 7.88e-253j)
| (-1.0558767922250993312 + 1.7341977574333016053e-780j)  +/-  (7.82e-253, 7.82e-253j)
| (-7.3512225939555800243 - 1.1231437494885298253e-801j)  +/-  (6.72e-247, 6.72e-247j)
| (-9.6160998511061804336 - 6.4013693509978690158e-832j)  +/-  (6.52e-248, 6.52e-248j)
| (-10.612288477642586681 - 1.3319453254699148863e-863j)  +/-  (6.78e-249, 6.78e-249j)
| (-8.7864717365715975543 - 9.4761929887799382352e-904j)  +/-  (2.36e-247, 2.36e-247j)
| (-6.6984486691885249844 - 1.3021670474477576655e-943j)  +/-  (7.68e-247, 7.68e-247j)
| (-8.0418815084029699112 - 3.9073468397095599249e-968j)  +/-  (4.75e-247, 4.75e-247j)
-------------------------------------------------
The weights are:
| (1.6046191917901400567e-25 - 6.7707327078831755377e-743j)  +/-  (9.02e-95, 3.93e-218j)
| (5.3540941980660238582e-18 - 4.4564939991723666426e-739j)  +/-  (4.51e-92, 1.96e-215j)
| (0.0063001959597203624085 - 2.8616800529237828635e-731j)  +/-  (5.73e-76, 2.5e-199j)
| (2.050985370117567337e-05 + 2.4629908262195448554e-731j)  +/-  (1.23e-83, 5.38e-207j)
| (1.5119240781611664958e-06 + 5.4217396681960349675e-732j)  +/-  (2.08e-85, 9.06e-209j)
| (7.4864601785189610172e-08 + 7.0581818591952300873e-734j)  +/-  (6.37e-87, 2.78e-210j)
| (4.592895709255708504e-11 + 1.5530226522031622088e-735j)  +/-  (1.34e-89, 5.84e-213j)
| (2.5785970044203139112e-15 + 1.036995601400779623e-737j)  +/-  (6.55e-92, 2.85e-215j)
| (0.00019314471461398673192 - 6.2524954163162131424e-731j)  +/-  (8.08e-85, 3.52e-208j)
| (2.9595426287091171414e-21 + 9.8531873676515086015e-741j)  +/-  (1.3e-94, 5.65e-218j)
| (0.060296580867740502845 - 1.0474137133646611108e-730j)  +/-  (6.95e-77, 3.03e-200j)
| (0.0012948310774983528932 + 8.1605659758245244483e-731j)  +/-  (1.32e-83, 5.77e-207j)
| (0.0063001959597203624085 - 1.2086031875693441426e-730j)  +/-  (3.16e-82, 1.38e-205j)
| (0.0012948310774983528932 + 1.212441940820675512e-731j)  +/-  (4.93e-84, 2.15e-207j)
| (7.4864601785189610172e-08 - 5.9638574200710162461e-733j)  +/-  (1.1e-90, 4.82e-214j)
| (0.022581561213936442563 + 5.8658454170367567144e-731j)  +/-  (7.1e-81, 3.1e-204j)
| (4.9211583184976970368e-13 - 1.5174900074902285605e-736j)  +/-  (7.88e-92, 3.44e-215j)
| (0.022581561213936442563 + 1.7267350500847865298e-730j)  +/-  (1.16e-82, 5.06e-206j)
| (2.3831233337056717398e-09 + 6.9955981804633928189e-734j)  +/-  (6.95e-93, 3.03e-216j)
| (2.050985370117567337e-05 + 1.3256530382857140218e-732j)  +/-  (4.48e-88, 1.95e-211j)
| (2.3831233337056717398e-09 - 1.1860626819200260793e-734j)  +/-  (1.28e-90, 5.56e-214j)
| (1.5119240781611664958e-06 - 3.3744627842843643298e-733j)  +/-  (4.09e-89, 1.78e-212j)
| (0.060296580867740502845 - 2.2693114538435981381e-730j)  +/-  (4.83e-85, 2.1e-208j)
| (0.18320856219115164582 - 2.8489174708987933198e-730j)  +/-  (4.26e-83, 1.86e-206j)
| (0.00019314471461398673192 - 4.3536655330217661517e-732j)  +/-  (1.13e-87, 4.91e-211j)
| (0.21034114541276070868 + 2.6790323962891645098e-730j)  +/-  (2.86e-83, 1.25e-206j)
| (0.18320856219115164582 - 2.2274461177062167519e-730j)  +/-  (9.82e-84, 4.28e-207j)
| (0.12093245219703023979 + 1.6310390611924633783e-730j)  +/-  (2.61e-84, 1.14e-207j)
| (0.12093245219703023979 + 2.6902849146664865141e-730j)  +/-  (8.38e-85, 3.65e-208j)
| (4.9211583184976970368e-13 + 5.8247735758152276193e-736j)  +/-  (7.36e-99, 3.21e-222j)
| (2.9595426287091171414e-21 - 2.5875488877734431841e-740j)  +/-  (1.27e-103, 5.55e-227j)
| (1.6046191917901400567e-25 + 1.6039485353345082056e-742j)  +/-  (1.7e-105, 7.41e-229j)
| (5.3540941980660238582e-18 + 1.3047207850368753021e-738j)  +/-  (1.69e-102, 7.39e-226j)
| (4.592895709255708504e-11 - 7.1677304451463545052e-735j)  +/-  (3.57e-99, 1.55e-222j)
| (2.5785970044203139112e-15 - 3.4351907307338472755e-737j)  +/-  (2.18e-101, 9.51e-225j)
