Starting with polynomial:
P : -1/13763753091226345046315979581580902400000000*t^37 + 37/371993326789901217467999448150835200000000*t^36 - 37/574063775910341384981480629862400000000*t^35 + 37/1405870471617162575464850522112000000*t^34 - 37/4864603708017863582923358208000000*t^33 + 37/22335186905499832795791360000000*t^32 - 37/130870235774413082787840000000*t^31 + 1147/29551343561964244500480000000*t^30 - 1147/262678609439682173337600000*t^29 + 33263/81520947757142743449600000*t^28 - 33263/1039808007106412544000000*t^27 + 33263/15689832754692096000000*t^26 - 33263/278517741207552000000*t^25 + 33263/5793169017117081600*t^24 - 33263/140806191388262400*t^23 + 765049/91830124818432000*t^22 - 765049/3035706605568000*t^21 + 765049/117022703616000*t^20 - 765049/5266021662720*t^19 + 765049/277159034880*t^18 - 765049/17108582400*t^17 + 13005833/21134131200*t^16 - 13005833/1816214400*t^15 + 565471/8072064*t^14 - 565471/988416*t^13 + 7351123/1900800*t^12 - 565471/26400*t^11 + 6220181/64800*t^10 - 6220181/18144*t^9 + 214489/224*t^8 - 214489/105*t^7 + 48433/15*t^6 - 145299/40*t^5 + 22015/8*t^4 - 1295*t^3 + 333*t^2 - 37*t + 1
Extension levels are: 37
-------------------------------------------------
Ending with final polynomial:
P : -1/13763753091226345046315979581580902400000000*t^37 + 37/371993326789901217467999448150835200000000*t^36 - 37/574063775910341384981480629862400000000*t^35 + 37/1405870471617162575464850522112000000*t^34 - 37/4864603708017863582923358208000000*t^33 + 37/22335186905499832795791360000000*t^32 - 37/130870235774413082787840000000*t^31 + 1147/29551343561964244500480000000*t^30 - 1147/262678609439682173337600000*t^29 + 33263/81520947757142743449600000*t^28 - 33263/1039808007106412544000000*t^27 + 33263/15689832754692096000000*t^26 - 33263/278517741207552000000*t^25 + 33263/5793169017117081600*t^24 - 33263/140806191388262400*t^23 + 765049/91830124818432000*t^22 - 765049/3035706605568000*t^21 + 765049/117022703616000*t^20 - 765049/5266021662720*t^19 + 765049/277159034880*t^18 - 765049/17108582400*t^17 + 13005833/21134131200*t^16 - 13005833/1816214400*t^15 + 565471/8072064*t^14 - 565471/988416*t^13 + 7351123/1900800*t^12 - 565471/26400*t^11 + 6220181/64800*t^10 - 6220181/18144*t^9 + 214489/224*t^8 - 214489/105*t^7 + 48433/15*t^6 - 145299/40*t^5 + 22015/8*t^4 - 1295*t^3 + 333*t^2 - 37*t + 1
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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:
| (117.14057111333492925 - 4.9113091929081495126e-594j)  +/-  (1.72e-240, 1.72e-240j)
| (81.992072000192307862 - 6.4347619130614673798e-590j)  +/-  (1.61e-237, 1.61e-237j)
| (106.41185731948361184 + 2.7941343173544752799e-595j)  +/-  (1.84e-239, 1.84e-239j)
| (97.28253366634952909 - 4.0751660657629725424e-594j)  +/-  (1.16e-238, 1.16e-238j)
| (33.690976143426304704 + 1.5808790454535330157e-593j)  +/-  (5.7e-237, 5.7e-237j)
| (75.394753301696875622 + 4.9195698123079353345e-592j)  +/-  (4e-237, 4e-237j)
| (69.331470026966007757 + 1.0569333516939901402e-607j)  +/-  (8.43e-237, 8.43e-237j)
| (16.967830861609724418 - 3.7333020238004707657e-621j)  +/-  (1.39e-239, 1.39e-239j)
| (130.80622535165002462 + 8.2828340315602957102e-622j)  +/-  (5.46e-242, 5.46e-242j)
| (40.909912529780507753 - 4.1706151407743316893e-625j)  +/-  (1.57e-236, 1.57e-236j)
| (9.2776089418061887243 + 1.6597175403192244006e-645j)  +/-  (2.43e-242, 2.43e-242j)
| (6.3460840606495494533 - 1.2904757902358116329e-647j)  +/-  (4.93e-244, 4.93e-244j)
| (19.296238948189429876 + 1.5641055893068600325e-639j)  +/-  (5.03e-239, 5.03e-239j)
| (14.80677283245776939 + 7.2670902725918983098e-645j)  +/-  (3.42e-240, 3.42e-240j)
| (63.724503575444959564 + 6.1140808032004460442e-645j)  +/-  (1.5e-236, 1.5e-236j)
| (0.038556734186015022592 + 2.1724018469317470959e-673j)  +/-  (4.31e-255, 4.31e-255j)
| (7.7386838135364333985 - 6.1457951542117596637e-663j)  +/-  (3.86e-243, 3.86e-243j)
| (21.79801837446760428 - 2.2209797956310174306e-655j)  +/-  (1.65e-238, 1.65e-238j)
| (89.23308272823344792 - 1.389676243651729718e-665j)  +/-  (5.08e-238, 5.08e-238j)
| (5.0969845446049991547 + 1.1445847423493054938e-683j)  +/-  (6.42e-245, 6.42e-245j)
| (1.4911150120426225625 - 6.8611962079591680014e-687j)  +/-  (3.15e-249, 3.15e-249j)
| (12.80775291254541338 - 6.5025913900620964955e-682j)  +/-  (7.94e-241, 7.94e-241j)
| (30.416909627456459507 - 3.8168225510125410315e-704j)  +/-  (2.64e-237, 2.64e-237j)
| (49.12787780671978805 + 3.7515010134816698732e-741j)  +/-  (2.47e-236, 2.47e-236j)
| (53.662301738694262913 + 1.0679144317420510879e-773j)  +/-  (2.27e-236, 2.27e-236j)
| (27.350001619637796275 + 2.3941465951070388497e-789j)  +/-  (1.19e-237, 1.19e-237j)
| (0.20322750994095859987 + 1.5137861777508224922e-814j)  +/-  (1.97e-253, 1.97e-253j)
| (3.0197574676425097513 + 4.6061461476641091476e-808j)  +/-  (5.59e-247, 5.59e-247j)
| (24.480008590749687594 + 7.9320704202023854629e-798j)  +/-  (4.67e-238, 4.67e-238j)
| (58.516203220150028755 + 5.4004190386694116929e-812j)  +/-  (1.9e-236, 1.9e-236j)
| (44.884780415154753613 + 1.020181482732295234e-825j)  +/-  (2.18e-236, 2.18e-236j)
| (0.49978706644227012338 - 6.8762789026537962067e-847j)  +/-  (5.6e-252, 5.6e-252j)
| (0.92882549934693066217 + 1.84164663918703439e-845j)  +/-  (1.34e-250, 1.34e-250j)
| (10.966079631310795661 - 3.077095369432599597e-835j)  +/-  (1.4e-241, 1.4e-241j)
| (37.184045639222585812 - 6.5905773898836779514e-830j)  +/-  (1.01e-236, 1.01e-236j)
| (2.1876690719353285022 - 7.2196150174621779527e-842j)  +/-  (4.08e-248, 4.08e-248j)
| (3.9889203029415885342 - 1.8640633548197326426e-840j)  +/-  (6.8e-246, 6.8e-246j)
-------------------------------------------------
The weights are:
| (1.5839224439544198206e-50 + 3.9499056088519992779e-627j)  +/-  (1.42e-85, 1.13e-202j)
| (1.6981579422487235672e-35 + 1.8694318315618491563e-619j)  +/-  (1.42e-80, 1.13e-197j)
| (5.9909906193811908853e-46 - 8.4018609349900796276e-625j)  +/-  (1.99e-84, 1.59e-201j)
| (4.8053496536420993648e-42 + 8.2275530893468558418e-623j)  +/-  (3.04e-83, 2.43e-200j)
| (7.8940023710878365192e-15 - 6.0545265991230751803e-608j)  +/-  (6.96e-71, 5.56e-188j)
| (1.1398881006626312678e-32 - 5.3791952551111033836e-618j)  +/-  (2.1e-80, 1.68e-197j)
| (4.5181021486852350767e-30 + 1.2016837748011932071e-616j)  +/-  (8.37e-80, 6.69e-197j)
| (9.5928412944538759599e-08 - 1.8461172728645501772e-605j)  +/-  (9.02e-65, 7.21e-182j)
| (2.5237731905450008162e-56 - 4.5273314173644303731e-630j)  +/-  (7.56e-90, 6.04e-207j)
| (6.5799472096910862977e-18 + 5.4997474740276040069e-610j)  +/-  (7.87e-75, 6.29e-192j)
| (0.0001508182894937998852 - 3.7077274638048622951e-604j)  +/-  (2.06e-59, 1.65e-176j)
| (0.0023154716429499836351 - 1.0727212370937962557e-603j)  +/-  (9.39e-56, 7.51e-173j)
| (1.0057541962375849333e-08 + 7.4057488140454914571e-606j)  +/-  (4.97e-67, 3.97e-184j)
| (7.7161064001032755824e-07 + 4.3313282398512488404e-605j)  +/-  (1.88e-64, 1.5e-181j)
| (1.1406116236355708115e-27 - 2.1722328165640376719e-615j)  +/-  (3.49e-80, 2.79e-197j)
| (0.095214651426979055171 + 4.3568856772859513977e-604j)  +/-  (5.88e-52, 4.7e-169j)
| (0.00063833255863661421187 + 6.5534769255219617795e-604j)  +/-  (1.17e-59, 9.33e-177j)
| (8.8440885796264389324e-10 - 2.8251117509211899317e-606j)  +/-  (4.1e-69, 3.28e-186j)
| (1.3428496035750324689e-38 - 4.7691865874076477262e-621j)  +/-  (4.74e-84, 3.79e-201j)
| (0.0072048771703099494171 + 1.6217563679361274622e-603j)  +/-  (7.98e-59, 6.38e-176j)
| (0.14165364252361854358 + 3.4538692447852601959e-603j)  +/-  (5.88e-52, 4.7e-169j)
| (5.2586849951351081141e-06 - 9.5097252625237022995e-605j)  +/-  (7.04e-65, 5.63e-182j)
| (1.954245790121932827e-13 + 1.8019805785613173275e-607j)  +/-  (2.45e-73, 1.96e-190j)
| (2.0228210532347099162e-21 + 4.9416627166136366433e-612j)  +/-  (7.82e-79, 6.25e-196j)
| (2.3218619944215189926e-23 - 4.2769726876634601322e-613j)  +/-  (8.6e-80, 6.87e-197j)
| (3.9295478116928752422e-12 - 3.9562563377653142923e-607j)  +/-  (1.14e-73, 9.15e-191j)
| (0.18812810086693704029 - 1.4129362853531032558e-603j)  +/-  (3.95e-61, 3.16e-178j)
| (0.04394862142283880303 + 2.8742072134974362827e-603j)  +/-  (1.41e-64, 1.12e-181j)
| (6.4813973464885699523e-11 + 1.0464664654759570824e-606j)  +/-  (7.4e-73, 5.92e-190j)
| (1.9401615214294621765e-25 + 3.2843870211024301067e-614j)  +/-  (4e-81, 3.2e-198j)
| (1.3187193066397206979e-19 - 5.259428044472021802e-611j)  +/-  (1.08e-78, 8.63e-196j)
| (0.22002905155139786799 + 2.4176874410779711469e-603j)  +/-  (9.08e-67, 7.25e-184j)
| (0.19573734237841640583 - 3.149357421985884511e-603j)  +/-  (2.7e-67, 2.15e-184j)
| (3.0485618916858805561e-05 + 1.9469811334048671245e-604j)  +/-  (1.87e-71, 1.49e-188j)
| (2.5604635963498163904e-16 - 6.7595980738156886579e-609j)  +/-  (3.97e-77, 3.17e-194j)
| (0.085713756436193989731 - 3.3262154623090667891e-603j)  +/-  (5.91e-70, 4.8e-187j)
| (0.019228710878365075492 - 2.2563512178541998676e-603j)  +/-  (2.45e-70, 1.94e-187j)
