Starting with polynomial:
P : 7113260368810144185/4294967296*t^34 - 59560284580634192355/4294967296*t^32 + 28405674184610153277/536870912*t^30 - 65378138996324955955/536870912*t^28 + 202565053611564207795/1073741824*t^26 - 223164889572062262825/1073741824*t^24 + 90048990529077755175/536870912*t^22 - 54029394317446653105/536870912*t^20 + 96845140757687397075/2147483648*t^18 - 32281713585895799025/2147483648*t^16 + 1976431444034436675/536870912*t^14 - 347882517228498525/536870912*t^12 + 85037948655855195/1073741824*t^10 - 6845630929362225/1073741824*t^8 + 166966608033225/536870912*t^6 - 4281195077775/536870912*t^4 + 347123925225/4294967296*t^2 - 583401555/4294967296
Extension levels are: 34 35
-------------------------------------------------
Trying to find an order 35 Kronrod extension for:
P1 : 7113260368810144185/4294967296*t^34 - 59560284580634192355/4294967296*t^32 + 28405674184610153277/536870912*t^30 - 65378138996324955955/536870912*t^28 + 202565053611564207795/1073741824*t^26 - 223164889572062262825/1073741824*t^24 + 90048990529077755175/536870912*t^22 - 54029394317446653105/536870912*t^20 + 96845140757687397075/2147483648*t^18 - 32281713585895799025/2147483648*t^16 + 1976431444034436675/536870912*t^14 - 347882517228498525/536870912*t^12 + 85037948655855195/1073741824*t^10 - 6845630929362225/1073741824*t^8 + 166966608033225/536870912*t^6 - 4281195077775/536870912*t^4 + 347123925225/4294967296*t^2 - 583401555/4294967296
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 7113260368810144185/4294967296*t^69 - 8710134237575418493755/304942678016*t^67 + 372364875759478920694336863/1580517900156928*t^65 - 138836583081902647093087598845/112216770911141888*t^63 + 3715313293871594261198081855589555/799726844994616557568*t^61 - 59574543452636153607578293309595719143/4485667873574804271398912*t^59 + 698680911777189792077705171040366925742327/23249216588738210538660560896*t^57 - 37844888063015916024844963093673644229317035963/685038166787171373521633426800640*t^55 + 22319035023048495031133746076598205603551086538808455/265581350820651610326404428622857240576*t^53 - 175868163849035470672233847471072374410435007759571349491/1640496004019164996986200155603389175037952*t^51 + 397899344405320052609176422926256736299755225254365001991655163/3435771203234086008805579976037231379797287895040*t^49 - 754909657996760976352533435387643851504468840934566495761079209581/7074252907458983092130689170660659411002615775887360*t^47 + 23717092840345904835944102773310446254089553077305100273898247290116571737/281318755756538904614573769726596132062145762928389573836800*t^45 - 25438405328611970202511323835997387591326644739532215437760993147201102343/443858481304761382836327503346407230586941092620347994275840*t^43 + 5142938812452858009151632275670269477191293447715696944761453952676411242388757/153070037295531879905245938485103266706939366646658873396895416320*t^41 - 26496044781202095615774050055373460983931683357224972480520203873432984049072925423719/1558304258131008540615171911167743764670989577150813961902983298102067200*t^39 + 1510654413774237716324155886284507224760297373587415133558940401452079071418537555669201357851/203392616464492556137468441368406786284208400112699459941235611856197534718361600*t^37 - 20803263184514034821884796051655485186863014561332466615815065363810849692540746022609031777401347/7437051021024170315166533558635794140482080150120855752751280147521862856976891904000*t^35 + 77856825878391633186638058336821032707775811947073916573642020770135608659219912633737566365813/85903904841776512731335360891194199697547022054871916716271471222712426583262494720*t^33 - 1162981677177658740115449635890809500820467796528507020094145088931251055607088950558270082083/4618489507622393157598675316730870951481022691122146060014595227027549816304435200*t^31 + 118902387075627903993602408712980315517664838590152556952525679751819169323040195589022729/1990728236044134981723566946866754720465958056518166405178704839236012851855360*t^29 - 6045604064365284441002014263264516511299846975068468041661508973118761761329443045499/502709150516195702455446198703725939511605569827819799287551727079801225216*t^27 + 9027921333614602342921450349255538928704623123465710595360969056148266495540251460807791/4423840524542522181607926548592788267702129014484814233730455198302250781900800*t^25 - 255936464702756169994905998631321840650312407200243403976282216087641026980443626479709/884768104908504436321585309718557653540425802896962846746091039660450156380160*t^23 + 89914349668684513223960789929125309911141417814933410670316217035236837459961216991387/2654304314725513308964755929155672960621277408690888540238273118981350469140480*t^21 - 2860310530528381197877718724083709005251575387703220508847415718025426498321034656849/884768104908504436321585309718557653540425802896962846746091039660450156380160*t^19 + 437397515872557851328245637188679179956064491308255961271669737099947213501639871859/1769536209817008872643170619437115307080851605793925693492182079320900312760320*t^17 - 12980343674571981417684341116850859085706994047483643285966755396892201189364000471051/875920423859419391958369456621372077005021544867993218278630129263845654816358400*t^15 + 4945738879266111939331629369236189328739090063469563921673116718582952458062632577/7299336865495161599653078805178100641708512873899943485655251077198713790136320*t^13 - 7556556618717609878673864464391604727157882115600357704217617902642626840127239/331788039340689163620594491144459120077659676086361067529784139872668808642560*t^11 + 1420592672586947970864927763443728331597532972106534247582041805658293423901309/2654304314725513308964755929155672960621277408690888540238273118981350469140480*t^9 - 7234096656486268841045781228915303101959779559965283018589897582076008499369/884768104908504436321585309718557653540425802896962846746091039660450156380160*t^7 + 116618621091273835703020372747152801045918807299406188142720857224465614843/1608669281651826247857427835851923006437137823449023357720165526655363920691200*t^5 - 18352768741426383412674893122403445347619273800856702162700727586213704217/60164231133778301669867801060861920440748954596993473578734190696910610633850880*t^3 + 2312887691345454491923809918022880113850289650812673770652742600818583/6016423113377830166986780106086192044074895459699347357873419069691061063385088*t
-------------------------------------------------
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: 0
  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:
| (0.99757175379084191924 + 1.8912587380929072919e-859j)  +/-  (1.29e-230, 1.29e-230j)
| (0.99345702264150973409 - 6.3843874288956946578e-859j)  +/-  (1.68e-230, 1.68e-230j)
| (-0.94216239740510709163 - 3.1821973774780921262e-860j)  +/-  (3.89e-231, 3.89e-231j)
| (-0.99959701578506607297 + 5.6955149380733737908e-860j)  +/-  (4.68e-231, 4.68e-231j)
| (0.9078096777183244688 + 1.985731536925338612e-876j)  +/-  (9.03e-232, 9.03e-232j)
| (0.88779659366471630376 - 2.416724545268639275e-877j)  +/-  (3.39e-232, 3.39e-232j)
| (0.99959701578506607297 + 7.4677419377324978098e-874j)  +/-  (4.94e-231, 4.94e-231j)
| (-0.92593952747053383288 + 4.9511451461162211805e-874j)  +/-  (1.94e-231, 1.94e-231j)
| (-0.99345702264150973409 - 2.2157712846543142281e-874j)  +/-  (1.67e-230, 1.67e-230j)
| (-0.96870826253334428176 - 1.9667979879581682625e-889j)  +/-  (1.03e-230, 1.03e-230j)
| (0.86593463833456446926 - 2.7074580317407119378e-912j)  +/-  (1.22e-232, 1.22e-232j)
| (-0.98722781640630948505 - 8.0974406403749205077e-908j)  +/-  (1.74e-230, 1.74e-230j)
| (-0.88779659366471630376 + 1.2045412779555991034e-925j)  +/-  (3.52e-232, 3.52e-232j)
| (-0.86593463833456446926 - 3.6956027894603880949e-929j)  +/-  (1.26e-232, 1.26e-232j)
| (0.26976800095077474706 + 6.0899625579160837335e-947j)  +/-  (7.33e-248, 7.33e-248j)
| (0.84227898672354964507 + 3.971319513321818904e-931j)  +/-  (3.63e-233, 3.63e-233j)
| (0.81688422790093366459 - 1.0618614714517770607e-932j)  +/-  (1.02e-233, 1.02e-233j)
| (0.97896771858276034585 - 9.8958843746231653076e-928j)  +/-  (1.5e-230, 1.5e-230j)
| (-0.76106487662987301419 + 5.5909236631566087552e-937j)  +/-  (6.08e-235, 6.08e-235j)
| (-0.22566669161644948387 + 7.4697888852975415188e-951j)  +/-  (3.8e-249, 3.8e-249j)
| (0.98722781640630948505 + 9.2717937981723883093e-930j)  +/-  (1.88e-230, 1.88e-230j)
| (0.92593952747053383288 + 7.2647295387919968329e-935j)  +/-  (2.02e-231, 2.02e-231j)
| (-0.97896771858276034585 + 5.6695437522405954995e-936j)  +/-  (1.43e-230, 1.43e-230j)
| (-0.81688422790093366459 - 2.4470906960595165016e-953j)  +/-  (1.01e-233, 1.01e-233j)
| (-0.84227898672354964507 + 1.7882188525105188942e-953j)  +/-  (3.89e-233, 3.89e-233j)
| (0.94216239740510709163 - 3.193126404566013077e-955j)  +/-  (3.83e-231, 3.83e-231j)
| (0.73075725701475890329 - 6.6096802061810148694e-962j)  +/-  (1.17e-235, 1.17e-235j)
| (0.76106487662987301419 - 3.2717910065446071152e-960j)  +/-  (5.75e-235, 5.75e-235j)
| (-0.99757175379084191924 + 3.411326741133705711e-954j)  +/-  (1.22e-230, 1.22e-230j)
| (-0.66567190278686411046 + 1.8770229380911821476e-970j)  +/-  (3.01e-237, 3.01e-237j)
| (-0.78979561521952921967 - 2.1234130947545764353e-967j)  +/-  (2.52e-234, 2.52e-234j)
| (0.78979561521952921967 + 7.8581856507714474736e-967j)  +/-  (2.62e-234, 2.62e-234j)
| (0.69893911321626290793 - 1.9524069337008208209e-969j)  +/-  (1.86e-236, 1.86e-236j)
| (0.045509821953102542749 + 2.1927417991079138513e-988j)  +/-  (2.03e-254, 2.03e-254j)
| (-0.63102172708052854532 + 7.0889745467860302882e-972j)  +/-  (4.13e-238, 4.13e-238j)
| (-0.73075725701475890329 + 5.5885072107806057596e-970j)  +/-  (1.07e-235, 1.07e-235j)
| (0.96870826253334428176 - 6.1579086086057666902e-963j)  +/-  (1.04e-230, 1.04e-230j)
| (0.63102172708052854532 - 2.2560040181224917954e-974j)  +/-  (4.43e-238, 4.43e-238j)
| (0.43968775243639376119 - 2.2582755571876976489e-979j)  +/-  (4.33e-243, 4.33e-243j)
| (-0.95643542933302095931 - 3.3296949559367326984e-966j)  +/-  (7.11e-231, 7.11e-231j)
| (-0.55787550066974664274 - 2.1733390298568078234e-980j)  +/-  (5.53e-240, 5.53e-240j)
| (2.8660886074363938442e-1017 - 4.0657378461182316192e-1017j)  +/-  (3.43e-1015, 3.43e-1015j)
| (0.66567190278686411046 - 1.8173681731778149059e-975j)  +/-  (2.75e-237, 2.75e-237j)
| (0.59506398775990817489 + 5.3248167072809719685e-978j)  +/-  (5.43e-239, 5.43e-239j)
| (0.95643542933302095931 - 3.0356144441616780255e-971j)  +/-  (7.04e-231, 7.04e-231j)
| (-0.51953046738386663267 - 1.5206226359592208193e-981j)  +/-  (5.6e-241, 5.6e-241j)
| (-0.48010654519032703419 + 6.1471129387899568134e-984j)  +/-  (5.29e-242, 5.29e-242j)
| (-0.59506398775990817489 + 3.8219045360963936956e-979j)  +/-  (5.21e-239, 5.21e-239j)
| (0.48010654519032703419 + 1.0633880845046309106e-983j)  +/-  (5.35e-242, 5.35e-242j)
| (0.356204949553047547 - 6.2678640933331823692e-986j)  +/-  (2.28e-245, 2.28e-245j)
| (-0.69893911321626290793 - 9.6508172544651979189e-977j)  +/-  (1.93e-236, 1.93e-236j)
| (-0.39835927775864594063 - 4.4305019415568742035e-985j)  +/-  (3.23e-244, 3.23e-244j)
| (0.090925172440993500491 - 1.8315482105678429487e-994j)  +/-  (4.99e-253, 4.99e-253j)
| (0.55787550066974664274 + 2.0905481469637931575e-980j)  +/-  (5.91e-240, 5.91e-240j)
| (0.51953046738386663267 + 7.0054953214120644944e-982j)  +/-  (5.96e-241, 5.96e-241j)
| (-0.13615235725918297589 - 3.1762454372516793023e-992j)  +/-  (1.04e-251, 1.04e-251j)
| (-0.43968775243639376119 + 3.4037038560731841017e-985j)  +/-  (4.45e-243, 4.45e-243j)
| (-0.090925172440993500491 - 1.7046337216978519131e-993j)  +/-  (4.61e-253, 4.61e-253j)
| (0.18109749528479873857 - 1.2547009166538860977e-991j)  +/-  (2.02e-250, 2.02e-250j)
| (0.39835927775864594063 + 6.0345593627390400147e-985j)  +/-  (3.28e-244, 3.28e-244j)
| (0.13615235725918297589 + 4.2485026583657649396e-992j)  +/-  (1.02e-251, 1.02e-251j)
| (-0.26976800095077474706 + 3.3852827113574621992e-989j)  +/-  (7.59e-248, 7.59e-248j)
| (-0.31331108133946324746 - 3.9409211096255680061e-987j)  +/-  (1.38e-246, 1.38e-246j)
| (-0.9078096777183244688 + 7.4510780613545160226e-991j)  +/-  (8.36e-232, 8.36e-232j)
| (0.31331108133946324746 + 2.4314680154393129208e-1007j)  +/-  (1.52e-246, 1.52e-246j)
| (0.22566669161644948387 + 4.0039571592911518162e-1010j)  +/-  (3.99e-249, 3.99e-249j)
| (-0.045509821953102542749 + 3.1277984989078835796e-1016j)  +/-  (2.12e-254, 2.12e-254j)
| (-0.356204949553047547 + 5.8856440675392250555e-1010j)  +/-  (2.21e-245, 2.21e-245j)
| (-0.18109749528479873857 - 4.2927382511793490241e-1013j)  +/-  (2.09e-250, 2.09e-250j)
-------------------------------------------------
The weights are:
| (0.0030413550983625059532 + 4.3848523368960660635e-859j)  +/-  (2.79e-32, 5.94e-141j)
| (0.0051855486830351059814 + 3.4040640557322360832e-859j)  +/-  (1.88e-32, 4.01e-141j)
| (0.015257161589203224395 - 2.3596511708398215068e-860j)  +/-  (1.42e-33, 3.03e-142j)
| (0.0010856644909045915616 + 6.0330445259353106676e-860j)  +/-  (2.24e-34, 4.76e-143j)
| (0.019075223395301179216 - 1.8158845126608502122e-859j)  +/-  (1e-33, 2.13e-142j)
| (0.020945414792823412182 + 1.6198481910225741754e-859j)  +/-  (6.11e-34, 1.3e-142j)
| (0.0010856644909045915616 - 2.0956508529812935064e-859j)  +/-  (4.67e-33, 9.95e-142j)
| (0.017181231733418095682 + 5.4364491651992867031e-860j)  +/-  (6.93e-34, 1.48e-142j)
| (0.0051855486830351059814 + 4.7015970603564170725e-860j)  +/-  (2.21e-34, 4.71e-143j)
| (0.011264093839933585148 - 1.1982815773187502483e-860j)  +/-  (6.98e-35, 1.49e-143j)
| (0.022768784004717144366 - 1.4622094915583830972e-859j)  +/-  (1.53e-35, 3.25e-144j)
| (0.0072564413076159254832 - 3.1009581276852132664e-860j)  +/-  (1.3e-34, 2.76e-143j)
| (0.020945414792823412182 + 3.2061596240379822887e-860j)  +/-  (1.83e-36, 3.9e-145j)
| (0.022768784004717144366 - 2.922855437517890568e-860j)  +/-  (6.47e-37, 1.38e-145j)
| (0.043837256886253744114 + 5.2661170767986647302e-860j)  +/-  (4.48e-40, 9.55e-149j)
| (0.024533241991697257459 + 1.3330868786630537098e-859j)  +/-  (5.52e-38, 1.18e-146j)
| (0.026249119132030782365 - 1.2246393935330972573e-859j)  +/-  (1.15e-38, 2.44e-147j)
| (0.0092588091267507075074 + 4.981889461257116563e-859j)  +/-  (8.01e-39, 1.71e-147j)
| (0.029530667610447976113 - 2.6017220902372527961e-860j)  +/-  (2.27e-42, 4.84e-151j)
| (0.044350363105479671927 - 3.5005233606131055505e-860j)  +/-  (5.77e-44, 1.23e-152j)
| (0.0072564413076159254832 - 8.6310451551575717356e-859j)  +/-  (2.54e-38, 5.41e-147j)
| (0.017181231733418095682 + 2.0654410098402033007e-859j)  +/-  (2.8e-39, 5.96e-148j)
| (0.0092588091267507075074 + 2.1387424966605142921e-860j)  +/-  (2.14e-39, 4.55e-148j)
| (0.026249119132030782365 - 2.6736711796623569782e-860j)  +/-  (4.36e-42, 9.29e-151j)
| (0.024533241991697257459 + 2.7648107400073383735e-860j)  +/-  (1.75e-41, 3.72e-150j)
| (0.015257161589203224395 - 2.3992690937517175184e-859j)  +/-  (1.02e-40, 2.17e-149j)
| (0.031073383922862539609 + 9.8146309246044601813e-860j)  +/-  (1.08e-44, 2.3e-153j)
| (0.029530667610447976113 - 1.0514011517310703797e-859j)  +/-  (3.61e-44, 7.68e-153j)
| (0.0030413550983625059532 - 8.9125017506891014841e-860j)  +/-  (2.04e-41, 4.34e-150j)
| (0.033970609709916557641 + 2.6467109062611071119e-860j)  +/-  (5.22e-47, 1.11e-155j)
| (0.027919633560120647129 + 2.6233529812155391862e-860j)  +/-  (4.38e-44, 9.34e-153j)
| (0.027919633560120647129 + 1.1317117745636761976e-859j)  +/-  (7.08e-44, 1.51e-152j)
| (0.032552895607225048848 - 9.1975145278288018693e-860j)  +/-  (2.98e-46, 6.34e-155j)
| (0.045478256346267700058 - 4.3194762177953995181e-860j)  +/-  (7.47e-51, 1.59e-159j)
| (0.03531698232965292086 - 2.6864346208022788858e-860j)  +/-  (1.69e-48, 3.59e-157j)
| (0.031073383922862539609 + 2.6017329855576822404e-860j)  +/-  (1.01e-46, 2.15e-155j)
| (0.011264093839933585148 - 3.626485974309655476e-859j)  +/-  (2.78e-44, 5.91e-153j)
| (0.03531698232965292086 - 8.153535815576144057e-860j)  +/-  (3.75e-49, 7.99e-158j)
| (0.040887655794005746369 + 6.2924682422917439791e-860j)  +/-  (8.25e-52, 1.76e-160j)
| (0.013279469346755367891 - 6.5538187495684705131e-861j)  +/-  (1.61e-45, 3.44e-154j)
| (0.037779151038287678113 - 2.7937298619471333063e-860j)  +/-  (4.73e-51, 1.01e-159j)
| (0.045525621850113425846 + 4.1625242089328943101e-860j)  +/-  (4.39e-53, 9.36e-162j)
| (0.033970609709916557641 + 8.6469203489553623169e-860j)  +/-  (9.42e-49, 2.01e-157j)
| (0.036585606961353932725 + 7.7095703169418741042e-860j)  +/-  (1.75e-50, 3.73e-159j)
| (0.013279469346755367891 + 2.8786294644600893653e-859j)  +/-  (2.09e-46, 4.45e-155j)
| (0.038898036460278521136 + 2.8588374637823218737e-860j)  +/-  (2.97e-52, 6.32e-161j)
| (0.039935677998485937215 - 2.9309925479905663301e-860j)  +/-  (4.06e-53, 8.65e-162j)
| (0.036585606961353932725 + 2.7359210575964362766e-860j)  +/-  (2.17e-51, 4.61e-160j)
| (0.039935677998485937215 - 6.6019473087655098721e-860j)  +/-  (3.02e-53, 6.42e-162j)
| (0.0425388848261948391 + 5.7416900095141350409e-860j)  +/-  (1.12e-54, 2.39e-163j)
| (0.032552895607225048848 - 2.617923797531993163e-860j)  +/-  (4.01e-51, 8.54e-160j)
| (0.041755419061723828874 - 3.0955166169052530287e-860j)  +/-  (1.7e-55, 3.63e-164j)
| (0.045336856600837521739 + 4.4859927807697083037e-860j)  +/-  (3.58e-56, 7.63e-165j)
| (0.037779151038287678113 - 7.3068257947992727018e-860j)  +/-  (4.71e-53, 1e-161j)
| (0.038898036460278521136 + 6.9389233008925773305e-860j)  +/-  (1.8e-53, 3.83e-162j)
| (0.04510186692646776879 - 3.7426938311223519461e-860j)  +/-  (4.17e-58, 8.89e-167j)
| (0.040887655794005746369 + 3.0100361487451952934e-860j)  +/-  (2.35e-56, 5e-165j)
| (0.045336856600837521739 + 3.8746941427860695473e-860j)  +/-  (4.17e-58, 8.88e-167j)
| (0.044772711231234264819 + 4.8511907000356816974e-860j)  +/-  (2.79e-58, 5.94e-167j)
| (0.041755419061723828874 - 6.0067252156918111046e-860j)  +/-  (5.04e-57, 1.07e-165j)
| (0.04510186692646776879 - 4.6628931473943479015e-860j)  +/-  (3.58e-58, 7.63e-167j)
| (0.043837256886253744114 + 3.3895676694925106857e-860j)  +/-  (1.11e-59, 2.36e-168j)
| (0.043233714565297556707 - 3.2851133292560673567e-860j)  +/-  (8.03e-60, 1.71e-168j)
| (0.019075223395301179216 - 3.7776734734534889115e-860j)  +/-  (2.43e-58, 5.17e-167j)
| (0.043233714565297556707 - 5.4954089209929935432e-860j)  +/-  (3.59e-59, 7.63e-168j)
| (0.044350363105479671927 - 5.0518995876228794443e-860j)  +/-  (1.51e-59, 3.2e-168j)
| (0.045478256346267700058 - 4.0144718017512862464e-860j)  +/-  (4.3e-60, 9.15e-169j)
| (0.0425388848261948391 + 3.1871575353222117409e-860j)  +/-  (1.68e-60, 3.68e-169j)
| (0.044772711231234264819 + 3.6181051065411305328e-860j)  +/-  (1.51e-60, 3.16e-169j)
