Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 3 50
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 50 Kronrod extension for:
P2 : 3/2*t^5 - 25/14*t^3 + 3/7*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^55 - 9090227048386963652162534097681486631773554373/448257390045035786868507593273060696264332784*t^53 + 197180133391548479408781467627085800181146847815/1522104763999077562004053256278854452150316816*t^51 - 93269699168876544311202978731565490286127199889975/179354678024557972722810942031525016278378998152*t^49 + 56561483503101466874426300329255327632266112517925/38433145290976708440602344721041074916795499604*t^47 - 69841796680509618543333371113193880718285071640192885/22368090559348444312430564627645905601574980769528*t^45 + 243481368527505877173252493611624992848853983928322655/47221524514180049104020080880585800714436070513448*t^43 - 2485543858983934179284575274864982558202019539223375525/365966814984895380556155626824539955536879546479222*t^41 + 207104611510620379986946402779148111275556619860940594075/28545411568821839683380138892314116531876604625379316*t^39 - 87179975846040803136984039658798301642917388473571287925/13714124856276079523999095068372234123276749320695056*t^37 + 1830501338676884612723638200138999104686087062171355146285/397709620832006306195973756982794789575025730300156624*t^35 - 1650170255607800275795391972627323980624298046947521000745/596564431248009459293960635474192184362538595450234936*t^33 + 5705492878815885003894770478929701225318045448019991043975/4126237316132065426783227728696495941840891951864124974*t^31 - 142476406104269180967313884307030152665468502526179977075/247849627442860437203886871356630457018251574416755004*t^29 + 151446814935213711009059783339085835583983323913756778339675/763624702151453007025175450649778438073233100778022167324*t^27 - 30753849623015660632451613621514120241895390933017619940/543892237999610403864085078810383502901163177192323481*t^25 + 7199606400069500379471429541568144072801137605382220315/543892237999610403864085078810383502901163177192323481*t^23 - 4806599451330427530532872039625335861899815650023572748575/1905798401950634855139754116151583794165675772881901477424*t^21 + 17433476919672130176038404033391784707743716290585312960575/45103895512831691571640847415587483128587659958205001632368*t^19 - 352700566892616517489483840997972239850325429081875563425/7517315918805281928606807902597913854764609993034166938728*t^17 + 1415226624084538403528360174552495980778811420654223355/320077778494533611280179717925896204944432977390171067932*t^15 - 6188532781703003208916213598614642827862041782275639376155/19642746495838201679449589049488348902499925911798278210896264*t^13 + 940037885818371479987748538581310882252710300968612275/57379006316956772189239305889449899423076706655691172962696*t^11 - 122747659548575989172453289178506906053728898648703206425/207382073581061013884958161310944298989854987030331821880424018*t^9 + 8068270932683336213991503043351648670134187419216025/583353230889060517257266276542740644134613184332860258454076*t^7 - 38603406690060475960424462667012127905050396107794055243/206644715097217241391144976737394274815668835965335086513738065936*t^5 + 740121915155245651575879296346934116465425314980125117/619934145291651724173434930212182824447006507896005259541214197808*t^3 - 3063290443331825233343003101185884650760390031166145/1343190648131912069042442348793062786301847433774678062339297428584*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: 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:
| (-0.99490660003376078704 - 2.8715910329667603543e-918j)  +/-  (1.89e-236, 1.89e-236j)
| (0.98750048491414285748 - 5.3654385983714428385e-921j)  +/-  (2.71e-236, 2.71e-236j)
| (-0.81617657680934203575 - 2.8903752523678082618e-942j)  +/-  (2.19e-238, 2.19e-238j)
| (0.99903253611157159595 + 1.9112000783613983043e-937j)  +/-  (6.21e-237, 6.21e-237j)
| (0.92582009977255146157 - 2.3766727846381327287e-946j)  +/-  (9.36e-237, 9.36e-237j)
| (0.94594083275500133444 + 1.1020974630394651838e-958j)  +/-  (1.55e-236, 1.55e-236j)
| (0.97684123594655413767 + 7.6869581482141657476e-981j)  +/-  (2.87e-236, 2.87e-236j)
| (-0.847756748841889274 - 1.3526009403996598237e-1004j)  +/-  (7.15e-238, 7.15e-238j)
| (-0.16722486550546443923 - 2.917410430499318504e-1018j)  +/-  (8.81e-252, 8.81e-252j)
| (0.99490660003376078704 - 5.1986559076896082017e-1001j)  +/-  (2.04e-236, 2.04e-236j)
| (0.847756748841889274 - 3.1032708237144641255e-1014j)  +/-  (7.38e-238, 7.38e-238j)
| (-0.57735026918962576451 + 3.3315275076579317257e-1020j)  +/-  (1.02e-242, 1.02e-242j)
| (-0.87663133586579625004 - 2.9672880672571956707e-1013j)  +/-  (1.98e-237, 1.98e-237j)
| (-0.9026866420702239195 - 5.3498323475098481908e-1014j)  +/-  (4.34e-237, 4.34e-237j)
| (0.96297003603050648595 - 1.1095519009511289769e-1012j)  +/-  (2.39e-236, 2.39e-236j)
| (0.81617657680934203575 + 1.4443212489060894901e-1021j)  +/-  (2.32e-238, 2.32e-238j)
| (0.9026866420702239195 - 1.373088780480471257e-1019j)  +/-  (4.52e-237, 4.52e-237j)
| (-0.96297003603050648595 - 8.9949245137625468244e-1020j)  +/-  (2.26e-236, 2.26e-236j)
| (-0.78201481258890047143 - 2.3717096079619740976e-1028j)  +/-  (6.22e-239, 6.22e-239j)
| (-0.97684123594655413767 - 1.0768767600731869075e-1022j)  +/-  (2.85e-236, 2.85e-236j)
| (-0.98750048491414285748 + 2.863552845780243065e-1022j)  +/-  (2.85e-236, 2.85e-236j)
| (0.70648628121742498691 + 1.9501834799491629998e-1028j)  +/-  (2.96e-240, 2.96e-240j)
| (-0.94594083275500133444 + 7.0262051630197856072e-1024j)  +/-  (1.67e-236, 1.67e-236j)
| (-0.70648628121742498691 - 3.3486603421268137424e-1029j)  +/-  (2.94e-240, 2.94e-240j)
| (-0.74540454456781020782 + 1.1131475175249718e-1028j)  +/-  (1.41e-239, 1.41e-239j)
| (0.87663133586579625004 - 1.2068000915140982613e-1026j)  +/-  (1.94e-237, 1.94e-237j)
| (0.74540454456781020782 - 5.36253272896597804e-1035j)  +/-  (1.42e-239, 1.42e-239j)
| (0.78201481258890047143 - 3.786253048291592414e-1034j)  +/-  (6.27e-239, 6.27e-239j)
| (1.7646416198361637885e-1050 - 9.2972420030335050878e-1052j)  +/-  (9.72e-1049, 9.72e-1049j)
| (-0.62231113728648091842 - 6.3290611966861098422e-1036j)  +/-  (7.78e-242, 7.78e-242j)
| (-0.92582009977255146157 - 1.547376737544010606e-1031j)  +/-  (9.67e-237, 9.67e-237j)
| (0.66540573822095799412 + 6.3125061134925004465e-1039j)  +/-  (5.13e-241, 5.13e-241j)
| (0.62231113728648091842 - 4.6190520243240223605e-1040j)  +/-  (7.54e-242, 7.54e-242j)
| (-0.99903253611157159595 - 7.2648881970825874767e-1042j)  +/-  (6.31e-237, 6.31e-237j)
| (-0.38166989357340029662 + 6.0495419714107637109e-1053j)  +/-  (7.91e-247, 7.91e-247j)
| (-0.66540573822095799412 + 4.6215013577106779262e-1050j)  +/-  (5.09e-241, 5.09e-241j)
| (0.16722486550546443923 + 8.4233853497567313946e-1061j)  +/-  (9.35e-252, 9.35e-252j)
| (0.57735026918962576451 - 1.247618415066233251e-1051j)  +/-  (9.99e-243, 9.99e-243j)
| (0.22208996406433972109 + 9.6217904598343147998e-1061j)  +/-  (1.95e-250, 1.95e-250j)
| (-0.27622392242547284538 - 4.1687954491395359185e-1059j)  +/-  (3.22e-249, 3.22e-249j)
| (-0.53066783933315184327 - 7.9506736421319875204e-1055j)  +/-  (1.06e-243, 1.06e-243j)
| (-0.22208996406433972109 - 2.0933047245186569411e-1061j)  +/-  (1.72e-250, 1.72e-250j)
| (0.38166989357340029662 - 3.5300663851500776193e-1057j)  +/-  (7.53e-247, 7.53e-247j)
| (0.53066783933315184327 + 5.015887860323496115e-1056j)  +/-  (1.06e-243, 1.06e-243j)
| (0.43269357527815656845 + 2.9995938214310525246e-1059j)  +/-  (9.53e-246, 9.53e-246j)
| (-0.48240382816486955273 + 6.0110599500440011186e-1058j)  +/-  (1.13e-244, 1.13e-244j)
| (-0.3294668164294661221 - 2.3958390316235475736e-1061j)  +/-  (5.92e-248, 5.92e-248j)
| (0.055995583431967660882 - 3.8147358568853638773e-1068j)  +/-  (1.87e-254, 1.87e-254j)
| (0.48240382816486955273 + 3.4044698698030983638e-1059j)  +/-  (1.07e-244, 1.07e-244j)
| (0.11179979568933184527 + 1.4823943225969217415e-1066j)  +/-  (4.47e-253, 4.47e-253j)
| (-0.11179979568933184527 - 7.1138315519539185247e-1066j)  +/-  (4.11e-253, 4.11e-253j)
| (-0.43269357527815656845 + 2.26817649381138621e-1058j)  +/-  (9.59e-246, 9.59e-246j)
| (-0.055995583431967660882 - 1.5283757162832380112e-1067j)  +/-  (2.03e-254, 2.03e-254j)
| (0.27622392242547284538 - 6.6992847095951981284e-1065j)  +/-  (3.37e-249, 3.37e-249j)
| (0.3294668164294661221 - 6.7778768063868086563e-1062j)  +/-  (5.46e-248, 5.46e-248j)
-------------------------------------------------
The weights are:
| (0.005769133730309282759 - 1.6474864078843572944e-918j)  +/-  (6.98e-46, 1.43e-159j)
| (0.0090384616687675087801 + 1.8544021548311965498e-920j)  +/-  (3.12e-46, 6.38e-160j)
| (0.032892438823036257736 + 1.6647194278832072774e-918j)  +/-  (7.98e-47, 1.63e-160j)
| (0.0024823558090147813213 + 1.7586132442759748021e-921j)  +/-  (1.46e-46, 2.97e-160j)
| (0.021641245714389076955 + 7.2840338862444865332e-920j)  +/-  (2.93e-47, 5.99e-161j)
| (0.018587081867537752444 - 5.6809090128735957473e-920j)  +/-  (3.23e-47, 6.6e-161j)
| (0.012273162762018658928 - 3.4057595399893970591e-920j)  +/-  (3.53e-47, 7.22e-161j)
| (0.03024722001064886654 - 1.6980017593669047052e-918j)  +/-  (6.5e-50, 1.33e-163j)
| (0.055174493062716119945 + 1.3044736036791959136e-918j)  +/-  (2.15e-51, 4.39e-165j)
| (0.005769133730309282759 - 5.0177486168673287351e-921j)  +/-  (6.17e-47, 1.26e-160j)
| (0.03024722001064886654 - 1.3822532583076934541e-919j)  +/-  (8.77e-50, 1.79e-163j)
| (0.045845402995841593211 + 1.6168290768836510024e-918j)  +/-  (1.36e-51, 2.78e-165j)
| (0.027482991133590576236 + 1.7488422165577283424e-918j)  +/-  (3.28e-51, 6.7e-165j)
| (0.024610517473467853522 - 1.8242842084836547364e-918j)  +/-  (7.27e-52, 1.48e-165j)
| (0.01546024265923506846 + 4.3498188189623456255e-920j)  +/-  (1.56e-48, 3.19e-162j)
| (0.032892438823036257736 + 1.6682965439870928833e-919j)  +/-  (2.18e-51, 4.46e-165j)
| (0.024610517473467853522 - 9.1584023512979848414e-920j)  +/-  (2.05e-50, 4.19e-164j)
| (0.01546024265923506846 + 2.3852006843852697957e-918j)  +/-  (1.59e-53, 3.25e-167j)
| (0.035408880475218483943 - 1.6442117262222771489e-918j)  +/-  (5.14e-53, 1.05e-166j)
| (0.012273162762018658928 - 2.9188213950008967433e-918j)  +/-  (6.14e-54, 1.25e-167j)
| (0.0090384616687675087801 + 4.4278713359691150741e-918j)  +/-  (3.19e-54, 6.51e-168j)
| (0.040023994634205613336 - 2.7826499488727071031e-919j)  +/-  (1.07e-56, 2.18e-170j)
| (0.018587081867537752444 - 2.1063485095243870449e-918j)  +/-  (4.5e-54, 9.19e-168j)
| (0.040023994634205613336 - 1.6273295772612786442e-918j)  +/-  (2.74e-56, 5.6e-170j)
| (0.037788200529786339798 + 1.6328051065190591424e-918j)  +/-  (1.43e-55, 2.92e-169j)
| (0.027482991133590576236 + 1.1326964846644240439e-919j)  +/-  (3.14e-55, 6.42e-169j)
| (0.037788200529786339798 + 2.3652744606571191476e-919j)  +/-  (5.97e-58, 1.22e-171j)
| (0.035408880475218483943 - 1.9947557380493608225e-919j)  +/-  (2.27e-57, 4.63e-171j)
| (0.056027600258688617587 - 1.114856400533280709e-918j)  +/-  (5.78e-63, 1.18e-176j)
| (0.044052186448754561164 - 1.6222533671430130935e-918j)  +/-  (1.17e-59, 2.4e-173j)
| (0.021641245714389076955 + 1.9360422859429892562e-918j)  +/-  (3.7e-57, 7.55e-171j)
| (0.042112337543801739576 + 3.2481437045003608449e-919j)  +/-  (4.68e-60, 9.55e-174j)
| (0.044052186448754561164 - 3.7607459511201477238e-919j)  +/-  (4.46e-61, 9.1e-175j)
| (0.0024823558090147813213 - 1.1418456591951786194e-918j)  +/-  (8.05e-59, 1.64e-172j)
| (0.051636039182568440169 + 1.5227449579486708336e-918j)  +/-  (5.36e-64, 1.09e-177j)
| (0.042112337543801739576 + 1.6247944874674979024e-918j)  +/-  (3.33e-60, 6.8e-174j)
| (0.055174493062716119945 + 9.3001993322052275066e-919j)  +/-  (7.86e-66, 1.6e-179j)
| (0.045845402995841593211 + 4.316575629897709942e-919j)  +/-  (5.42e-64, 1.11e-177j)
| (0.054527148112634477877 - 8.6867634493973216651e-919j)  +/-  (5.15e-66, 1.05e-179j)
| (0.053714115026806490212 + 1.4242403005443703963e-918j)  +/-  (1.11e-65, 2.26e-179j)
| (0.04749612717106619016 - 1.6058819933321969049e-918j)  +/-  (2.29e-64, 4.67e-178j)
| (0.054527148112634477877 - 1.3660325898127978858e-918j)  +/-  (8.78e-66, 1.79e-179j)
| (0.051636039182568440169 + 6.8018065530392473961e-919j)  +/-  (2.36e-67, 4.83e-181j)
| (0.04749612717106619016 - 4.9086803322768209355e-919j)  +/-  (1.67e-66, 3.41e-180j)
| (0.050389060695085950022 - 6.1620622588314480083e-919j)  +/-  (2.46e-67, 5.03e-181j)
| (0.049009374759925401316 + 1.587279522885343111e-918j)  +/-  (1.03e-66, 2.11e-180j)
| (0.052746914843829414078 - 1.4771135926847990494e-918j)  +/-  (3.23e-67, 6.6e-181j)
| (0.055931610847898047787 + 1.0526726314094179964e-918j)  +/-  (4.07e-69, 8.31e-183j)
| (0.049009374759925401316 + 5.5274954269977980766e-919j)  +/-  (2.85e-68, 5.81e-182j)
| (0.055645461888501144931 - 9.9118560721569426337e-919j)  +/-  (2.82e-69, 5.77e-183j)
| (0.055645461888501144931 - 1.2413061266255355349e-918j)  +/-  (1.28e-69, 2.62e-183j)
| (0.050389060695085950022 - 1.5596835348537273506e-918j)  +/-  (4e-69, 8.18e-183j)
| (0.055931610847898047787 + 1.1778357189881633893e-918j)  +/-  (8.19e-70, 1.67e-183j)
| (0.053714115026806490212 + 8.0669888728703249575e-919j)  +/-  (5.71e-71, 1.17e-184j)
| (0.052746914843829414078 - 7.4383821330625937049e-919j)  +/-  (5.24e-71, 1.07e-184j)
