Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 4 6 31
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P2 : 3/2*t^6 - 25/14*t^4 + 45/98*t^2 - 1/98
Solvable: 1
-------------------------------------------------
Trying to find an order 31 Kronrod extension for:
P3 : 3/2*t^12 - 1595/364*t^10 + 318813/66248*t^8 - 10310751/4183088*t^6 + 2471775/4183088*t^4 - 33827/597584*t^2 + 31245/29281616
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^43 - 4612322985590771338966053261923299066108795551399896542932253171716134683168935374701805417301936773484820358719336948254626017/293529862219594304324924962232353985178107404205032827393431251080691822389425973264404766291370484367168449029146218661670851*t^41 + 1741415359582828494893179151824832388607320969716131926846083242695964512825228303236287488053588013351521021888067755637606096602429/22757957277609585602920082171798869178829023262824605173467511758788198373496974559135830340102536393955304190127764625276664419732*t^39 - 5912109209428796130894262435341561738329492573420556053230139755842304650689706538686740742104765836960023913340192795758419107104291319/25706377076019894137698395039834144896886205609986104021496747171093424962774471485352761248609153886772180266315428353395841165666168*t^37 + 3291241175795226109835292085247845446791415378215097154873863439339610254457818905145353019884868199516017097957638765475440185234666869491/6889309056373331628903169870675550832365503103476275877761128241853037890023558358074540014627253241654944311372534798710085432398533024*t^35 - 1643130641973313618824497475614270956579866470835237211621781626345410844274354288815888161290883816649798143142828596432545271149040795187/2257840783181175911993475839969298171951719504500628228846084045649314938747216604747118156054309885920527967592679471846162452634813344*t^33 + 1814528946915400133163386220891611231247179495596489461411446494034274894636410187455302654873716276015289962524644852452604530729725700553/2155211656672940643266499665425239164135732254296054218443989316301618805167797668167703694415477618378685787247557677671336886605958192*t^31 - 33123502076692433010434387780142078264687427019841897687970027062458791741796585578639775937352019459160213188173524949990459878224485897211/43822637019016459746418826530313196337426555837353102441694449431466249038411885919409975119781378240366611007367006112650516694321149904*t^29 + 197069530152661505447194495657574621595135076686973092399550952242180241600711226473026688310997866381493019360923918568464697393342336992453/369362226303138732148387252184068369129738113486261863437138930922358384752328752749312647438157330883090007062093337235197212137849692048*t^27 - 19772061812228437946417686048713079988457123542004336900264326293015794639955247898681613859008620528104613042820454223735474263235625511497/66295784208255669872787455520217399587388892164200847283589038883500222904264135108850988001720546568759744857298804119137961152947380624*t^25 + 96512250190063580730408228263933757635162280449152226907590800872456025710634173788721229959259273252552424131246218325148347404021150072085/729253626290812368600662010722391395461277813806209320119479427718502451946905486197360868018926012256357193430286845310517572682421186864*t^23 - 21331862925603600658828639111191357708426594053103839842874707377751773303345006176073555706280315252767444304333173283998329831470313363815/458305638657071804772748062074546371060644950178605857308289442716371106164260760100317699664068126279686931839587384997518948839940587792*t^21 + 774310087574003563443293554257850969971203319093923050782809414832814369996171774813213914736279944565062677698893810794694230169650170985/60016214586045117291669389081190596210322552999579338457037903212858121045319861441708270194104159393768526788517395654437005205230315068*t^19 - 683953797688604804745645831530894186263923510029742632629171041687650070566285266974895982606235007181050360863070529461140896554891324430/245066209559684228940983338748194934525483758081615632032904771452503994268389434220308769959258650857888151053112698922284437921357119861*t^17 + 256640355952329927030953235716196278095905438877745809866565410813928119111873382197367146892618638798621672891092184936390472437748226345465/552869368766647620490858412215927772289491358232124865866233164396849011069486563601016585028087516335395668775822248768673691950581662406416*t^15 - 1966992227907094185794385882824730979364370325487348149269810682583322428797937581919565843962433122214812206357187938823383719841450013695/33849145026529446152501535441791496262621919891762746889769377412051980269560401853123464389474745898085449108723811149102470935749897698352*t^13 + 2936662430756200438442168003584030504134974425020577827553447582603952323570263040254581624288377037971532948189914705757921807816923450955/552869368766647620490858412215927772289491358232124865866233164396849011069486563601016585028087516335395668775822248768673691950581662406416*t^11 - 84847399597421218715714113930637981663455584262573045517752908094940748544818408892230038472101757529434445595290375487780345688066005/250053988587357585025263868030722646897101473646370359957590757302962013147664660154236356864806655963543947885944029293837038421791796656*t^9 + 174846140475763735627942423142600313483442349285567530940404960986343283995145818022145222725312292267704326264138723127830252455788195/12328133437335195654170084663476948610228795295055957557909144317596976233110335037415464160146033811938496902376825444241437384832867257776*t^7 - 32555034878589207842713650176369105794644526541279784678496037010284988638433150861754764165258810066812577952201956955430480749072315/93341581739823624238716355309182610906018021519709392938454949833234248622121108140431371498248541718962905117995964077828025913734566380304*t^5 + 277127470845695954556151942755230078072104706653942374212798236276514928371155683101216846196325180067973913067668959906665576540168125/66645889362234067706443477690756384186896867365072506558056834180929253516194471212267999249749458787339514254249118351569210502406480395537056*t^3 - 3737481304936551651360398051930679924912378467268640578714374720138625134361724007581088829704173465776267501157587513809461847076125/244368260994858248256959418199440075351955180338599190712875058663407262892713061111649330582414682220244885598913433955753771842157094783635872*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:
| (-0.97851071377793355581 - 1.8756469821540660807e-906j)  +/-  (7.56e-241, 7.56e-241j)
| (0.99105250481616767714 - 2.2970707852537387154e-921j)  +/-  (5.56e-241, 5.56e-241j)
| (-0.93950971544220319294 - 1.3459656296377596449e-937j)  +/-  (5.85e-241, 5.85e-241j)
| (0.99828029537769456017 + 1.4891923853917556127e-944j)  +/-  (1.74e-241, 1.74e-241j)
| (0.93950971544220319294 - 5.1960837915353217627e-948j)  +/-  (5.89e-241, 5.89e-241j)
| (0.91248695683407599658 - 4.643378851704613556e-952j)  +/-  (3.12e-241, 3.12e-241j)
| (-0.96127891496452473422 - 3.5854594154814604311e-953j)  +/-  (8.15e-241, 8.15e-241j)
| (-0.91248695683407599658 - 3.9997992096468926383e-960j)  +/-  (3.05e-241, 3.05e-241j)
| (-0.99105250481616767714 - 3.4783842761797249497e-965j)  +/-  (5.44e-241, 5.44e-241j)
| (-0.99828029537769456017 - 7.9014439724858778469e-979j)  +/-  (1.85e-241, 1.85e-241j)
| (0.84063368496338677751 + 1.9463134835451948085e-985j)  +/-  (4.3e-242, 4.3e-242j)
| (0.96127891496452473422 + 2.2520820799666730575e-986j)  +/-  (7.83e-241, 7.83e-241j)
| (-0.87953320567409313479 - 1.8414359647356766211e-991j)  +/-  (1.24e-241, 1.24e-241j)
| (-0.74677180221832073614 + 7.6158876722043916104e-997j)  +/-  (3.24e-243, 3.24e-243j)
| (0.97851071377793355581 + 2.553872949757520777e-994j)  +/-  (8.2e-241, 8.2e-241j)
| (0.87953320567409313479 + 3.9275117931629749252e-995j)  +/-  (1.28e-241, 1.28e-241j)
| (0.7961868862601447813 + 9.4810980399143060887e-997j)  +/-  (1.31e-242, 1.31e-242j)
| (-0.37491479569986842758 + 2.387472477668420781e-1003j)  +/-  (1.32e-248, 1.32e-248j)
| (-0.7961868862601447813 - 2.3201003715154053518e-998j)  +/-  (1.23e-242, 1.23e-242j)
| (-0.84063368496338677751 + 1.0460398506137296806e-1005j)  +/-  (4.08e-242, 4.08e-242j)
| (0.74677180221832073614 - 4.6275378722999587101e-1010j)  +/-  (3.05e-243, 3.05e-243j)
| (0.69311793494118157127 - 3.6457373202158413188e-1011j)  +/-  (7.18e-244, 7.18e-244j)
| (0.15655801081562154215 + 1.072522518768304583e-1020j)  +/-  (6.16e-253, 6.16e-253j)
| (-0.69311793494118157127 + 2.4743782176525443556e-1011j)  +/-  (7.32e-244, 7.32e-244j)
| (-0.57735026918962576451 - 4.4828358417425121478e-1014j)  +/-  (2.66e-245, 2.66e-245j)
| (0.23258688052317872059 - 8.9355499818290439337e-1021j)  +/-  (1.81e-251, 1.81e-251j)
| (0.63617777805726890931 + 8.1361726385644267459e-1014j)  +/-  (1.47e-244, 1.47e-244j)
| (0.43693939954921891801 - 1.5218025467269456086e-1016j)  +/-  (3.11e-247, 3.11e-247j)
| (-0.15655801081562154215 + 3.8617028456872299687e-1021j)  +/-  (7.11e-253, 7.11e-253j)
| (-0.63617777805726890931 - 1.0995348800114065685e-1016j)  +/-  (1.4e-244, 1.4e-244j)
| (-0.23258688052317872059 - 1.9220398611100642642e-1021j)  +/-  (1.82e-251, 1.82e-251j)
| (0.47886125467391336044 - 3.035697976979834786e-1017j)  +/-  (2.06e-246, 2.06e-246j)
| (0.57735026918962576451 - 9.9317707632771409178e-1017j)  +/-  (2.86e-245, 2.86e-245j)
| (-2.2097316026680357697e-1025 - 2.1631523890743070415e-1026j)  +/-  (9.55e-1024, 9.55e-1024j)
| (-0.52014184021459586686 + 1.1080873803369083311e-1019j)  +/-  (6.68e-246, 6.68e-246j)
| (-0.43693939954921891801 + 2.4261923198492201674e-1022j)  +/-  (2.97e-247, 2.97e-247j)
| (0.078719371864730251469 + 1.5812962524971180059e-1029j)  +/-  (2.95e-254, 2.95e-254j)
| (0.52014184021459586686 + 5.541203551854658934e-1023j)  +/-  (6.89e-246, 6.89e-246j)
| (0.30578417921728074886 - 7.964682769334054584e-1027j)  +/-  (5.28e-250, 5.28e-250j)
| (-0.30578417921728074886 - 9.1578744018002352357e-1025j)  +/-  (4.53e-250, 4.53e-250j)
| (-0.47886125467391336044 + 5.4849456808427325654e-1031j)  +/-  (2e-246, 2e-246j)
| (-0.078719371864730251469 - 1.6293585203671567729e-1035j)  +/-  (2.95e-254, 2.95e-254j)
| (0.37491479569986842758 - 6.0156490028438116968e-1046j)  +/-  (1.27e-248, 1.27e-248j)
-------------------------------------------------
The weights are:
| (0.014982433111327931698 - 8.9507739228108844038e-907j)  +/-  (3.85e-66, 5e-183j)
| (0.0099846054212444754577 + 6.6169193335189385265e-909j)  +/-  (1.36e-66, 1.76e-183j)
| (0.024237547798648933491 - 1.7268437465644878196e-906j)  +/-  (1.06e-66, 1.38e-183j)
| (0.0044005137051169653483 - 1.7577317248561031925e-909j)  +/-  (1.01e-66, 1.31e-183j)
| (0.024237547798648933491 - 3.5113614568337105654e-908j)  +/-  (2.03e-67, 2.64e-184j)
| (0.029931800983140164318 + 4.4267057231111677175e-908j)  +/-  (1.29e-67, 1.67e-184j)
| (0.019443135360818683932 + 2.7653943221039376268e-906j)  +/-  (6.88e-68, 8.94e-185j)
| (0.029931800983140164318 + 1.2678603276099227074e-906j)  +/-  (1.25e-68, 1.62e-185j)
| (0.0099846054212444754577 - 1.0391211988758355502e-906j)  +/-  (7.99e-69, 1.04e-185j)
| (0.0044005137051169653483 + 1.7575831095215676825e-907j)  +/-  (2.8e-69, 3.64e-186j)
| (0.041758102849070181169 + 6.4758776067658867095e-908j)  +/-  (5.85e-72, 7.61e-189j)
| (0.019443135360818683932 + 2.4565920908205008889e-908j)  +/-  (7.11e-71, 9.25e-188j)
| (0.035970751024870804203 - 9.9748834951265173008e-907j)  +/-  (3.55e-71, 4.62e-188j)
| (0.051670979794316477957 + 8.5075313916994011313e-907j)  +/-  (4.62e-73, 6e-190j)
| (0.014982433111327931698 - 1.4359452101498712766e-908j)  +/-  (2.89e-71, 3.76e-188j)
| (0.035970751024870804203 - 5.3135940525289012412e-908j)  +/-  (1.63e-72, 2.13e-189j)
| (0.047038811200711576942 - 8.3058839233741035458e-908j)  +/-  (5.69e-74, 7.39e-191j)
| (0.066496779422619324486 - 1.8286573640248507877e-906j)  +/-  (3.58e-77, 4.65e-194j)
| (0.047038811200711576942 - 8.0847536307718570205e-907j)  +/-  (8.26e-75, 1.07e-191j)
| (0.041758102849070181169 + 8.5442488691338461297e-907j)  +/-  (2.87e-74, 3.73e-191j)
| (0.051670979794316477957 + 1.1427265079732377293e-907j)  +/-  (5.27e-76, 6.85e-193j)
| (0.055480656980511512416 - 1.7113869076479513063e-907j)  +/-  (5.06e-77, 6.58e-194j)
| (0.077094907300506992942 + 3.5463063181850562233e-907j)  +/-  (5.82e-80, 7.57e-197j)
| (0.055480656980511512416 - 1.0024091694007140933e-906j)  +/-  (1.88e-77, 2.44e-194j)
| (0.059034258084223677258 - 2.1035391359548668138e-906j)  +/-  (8.62e-79, 1.12e-195j)
| (0.074793375656648522718 - 4.1489629921092364448e-907j)  +/-  (1.99e-80, 2.58e-197j)
| (0.058179144861215203128 + 2.8423758730496500434e-907j)  +/-  (3.19e-79, 4.14e-196j)
| (0.05519950899261649427 + 1.481415125740789991e-906j)  +/-  (8.99e-81, 1.17e-197j)
| (0.077094907300506992942 + 4.8972421102737593763e-907j)  +/-  (4.81e-82, 6.26e-199j)
| (0.058179144861215203128 + 1.3406690191878685682e-906j)  +/-  (4.7e-80, 6.11e-197j)
| (0.074793375656648522718 - 6.7363434101075520264e-907j)  +/-  (5.13e-82, 6.68e-199j)
| (0.032109027375116059432 - 1.8579333623078588548e-906j)  +/-  (1.54e-81, 2.01e-198j)
| (0.059034258084223677258 - 5.423728110843430964e-907j)  +/-  (2.97e-81, 3.87e-198j)
| (0.078864517832324657989 + 3.464231515916797221e-907j)  +/-  (2.85e-83, 3.71e-200j)
| (0.052927434469840109776 + 4.0561343871116068595e-906j)  +/-  (1.54e-82, 2.01e-199j)
| (0.05519950899261649427 + 3.8718247302308334722e-906j)  +/-  (5.6e-83, 7.28e-200j)
| (0.078428255085479012173 - 3.3455318087267050632e-907j)  +/-  (6.34e-84, 8.24e-201j)
| (0.052927434469840109776 + 1.2405849141542540881e-906j)  +/-  (4.73e-83, 6.15e-200j)
| (0.07140571160579456789 + 5.4212095009593794641e-907j)  +/-  (3.07e-84, 3.99e-201j)
| (0.07140571160579456789 + 1.0349571955692671123e-906j)  +/-  (1.58e-84, 2.06e-201j)
| (0.032109027375116059432 - 5.4191993049175794906e-906j)  +/-  (7.71e-84, 1e-200j)
| (0.078428255085479012173 - 3.9309078848655760715e-907j)  +/-  (4.61e-85, 5.98e-202j)
| (0.066496779422619324486 - 8.1553813841935797749e-907j)  +/-  (1.01e-84, 1.31e-201j)
