Starting with polynomial:
P : 5/2*t^3 - 3/2*t
Extension levels are: 3 18 22
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P1 : 5/2*t^3 - 3/2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P2 : 5/2*t^21 - 492974097/38114128*t^19 + 1092720951/38114128*t^17 - 62676676797/1762778420*t^15 + 104814789093/3878112524*t^13 - 239868945099/18495613576*t^11 + 190151996979/48761163064*t^9 - 17182210131/24380581532*t^7 + 42668603943/609514538300*t^5 - 107290416779/33645202514160*t^3 + 479989951/11215067504720*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 5/2*t^43 - 88186444764315217611843095555521587690799414053147879926410892410827896054407913547944858522059749780552782483/3251837442113635427153919942607500210649489840377556518165782073609838642813535557169513764276317943602810672*t^41 + 8012264149779481236318049782373213159109936363964618512260306206509746539568623881306840719228975038012478824521/58533073958045437688770558966935003791690817126796017326984077324977095570643640029051247756973722984850592096*t^39 - 1638479810486437760498107329226996319982472287865658552941291157541814339008261387213423326857624870028020445441/3838574506287985101886761222574610316009500591441780647108136939071521687546640696694250561871725895851598560*t^37 + 867996566660490583575845876696447463343943066324233895236633559381262670835637739741794459491396748725930559726633467/942765206977334151574094114560898905301783211084168006770043156206948396619939889806376577814918691321764709693920*t^35 - 3756941176802135826528008773478659716728222357477828553864269087375545687785015287309834629667060726247900952933813680251/2577708628917427037233888128032409786876135655746332164110651997701038306038239646708594839061550685811969069245116064*t^33 + 151914677784456496098243684931116622638883338679496865684991855224783214660616518555488852911320016300994157031556556546963/86646160503838058819748194121816683517950105337473301607264870559087173968876282670045721976637124188997778486671060424*t^31 - 307795225452439297277127615199942551311993912944050911764792478382922986446278298847679174575046610709402184607842139859784097/187985832806665687807735622324226602689250652731691672458058496748146001923377811081911778160731711663852373796065661643128*t^29 + 33318685285176206700201806009128596640655497570725186906356091905229715355317819067171377536472623655378675771690035852390571553/27711704663741235013036889152967887120570570359585582750282761158562902007670349737074925918521657495274789585454507018081800*t^27 - 1931833409951959689969177808013171404429517591432333701013128395956437968418468816614016223360718719814636083565671139737845774656911/2763951567309218909582792805672440577462148402379886230721827456574484564794036847600984573650390857749959875858439802729969691100*t^25 + 11031948203331092399844940285494290007042384222080530865837767925317611456286978657710056864657811958546750212624064552385949817198324219/34232756299814292251503105327087672425722791308771938117431350653755884108182655733751138377872496945210663044852154670323875810937584*t^23 - 453804740241924698961932761216667816560801109190611761445676069564725453303467840695264454458966687785861806365471661963140297206955163/3859699125918634277435501190158005807763881407694993759739864885795615525830468922081005285051210046143869893782151558260540161439536*t^21 + 365680012087117870586125462655994560267105292704574942799114729605288334158405250500563413696136216720560352266635459959258896891975639/10843916591866639160414027153301063936098523954952601515459620393425776953523698400132348181810542510594682082530806758922469977377744*t^19 - 420759514422391430296571837823320681353174235599795397612006945905541638137056108308801362587552553565989587091756597324206181965597/55954161980736012179638942999489493994316429076122814837252943206531356829327649123489928698712809652191342015122841893304798644880*t^17 + 1399294096324799470310836557644350347217319657030480017739059706585826754656423597487240925098520368864503936035879706270925656995809/1091106158624352237502959388490045132889170366984394889326432392527361458171889157908053609624899788217731169294895416919443573575160*t^15 - 6308164446426024289129195136421625030497533582231975208047988823145360401473041021457518913164396081652940835971613028817792043531/38598888010439927045954321696258006874045401074545738370782962517047902083959920666543052509112056827867586779923723136567886522824*t^13 + 240093880966180187919444829822334962377523078641911908410762488225583944029231476256174594177848904501085373376842337193523844461509/15941340748311689869979134860554556838980750643787389947133363519540783560675447235282280686263279469909313340108497655402537133926312*t^11 - 8329672436450669111527808781280720208195208531618492550916744901571608878124415731309168913321065895702071909758453985667631243563/8695276771806376292715891742120667366716773078429485425709107374294972851277516673790334919779970619950534549150089630219565709414352*t^9 + 221721652019643817699415474866257500798028284676440849186995745581351547821795414284439533956262952377541370624516259750010322113/5651018447085904928180139287332089902897693195625032456959797245348934138146813771226423113483838348395525597980142107689864507166560*t^7 - 16993699496896892386539037154573750890468337544403823501118881112510742009351802340405909532129235092413286421839444916350792363/18336978226258344562870247891546985603280269757232248176665464530826133223782518155612270919263883620303848368955971329034458298764960*t^5 + 29731237943723201170363927581221467729466965216672635474582269668469866125233819191731458813886057645472702316712362070193492051/2871570790232056758545480819816257945473690243982570064465811745527372462844342343168881625956724174939582654578505110126796169586592736*t^3 - 232019873271156359790595157336686293162060178708399486327569234244649345848079926911391178311675499171024198664550178091449981/6700331843874799103272788579571268539438610569292663483753560739563869079970132134060723793899023074859026194016511923629191062368716384*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:
| (-0.96863851499355040942 - 2.0720785110092411055e-920j)  +/-  (3.3e-240, 3.3e-240j)
| (-0.9990130266325466666 - 1.5513191062053301069e-922j)  +/-  (1.33e-240, 1.33e-240j)
| (-0.92316618973895636051 - 2.2393558514146016503e-927j)  +/-  (1.1e-240, 1.1e-240j)
| (0.9990130266325466666 + 4.9117272888239382034e-924j)  +/-  (1.4e-240, 1.4e-240j)
| (0.8930681618696741024 + 3.1459663353983424358e-939j)  +/-  (4.83e-241, 4.83e-241j)
| (0.96863851499355040942 - 2.0471871148490326575e-950j)  +/-  (3.44e-240, 3.44e-240j)
| (-0.81860060849733478918 - 1.1989177633138055654e-966j)  +/-  (5.04e-242, 5.04e-242j)
| (-0.8930681618696741024 - 2.6718908822022248886e-964j)  +/-  (4.88e-241, 4.88e-241j)
| (-0.9940396115810441603 + 2.0696594449615655207e-962j)  +/-  (3.39e-240, 3.39e-240j)
| (0.94835757651647283262 + 2.2440045007133781416e-975j)  +/-  (2.14e-240, 2.14e-240j)
| (0.85815313192946415361 - 1.8674716276446627823e-992j)  +/-  (1.72e-241, 1.72e-241j)
| (0.9940396115810441603 - 6.3661972166288518786e-1001j)  +/-  (3.59e-240, 3.59e-240j)
| (-0.94835757651647283262 - 4.8495398504021987992e-1012j)  +/-  (2.19e-240, 2.19e-240j)
| (-0.85815313192946415361 + 1.6159564058219765314e-1015j)  +/-  (1.67e-241, 1.67e-241j)
| (-0.074149897046529985022 + 9.7911039554193805899e-1029j)  +/-  (2.69e-254, 2.69e-254j)
| (0.81860060849733478918 - 2.120356533740573831e-1014j)  +/-  (4.83e-242, 4.83e-242j)
| (0.92316618973895636051 + 1.1130946471526716588e-1021j)  +/-  (1.12e-240, 1.12e-240j)
| (-0.29239730601748887918 - 3.9545990901867994018e-1037j)  +/-  (1.61e-250, 1.61e-250j)
| (-0.72632446049439515791 + 1.0680128865784048741e-1028j)  +/-  (2.28e-243, 2.28e-243j)
| (-0.98393195261383823874 - 7.2245668293605257677e-1029j)  +/-  (3.96e-240, 3.96e-240j)
| (0.49574951572269775249 + 1.746129416677504006e-1038j)  +/-  (5.53e-247, 5.53e-247j)
| (0.77459666924148337704 + 7.6910667551641490444e-1035j)  +/-  (1.28e-242, 1.28e-242j)
| (0.43027365915780572809 + 1.4468823112431967489e-1045j)  +/-  (4.68e-248, 4.68e-248j)
| (-0.61794311282460414893 + 8.1032743609634225141e-1044j)  +/-  (5.2e-245, 5.2e-245j)
| (-0.77459666924148337704 - 3.7403278043680480933e-1042j)  +/-  (1.21e-242, 1.21e-242j)
| (0.98393195261383823874 + 2.260691570981132198e-1042j)  +/-  (3.88e-240, 3.88e-240j)
| (0.67401253888417823604 - 1.0778919311950452868e-1047j)  +/-  (3.84e-244, 3.84e-244j)
| (0.72632446049439515791 + 2.2126964033187223562e-1050j)  +/-  (2.36e-243, 2.36e-243j)
| (6.2303560462833989044e-1073 + 9.0073240652066901924e-1073j)  +/-  (4.71e-1071, 4.71e-1071j)
| (-0.67401253888417823604 + 2.5230090397828358231e-1053j)  +/-  (3.92e-244, 3.92e-244j)
| (-0.36236130384595011635 - 5.2900497528656093483e-1060j)  +/-  (2.97e-249, 2.97e-249j)
| (0.074149897046529985022 + 8.496759582932205149e-1065j)  +/-  (2.26e-254, 2.26e-254j)
| (0.61794311282460414893 - 1.0633308782781393779e-1054j)  +/-  (5.28e-245, 5.28e-245j)
| (0.14788136810434884046 - 1.0687677754336872135e-1064j)  +/-  (4.93e-253, 4.93e-253j)
| (-0.43027365915780572809 + 2.5614584203399053174e-1060j)  +/-  (4.38e-248, 4.38e-248j)
| (-0.55841853871864983226 + 2.8822829560807248057e-1059j)  +/-  (5.96e-246, 5.96e-246j)
| (0.22077021219003756334 + 2.2755384410824253854e-1063j)  +/-  (9.68e-252, 9.68e-252j)
| (0.55841853871864983226 - 7.2427000384973796605e-1059j)  +/-  (5.86e-246, 5.86e-246j)
| (0.29239730601748887918 - 7.2393491359523208576e-1064j)  +/-  (1.75e-250, 1.75e-250j)
| (-0.14788136810434884046 + 3.2026849176652961966e-1067j)  +/-  (4.14e-253, 4.14e-253j)
| (-0.49574951572269775249 + 1.9384996103698715837e-1060j)  +/-  (5.49e-247, 5.49e-247j)
| (-0.22077021219003756334 + 2.4672677869773256953e-1066j)  +/-  (8.48e-252, 8.48e-252j)
| (0.36236130384595011635 + 2.272530350691826758e-1062j)  +/-  (2.98e-249, 2.98e-249j)
-------------------------------------------------
The weights are:
| (0.017813952893785077277 - 2.0476711726903609705e-921j)  +/-  (8.3e-78, 5.73e-193j)
| (0.0026617889964950861575 - 2.1365070907283060729e-921j)  +/-  (2.59e-78, 1.79e-193j)
| (0.027649021313224054814 - 1.1477368832558279555e-920j)  +/-  (2.43e-78, 1.68e-193j)
| (0.0026617889964950861575 + 2.5075889638044012165e-923j)  +/-  (2.4e-79, 1.66e-194j)
| (0.032531813429758549638 + 3.0835346014669929027e-922j)  +/-  (1.18e-79, 8.15e-195j)
| (0.017813952893785077277 - 1.8659142718319854126e-922j)  +/-  (7.99e-80, 5.52e-195j)
| (0.041807558748801225577 + 4.364438659228832852e-921j)  +/-  (2.31e-79, 1.6e-194j)
| (0.032531813429758549638 + 7.6400993336126905701e-921j)  +/-  (8.79e-79, 6.07e-194j)
| (0.007472563950188274285 + 7.0828852685429760812e-921j)  +/-  (1.37e-78, 9.43e-194j)
| (0.022736637760304238617 + 2.3294830570747476781e-922j)  +/-  (2.21e-80, 1.53e-195j)
| (0.037266423512152878636 - 3.3850903525295556685e-922j)  +/-  (3.38e-81, 2.33e-196j)
| (0.007472563950188274285 - 8.0326519772115482203e-923j)  +/-  (1.47e-80, 1.01e-195j)
| (0.022736637760304238617 + 2.2293212573328037151e-920j)  +/-  (2.5e-79, 1.72e-194j)
| (0.037266423512152878636 - 5.6206643463972548311e-921j)  +/-  (3.9e-80, 2.69e-195j)
| (0.074010973440796506113 + 8.0473724370459439109e-922j)  +/-  (3.11e-84, 2.15e-199j)
| (0.041807558748801225577 + 3.6521779847276506923e-922j)  +/-  (2.99e-82, 2.06e-197j)
| (0.027649021313224054814 - 2.7363543117525844445e-922j)  +/-  (5.23e-81, 3.61e-196j)
| (0.070860908095510444666 - 1.0680453883453506116e-921j)  +/-  (1.33e-84, 9.16e-200j)
| (0.050335499902022833397 + 2.8767419871484275604e-921j)  +/-  (4.53e-83, 3.13e-198j)
| (0.012734248983796552195 - 1.81673247703986811e-920j)  +/-  (2.9e-80, 2e-195j)
| (0.06413179469971093787 + 4.931684803233075917e-922j)  +/-  (1.77e-85, 1.22e-200j)
| (0.046170935878571123623 - 3.8895781261673996426e-922j)  +/-  (9.23e-84, 6.38e-199j)
| (0.066757780967964901355 - 5.1670933783398360873e-922j)  +/-  (4.53e-86, 3.13e-201j)
| (0.057847719023109082579 + 2.0427233235483793378e-921j)  +/-  (4.03e-85, 2.78e-200j)
| (0.046170935878571123623 - 3.5030819852918488592e-921j)  +/-  (5.09e-83, 3.52e-198j)
| (0.012734248983796552195 + 1.3635746556389783657e-922j)  +/-  (1.16e-82, 8.01e-198j)
| (0.054240530437645388052 - 4.3079151123905577678e-922j)  +/-  (1.26e-85, 8.69e-201j)
| (0.050335499902022833397 + 4.1044683213261089531e-922j)  +/-  (5.92e-85, 4.09e-200j)
| (0.074219237735797928649 - 7.4293358786224511672e-922j)  +/-  (2.66e-88, 1.84e-203j)
| (0.054240530437645388052 - 2.4056577336210943229e-921j)  +/-  (3.98e-86, 2.75e-201j)
| (0.069002567701666013858 + 1.1925699527840256329e-921j)  +/-  (3.32e-88, 2.3e-203j)
| (0.074010973440796506113 + 6.9022550089648739199e-922j)  +/-  (7.81e-89, 5.4e-204j)
| (0.057847719023109082579 + 4.5093821240006503193e-922j)  +/-  (7.82e-88, 5.4e-203j)
| (0.073381036795249722082 - 6.4507470098016052919e-922j)  +/-  (2.28e-89, 1.58e-204j)
| (0.066757780967964901355 - 1.3435557211175686665e-921j)  +/-  (1.99e-89, 1.37e-204j)
| (0.061150108261918899481 - 1.7570700592892198018e-921j)  +/-  (4.97e-89, 3.43e-204j)
| (0.072326516339429245402 + 6.0622513334024671604e-922j)  +/-  (2.44e-90, 1.68e-205j)
| (0.061150108261918899481 - 4.7151562686918051322e-922j)  +/-  (8.2e-90, 5.66e-205j)
| (0.070860908095510444666 - 5.725124881854482389e-922j)  +/-  (9.01e-91, 6.24e-206j)
| (0.073381036795249722082 - 8.7770061800312133068e-922j)  +/-  (2.65e-91, 1.85e-206j)
| (0.06413179469971093787 + 1.5284820503379654214e-921j)  +/-  (2.56e-91, 1.78e-206j)
| (0.072326516339429245402 + 9.6442801009464438531e-922j)  +/-  (1.66e-91, 1.16e-206j)
| (0.069002567701666013858 + 5.4292971645925591865e-922j)  +/-  (1.19e-91, 7.76e-207j)
