Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 4 16 22
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 16 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 22 Kronrod extension for:
P3 : 3/2*t^22 - 21703940836137923/2794208237943850*t^20 + 42027029201559237/2431716358426810*t^18 - 262592289065984469/12158581792134050*t^16 + 662392414045240323/39845409473079301*t^14 - 3613046556074683491/444429567199730665*t^12 + 577469291852421331/229877362344688275*t^10 - 1047921046375098841/2222147835998653325*t^8 + 25219697121887517513/511094002279690264750*t^6 - 345233232267838651/143106320638313274130*t^4 + 76767549244621411/2146594809574699111950*t^2 - 2147720438279/511094002279690264750
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^44 - 11161971547131484425715468640881380044567344581596880471992287041047534655876882233710733159256609484831366014781182427624033254198010855587882154950545617122897669068472807346807891145986545856911154755027271424559857/685397183779311920071006963989637017948477101795615166075170050756880156708760902769880264858340549242701763104428919788593819982341721148767387254523925841092654164638623498867737358723116250771311689801145811011650*t^42 + 2657085631367615609089163520136036273099482857042698329699545760313337770529234525551851985560943473192291476197293605157761954116256055826378357599672956496188606427235264133690578937818574869835212878173862827408399639863/32256881094214721738785706649023018177514931426055904639784317131456453589826205038322424655284903627084845891703889687567653808064069512264495583793184132782555343567663861562504951008091323676696621145486437554656455250*t^40 - 9401587080918869423498454710187120805649983768912723152546323069693449068955622399720351793952682315536107645095248182534609262566843742074817291924848793406246045248605751403227706230271091010284279799172647725231817210081/36475088621919723812319222133895259016113037843309369092679189371723835982341939543333818648668314101395941123695936800557270075272447833099083467827677442454120273111127597305294059986072496772880025449126971696419222475*t^38 + 28460267606991421616669283175927613133708394237741509356685263922651246194654732642115616594227974971476399024030009380284275159021683338961691143027834284809481857132030244777634918487609819339737309106146608063576214627356/50933682309887902620806120997781667995473160952368938823110579753308059254621627290240917932825123294742079947503335171949341096101165893066287725344954987210708489479502500741626840521092225223391026528060185702207022375*t^36 - 67199806984844125972268454861463537033235554185917090869620742579672733166116785110820458930035690436460705863277436192930855696847483091746283849357882807372925751089214591017645181076600330145318274199119053482339639441/75455379785280027381337769606685314391393408475834549608960527845824306831704282977036940055269524433476555821184476513321799789887043033328514931164143681086590186452737989911224662211012466168340005073369537706010250*t^34 + 42036116352124904560355709552494361782301811030360884308631823270588172766597082984523395466206646523310182362375976210306565527406655265289951041775063606818229621802880986099275507564652594542133682854923826684151824810419/38892217920659502113254197714272500547803875842060988020111888069332708551288110922464073469154421877161599422099185344183166338367444880811960879353038458021398135103956251266575565058962858812034716614983772051601216525*t^32 - 1221568264944227447517492690018256125911654865517342386551098119696228651720897089382702378567431275300014061032595533093624485945644457805863159498894997271287154015906902700632150370822453711911681391978734739813542694133447/1196876641816424677936919503852127920084028953333102663586669071553013030900930897420346002889461886155231156409116865108088409251694916654664860609767699643626252286747556893816551260201631203441326440344984468942824534350*t^30 + 91957704838174456543084400030263853169604442455630188065640440771858463684704506431245172122219382301070458348914255613741248268663765818176795295904329258877829008719178657897915443364262887188177739644303717779433840211040339/121028991452643633381035049829185004332634996746528398654065760425145197004033788161557401843908516591386736764473627825154112418296391141027748404763578593273585683823696916935070226570389086347989302976264377764649411964875*t^28 - 3063300305200323873119450201000031300420610355182244609855644038451479364090176620742392528510981609320144288157187210353990018078587460239454532586898136732093534599465511408287154023854796605651694809262949744687490660430121/6821279711501654055291830505670652418103421716793065946686476030402708365766799654838178847885343125118415115550043436200312294106881948367103372249154993179670690714701114481042605362260254464057368122655802289472994233125*t^26 + 3027072239003791674561557559056328671402703176856437044225773270983405736402429234625964291342997473873396445224963533682791527191750965422335759101848658195856869129401690754378491312162770200106858739512759971472288197389791989/14331203722536696272692722845873787218915420874011363158098904862124142861278517676712797464352729855239961334506651963397355410074822430561592479297656443153145971207766854886611361373163187699961431390419063056668643267582850*t^24 - 1147179253209199953219092713296141866845706258273042734197936249417182085049094448732656085487645584573291391519777688610588025540259353606924384260886097561246028615186305499941426405009659521914598191488033725860797932164046448064/14538383080699455034026215469623919142841045980124788299406204247630937535251348421387015079870003015103756427712019866781251961111773667872972022748372563472642537965444353984428677793014351174319569474650121250857439958298993375*t^22 + 920627075186998008069911605677457604084279727933577654570661012682451909866247294721006554038072115575779078277686258080222572601107251406969289840370053562071528996252133405558553153990267540123405314816717598637998676451973503/39560226069930489888506708760881412633581077496938199454166542170424319823813192983366027428217695279193895041393251338180277445202105218701964687750673642102428674735903004039261708280311159658012433944626180274442013491970050*t^20 - 20292193497739394383066325840841462891882038466313239497338498773977062439974037088970368673355556067488791392446297212513474822705790827580006839469191907837460117936235625937249079504183291188825992710153890885700756257260608071/3784594960690016866000475138124321808612589747207087747781932534303926596478128795408683290632826181709549292293287711352579875591001399255821288461481111761132343216401387386422703425483100940616522847369237912921619290731801450*t^18 + 20620379785019286462394739960422660138349471919619292175842415116971116705919764903730949014103991642970764857229746904397411684720107479561627603137943640691644170667595186984347971136996040960179300229967738004879568908006669538/21705765215722155555002725056889492725866323550158297376984613064390167244506915150138036519805914865687120941093855991580972815889566848673092683823200493924141380211713839422130210822623667159418292801088276265285757696844155375*t^16 - 13551987086100176975984085109103245533170646712696520312150230231675888318636386713616957522956452969399219555928094154506571053400016139319328380296098055083147052177768856348693708511746356436873888686911522562326620539865047669/107081775064229300738013443613988164114273862847447600393124091117658158406234114740680980164375846670723129976063022891799465891721863120120590573527789103359097475711121607815842373391610091319796911152035496242076404637764499850*t^14 + 1517291474811817774829327451300104572454339094934015990469693509381299199371297503672944763808065239625762168953026062002487976181964297571968201478458089228515195066207221869503302921602284718669245946434217340984923439326122959/123555894304879962390015511862294035516469841747054923530527797443451721237962440085401130958895207696988226895457334105922460644294457446292989123301295119260497087358986470556741200067242413061304128252348649510088159197420576750*t^12 - 86068434545215047762033883493707909313655559614104571438368725691619321713799991927668703690872797671049220132627350967556743288918586630253400106291362386131698515732569218309506580246130496115578297162445443395974274889980933/103786951216099168407613029964326989833834667067526135765643349852499445839888449671736950005471974465470110592184160648974866941207344254886110863573087900178817553381548635267662608056483626971495467731972865588474053725833284470*t^10 + 1415253046411873960799209838065762048186892133502746002362659037279623876046680583678910427231388479825640323502720525831018363580730408545709030743587413374173322504815930864237856128691800765326304915168369024109142183758367/38857433426317321505265747933504066242136167621899881748006568181491338418315723910916007852290231985864413385962668842007498492481010530210983535878813102723953431821594295812772232484915367585946370769216894121288594993971398775*t^8 - 41998617833730908005222461775626808822241922849393686611980197973249410653644742451837463287792494201075762902640737906692257663623593406508466992497439495448887107382971920104768624862604884684339060394400798988470066957164812/44959636491940011076347787328367612971385918843339057055168007817339825135232856472028225820114177600787406467697010408114594429208385551230851256462230793039480404431128338798063708586372995209902642668586771677682793738432825582625*t^6 + 7846751517784804287036079514355355306319518417386543914014716286104763796884622897152566615157572183640243175239983353443538430878586394520648642616277194760087730635452735192098202340343401636091241376271331475801371709248151/679789703758132967474378544404918308127355092911286542674140278198178156044720789857066774400126365323905585791578797370692667769630789534610470997708929590756943714998660482626723273825959687573727957149031987766563841325104322809290*t^4 - 630977307399777036731964275577616037539896394405932741156831893451373451065768161008995674488911474486433760952313923308152142360601005805694844486469197112985223941682451705944779706029632911444079615502517984977337779767469/14162285494961103489049553008435798085986564435651802972377922462462044917598349788688891133335965944248033037324558278556097245200641448637718145785602699807436327395805426721390068204707493491119332440604833078470080027606340058526875*t^2 + 933734220991223947477716046139786117792162838633584404633976507182174403289733247108028782349181367700367900786467274821906756191285717810487203002963734847228710267695759342679103359577073947440618053738331448890278792/182483230467285927309882195626903840883860494128846760988623090552732231431239240974702798916934014967901826251240806950582765624434035472642866864464348512924949876808697375121552699556455098204898961419558073280006633408933233247125
-------------------------------------------------
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:
| (-0.99297295782023808726 + 9.2986638744996591278e-938j)  +/-  (1.9e-240, 1.9e-240j)
| (-0.010883346134298060289 - 7.6547478096794017495e-950j)  +/-  (1.18e-255, 1.18e-255j)
| (-0.91248695683407599658 - 3.2223149491799372121e-940j)  +/-  (1.06e-240, 1.06e-240j)
| (0.99297295782023808726 - 3.6960863763933484929e-940j)  +/-  (1.78e-240, 1.78e-240j)
| (0.98118099749353905881 + 1.9179659954039428294e-956j)  +/-  (2.51e-240, 2.51e-240j)
| (0.94030397197484975539 + 1.4765171285183845772e-971j)  +/-  (1.72e-240, 1.72e-240j)
| (-0.94030397197484975539 - 2.9689723981427289393e-981j)  +/-  (1.66e-240, 1.66e-240j)
| (-0.88059034847484895104 + 2.4331735747569684687e-982j)  +/-  (5.4e-241, 5.4e-241j)
| (0.15655801081562154215 + 5.6520401129549768063e-995j)  +/-  (5.5e-253, 5.5e-253j)
| (-0.9988182618907404702 - 2.7618038853684118265e-982j)  +/-  (7.27e-241, 7.27e-241j)
| (0.80812924328754771174 - 2.0539637366328335847e-983j)  +/-  (1.1e-241, 1.1e-241j)
| (-0.15655801081562154215 - 6.1803194250320390293e-999j)  +/-  (6.14e-253, 6.14e-253j)
| (-0.98118099749353905881 + 7.7699424976912651769e-988j)  +/-  (2.54e-240, 2.54e-240j)
| (-0.84532601780352374363 + 3.0550375487773091035e-990j)  +/-  (2.89e-241, 2.89e-241j)
| (0.96343728160335037502 - 8.3859893805665422735e-989j)  +/-  (2.19e-240, 2.19e-240j)
| (0.84532601780352374363 + 9.9458173343211390719e-1002j)  +/-  (2.9e-241, 2.9e-241j)
| (0.88059034847484895104 - 4.8092901306001053676e-1007j)  +/-  (5.77e-241, 5.77e-241j)
| (0.51560983185369037392 - 9.7935291384902820973e-1019j)  +/-  (1.8e-246, 1.8e-246j)
| (-0.80812924328754771174 - 6.2961383867505766412e-1013j)  +/-  (1.17e-241, 1.17e-241j)
| (-0.96343728160335037502 + 2.7319391454590742469e-1013j)  +/-  (2.15e-240, 2.15e-240j)
| (0.68481696369423821128 + 5.1024586151935438286e-1016j)  +/-  (1.67e-243, 1.67e-243j)
| (0.73005911348187219287 - 9.3745741359481017208e-1014j)  +/-  (9.3e-243, 9.3e-243j)
| (0.44953072961765315134 + 8.3638070586900647389e-1023j)  +/-  (1.05e-247, 1.05e-247j)
| (-0.73005911348187219287 - 1.0121039009418312791e-1021j)  +/-  (1.05e-242, 1.05e-242j)
| (-0.77028730284858275563 + 4.8237253142519819526e-1021j)  +/-  (3.84e-242, 3.84e-242j)
| (0.010883346134298060289 - 1.8061976360949416623e-1024j)  +/-  (1.18e-255, 1.18e-255j)
| (0.77028730284858275563 - 2.0263848739195206893e-1019j)  +/-  (3.91e-242, 3.91e-242j)
| (-0.68481696369423821128 - 5.7766026082774058573e-1033j)  +/-  (1.74e-243, 1.74e-243j)
| (0.9988182618907404702 + 3.8236640446206415578e-1035j)  +/-  (7.31e-241, 7.31e-241j)
| (-0.63391240132195075352 - 8.970313089708796689e-1058j)  +/-  (2.09e-244, 2.09e-244j)
| (-0.37992906516324059686 - 3.2849645002349959001e-1062j)  +/-  (6.01e-249, 6.01e-249j)
| (0.91248695683407599658 - 3.75444101321897765e-1060j)  +/-  (1.09e-240, 1.09e-240j)
| (0.63391240132195075352 - 1.8760518124839830738e-1070j)  +/-  (2.13e-244, 2.13e-244j)
| (0.23280045503407815822 + 1.8681637389635792829e-1078j)  +/-  (1.26e-251, 1.26e-251j)
| (-0.51560983185369037392 - 4.5402157987129481339e-1071j)  +/-  (1.65e-246, 1.65e-246j)
| (-0.44953072961765315134 - 3.0272969272323007238e-1073j)  +/-  (1.1e-247, 1.1e-247j)
| (-0.079727518863151580004 - 1.6123767260873912491e-1081j)  +/-  (2.41e-254, 2.41e-254j)
| (0.57735026918962576451 + 5.3210206786208240588e-1073j)  +/-  (2.18e-245, 2.18e-245j)
| (0.079727518863151580004 + 2.5568055438234966352e-1081j)  +/-  (2.41e-254, 2.41e-254j)
| (-0.30748033069781296176 + 1.513620323120168503e-1076j)  +/-  (3.27e-250, 3.27e-250j)
| (-0.57735026918962576451 + 2.9949984894617331866e-1075j)  +/-  (2.17e-245, 2.17e-245j)
| (-0.23280045503407815822 + 1.2861618448136345e-1081j)  +/-  (1.24e-251, 1.24e-251j)
| (0.30748033069781296176 - 2.4170803372469424255e-1081j)  +/-  (2.93e-250, 2.93e-250j)
| (0.37992906516324059686 + 3.4831380517275088887e-1079j)  +/-  (5.85e-249, 5.85e-249j)
-------------------------------------------------
The weights are:
| (0.0087371635794000568715 + 3.4637246851219637781e-938j)  +/-  (1.05e-72, 9.72e-189j)
| (0.041668921005997305377 + 1.608186120811516444e-937j)  +/-  (7.76e-74, 7.21e-190j)
| (0.029947420659721537056 + 7.5675120030483964355e-938j)  +/-  (2.72e-73, 2.53e-189j)
| (0.0087371635794000568715 - 2.707990662255881441e-940j)  +/-  (2.7e-73, 2.51e-189j)
| (0.014832845558953025632 + 2.4587874194653021731e-940j)  +/-  (1.92e-73, 1.78e-189j)
| (0.025588662900128701614 + 1.6765866619084842191e-939j)  +/-  (8.04e-74, 7.48e-190j)
| (0.025588662900128701614 - 7.2401688631949678228e-938j)  +/-  (7.59e-74, 7.06e-190j)
| (0.033742048296001608104 - 8.6263668872240225314e-938j)  +/-  (4.5e-74, 4.18e-190j)
| (0.076759245420190602627 - 2.0931616836880310612e-938j)  +/-  (3.9e-75, 3.63e-191j)
| (0.0031654784089832044852 + 4.5056310186076893876e-938j)  +/-  (1.16e-74, 1.08e-190j)
| (0.037557866220064404907 + 1.2454279666014621824e-938j)  +/-  (6.08e-77, 5.65e-193j)
| (0.076759245420190602627 + 2.8840527107331093392e-938j)  +/-  (2.5e-76, 2.32e-192j)
| (0.014832845558953025632 - 1.2368305775559926436e-937j)  +/-  (1.51e-74, 1.4e-190j)
| (0.036541679348785337215 + 1.0436383574821354318e-937j)  +/-  (1.35e-75, 1.25e-191j)
| (0.020555104941146761678 - 8.8944541036077862474e-940j)  +/-  (1.53e-76, 1.42e-192j)
| (0.036541679348785337215 - 7.9838170812913281188e-939j)  +/-  (1.5e-77, 1.39e-193j)
| (0.033742048296001608104 + 4.8511342581474760509e-939j)  +/-  (1.32e-77, 1.23e-193j)
| (0.064057017077100297067 + 1.0621696103177068573e-938j)  +/-  (1.26e-79, 1.17e-195j)
| (0.037557866220064404907 - 1.2605493582173706892e-937j)  +/-  (1.64e-78, 1.52e-194j)
| (0.020555104941146761678 + 8.0219701515809990835e-938j)  +/-  (8.23e-77, 7.66e-193j)
| (0.04805215746761888261 - 1.6555816703890356355e-938j)  +/-  (1.11e-79, 1.03e-195j)
| (0.042491548379294180742 + 1.8007693782982600754e-938j)  +/-  (1.95e-79, 1.81e-195j)
| (0.067963711290783555447 - 1.0050958068139138206e-938j)  +/-  (1.09e-80, 1.01e-196j)
| (0.042491548379294180742 - 1.2102818017121119122e-937j)  +/-  (6.33e-81, 5.88e-197j)
| (0.038469844054841778487 + 1.3584804164554901338e-937j)  +/-  (2.31e-80, 2.14e-196j)
| (0.041668921005997305377 - 1.5730452127491535093e-937j)  +/-  (3.72e-82, 3.46e-198j)
| (0.038469844054841778487 - 1.6637669262062831949e-938j)  +/-  (5.22e-81, 4.86e-197j)
| (0.04805215746761888261 + 9.2025698170929288994e-938j)  +/-  (6.21e-82, 5.77e-198j)
| (0.0031654784089832044852 + 3.1113081642994734367e-940j)  +/-  (1.73e-82, 1.61e-198j)
| (0.053764667077434040298 - 6.5165069393209088938e-938j)  +/-  (5.33e-83, 4.95e-199j)
| (0.071128856584537636965 - 2.3204928215636883006e-938j)  +/-  (4.31e-85, 4.01e-201j)
| (0.029947420659721537056 - 2.8958621515456234961e-939j)  +/-  (8.83e-82, 8.21e-198j)
| (0.053764667077434040298 + 1.4140487337382250885e-938j)  +/-  (5.34e-83, 4.97e-199j)
| (0.075582615582393916116 + 1.4346488958407687253e-938j)  +/-  (7.06e-85, 6.57e-201j)
| (0.064057017077100297067 - 3.3944151999628127458e-938j)  +/-  (2.93e-85, 2.73e-201j)
| (0.067963711290783555447 + 2.6918712230217102048e-938j)  +/-  (1.79e-85, 1.66e-201j)
| (0.076449279843298419831 - 4.8661952431449357499e-938j)  +/-  (1.19e-85, 1.1e-201j)
| (0.05927605371192157888 - 1.2006340951391212309e-938j)  +/-  (2.46e-85, 2.29e-201j)
| (0.076449279843298419831 + 4.1375957414444279549e-938j)  +/-  (8.37e-86, 7.78e-202j)
| (0.073667812591403167992 + 2.1947388474417633287e-938j)  +/-  (6.67e-87, 6.2e-203j)
| (0.05927605371192157888 + 4.5993570822703894323e-938j)  +/-  (1.69e-86, 1.57e-202j)
| (0.075582615582393916116 - 2.3223841812265772918e-938j)  +/-  (5.59e-87, 5.19e-203j)
| (0.073667812591403167992 - 1.150685579791593125e-938j)  +/-  (3.04e-88, 2.84e-204j)
| (0.071128856584537636965 + 1.028907910460046133e-938j)  +/-  (2.7e-88, 2.5e-204j)
