Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 4 9 28
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 9 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 28 Kronrod extension for:
P3 : 3/2*t^15 - 1280116003/245021714*t^13 + 12427268373/1715151998*t^11 - 61055366515/12006063986*t^9 + 7331508745275/3877958667478*t^7 - 195050681397/553994095354*t^5 + 14996878941/553994095354*t^3 - 264841293/553994095354*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^43 - 15915981797918979561124210287180742373373616171983736461177355083335775541642432868028466661370278827844653598682213338453621492813749530752531137079408998947104953/975131006225130687613909649720919129569525728606593332296786238408432610704701027006297281110912342410155526149318902750872843112253077331479564162663193222867218*t^41 + 305221890909902062559330895704101198246941108287470687538698293339409488674056714788000160935238137739860146500266810281888521449165493163810636927044964247177745995803/3689408162052781956587227159719097526726300594183045872744890733018304782601236335678325763083136847508823433185948068557927401915209518083652931009436191558718119303*t^39 - 448778735572186461378095732464442641457531955542736510471926869539216152481374244662654797600484571919481214750427907442345759746831607950742945682374869740501401345681685/1730332428002754737639409537908256740034634978671848514317353753785584943039979841433134782885991181481638190164209644153667951498233263981233224643425573841038797953107*t^37 + 629531610674523004987745964468234353147243483142665121768525842869588246348372137027688114379227699043659493586117355866313330250942100671664199755788713928910657561493498839/1117794748489779560515058561488733854062374196222014140249010524945487873203826977565805069744350303237138270846079430123269496667858688531876663119652920701311063477707122*t^35 - 1101319124734609712108644019274345371314911240873214371570335005127216760311302348639639190050542154095048347407608868857200819751151147317973675328019710749253604727587079/1225204327902571677583184393301498561266760171233482798957629366034513562152532310083089225149086923533582320985837884680236934601233491266214829871742331788064738923318*t^33 + 2815834283251321160521764544920527610550683794924784555444922249441437561767383309972409420325172448661123169918815315169915371270899203348770650171684445736751875495031221012/2578442508070962095473811555703003722185896780360864550406331000819633791550004246569861274326253430576423994514695828309558628868295882369749109465081737247982243064122731*t^31 - 17442829017839567257627435980151057282992358566993100759406189007228233963727863256482643358553135312166932288205469875945033092786842251624446573573806327090419230161275993652/16903123108465195959217209087386357734329767782365667608219281005373154855716694505291312798360994711556557297374117096695995455914384117757244162048869166403439148975915681*t^29 + 317272019430889908564553454551576731840119773102242168620462068114691830389906391033934138204925755969140791335758715369970132291116754211400563650308845983124869329589845751935/412919150221078358432306107706152453224341470112075594429356721702687068618222108629259212645675727953738756835853431933573603280194240590926964530050946779284013496411654493*t^27 - 145798270907866482394575635573013190095902941749270321145668093215082623076219791186741791788036700742155259488389029180787516214002530186021297813908064876220794426324229822571/321159339060838723225126972660340796952265587864947684556166339102089942258617195600534943168858899519574588650108224837223913662373298237387639078928514161665343830542397939*t^25 + 20848958061180100497053549858194643368329159756260911344517777708587496563319950783820977597531165162148404721212271871810613541499757586188549520714733363247497097998867278890/97744146670690046198951687331408068637646048480636251821441929291940417209144363878423678355739665071174874806554677124372495462461438593987542328369547788332930731034642851*t^23 - 132160827025013224200510011433584882821063555453242408595502528889792154350719280466252657467402218544255878952259550688497958551401102955646850583311070825707285002048953278270/1661650493401730785382178684633937166839982824170816280964512797962987092555454185933202532047574306209972871711429511114332422861844456097788219582282312401659822427588928467*t^21 + 292240416444238829937730120616124800393108955598333085405181717378182483117990410641250798501021091161461886910338863245714241031460680076914715054520813266509053129946171765/12493612732343840491595328455894264412330697926096363014770772917014940545529730721302274677049430873759194524146086549731822728284544782690136989340468514298194153590894199*t^19 - 3152222249216214631879802834573941489856470629887696881496527414955659368724663655945727301200018187999588695766419866879660272193039749337415163077173928435178129079806170825/587199798420160503104980437427030427379542802526529061694226327099702205639897343901206909821323251066682142634866067837395668229373604786436438499002020172015125218772027353*t^17 + 1732177570837749362981215322750953886240028387422699448952338817534158607115510353904406040637329856443495735437768648264250096030984491503139308365640239593121689608329001740/1830681724486382744974350775507800744183280501994472957046705608016718641112621130986115660031184253325538444685170682081292377420988297275360661202771004065694213917348085277*t^15 - 687691171357768736200290941542041891337111988561689854988813427313941883694543821454613204243015901839718481675355145390435719601343680742373633009730857097156120898463150060/5492045173459148234923052326523402232549841505983418871140116824050155923337863392958346980093552759976615334055512046243877132262964891826081983608313012197082641752044255831*t^13 + 370784213218528841777818497692043048270619725310659902194866505419717359752925049575749753171488373394477091762130918672675942763431033988128571395991896780989841378993965/30767760075401390671837828159794970490475302554528957261289169882633926741388590436741439664389651316395604112355809782878863486067030206308582541223042085137717880963833366*t^11 - 433773573895473612334898141229879780290559112310422803643341327875647284958427090952764815256901166448165954631953528472864105244047122288693532337451116841639678864655800395/538220426998996527022459127999293418789884467586375049371731448756915280487110612509918004049168170477708302737440180531899958961770559398956034393614675195314098891700337071438*t^9 + 3140101470908663771855523677826712628233579249783261370095238177216547878418057004949145738269094618344668220508864176313615306454562252106567681764518614674640233948766025/89703404499832754503743187999882236464980744597729174895288574792819213414518435418319667341528028412951383789573363421983326493628426566492672398935779199219016481950056178573*t^7 - 11363021138359132086643305724229192854203524353875815199176725045473519417123004105929507293828698877524607828493442651468805969785182185244941983450034795532774507272445/12814772071404679214820455428554605209282963513961310699326939256117030487788347916902809620218289773278769112796194774569046641946918080927524628419397028459859497421436596939*t^5 + 12023362040521954305848173292662685481736402686554934074386547985558616397776009620039232417819321705464921496959015817246897893142312417212176439596190967440564206575/1114328006209102540419170037265617844285475088170548756463212109227567868503334601469809532192894762893806009808364763006004055821471137471958663340817132909552999775777095386*t^3 - 921619496542658038233402519276126713773907368035830835630196245149540084295504054242118527804643605411727524064574022927293513124889886337201186448031825921878823825/22931697390934689121257657082676661953453724182878134935637680774104159820252833114457659320390623804814639465003716965018293990852379723765044071908394682507116995385728647154*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:
| (-0.99481595896889972905 + 8.8460726713891224278e-890j)  +/-  (2.37e-240, 2.37e-240j)
| (-0.99996842064316502869 + 5.6135944518152232677e-890j)  +/-  (8.63e-241, 8.63e-241j)
| (-0.94015168715445181499 + 1.0880230749238868261e-890j)  +/-  (1.83e-240, 1.83e-240j)
| (0.99996842064316502869 - 4.82482013538691897e-892j)  +/-  (8.52e-241, 8.52e-241j)
| (0.91248695683407599658 - 6.4358168603125757518e-913j)  +/-  (1.27e-240, 1.27e-240j)
| (0.94015168715445181499 + 2.3737760331619288924e-922j)  +/-  (1.81e-240, 1.81e-240j)
| (-0.96431117655741220906 - 2.0896961289357469597e-936j)  +/-  (2.2e-240, 2.2e-240j)
| (-0.91248695683407599658 + 8.0990767008407215662e-936j)  +/-  (1.31e-240, 1.31e-240j)
| (-0.98280708179129512709 - 7.8455934058124816594e-936j)  +/-  (2.22e-240, 2.22e-240j)
| (0.99481595896889972905 - 2.1975277451274196006e-932j)  +/-  (2.1e-240, 2.1e-240j)
| (0.88436740236853663905 + 3.0351211399121932826e-949j)  +/-  (7.39e-241, 7.39e-241j)
| (0.96431117655741220906 + 9.7247063132344016402e-968j)  +/-  (2.09e-240, 2.09e-240j)
| (-0.85200993562103111583 - 1.3813090284784760752e-986j)  +/-  (3.14e-241, 3.14e-241j)
| (-0.81106721229304993576 + 7.9134601012994268897e-991j)  +/-  (8.87e-242, 8.87e-242j)
| (0.98280708179129512709 + 1.0545986299556601345e-993j)  +/-  (2.3e-240, 2.3e-240j)
| (0.85200993562103111583 - 3.9660528924246077296e-1005j)  +/-  (3.28e-241, 3.28e-241j)
| (0.81106721229304993576 - 9.6773995359328355764e-1011j)  +/-  (9.94e-242, 9.94e-242j)
| (-0.37314303819498557267 - 5.4000648133181226269e-1018j)  +/-  (4.57e-249, 4.57e-249j)
| (-0.76471043608676504393 - 1.0806117129927168327e-1009j)  +/-  (3.2e-242, 3.2e-242j)
| (-0.88436740236853663905 - 3.4938966674372887848e-1011j)  +/-  (8.44e-241, 8.44e-241j)
| (0.76471043608676504393 + 2.4111154404506397009e-1015j)  +/-  (3.27e-242, 3.27e-242j)
| (0.72770080257399915914 + 1.7779360874619832071e-1016j)  +/-  (1.17e-242, 1.17e-242j)
| (0.23146399278060456919 - 1.7567700406510431543e-1025j)  +/-  (1.33e-251, 1.33e-251j)
| (-0.69549768905361272692 + 1.3677697728222701567e-1013j)  +/-  (2.97e-243, 2.97e-243j)
| (-0.72770080257399915914 + 1.0368170629444212327e-1016j)  +/-  (1.31e-242, 1.31e-242j)
| (0.15655801081562154215 - 8.8853425691486555948e-1028j)  +/-  (6.11e-253, 6.11e-253j)
| (0.69549768905361272692 - 2.2769048929071066311e-1019j)  +/-  (3.16e-243, 3.16e-243j)
| (0.51079795216019729642 + 4.9594063603685119067e-1023j)  +/-  (1.09e-246, 1.09e-246j)
| (-0.078988869177377193764 - 9.3649183710382277402e-1031j)  +/-  (2.52e-254, 2.52e-254j)
| (-0.64029743779323613123 + 2.9834038700304644508e-1021j)  +/-  (1.99e-244, 1.99e-244j)
| (-0.30330416161656652066 + 3.0314269990705254183e-1027j)  +/-  (2.68e-250, 2.68e-250j)
| (0.30330416161656652066 + 2.1887438318120962107e-1027j)  +/-  (2.86e-250, 2.86e-250j)
| (0.64029743779323613123 - 9.1057653362670527607e-1023j)  +/-  (2.28e-244, 2.28e-244j)
| (0.078988869177377193764 + 4.0360825310833600693e-1033j)  +/-  (2.52e-254, 2.52e-254j)
| (-0.51079795216019729642 - 2.3877981060293112533e-1025j)  +/-  (9.93e-247, 9.93e-247j)
| (-0.4423281445660645251 + 7.8496468142701689213e-1027j)  +/-  (6.68e-248, 6.68e-248j)
| (1.1037314317547756905e-1040 + 1.2966231836818100978e-1041j)  +/-  (4.78e-1039, 4.78e-1039j)
| (0.57735026918962576451 + 1.5625032861889851749e-1027j)  +/-  (1.4e-245, 1.4e-245j)
| (0.37314303819498557267 + 2.2852090617887354884e-1030j)  +/-  (4.33e-249, 4.33e-249j)
| (-0.23146399278060456919 + 5.7752419028106295588e-1034j)  +/-  (1.31e-251, 1.31e-251j)
| (-0.57735026918962576451 - 2.8554692120229140726e-1027j)  +/-  (1.52e-245, 1.52e-245j)
| (-0.15655801081562154215 + 1.1895399251360981075e-1034j)  +/-  (6.19e-253, 6.19e-253j)
| (0.4423281445660645251 + 2.5687349910775419415e-1031j)  +/-  (7.09e-248, 7.09e-248j)
-------------------------------------------------
The weights are:
| (0.0086308205031379994075 - 2.91779001102522764e-890j)  +/-  (9.91e-73, 4.67e-188j)
| (0.0014391162256075776998 + 8.4880539522480471886e-890j)  +/-  (7.36e-73, 3.47e-188j)
| (0.026451303393870189206 - 4.1687982236852912431e-890j)  +/-  (8.44e-74, 3.98e-189j)
| (0.0014391162256075776998 + 1.6647792401877110473e-892j)  +/-  (3.45e-74, 1.62e-189j)
| (0.028167820406835989696 + 1.9301595876805656354e-891j)  +/-  (1.54e-74, 7.27e-190j)
| (0.026451303393870189206 - 1.0031580899494953907e-891j)  +/-  (1.13e-74, 5.33e-190j)
| (0.021533807687542392157 + 5.6333336796088761655e-890j)  +/-  (5.85e-74, 2.76e-189j)
| (0.028167820406835989696 + 3.7692416617730522346e-890j)  +/-  (1.02e-74, 4.79e-190j)
| (0.015333916109215940944 - 8.4417244814530253684e-890j)  +/-  (3.14e-74, 1.48e-189j)
| (0.0086308205031379994075 - 1.1772489982679720881e-892j)  +/-  (5.43e-75, 2.56e-190j)
| (0.028855398097816041061 - 2.9710998818780155235e-891j)  +/-  (8.05e-76, 3.79e-191j)
| (0.021533807687542392157 + 5.0838783228342369082e-892j)  +/-  (1.7e-75, 8e-191j)
| (0.036731763781328680692 + 4.5305943147896415289e-890j)  +/-  (8.17e-77, 3.85e-192j)
| (0.044566293122452569527 - 4.1957791559268062371e-890j)  +/-  (1.24e-77, 5.85e-193j)
| (0.015333916109215940944 - 2.1907951421805087874e-892j)  +/-  (1.79e-75, 8.43e-191j)
| (0.036731763781328680692 + 3.557576895931864515e-891j)  +/-  (2.68e-77, 1.26e-192j)
| (0.044566293122452569527 - 4.2853572457978230038e-891j)  +/-  (2.84e-78, 1.34e-193j)
| (0.069379669757998802625 - 5.2654847090381707105e-891j)  +/-  (9.91e-82, 4.67e-197j)
| (0.046302567696036445374 + 5.4866476409749429041e-890j)  +/-  (1.48e-79, 6.98e-195j)
| (0.028855398097816041061 - 4.8267597770671693304e-890j)  +/-  (1.27e-77, 6.01e-193j)
| (0.046302567696036445374 + 7.1718860486013721816e-891j)  +/-  (3.8e-80, 1.79e-195j)
| (0.025296393976655824394 - 1.0713806322122317423e-890j)  +/-  (6.54e-81, 3.08e-196j)
| (0.073319706226813893594 - 2.2812748020111848059e-891j)  +/-  (1.64e-84, 7.74e-200j)
| (0.046765994413805496479 + 4.8434163796917992297e-890j)  +/-  (3.31e-82, 1.56e-197j)
| (0.025296393976655824394 - 6.9210307857722116985e-890j)  +/-  (1.47e-81, 6.92e-197j)
| (0.076407376150170196089 + 2.15986971176720439e-891j)  +/-  (2.88e-85, 1.36e-200j)
| (0.046765994413805496479 + 8.5573267626032943922e-891j)  +/-  (1.01e-82, 4.74e-198j)
| (0.067756434345147531982 - 2.4418797687642366634e-891j)  +/-  (4.44e-85, 2.09e-200j)
| (0.078512357110604447625 - 2.4807320758923258367e-891j)  +/-  (1.74e-86, 8.18e-202j)
| (0.060326080236546022719 - 1.9298916144369018064e-890j)  +/-  (1.8e-84, 8.48e-200j)
| (0.070561415492023249676 + 4.4752583364101792577e-891j)  +/-  (2.17e-86, 1.02e-201j)
| (0.070561415492023249676 + 2.3810323000240800152e-891j)  +/-  (1.92e-86, 9.03e-202j)
| (0.060326080236546022719 - 4.1737931858682441391e-891j)  +/-  (4.07e-85, 1.92e-200j)
| (0.078512357110604447625 - 2.1151111558304831468e-891j)  +/-  (7.29e-87, 3.44e-202j)
| (0.067756434345147531982 - 7.6123960635614345197e-891j)  +/-  (4.44e-87, 2.09e-202j)
| (0.068967897885292419739 + 6.1471392048846705086e-891j)  +/-  (3.87e-87, 1.82e-202j)
| (0.079227230394750955267 + 2.2083812552066781142e-891j)  +/-  (7.7e-88, 3.62e-203j)
| (0.065080252183722811679 + 2.859055990761370095e-891j)  +/-  (1.57e-87, 7.39e-203j)
| (0.069379669757998802625 - 2.3892086656057746594e-891j)  +/-  (2.62e-88, 1.24e-203j)
| (0.073319706226813893594 - 3.6681409409853569128e-891j)  +/-  (5.96e-89, 2.84e-204j)
| (0.065080252183722811679 + 1.0793306054127762541e-890j)  +/-  (1.42e-88, 6.78e-204j)
| (0.076407376150170196089 + 2.9684909775835571298e-891j)  +/-  (4.4e-89, 2.1e-204j)
| (0.068967897885292419739 + 2.3587626422676579772e-891j)  +/-  (4e-89, 1.76e-204j)
