Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 4 6 22
-------------------------------------------------
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 22 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^34 - 21259245294933518877534799704140846651572732824530222048069863340719247502056757129186773/1667895996219657521686226478874808654216690924475431876040686551934279460764502885941572*t^32 + 2386262681858769790540038674695540292685342264252789312686924635430737847905044264787117112593/48265574338604449362556021845679212835722601972470047628865387439874179035603184513377210536*t^30 - 7420062853499545743310677006754539568953098344612507804584494628976736544863125122429105112097623/64000151572989499854749284967370636220168170215495283155875503745273161401209822664738181170736*t^28 + 6524545050924956715371519788005715061393328089520217514307060524114768058944150640081175201256751/35555639762771944363749602759650353455648983453052935086597502080707311889561012591521211761520*t^26 - 4662450006919189797788708749002273514659795060423665619069142074434977371845631981325090252936545/22495779772984557107064652515240319782516376069335414699020342662601356945510717581943228210654*t^24 + 92981256151935782090794830806531270573714963864975423333607343814613270080460064210089788571534169/539898714551629370569551660365767674780393025664049952776488223902432566692257221966637477055696*t^22 - 671931985934414365539150485245430765829343625269621039944169577470175620032798910883116768466920/6281289157391791919505065312696972406806520590788459948427758016180898367902343220932200084793*t^20 + 3014095534894833976276902641011697998471116867489276538931865184419775478850814166094169819305/60324505713246501027659690878242231998141854413334549324636331487931797050682768028160384968*t^18 - 9419244759701058947632340323359167189089331346737038483514493955948900999002878944164398998555763/537973941950732296164669123252164224959429057658117510877106804209375766097988925275134313144624*t^16 + 22673736486631398638196366267940578585724960234904780914260804459734095661862000439536944138633775/4976258963044273739523189390082519080874718783337586975613237938936725836406397558794992396587772*t^14 - 7746870127936361125171368623126516832165212768520452433996808779752249234567836608820482144473561/8968202966365504321778055604104759662235756928212794109896384856984868540336804391674491791652688*t^12 + 239623229476076817645418294768104745255854225811717570856590528367852444725865960402869647948920455/2071654885230431498330730844548199481976459850417155439386064901963504632817801814476807603871770928*t^10 - 76567030021443194324315526411012294744278001427728695801468271898468978086628140386806002594975/7346293919256849284860747675702835042469715781621118579383208872211009336233339767648253914438904*t^8 + 57684152159317487512280958920723262060318707707375175962296589820475625798423246429100038453587/98650232630020547539558611645152356284593326210340735208860233426833553943704848308419409708179568*t^6 - 7922169264628429005922569118953020089803675534320555223041526417041447928020159195874545833265/443926046835092463928013752403185603280669967946533308439871050420750992746671817387887343686808056*t^4 + 1892100840716277323667271623563060594497192043517751809056950904148335458269569872252453523419/8416097971248627961968594055977060395529368142319693972505888664226737570822319871312030890729069395*t^2 - 4452128624755336138660113833184709761874980992710244011570675114237805640552076338002406109/8977171169331869826099833659708864421897992685141006904006281241841853408877141196066166283444340688
-------------------------------------------------
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: 1
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (-0.97543045249072415158 + 3.4443146120288893069e-438j)  +/-  (3.98e-116, 3.98e-116j)
| (0.99835768318550801462 - 4.9779142889151660195e-451j)  +/-  (1.97e-116, 1.97e-116j)
| (-0.94932275186407481078 - 9.1767872572384771324e-448j)  +/-  (2.56e-116, 2.56e-116j)
| (0.3523124687524059471 - 1.443884462785447339e-461j)  +/-  (5.71e-123, 5.71e-123j)
| (0.86549938609357694638 - 2.2613518380386326058e-455j)  +/-  (4.29e-117, 4.29e-117j)
| (0.97543045249072415158 + 6.0958877626137412256e-455j)  +/-  (3.64e-116, 3.64e-116j)
| (0.94932275186407481078 - 8.4254328378222068849e-457j)  +/-  (2.24e-116, 2.24e-116j)
| (-0.86549938609357694638 - 5.4460011751020427425e-454j)  +/-  (4.3e-117, 4.3e-117j)
| (-0.99835768318550801462 + 1.2067595025627463705e-454j)  +/-  (1.97e-116, 1.97e-116j)
| (-0.99105250481616767714 - 7.1185950011161660144e-475j)  +/-  (4.36e-116, 4.36e-116j)
| (0.91248695683407599658 - 1.1351806320595937349e-486j)  +/-  (1.09e-116, 1.09e-116j)
| (-0.68401217235521649532 - 1.1415814351992191521e-487j)  +/-  (2.24e-118, 2.24e-118j)
| (-0.91248695683407599658 - 1.2281190521496859201e-490j)  +/-  (1.15e-116, 1.15e-116j)
| (-0.80949270909121460968 - 6.5289807476363069439e-499j)  +/-  (1.59e-117, 1.59e-117j)
| (0.99105250481616767714 - 6.6995494519437786414e-498j)  +/-  (4.33e-116, 4.33e-116j)
| (0.74677180221832073614 + 3.5823884618103874114e-499j)  +/-  (5.52e-118, 5.52e-118j)
| (0.80949270909121460968 - 5.3037986773491555377e-502j)  +/-  (1.62e-117, 1.62e-117j)
| (-0.3523124687524059471 - 2.8615993899399673669e-507j)  +/-  (5.03e-123, 5.03e-123j)
| (-0.74677180221832073614 + 2.1742540085571723998e-502j)  +/-  (5.52e-118, 5.52e-118j)
| (-0.43693939954921891801 - 1.084329011219962535e-506j)  +/-  (1.17e-121, 1.17e-121j)
| (0.15655801081562154215 + 1.3375520466964582815e-511j)  +/-  (6.24e-126, 6.24e-126j)
| (0.68401217235521649532 - 7.3600455074458692725e-504j)  +/-  (2.2e-118, 2.2e-118j)
| (0.25746215955965288222 + 6.4102340440801301262e-510j)  +/-  (2.01e-124, 2.01e-124j)
| (-0.50992493118502290047 + 3.3876801617255256117e-505j)  +/-  (1.66e-120, 1.66e-120j)
| (-0.57735026918962576451 + 1.5400456500568108981e-503j)  +/-  (1.57e-119, 1.57e-119j)
| (-0.052513218848459454265 + 1.010941032185294485e-513j)  +/-  (2.73e-127, 2.73e-127j)
| (0.63352702761174118591 + 1.1731893180041580825e-504j)  +/-  (7.19e-119, 7.19e-119j)
| (0.43693939954921891801 - 7.1500811474899576933e-510j)  +/-  (1.18e-121, 1.18e-121j)
| (-0.15655801081562154215 - 4.7453404790456298914e-513j)  +/-  (6.31e-126, 6.31e-126j)
| (-0.63352702761174118591 + 1.9793017608889084442e-507j)  +/-  (7.72e-119, 7.72e-119j)
| (-0.25746215955965288222 + 1.6688614970771684421e-513j)  +/-  (1.67e-124, 1.67e-124j)
| (0.50992493118502290047 - 4.0823811129321922598e-508j)  +/-  (1.61e-120, 1.61e-120j)
| (0.57735026918962576451 + 7.5950944755493070872e-510j)  +/-  (1.57e-119, 1.57e-119j)
| (0.052513218848459454265 - 1.7898993765113614264e-519j)  +/-  (3.23e-127, 3.23e-127j)
-------------------------------------------------
The weights are:
| (0.02070683733836592008 - 3.448335797169128132e-439j)  +/-  (3.78e-20, 1.37e-74j)
| (0.0041961171539922690366 - 1.0352079140456718536e-440j)  +/-  (6.68e-21, 2.41e-75j)
| (0.031523819556222345945 - 3.1234924839180309462e-438j)  +/-  (2.27e-20, 8.21e-75j)
| (0.090503466930519416987 + 2.6130302008874146387e-439j)  +/-  (4.1e-21, 1.48e-75j)
| (0.051744846507392038034 + 6.9787943280974565077e-440j)  +/-  (1.6e-21, 5.79e-76j)
| (0.02070683733836592008 - 3.6558660976980886852e-440j)  +/-  (1.33e-21, 4.79e-76j)
| (0.031523819556222345945 + 4.236761706643132598e-440j)  +/-  (8.04e-22, 2.9e-76j)
| (0.051744846507392038034 - 1.1686842617259426369e-438j)  +/-  (1.63e-22, 5.88e-77j)
| (0.0041961171539922690366 - 8.912027473413170862e-439j)  +/-  (1.25e-22, 4.52e-77j)
| (0.010911624644528342947 + 3.4342207613872147909e-438j)  +/-  (2.53e-22, 9.13e-77j)
| (0.042049151286488512357 - 5.146764797650352276e-440j)  +/-  (2.03e-23, 7.35e-78j)
| (0.057845222405419045384 + 2.6397001672141717613e-438j)  +/-  (3.1e-25, 1.12e-79j)
| (0.042049151286488512357 + 1.5437126210155732252e-438j)  +/-  (1.19e-23, 4.32e-78j)
| (0.059921959530203157756 + 1.1822137088923054191e-438j)  +/-  (1.28e-24, 4.62e-79j)
| (0.010911624644528342947 + 2.7281994101629892006e-440j)  +/-  (1.35e-24, 4.9e-79j)
| (0.064584297420771333623 + 2.1033784512453286483e-439j)  +/-  (5.86e-27, 2.12e-81j)
| (0.059921959530203157756 - 1.0990606166124312649e-439j)  +/-  (2.62e-26, 9.48e-81j)
| (0.090503466930519416987 - 5.5678578420061898637e-439j)  +/-  (6.14e-29, 2.22e-83j)
| (0.064584297420771333623 - 1.5842143330567253744e-438j)  +/-  (3.24e-27, 1.17e-81j)
| (0.078265133916334660616 + 1.0271517527518451128e-438j)  +/-  (8.16e-29, 2.95e-83j)
| (0.10287268496633279485 + 1.5706796775753763899e-439j)  +/-  (2.88e-30, 1.04e-84j)
| (0.057845222405419045384 - 4.6356341054665201839e-439j)  +/-  (1.04e-29, 3.78e-84j)
| (0.098465813652213679995 - 1.8828648351133693762e-439j)  +/-  (3.7e-30, 1.34e-84j)
| (0.069290847746396787111 - 1.7336379815716823188e-438j)  +/-  (1.66e-29, 5.99e-84j)
| (0.064404302777188892695 + 2.6757420007142663865e-438j)  +/-  (1.78e-29, 6.45e-84j)
| (0.10486568120365065239 + 1.6917554200500067873e-439j)  +/-  (8.62e-32, 3.12e-86j)
| (0.047848192963980150189 + 7.0080797201144779117e-439j)  +/-  (2.35e-31, 8.53e-86j)
| (0.078265133916334660616 - 3.916198211571480816e-439j)  +/-  (6.57e-32, 2.37e-86j)
| (0.10287268496633279485 - 2.1712676896708814241e-439j)  +/-  (2.1e-32, 7.56e-87j)
| (0.047848192963980150189 - 3.2979202507530261232e-438j)  +/-  (6.04e-31, 2.18e-85j)
| (0.098465813652213679995 + 3.2332488322532467221e-439j)  +/-  (2.48e-32, 8.92e-87j)
| (0.069290847746396787111 + 5.4331647579024623597e-439j)  +/-  (9.67e-33, 3.53e-87j)
| (0.064404302777188892695 - 6.85969275132216418e-439j)  +/-  (1.23e-32, 4.52e-87j)
| (0.10486568120365065239 - 1.5189064107336168662e-439j)  +/-  (2.04e-33, 6.93e-88j)
