Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 6 37
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 37 Kronrod extension for:
P2 : 3/2*t^8 - 161/52*t^6 + 105/52*t^4 - 245/572*t^2 + 25/1716
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^45 - 157543480808011278868201576362854900425409323721740015894616339/9579292742070825975592936657166888462542348075011902328019768*t^43 + 427307252869453480345776877800386878224033934040580316123625919303/5081130564472710978196653401151522408774248343217027620562485512*t^41 - 42461252613583296221710742082721221927735998239272800879297886979201943/159405228068637888807985410500925561008065719023404590512286295482464*t^39 + 3768877948257858489248474665005546919770454722290606216180708040596150131/6437518825848837817245564654845070733018038652868262309150023471407200*t^37 - 848468705166004665120442265613234085355862607298210244395867552873562993/895121665308505067921764228197505073352984422208348854415146120786144*t^35 + 372221022925769685126985611108084750074518098153221991935189790251049143623/317768191184519299112226301010114301040309469883963843317376872879081120*t^33 - 187639728353711492259575643864025388208387802476349228777005356308717983269/166106099937362360899572839164377930089252677439344736279537910823156040*t^31 + 94184014885447669333461339565859574843491279904596855349779475100030500141/109261936704941020002664321974885342513126936492360001844464628577924520*t^29 - 36728411885152327998957425860128389819507976929571139854513294554203865473511/70005683731665782101707069151051537310196330024033515467489122738855924600*t^27 + 91754495980938392341884184773926173323727503805550896329228937517287131933/359003506316234780008754200774623268257417077046325720346098065327466280*t^25 - 6108067988627205407401629850356194632054040766572899994068523962414320289617/61317798878812900425495217492305654218366836759512433035113549557931240624*t^23 + 695173208534895344440149636922106840070135221925680799944497558889464072791/22470497725776156056547936845006419868842505396343065522184468471540019856*t^21 - 170699302089972207313399282497395342988196732833085531612009228034810226113/22470497725776156056547936845006419868842505396343065522184468471540019856*t^19 + 23409457865059101473836913142626662383590402470573315881014856269730797587887/16066405873929951580431774844179590206222391358385291848361894957151114197040*t^17 - 127877653066571978080295913844196667866850364940089229584636135282057321979277/596063657922801203634018846719062796650850719396094327574226302910306336710184*t^15 + 2015472314200485851588787364152860052185668574633273238456659504321992779675/85151951131828743376288406674151828092978674199442046796318043272900905244312*t^13 - 21682067849228596885054114491950727743367060448830835865627158351833433107/11462762652361561608346516283058899935593283065309506299504351979044352629042*t^11 + 1007621817899186235183190834942706707404058107296722563007305951052926973/9657487612360957155303466983678304939334673824550134628775753651998955223956*t^9 - 14488643309895385137345021096454659925613606290629180371903790741693985149/3918180688443588331580263747663769432530067665960340335103305767382433262290720*t^7 + 58885308032635671885003563469416494492444399066194465835760977337486781/783636137688717666316052749532753886506013533192068067020661153476486652458144*t^5 - 1585032911526683231146809408935779784489953609715778609655624174107/2219932401384469309677203256466724890951879697427954864081193069338489100448*t^3 + 141781661415302928922317147641652747070678308676356891805459368617365/71310888529673307634760800207480603672047231520478194098880164966360285373691104*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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:
| (0.53531499821654679923 + 1.187923009844381713e-893j)  +/-  (2.19e-245, 2.19e-245j)
| (0.98219129046748981137 - 3.4436903479465425487e-903j)  +/-  (4.96e-240, 4.96e-240j)
| (-0.91889438794512440954 - 2.7773026146760150642e-922j)  +/-  (1.57e-240, 1.57e-240j)
| (0.99867105905751390207 - 1.0011721970914193158e-922j)  +/-  (1.41e-240, 1.41e-240j)
| (0.94522139973198429664 + 1.0200446316438920131e-931j)  +/-  (2.83e-240, 2.83e-240j)
| (0.91889438794512440954 - 4.4916070025183406102e-938j)  +/-  (1.57e-240, 1.57e-240j)
| (-0.99867105905751390207 - 5.8687183595825238509e-943j)  +/-  (1.48e-240, 1.48e-240j)
| (-0.8874631314285859086 - 1.2498861605531591293e-943j)  +/-  (6.35e-241, 6.35e-241j)
| (-0.96633081533827669672 + 2.4453529711217631065e-943j)  +/-  (3.87e-240, 3.87e-240j)
| (-0.9928922753995256145 + 1.4940245607818437308e-943j)  +/-  (3.65e-240, 3.65e-240j)
| (0.85110112875893547946 - 1.2631798167950952804e-944j)  +/-  (2.42e-241, 2.42e-241j)
| (-0.2041968861768067152 + 2.5450894199282708257e-962j)  +/-  (7.37e-252, 7.37e-252j)
| (-0.71507302018336741422 + 2.4768089033635536252e-955j)  +/-  (5.49e-243, 5.49e-243j)
| (-0.76455726786809476552 + 1.5906923054840879215e-955j)  +/-  (2.24e-242, 2.24e-242j)
| (0.9928922753995256145 - 3.3214931309884003656e-952j)  +/-  (3.72e-240, 3.72e-240j)
| (0.8874631314285859086 + 2.7371168196253940066e-965j)  +/-  (6.59e-241, 6.59e-241j)
| (0.76455726786809476552 - 3.0288772529932425497e-971j)  +/-  (2.13e-242, 2.13e-242j)
| (-0.98219129046748981137 - 4.090532120186182546e-970j)  +/-  (4.38e-240, 4.38e-240j)
| (-0.81003555167718283955 - 2.2828746441586071242e-972j)  +/-  (8.81e-242, 8.81e-242j)
| (-0.85110112875893547946 - 1.5343622229706810275e-971j)  +/-  (2.43e-241, 2.43e-241j)
| (0.81003555167718283955 + 5.1478775742070148382e-972j)  +/-  (8.65e-242, 8.65e-242j)
| (0.71507302018336741422 - 3.0789352121869350868e-975j)  +/-  (5.64e-243, 5.64e-243j)
| (0.2041968861768067152 + 3.3774462316794302634e-986j)  +/-  (6.39e-252, 6.39e-252j)
| (-0.94522139973198429664 + 3.9876626098513054147e-976j)  +/-  (2.88e-240, 2.88e-240j)
| (-0.6623746154360437402 - 1.8781113786197466952e-980j)  +/-  (1.51e-243, 1.51e-243j)
| (-3.7651461234213038837e-988 + 4.2514334615445869391e-988j)  +/-  (2.56e-986, 2.56e-986j)
| (0.6623746154360437402 + 4.0018571982692307209e-979j)  +/-  (1.57e-243, 1.57e-243j)
| (0.96633081533827669672 - 3.2856943857520466758e-995j)  +/-  (4.1e-240, 4.1e-240j)
| (-0.53531499821654679923 - 1.1409648195792404443e-1015j)  +/-  (2.13e-245, 2.13e-245j)
| (-0.61014817769363763382 - 7.6807026871060451676e-1016j)  +/-  (5.08e-244, 5.08e-244j)
| (-0.27355932869414784702 - 2.0618389218389593951e-1022j)  +/-  (1.55e-250, 1.55e-250j)
| (0.27355932869414784702 + 7.1615095848254078151e-1022j)  +/-  (1.47e-250, 1.47e-250j)
| (0.61014817769363763382 - 1.8147795148219512687e-1016j)  +/-  (4.88e-244, 4.88e-244j)
| (0.067062324374096494082 + 3.5031749591739080374e-1027j)  +/-  (2.33e-254, 2.33e-254j)
| (-0.47477402602494021004 - 1.4350040003196067274e-1022j)  +/-  (1.13e-246, 1.13e-246j)
| (-0.40972267876428466373 + 1.0104156871860476648e-1024j)  +/-  (4.85e-248, 4.85e-248j)
| (0.13512582097270343453 - 4.9049119027170823432e-1028j)  +/-  (3.7e-253, 3.7e-253j)
| (0.57735026918962576451 + 3.0173495320824367875e-1023j)  +/-  (1.88e-244, 1.88e-244j)
| (0.3423438407211751372 - 1.1666383645543917874e-1027j)  +/-  (2.86e-249, 2.86e-249j)
| (-0.3423438407211751372 - 1.8685095941839552722e-1027j)  +/-  (2.92e-249, 2.92e-249j)
| (-0.57735026918962576451 + 1.3178521653764866256e-1027j)  +/-  (1.8e-244, 1.8e-244j)
| (-0.13512582097270343453 + 1.1005715414594692437e-1031j)  +/-  (4.11e-253, 4.11e-253j)
| (0.47477402602494021004 + 1.8507822209337973935e-1027j)  +/-  (1.1e-246, 1.1e-246j)
| (0.40972267876428466373 + 4.0477940902816036838e-1029j)  +/-  (5.82e-248, 5.82e-248j)
| (-0.067062324374096494082 - 6.695701119588299778e-1036j)  +/-  (2.01e-254, 2.01e-254j)
-------------------------------------------------
The weights are:
| (0.055964664413782646983 + 1.0197252451060984053e-893j)  +/-  (1.25e-70, 5.15e-187j)
| (0.013253514708407263028 + 2.5346926903815986754e-896j)  +/-  (5.85e-71, 2.4e-187j)
| (0.02890348286997879806 + 2.0269384877984055953e-896j)  +/-  (2.33e-72, 9.6e-189j)
| (0.0034241597450398957474 + 4.1096655611244323949e-897j)  +/-  (2.52e-71, 1.03e-187j)
| (0.023731298319870758549 + 5.4988695525894276838e-896j)  +/-  (2.43e-71, 1e-187j)
| (0.02890348286997879806 - 7.6844406506692903695e-896j)  +/-  (1.46e-71, 5.99e-188j)
| (0.0034241597450398957474 - 1.2413663387246265055e-897j)  +/-  (7.35e-74, 3.02e-190j)
| (0.033930007737677239101 - 2.6965595784161232207e-896j)  +/-  (1.39e-73, 5.7e-190j)
| (0.018481624870714902627 + 1.1105862797198859395e-896j)  +/-  (4.85e-74, 1.99e-190j)
| (0.0081891106420813277618 + 4.101285095518918261e-897j)  +/-  (6.72e-74, 2.76e-190j)
| (0.038756263928916608266 - 1.6044237167474174335e-895j)  +/-  (4.03e-75, 1.66e-191j)
| (0.069361923099259816259 + 3.7964986225728082656e-895j)  +/-  (2.44e-76, 1e-192j)
| (0.051289950674247667061 - 1.2517577564947110731e-895j)  +/-  (6.01e-76, 2.47e-192j)
| (0.047564541844485960492 + 7.6459897116755235513e-896j)  +/-  (9.79e-76, 4.02e-192j)
| (0.0081891106420813277618 - 1.3697386138505397679e-896j)  +/-  (5.93e-75, 2.44e-191j)
| (0.033930007737677239101 + 1.0894864123499488214e-895j)  +/-  (2.12e-75, 8.71e-192j)
| (0.047564541844485960492 - 4.3355049921938542913e-895j)  +/-  (4.88e-77, 2e-193j)
| (0.013253514708407263028 - 7.4641801203707175345e-897j)  +/-  (8.18e-76, 3.36e-192j)
| (0.043327061815317275563 - 5.1345298515628482786e-896j)  +/-  (3.01e-77, 1.24e-193j)
| (0.038756263928916608266 + 3.6544204942683639928e-896j)  +/-  (5.2e-77, 2.14e-193j)
| (0.043327061815317275563 + 2.514461527374044565e-895j)  +/-  (8.28e-78, 3.4e-194j)
| (0.051289950674247667061 + 8.7071658467596088833e-895j)  +/-  (4.73e-79, 1.95e-195j)
| (0.069361923099259816259 + 8.4790162501756091467e-895j)  +/-  (6.37e-82, 2.62e-198j)
| (0.023731298319870758549 - 1.5224358726672032798e-896j)  +/-  (2.57e-77, 1.06e-193j)
| (0.053721956555937524496 + 2.4327447666851806071e-895j)  +/-  (5.47e-80, 2.25e-196j)
| (0.06684380584010837293 - 6.3364393213122862891e-895j)  +/-  (7.6e-83, 3.12e-199j)
| (0.053721956555937524496 - 2.2931543606869755823e-894j)  +/-  (1.58e-80, 6.48e-197j)
| (0.018481624870714902627 - 3.8692487817837223939e-896j)  +/-  (9.8e-79, 4.03e-195j)
| (0.055964664413782646983 - 6.2095880582316191334e-895j)  +/-  (3.16e-82, 1.3e-198j)
| (0.046983650562060578842 - 6.3014682968756276217e-895j)  +/-  (1.86e-81, 7.65e-198j)
| (0.06921541032075968591 - 3.305663362473900549e-895j)  +/-  (2.28e-83, 9.39e-200j)
| (0.06921541032075968591 - 1.0215122503949630411e-894j)  +/-  (4.84e-84, 1.99e-200j)
| (0.046983650562060578842 + 9.6455876463444050051e-894j)  +/-  (9.33e-83, 3.84e-199j)
| (0.067468920320153799248 + 7.0186369677542097865e-895j)  +/-  (4.27e-84, 1.75e-200j)
| (0.063437221562316781106 + 3.8412883403086666866e-895j)  +/-  (1.21e-83, 4.98e-200j)
| (0.066396577677209964682 - 3.1801551558800358008e-895j)  +/-  (3.88e-84, 1.6e-200j)
| (0.068650062355409102436 - 7.6085272158139087841e-895j)  +/-  (8.16e-85, 3.36e-201j)
| (0.026309232011556980347 - 2.2991278827960673265e-893j)  +/-  (1.99e-84, 8.18e-201j)
| (0.068217461044761236973 + 1.4026579737299146561e-894j)  +/-  (8.11e-86, 3.33e-202j)
| (0.068217461044761236973 + 3.0840290139916824774e-895j)  +/-  (1.63e-85, 6.7e-202j)
| (0.026309232011556980347 + 8.6858524362965650116e-895j)  +/-  (1.45e-84, 5.95e-201j)
| (0.068650062355409102436 - 4.5415645316024570366e-895j)  +/-  (1.67e-86, 6.83e-203j)
| (0.063437221562316781106 + 6.4089542338141668242e-894j)  +/-  (1.3e-86, 5.39e-203j)
| (0.066396577677209964682 - 2.3929540115381494096e-894j)  +/-  (8.56e-87, 3.54e-203j)
| (0.067468920320153799248 + 5.4558752509465734851e-895j)  +/-  (7.11e-87, 2.89e-203j)
