Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 10 37
-------------------------------------------------
Trying to find an order 10 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^12 - 3091/728*t^10 + 61875/13832*t^8 - 36135/16796*t^6 + 7755/16796*t^4 - 15543/436696*t^2 + 189/436696
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^49 - 446873448013751033502549529029101410497260689304211289995566372796209827372585149879614042085920498093681/25196717250738747996614853289874370063042161847404882224393546921538730331659540042967226062386075661960*t^47 + 207073401918373533893664098983799135357842194049314242540308348704752561009160255805819466235251480233146888453/2105966824533995296305066052820989724239126929367947461197037045249128619850436016331243721520290589902278760*t^45 - 17026107653299804887178472317302705186601551707894341525504246110119507003729891075461142572715315799227798552895/50122010423909088052060572057139555436891220918957149576489481676929261152440377188683600572182916039674234488*t^43 + 658878156916893077967755963777580252619308960193549473998285058030957837812205627350178621610253814760434176365686803/803806681168230045090895394080347050541424509877315807758161817652914561101686328974918902376097424528255698484056*t^41 - 536807831660565443267067897405844337443478315158129751523488446994329379677493523357932232353199715890899993755383552867/365732039931544670516357404306557907996348151994178692529963627032076125301267279683588100581124328160356342810245480*t^39 + 973278430210022844742104047038791640534177877727514408446588848498080142916418936755663816716080079506125056800729586289/481226368330979829626786058298102510521510726308129858592057403989573849080614841688931711290953063368889924750323000*t^37 - 1943900066759355725175015357422712911106859910165065123414202223301903989163771718066443689544922307135509191501364053597/885618274491467081414001233338524788270679403877986882618996398938795570997097901931731468678308578804931878322023000*t^35 + 319364757258843254966270195951674269437402937538831369764572942137681068150162455682663417197511233419181670888494871337/167677059970384434081050900178760693245915300467565516442529984865745294775450536099074491403093090920400435628969688*t^33 - 8388116234223881186320722152237303504388202559145676755186714844024235451021632166755374099798145493040437059309810704541/6287889748889416278039408756703525996721823767533706866594874432465448554079395103715293427615990909515016336086363300*t^31 + 4415762978362470416557473830704040720577313049045987340370568268402941147439981419172156335004263561411169556149879519749/5824266541598030746018069862200040208945099434443663963988800741592420089262481179017391608068268077477042781351884900*t^29 - 3556793447713236320660868926004403211537251435972657018937625538713292402351086970070000014397589923786412731756575907007/10153414852211126396315026004984744425555633113685314573237181369442724676683635771850242075368053545027028603506159500*t^27 + 718582519125547658934056621990153945396138138729491917476971202111854347661715071272699564175033496417421263417879872629/5467223381959837290323475541145631613760725522753630924050789968161467133598880800227053425198182678091476940349470500*t^25 - 106408999576153332877050327922597382191534505119488298209763379472390050483989609497393748049616435406356376611498362279/2668005010396400597677856064079068227515234055103771890936785504462795961196253830510802071496713146908640746890541604*t^23 + 18521094858566590384459200502964716429718329792762733342306071386056394521213326273389273726936900235561231923516675981/1905717864568857569769897188627905876796595753645551350669132503187711400854467021793430051069080819220457676350386860*t^21 - 3586363054321968661529219116134959911946960191176032127527478766540362633019520423354631286189012214027469433698672141/1905717864568857569769897188627905876796595753645551350669132503187711400854467021793430051069080819220457676350386860*t^19 + 2719310674806162611922649755312675134729632116456717057783198335489231516642231735470376719398528303661107011359254679/9528589322844287848849485943139529383982978768227756753345662515938557004272335108967150255345404096102288381751934300*t^17 - 4795244207960876656311116501898594465232704065383558518426250642196992967030239122763429857099044421135673042534651161/144290066888784930282577929996112873528885107061734602264948603812783863207552503078645418152373262026691795495100719400*t^15 + 6899483887524059034617999218263347672129013247212234129411361147932195123382208430500853425401880319145370431889283253/2383671905002727048268187403535784670697181968659855629416950934987189420188767350859222307877206288680948461579063884488*t^13 - 318751440717525501856207947699762313840971610249579612063607447400289709747017540940530761789018172854010109871664333619/1751998850177004380477117741598801732962428746964993887621458937215584223838744002881528396289746622180497119260611955098680*t^11 + 77998230057370054396747529849177314574108749260480920059192780341268734924299750894762596989368075958817956379890558057/9927993484336358156037000535726543153453762899468298696521600644221643935086216016328660912308564192356150342476801078892520*t^9 - 412201300288685588321472204407746287649081817836406112014762597832549880677209015278600574651419076654987240433891609/1897704991975762625399426661758594767762791701105610414828072557748603971495353162074894942996606837573107208320515296770200*t^7 + 465367285107581711451041173276008912083509551806142723801724301572222136292748597567495477202588325862234547730695047/134737054430279146403359292984860228511158210778498339452793151600150881976170074507317540952759085467690611790756586070684200*t^5 - 141564430854582129473967529895684301115932028369734958087250714987792559949779980186307944055344264372374071592911/5389482177211165856134371719394409140446328431139933578111726064006035279046802980292701638110363418707624471630263442827368*t^3 + 184679430555556639077969412133282176379316140982280449554074305438525842789652147993064384451479955993880875277/2943834802678367904611211443366694068311019731294921702329934404709178933933127678311139550228349766520971350050143897342680*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:
| (-0.99850495894663499841 - 1.1163172260000386485e-912j)  +/-  (1.07e-239, 1.07e-239j)
| (-0.99213874716681282044 - 1.6535076261383448032e-913j)  +/-  (3.36e-239, 3.36e-239j)
| (-0.90030150467747382532 - 3.8543428129329671627e-916j)  +/-  (5.72e-239, 5.72e-239j)
| (0.99850495894663499841 - 2.2522485123081428596e-917j)  +/-  (1.08e-239, 1.08e-239j)
| (0.94384458840419364444 - 3.4822770359473208307e-932j)  +/-  (6.93e-239, 6.93e-239j)
| (0.92040938117918596669 + 1.4828373084372600515e-948j)  +/-  (7.46e-239, 7.46e-239j)
| (-0.87803389693475914942 - 4.7365039119670159531e-954j)  +/-  (2.42e-239, 2.42e-239j)
| (-0.92040938117918596669 + 1.8094382743019759348e-959j)  +/-  (6.87e-239, 6.87e-239j)
| (0.96451946280784400487 - 1.64419231255731854e-969j)  +/-  (6.25e-239, 6.25e-239j)
| (-0.98075725178499407913 - 1.0813170514082260614e-979j)  +/-  (5.65e-239, 5.65e-239j)
| (0.84512275620248525694 + 6.8323414450655069926e-987j)  +/-  (5.59e-240, 5.59e-240j)
| (0.99213874716681282044 - 1.8391609403292798108e-993j)  +/-  (3.35e-239, 3.35e-239j)
| (-0.8059878668603262635 - 1.3316250083772070128e-1008j)  +/-  (1.24e-240, 1.24e-240j)
| (-0.84512275620248525694 + 9.3690144655852778369e-1008j)  +/-  (5.28e-240, 5.28e-240j)
| (0.98075725178499407913 - 4.8110070148409841831e-1008j)  +/-  (5.36e-239, 5.36e-239j)
| (0.8059878668603262635 + 8.3888232200913076858e-1016j)  +/-  (1.15e-240, 1.15e-240j)
| (0.90030150467747382532 - 8.7659068920343464476e-1016j)  +/-  (5.76e-239, 5.76e-239j)
| (-0.96451946280784400487 + 3.837123902098543028e-1021j)  +/-  (7.07e-239, 7.07e-239j)
| (-0.71460006907976081269 + 7.4380123813643233357e-1029j)  +/-  (5.56e-242, 5.56e-242j)
| (-0.94384458840419364444 + 3.8205115267490195811e-1028j)  +/-  (6.62e-239, 6.62e-239j)
| (0.87803389693475914942 - 1.9066298094114616059e-1032j)  +/-  (2.44e-239, 2.44e-239j)
| (0.7622702556366203736 + 9.2880361475809606454e-1039j)  +/-  (2.58e-241, 2.58e-241j)
| (0.17241534909934102453 - 7.1612833274654430195e-1051j)  +/-  (6.38e-252, 6.38e-252j)
| (-0.61138960967487175826 + 1.2191689841065743365e-1038j)  +/-  (3.1e-243, 3.1e-243j)
| (-0.7622702556366203736 - 3.1708020536919118846e-1039j)  +/-  (2.35e-241, 2.35e-241j)
| (-0.064202495068776816539 + 3.9639030680256428444e-1053j)  +/-  (2.32e-254, 2.32e-254j)
| (0.71460006907976081269 - 2.2625229949793655696e-1040j)  +/-  (5.46e-242, 5.46e-242j)
| (0.66360847523580159924 + 2.0386146717217931742e-1042j)  +/-  (1.08e-242, 1.08e-242j)
| (-0.17241534909934102453 + 7.5009284499925128045e-1052j)  +/-  (6.61e-252, 6.61e-252j)
| (-0.66360847523580159924 - 1.4898365243155764215e-1043j)  +/-  (1.09e-242, 1.09e-242j)
| (-0.29390379477602130466 - 1.1224497952322349933e-1050j)  +/-  (1.12e-249, 1.12e-249j)
| (0.54347519003464580297 + 5.45154752522419595e-1044j)  +/-  (2.09e-244, 2.09e-244j)
| (0.57735026918962576451 - 3.5235050875703904575e-1043j)  +/-  (1.16e-243, 1.16e-243j)
| (0.12172613438315505292 - 1.7020767203898658376e-1055j)  +/-  (5.79e-253, 5.79e-253j)
| (-0.54347519003464580297 + 1.8377869689403965848e-1046j)  +/-  (2.04e-244, 2.04e-244j)
| (-0.57735026918962576451 - 1.6153041705296835981e-1046j)  +/-  (1.18e-243, 1.18e-243j)
| (0.064202495068776816539 - 1.794257156851921613e-1056j)  +/-  (2.32e-254, 2.32e-254j)
| (0.61138960967487175826 - 9.4078594529555156885e-1049j)  +/-  (3.15e-243, 3.15e-243j)
| (0.29390379477602130466 + 3.0419819352330295619e-1056j)  +/-  (1.19e-249, 1.19e-249j)
| (-0.23000375096015989415 - 8.800637639286965345e-1057j)  +/-  (7.54e-251, 7.54e-251j)
| (-0.48573276128312239515 + 8.5692169941308035693e-1053j)  +/-  (8.86e-246, 8.86e-246j)
| (-0.12172613438315505292 + 6.6413798712994012251e-1060j)  +/-  (5.61e-253, 5.61e-253j)
| (0.35909882564439703209 + 1.9229529155132838836e-1054j)  +/-  (2.19e-248, 2.19e-248j)
| (0.48573276128312239515 - 4.5495483615461806244e-1053j)  +/-  (8.73e-246, 8.73e-246j)
| (-2.7633594492232948955e-1070 + 4.6241590726258879008e-1070j)  +/-  (2.64e-1068, 2.64e-1068j)
| (-0.35909882564439703209 + 7.8748388601259501578e-1056j)  +/-  (2.29e-248, 2.29e-248j)
| (-0.42344636948498446212 + 1.2966739441266287337e-1054j)  +/-  (4.21e-247, 4.21e-247j)
| (0.23000375096015989415 - 9.8939204990916096944e-1060j)  +/-  (7.12e-251, 7.12e-251j)
| (0.42344636948498446212 - 1.0015514429927143333e-1054j)  +/-  (3.99e-247, 3.99e-247j)
-------------------------------------------------
The weights are:
| (0.003834978456964614257 - 1.5569490059386793777e-912j)  +/-  (3.31e-65, 6.78e-180j)
| (0.0088899951398229892604 + 2.4759686175839634674e-912j)  +/-  (2.57e-65, 5.26e-180j)
| (0.017881656922667645414 - 6.8998222161036084309e-912j)  +/-  (4.85e-66, 9.92e-181j)
| (0.003834978456964614257 - 1.9220362845688495828e-915j)  +/-  (3.66e-67, 7.5e-182j)
| (0.022573204027681001466 - 8.6512917997676586434e-914j)  +/-  (3.97e-67, 8.12e-182j)
| (0.023153322568272092869 + 2.1476424093220905974e-913j)  +/-  (2.14e-67, 4.38e-182j)
| (0.028364900695893604623 + 5.5064106599058303259e-912j)  +/-  (5.33e-67, 1.09e-181j)
| (0.023153322568272092869 + 5.2355496703069118972e-912j)  +/-  (5.82e-67, 1.19e-181j)
| (0.018567292845428340061 + 3.8495782665913329238e-914j)  +/-  (1.26e-67, 2.57e-182j)
| (0.01384820510302483107 - 1.8907138554058185742e-912j)  +/-  (2.64e-67, 5.39e-182j)
| (0.036495610943764216086 - 2.8643464198335442201e-913j)  +/-  (3.83e-69, 7.84e-184j)
| (0.0088899951398229892604 + 7.4992920201379411959e-915j)  +/-  (2.94e-68, 6.02e-183j)
| (0.041559251759618385916 + 2.659567483835224698e-912j)  +/-  (1.5e-69, 3.07e-184j)
| (0.036495610943764216086 - 3.4304499757918517175e-912j)  +/-  (7.02e-69, 1.44e-183j)
| (0.01384820510302483107 - 1.7884633192272074919e-914j)  +/-  (3.57e-68, 7.3e-183j)
| (0.041559251759618385916 + 2.8453497316994876021e-913j)  +/-  (7.79e-71, 1.59e-185j)
| (0.017881656922667645414 - 3.5901230715469872909e-913j)  +/-  (3.38e-69, 6.92e-184j)
| (0.018567292845428340061 + 2.1768806048421858686e-912j)  +/-  (9.91e-70, 2.03e-184j)
| (0.049464791106294069158 + 2.8873687534154992273e-912j)  +/-  (6.22e-73, 1.27e-187j)
| (0.022573204027681001466 - 3.0379046082481097538e-912j)  +/-  (7.82e-70, 1.6e-184j)
| (0.028364900695893604623 + 3.5518602244694420881e-913j)  +/-  (1.72e-70, 3.52e-185j)
| (0.04578137988212780661 - 3.3937366514254536071e-913j)  +/-  (4.69e-73, 9.61e-188j)
| (0.052556713052330589424 + 5.0364813110447960605e-912j)  +/-  (8.61e-77, 1.76e-191j)
| (0.049943246585814121083 + 9.1380041329113888255e-912j)  +/-  (5.22e-75, 1.07e-189j)
| (0.04578137988212780661 - 2.5239942985603842126e-912j)  +/-  (1.14e-72, 2.34e-187j)
| (0.062104438499299059014 + 6.1389145691618177023e-912j)  +/-  (1.6e-77, 3.28e-192j)
| (0.049464791106294069158 + 4.7934603764576360915e-913j)  +/-  (9.7e-75, 1.98e-189j)
| (0.052292082794591268077 - 8.427143643603404619e-913j)  +/-  (9.7e-76, 1.99e-190j)
| (0.052556713052330589424 + 7.1373460304219877406e-912j)  +/-  (2.85e-78, 5.83e-193j)
| (0.052292082794591268077 - 4.1765495882326172329e-912j)  +/-  (1.48e-75, 3.02e-190j)
| (0.065072159432865605755 + 3.7895117669444666466e-912j)  +/-  (1.03e-78, 2.12e-193j)
| (0.052263075638014899819 + 2.9177963441966361031e-912j)  +/-  (5.24e-78, 1.07e-192j)
| (0.019268663858928871618 - 3.6331666836407007276e-912j)  +/-  (1.25e-77, 2.55e-192j)
| (0.052311279649329446798 - 5.8983601293050464744e-912j)  +/-  (1.77e-79, 3.62e-194j)
| (0.052263075638014899819 + 9.8786557155549457267e-912j)  +/-  (9.11e-79, 1.86e-193j)
| (0.019268663858928871618 - 1.3580464678023763284e-911j)  +/-  (3.15e-78, 6.45e-193j)
| (0.062104438499299059014 + 5.3975693446311049838e-912j)  +/-  (3.61e-80, 7.38e-195j)
| (0.049943246585814121083 + 2.199871141700058362e-912j)  +/-  (7.24e-79, 1.48e-193j)
| (0.065072159432865605755 + 2.0667646086983164249e-912j)  +/-  (3.33e-81, 6.81e-196j)
| (0.061880255201310049972 - 5.1543823978875857491e-912j)  +/-  (1.14e-80, 2.33e-195j)
| (0.06078347394927139526 - 4.7447780395757597158e-912j)  +/-  (1.28e-80, 2.62e-195j)
| (0.052311279649329446798 - 7.5350448183601146761e-912j)  +/-  (1.09e-80, 2.22e-195j)
| (0.064999297058428133832 - 1.5585231366996663325e-912j)  +/-  (1.9e-82, 3.88e-197j)
| (0.06078347394927139526 - 1.6404491351773260629e-912j)  +/-  (4.32e-82, 8.84e-197j)
| (0.065194615540871556525 - 5.2138669527700204133e-912j)  +/-  (1.07e-81, 2.2e-196j)
| (0.064999297058428133832 - 3.3074916615214616382e-912j)  +/-  (1.27e-82, 2.61e-197j)
| (0.063513417057821184295 + 3.5023072840501475405e-912j)  +/-  (1.26e-82, 2.59e-197j)
| (0.061880255201310049972 - 3.2252760667205158316e-912j)  +/-  (3.51e-83, 7.29e-198j)
| (0.063513417057821184295 + 1.4172474259922881806e-912j)  +/-  (1.54e-83, 3.08e-198j)
