Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 5 36
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 36 Kronrod extension for:
P2 : 4*t^7 - 106/3*t^5 + 215/3*t^3 - 55/2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^43 - 9927754837833699314402484607543676023535101344710/5704955889151219891120510691412034070932977681*t^41 + 15582483346496486490146577962603997837003716930886671/45639647113209759128964085531296272567463821448*t^39 - 6098197867015311851302895372023274867119083006213349151/152132157044032530429880285104320908558212738160*t^37 + 958755324443548580784883270884038062551581739582485706261/304264314088065060859760570208641817116425476320*t^35 - 21400844444821631737887886127101785992104982501566278597507/121705725635226024343904228083456726846570190528*t^33 + 438560054185789614916890757605792370210730449806796730511453/60852862817613012171952114041728363423285095264*t^31 - 26950647391760341575932409362302311285899659501015124873979315/121705725635226024343904228083456726846570190528*t^29 + 1256614490418651424966435124563143819375658223621237949384904401/243411451270452048687808456166913453693140381056*t^27 - 3440163093652938825686381758241429672005321207156749649437778407/37447915580069545951970531717986685183560058624*t^25 + 187142943638192877313609691564139295689213261169766167431961767975/149791662320278183807882126871946740734240234496*t^23 - 3879670590354472266801737459360912055340512656067517936562270346225/299583324640556367615764253743893481468480468992*t^21 + 60904767454619854786240470099389781386333450509724287913924324839875/599166649281112735231528507487786962936960937984*t^19 - 716540752497881027313646401673761843524131047574813903695488220518025/1198333298562225470463057014975573925873921875968*t^17 + 3112645351439508528769245877520381132248487586482380458714351206243325/1198333298562225470463057014975573925873921875968*t^15 - 19569309231432629396867756692871929381723400628749110895560383104479875/2396666597124450940926114029951147851747843751936*t^13 + 86566293968857084684664941464214117504673857996615502967439242030349875/4793333194248901881852228059902295703495687503872*t^11 - 258734046356154026641315762276189376618199346518697208461050830465840625/9586666388497803763704456119804591406991375007744*t^9 + 1963800493752519211236203222740846003672776216396516615593185675763966625/76693331107982430109635648958436731255931000061952*t^7 - 2131985069593241770535663888532769843616952462237571678837582175321160375/153386662215964860219271297916873462511862000123904*t^5 + 1089735668106867422489501006172284041531174632245315294887706724318658125/306773324431929720438542595833746925023724000247808*t^3 - 165734756789443697915182301854446094650607802136733150841421471262164375/613546648863859440877085191667493850047448000495616*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:
| (-5.6335191884622061353 + 1.371328296105663446e-891j)  +/-  (2.88e-245, 2.88e-245j)
| (7.7683844835622970708 - 3.380734180648505114e-899j)  +/-  (4.94e-247, 4.94e-247j)
| (8.7173667676509224921 - 5.8523515982350363951e-902j)  +/-  (2.69e-248, 2.69e-248j)
| (6.0959818384438232642 - 1.869731650646238161e-897j)  +/-  (1.92e-245, 1.92e-245j)
| (-7.1355236175259249618 - 2.011521667736911577e-906j)  +/-  (2.91e-246, 2.91e-246j)
| (-6.0959818384438232642 - 7.2606998570194295157e-922j)  +/-  (1.87e-245, 1.87e-245j)
| (-7.7683844835622970708 + 5.4402885203329006075e-932j)  +/-  (5.15e-247, 5.15e-247j)
| (6.5911124693884797789 + 6.3333799403991063352e-939j)  +/-  (8.93e-246, 8.93e-246j)
| (-5.1946641820043892258 + 6.0230763352974060424e-948j)  +/-  (3.49e-245, 3.49e-245j)
| (3.5850768638956568877 - 4.4394548216144555225e-956j)  +/-  (4.16e-246, 4.16e-246j)
| (-6.5911124693884797789 - 2.2545133254324822862e-957j)  +/-  (8.97e-246, 8.97e-246j)
| (3.2060478821792656191 - 1.592332294054036365e-960j)  +/-  (1.61e-246, 1.61e-246j)
| (-8.7173667676509224921 + 5.3363819066016095751e-965j)  +/-  (2.83e-248, 2.83e-248j)
| (-4.7737622206307793749 + 5.7959246073162406774e-961j)  +/-  (2.74e-245, 2.74e-245j)
| (-3.9714525686314635053 + 1.5850341631768095136e-964j)  +/-  (9.44e-246, 9.44e-246j)
| (1.0673767481200508411 - 3.3401896729498303883e-974j)  +/-  (5.37e-251, 5.37e-251j)
| (-3.2060478821792656191 + 4.190180845638300629e-969j)  +/-  (1.5e-246, 1.5e-246j)
| (-4.3669598826285768923 + 1.3748936763659816113e-968j)  +/-  (1.72e-245, 1.72e-245j)
| (-1.6608104860778252541 - 2.9573663629461146008e-972j)  +/-  (3.1e-248, 3.1e-248j)
| (7.1355236175259249618 - 1.8122483543468254679e-968j)  +/-  (2.89e-246, 2.89e-246j)
| (2.8327170744005957913 - 6.3506911180221938333e-971j)  +/-  (4.55e-247, 4.55e-247j)
| (1.6608104860778252541 + 3.2540194370747261069e-972j)  +/-  (3.18e-248, 3.18e-248j)
| (-2.4631197782145911371 - 7.0057177253493507577e-972j)  +/-  (1.3e-247, 1.3e-247j)
| (3.9714525686314635053 - 5.1896894281242992576e-969j)  +/-  (9.59e-246, 9.59e-246j)
| (1.5638209050585896891 - 1.1459915290210029493e-980j)  +/-  (4.25e-248, 4.25e-248j)
| (-2.0929770949463074706 - 7.482738162277194131e-982j)  +/-  (3.73e-248, 3.73e-248j)
| (1.5054482028623358456 + 8.8927924284690931755e-981j)  +/-  (2.03e-248, 2.03e-248j)
| (5.6335191884622061353 + 9.93678425595506248e-977j)  +/-  (2.97e-245, 2.97e-245j)
| (4.7737622206307793749 + 5.2185754490016195565e-983j)  +/-  (2.76e-245, 2.76e-245j)
| (-0.7071067811865475244 - 3.9964090376705403633e-997j)  +/-  (2.05e-252, 2.05e-252j)
| (-1.5054482028623358456 + 2.28279267718995919e-993j)  +/-  (2.02e-248, 2.02e-248j)
| (4.3669598826285768923 + 1.9596685296470851696e-990j)  +/-  (1.72e-245, 1.72e-245j)
| (2.4631197782145911371 - 2.3558581316615492123e-994j)  +/-  (1.46e-247, 1.46e-247j)
| (-3.5850768638956568877 - 1.060212156739017989e-994j)  +/-  (4.37e-246, 4.37e-246j)
| (-1.0673767481200508411 + 9.4874981170937365873e-1003j)  +/-  (5.37e-251, 5.37e-251j)
| (-2.8327170744005957913 + 2.5641955614258760014e-999j)  +/-  (4.71e-247, 4.71e-247j)
| (2.0929770949463074706 - 4.0507131166245258254e-1004j)  +/-  (4e-248, 4e-248j)
| (1.3752035540236892025e-1013 + 1.6926856092507848499e-1013j)  +/-  (9.38e-1012, 9.38e-1012j)
| (0.35268321296490598442 + 5.0133503354883476981e-1011j)  +/-  (8.86e-254, 8.86e-254j)
| (-1.5638209050585896891 - 3.4935947218134712694e-1009j)  +/-  (4.15e-248, 4.15e-248j)
| (-0.35268321296490598442 - 1.1412208945689101363e-1017j)  +/-  (8.86e-254, 8.86e-254j)
| (5.1946641820043892258 + 2.1075674745421965064e-1011j)  +/-  (3.44e-245, 3.44e-245j)
| (0.7071067811865475244 - 4.3095610215824588767e-1026j)  +/-  (2.15e-252, 2.15e-252j)
-------------------------------------------------
The weights are:
| (4.1798400577059891453e-15 + 3.3848194793093561002e-905j)  +/-  (4.31e-83, 1.28e-204j)
| (2.4647177420520246851e-27 + 2.5509539360359363442e-913j)  +/-  (2.87e-89, 8.52e-211j)
| (1.026433484037589008e-33 - 2.3915429932726559831e-916j)  +/-  (1.77e-91, 5.26e-213j)
| (1.9543817664683143071e-17 - 2.9867125737229030332e-908j)  +/-  (1.68e-85, 5e-207j)
| (2.5195699467792154589e-23 + 2.2845010762151392621e-910j)  +/-  (2.65e-89, 7.89e-211j)
| (1.9543817664683143071e-17 + 7.5752968989519062198e-907j)  +/-  (1.54e-86, 4.57e-208j)
| (2.4647177420520246851e-27 - 1.601394288138781398e-912j)  +/-  (1.97e-91, 5.85e-213j)
| (3.9546525847342714403e-20 + 1.1783112656691353777e-909j)  +/-  (2.86e-89, 8.51e-211j)
| (4.6213481500831988188e-13 - 1.5664669666189939697e-904j)  +/-  (4.76e-85, 1.41e-206j)
| (5.6504344959624833533e-07 - 1.7359764568025658997e-902j)  +/-  (4.7e-82, 1.4e-203j)
| (3.9546525847342714403e-20 - 1.5042277870739180787e-908j)  +/-  (2.8e-88, 8.33e-210j)
| (7.286144470213214302e-06 + 8.4902954983034814692e-902j)  +/-  (5.71e-81, 1.7e-202j)
| (1.026433484037589008e-33 + 1.1129195273544107718e-915j)  +/-  (1.06e-94, 3.16e-216j)
| (2.9556520149185959853e-11 + 7.4344808683325096472e-904j)  +/-  (4.3e-85, 1.28e-206j)
| (3.1138511585817812504e-08 + 1.8024728397391219151e-902j)  +/-  (2.12e-84, 6.3e-206j)
| (0.066278467616304991728 - 5.8594997050583952293e-899j)  +/-  (3.76e-72, 1.12e-193j)
| (7.286144470213214302e-06 + 3.0917176328463570048e-901j)  +/-  (2.9e-83, 8.62e-205j)
| (1.1807471553893766793e-09 - 3.7865218619206255871e-903j)  +/-  (5.98e-85, 1.78e-206j)
| (0.037308480979434625262 + 4.160149546158396495e-898j)  +/-  (4.5e-78, 1.34e-199j)
| (2.5195699467792154589e-23 - 2.6872296870835505221e-911j)  +/-  (2.87e-95, 8.53e-217j)
| (6.8544835520986175004e-05 - 3.7665231909368450981e-901j)  +/-  (1.19e-84, 3.54e-206j)
| (0.037308480979434625262 + 2.2657408000952389322e-898j)  +/-  (4.01e-80, 1.19e-201j)
| (0.00048222831412944683849 + 4.0726308478536831456e-900j)  +/-  (4.36e-83, 1.29e-204j)
| (3.1138511585817812504e-08 + 3.1190394461250307722e-903j)  +/-  (8.91e-89, 2.65e-210j)
| (-0.09592021838810562758 - 6.9696332270863123244e-898j)  +/-  (5.44e-80, 1.62e-201j)
| (0.0026432337438312424481 - 1.5978209212558564038e-899j)  +/-  (8.53e-83, 2.54e-204j)
| (0.091860293314295952829 + 5.0748429084774430823e-898j)  +/-  (5.92e-80, 1.76e-201j)
| (4.1798400577059891453e-15 + 5.0873336775509826982e-907j)  +/-  (8.51e-94, 2.53e-215j)
| (2.9556520149185959853e-11 + 6.1417014516081176449e-905j)  +/-  (2.79e-92, 8.25e-214j)
| (0.12188756671269131929 + 7.2762279822913921106e-899j)  +/-  (2.04e-82, 6e-204j)
| (0.091860293314295952829 + 8.7762884869726015039e-898j)  +/-  (4.53e-84, 1.33e-205j)
| (1.1807471553893766793e-09 - 4.795621923796174841e-904j)  +/-  (3.9e-91, 1.15e-212j)
| (0.00048222831412944683849 + 1.5947189924822010607e-900j)  +/-  (3.32e-87, 9.74e-209j)
| (5.6504344959624833533e-07 - 7.8124100908583636761e-902j)  +/-  (9.98e-90, 2.93e-211j)
| (0.066278467616304991728 - 8.5989215456814055871e-899j)  +/-  (1.32e-85, 3.86e-207j)
| (6.8544835520986175004e-05 - 1.1385410861401380042e-900j)  +/-  (1.85e-88, 5.44e-210j)
| (0.0026432337438312424481 - 7.3217550857084698888e-900j)  +/-  (4.49e-87, 1.29e-208j)
| (0.19884010517070712544 + 6.4655028449699421484e-899j)  +/-  (1.7e-86, 4.94e-208j)
| (0.17596346674934209523 - 6.0312224165930644668e-899j)  +/-  (1.2e-86, 3.43e-208j)
| (-0.09592021838810562758 - 1.2325932464399366811e-897j)  +/-  (8.58e-86, 2.59e-207j)
| (0.17596346674934209523 - 6.8368188526465726946e-899j)  +/-  (1.1e-86, 3.27e-208j)
| (4.6213481500831988188e-13 - 6.3487197119245925662e-906j)  +/-  (1.07e-94, 4.03e-216j)
| (0.12188756671269131929 + 5.6533374291353678112e-899j)  +/-  (4.19e-87, 1.04e-208j)
