Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 4 6 29
-------------------------------------------------
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 29 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^41 - 200878654664870721002356981670774076294062513277236691787769718660280181776686150147511416482124742715746383335039744459/13098896957413181817464871223832828865583339979972714427224843514161912270225101895778436692789697406609026877724435820*t^39 + 2295302302975720884225651232683393379303410141210102984129085542936241618827088569792657772341529950532286020195007285589685563/31594188410842135870452561333335984503973418398182723929719672930352352856534103739886782440905383380850475707151016182960024*t^37 - 14776021912362221081063870549817506301993151090670429892735738907373725397122950835413073895082091615464125766820377812195109881427/69823156387961120273700160546672525753781254659983819884680477176078699812940369265149789194400897271679551312803745764341653040*t^35 + 35551421321614917583385162262057209079390946084386077382347846196329495777619545373612089410279599953788081275077301648669908793/83821316192030156390996591292524040520745803913546002262521581243791956558151703799699626884034690602256364121012900077240880*t^33 - 2219486859970114367437194513661428323725230974062928460313806836273463245491065557557473267456055017098277022524077074602156670397/3579170201399687677895554448190776530235845827108414296609671519109916545033077752247174067948281288716346747967250833298185576*t^31 + 5057192984323960857602962985343288659888489067636335439194814104001132813685905130208909954610044330394985527937543456214614030304181/7390986465890355054854319935513953534937021632978875522498971686961977665493305558390414450313200861199256034552372970760753214440*t^29 - 122790717808097070962475171046624280030327441233311728102911758959025475600158721945973653070353835958243030088417244900618940746913/211171041882581572995837712443255815283914903799396443499970619627485076156951587382583270008948596034264458130067799164592948984*t^27 + 6253760023184224830464403033974554949945314612629956463201325302008729494289647621011937528683941474990308074351397382998864222293/16243926298660120999679824034096601175685761830722803346151586125191159704380891337121790000688353541097266010005215320353303768*t^25 - 1202994473361673679769802528231559763575613761601924736277490683069995958861306183893540915403437666204153178796931817878535221630377/6026496656802904890881214716649839036179417639198160041422238452445920250325310686072184090255379163747085689711934883851075697928*t^23 + 361014699688345899241077046278861031544366710182037906980379941749505305334833857533175997900610393330271459331798227857512571643425/4454367094158668832390463051436837548480439124624726987138176247460028011110012246227266501493106338421758988047951870672534211512*t^21 - 14277052664657074335063685526487999126647667038908176107728506812917929598569742088227598637966709179082724294709718760120891512128/556795886769833604048807881429604693560054890578090873392272030932503501388751530778408312686638292302719873505993983834066776439*t^19 + 13940926389762880860449577034111517217954999352486534511651394818309763025799547738286244549093218208495180279058087748632730042575/2227183547079334416195231525718418774240219562312363493569088123730014005555006123113633250746553169210879494023975935336267105756*t^17 - 2129347366776518885319525939721855642072168583853239261788032811250023209837268816080458362172795132986127894472180075029807108403/1834151156418275401572543609415168402315474933669005229998072572483540945751181513152403853555984962879547818607980182041631734152*t^15 + 84714269755935830610783758720633677314948821290562739337775784646808072852191958342971339018615288443487625231067105193185405276633/529545641017333512368301519232579334439939262992151367118014952712748035909019691154429741148092229997080877343818278272305390674456*t^13 - 8402617301659407497753974641976470890898897368504232110045145726918406536122470655708304721018257940988725511024444663909893156755/529545641017333512368301519232579334439939262992151367118014952712748035909019691154429741148092229997080877343818278272305390674456*t^11 + 52182695521120303529417194088202094239780456917500216826561072225074469573694784644001896942281057497223116534406672053054585785453/48188653332577349625515438250164719434034472932285774407739360696860071267720791895053106444476392929734359838287463322779790551375496*t^9 - 2292387538373890546262498328937135861526864145876677713076169144123855829494642001142675857660726325857845560379096611122852651185/48188653332577349625515438250164719434034472932285774407739360696860071267720791895053106444476392929734359838287463322779790551375496*t^7 + 2083995789649506032397264057916930218226218966072953845396206159562919856155861571386384450790558137422083876991056017186479083/1721023333306333915196979937505882836929802604724491943133548596316431116704313996251896658731299747490512851367409404384992519691982*t^5 - 203609874592532875451378189184252401014214549605873128554173998378707760397699603882150892520806429544751748481692156833063113/13768186666450671321575839500047062695438420837795935545068388770531448933634511970015173269850397979924102810939275235079940157535856*t^3 + 91374323838570304703853779495263468018464413181294175237794053309382828436189406729724568302318755831710206533275762711359705/1638414213307629887267524900505600460757172079697716329863138263693242423102506924431805619112197359610968234501773752974512878746766864*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:
| (0.98022284459131522569 - 3.4027217740990359265e-898j)  +/-  (6.09e-241, 6.09e-241j)
| (-0.99819248007898231313 - 3.6104926188189550752e-907j)  +/-  (1.43e-241, 1.43e-241j)
| (-0.96495734653674844542 + 1.2473229653352322131e-920j)  +/-  (4.83e-241, 4.83e-241j)
| (0.99819248007898231313 + 4.6076067721998743888e-926j)  +/-  (1.32e-241, 1.32e-241j)
| (0.96495734653674844542 + 6.1985896143244821693e-935j)  +/-  (4.69e-241, 4.69e-241j)
| (0.94237624791752907847 + 1.2596709307430741448e-936j)  +/-  (2.67e-241, 2.67e-241j)
| (-0.87625707217871741571 - 6.3411791612641724674e-936j)  +/-  (4.37e-242, 4.37e-242j)
| (-0.91248695683407599658 - 8.5238097502308566253e-940j)  +/-  (1.24e-241, 1.24e-241j)
| (-0.98022284459131522569 + 2.6854670677772227691e-950j)  +/-  (5.95e-241, 5.95e-241j)
| (0.79131145092211922853 - 6.9852635625366930179e-965j)  +/-  (5.16e-243, 5.16e-243j)
| (0.91248695683407599658 + 1.8817758536775181391e-962j)  +/-  (1.23e-241, 1.23e-241j)
| (-0.99105250481616767714 + 1.902842354335909343e-968j)  +/-  (4.51e-241, 4.51e-241j)
| (-0.94237624791752907847 - 5.8987257728194379567e-982j)  +/-  (2.48e-241, 2.48e-241j)
| (-0.79131145092211922853 + 4.4520474157275916569e-991j)  +/-  (4.93e-243, 4.93e-243j)
| (0.99105250481616767714 + 4.7408714135693718459e-989j)  +/-  (4.52e-241, 4.52e-241j)
| (0.87625707217871741571 - 5.2966951820487540777e-1005j)  +/-  (4.53e-242, 4.53e-242j)
| (0.83508083966415356444 - 5.2126191460832254032e-1015j)  +/-  (1.54e-242, 1.54e-242j)
| (-0.83508083966415356444 - 3.2359981380248764285e-1020j)  +/-  (1.55e-242, 1.55e-242j)
| (-0.74677180221832073614 + 6.5449262713758148551e-1023j)  +/-  (1.41e-243, 1.41e-243j)
| (-0.22730163529496603266 + 3.227082442167014434e-1031j)  +/-  (1.29e-251, 1.29e-251j)
| (0.50865952693448286855 + 2.3361542153894057497e-1025j)  +/-  (2.82e-247, 2.82e-247j)
| (0.74677180221832073614 - 9.5947667968017769946e-1023j)  +/-  (1.39e-243, 1.39e-243j)
| (0.15655801081562154215 - 1.2197890978008102917e-1034j)  +/-  (5.57e-253, 5.57e-253j)
| (-0.57735026918962576451 - 9.844869386356025533e-1029j)  +/-  (3.12e-246, 3.12e-246j)
| (-0.69795429855773288377 - 1.8980187830192227958e-1027j)  +/-  (2.6e-244, 2.6e-244j)
| (0.079862463709358007857 + 5.6928417603256544947e-1036j)  +/-  (1.93e-254, 1.93e-254j)
| (0.69795429855773288377 - 4.4304742506602739749e-1028j)  +/-  (2.63e-244, 2.63e-244j)
| (0.43693939954921891801 + 1.482059551106229046e-1033j)  +/-  (2.25e-248, 2.25e-248j)
| (-0.15655801081562154215 - 6.0926823053226198239e-1040j)  +/-  (6.27e-253, 6.27e-253j)
| (-0.64112778535063222988 - 3.9843662937911216806e-1032j)  +/-  (3.28e-245, 3.28e-245j)
| (-0.079862463709358007857 - 5.72190155401601253e-1040j)  +/-  (2.32e-254, 2.32e-254j)
| (0.36454779814427719704 - 5.7416121579460589443e-1035j)  +/-  (1.98e-249, 1.98e-249j)
| (0.64112778535063222988 + 6.9553878104176573345e-1032j)  +/-  (3.36e-245, 3.36e-245j)
| (2.9909759029289737287e-1044 - 2.1394973301201493033e-1044j)  +/-  (1.51e-1042, 1.51e-1042j)
| (-0.43693939954921891801 - 5.4908139501477086835e-1038j)  +/-  (2.13e-248, 2.13e-248j)
| (-0.36454779814427719704 - 6.0455674984676131357e-1039j)  +/-  (1.78e-249, 1.78e-249j)
| (0.22730163529496603266 - 9.3809812994284174434e-1040j)  +/-  (1.23e-251, 1.23e-251j)
| (0.57735026918962576451 + 3.368749016373130522e-1036j)  +/-  (3.34e-246, 3.34e-246j)
| (0.29459807959422975131 - 1.8806257881500756273e-1040j)  +/-  (1.68e-250, 1.68e-250j)
| (-0.29459807959422975131 - 3.5731907704183164114e-1041j)  +/-  (1.66e-250, 1.66e-250j)
| (-0.50865952693448286855 + 1.4356552734617357094e-1037j)  +/-  (2.77e-247, 2.77e-247j)
-------------------------------------------------
The weights are:
| (0.012448186212345337553 + 7.713534244606518446e-899j)  +/-  (1.1e-73, 6.97e-190j)
| (0.0045776449992847610002 + 2.8444266125466834308e-901j)  +/-  (2.9e-74, 1.84e-190j)
| (0.018709110330984077021 - 2.7021806302615576104e-900j)  +/-  (2.68e-74, 1.7e-190j)
| (0.0045776449992847610002 - 3.1316536017893137896e-899j)  +/-  (1.72e-74, 1.09e-190j)
| (0.018709110330984077021 - 3.4432084164137958123e-898j)  +/-  (2.73e-74, 1.73e-190j)
| (0.026377405820556032963 + 1.4390973622482209459e-898j)  +/-  (7.04e-75, 4.47e-191j)
| (0.038999301978754667166 + 3.7831312630222790296e-900j)  +/-  (5.76e-76, 3.66e-192j)
| (0.033240526616905596241 - 3.1109263658589123907e-900j)  +/-  (6.74e-76, 4.28e-192j)
| (0.012448186212345337553 + 2.1606158708968562135e-900j)  +/-  (5.37e-76, 3.41e-192j)
| (0.044137853400692980915 + 6.4256182411872103807e-899j)  +/-  (2.27e-78, 1.44e-194j)
| (0.033240526616905596241 - 8.6927054481943277387e-899j)  +/-  (4.25e-77, 2.7e-193j)
| (0.0093116168452263077282 - 1.1283752230937286509e-900j)  +/-  (3.21e-76, 2.04e-192j)
| (0.026377405820556032963 + 2.83288035185234184e-900j)  +/-  (1.17e-76, 7.44e-193j)
| (0.044137853400692980915 + 6.8520969086036335517e-900j)  +/-  (2.14e-79, 1.36e-195j)
| (0.0093116168452263077282 + 2.0539333826258691924e-898j)  +/-  (3.46e-77, 2.2e-193j)
| (0.038999301978754667166 + 6.7554035931538967218e-899j)  +/-  (8.55e-79, 5.43e-195j)
| (0.042955171734225994544 - 6.3086811080172244297e-899j)  +/-  (2.18e-79, 1.38e-195j)
| (0.042955171734225994544 - 5.0440849246842411549e-900j)  +/-  (9.89e-80, 6.28e-196j)
| (0.045658093774198748202 - 8.1678283940449639152e-900j)  +/-  (2.92e-81, 1.85e-197j)
| (0.067894878833935198755 - 1.7758438197762448185e-899j)  +/-  (2.01e-84, 1.28e-200j)
| (0.070532115533134733304 - 2.4026452713324227475e-899j)  +/-  (3.43e-84, 2.18e-200j)
| (0.045658093774198748202 - 6.0422930856147719924e-899j)  +/-  (3.94e-82, 2.5e-198j)
| (0.073980565146035973229 + 2.3868652343236447096e-899j)  +/-  (2.58e-85, 1.64e-201j)
| (0.066547960905323744985 + 7.085528323828443571e-900j)  +/-  (1.86e-84, 1.18e-200j)
| (0.052706009516691696077 + 8.0698210217249465124e-900j)  +/-  (4.47e-83, 2.84e-199j)
| (0.07884430107171955669 - 1.9215773200978813095e-899j)  +/-  (7.17e-86, 4.55e-202j)
| (0.052706009516691696077 + 4.7977677973540313085e-899j)  +/-  (4.2e-84, 2.67e-200j)
| (0.072527953547909851093 + 2.3841741763719329354e-899j)  +/-  (1.21e-85, 7.66e-202j)
| (0.073980565146035973229 + 1.7294247553897136594e-899j)  +/-  (1.7e-86, 1.08e-202j)
| (0.060661863466092887896 - 7.3484400611905534885e-900j)  +/-  (2.94e-85, 1.87e-201j)
| (0.07884430107171955669 - 1.632049866787569282e-899j)  +/-  (9.28e-87, 5.9e-203j)
| (0.071687923274128312309 - 2.6167591314699833173e-899j)  +/-  (3.22e-87, 2.04e-203j)
| (0.060661863466092887896 - 3.5135864558550390547e-899j)  +/-  (1.69e-86, 1.08e-202j)
| (0.080362141675286558815 + 1.6735183177466682941e-899j)  +/-  (3.65e-87, 2.32e-203j)
| (0.072527953547909851093 + 9.1399722036758226966e-900j)  +/-  (1.34e-88, 8.53e-205j)
| (0.071687923274128312309 - 1.1980283036422092974e-899j)  +/-  (1.19e-88, 7.58e-205j)
| (0.067894878833935198755 - 2.8480734296678374635e-899j)  +/-  (1.3e-88, 8.29e-205j)
| (0.066547960905323744985 + 2.7393844107653891224e-899j)  +/-  (1.05e-88, 6.64e-205j)
| (0.068020446154210262921 + 2.9069001796523190743e-899j)  +/-  (8.37e-89, 5.31e-205j)
| (0.068020446154210262921 + 1.5633903611333292619e-899j)  +/-  (1.38e-89, 8.8e-206j)
| (0.070532115533134733304 - 7.6097305461527538772e-900j)  +/-  (6.79e-90, 4.24e-206j)
