Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 10 30
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P2 : 4*t^12 - 8477/76*t^10 + 155745/152*t^8 - 563535/152*t^6 + 1500975/304*t^4 - 2132865/1216*t^2 + 110565/2432
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^42 - 61207353021989050186093439767945403405255979935645700964984353136634333843/46168491920911358877925303948092177126149890934417148276370911268505659*t^40 + 13420370807049796208295901872713657202189000795399043272735951035099306363972295/67960020107581520268306047411591684729692639455462042262817981387240330048*t^38 - 26214145493621980678309982576576547995642860370641859169536765486511102402132729195/1495120442366793445902733043055017064053238068020164929781995590519287261056*t^36 + 3103346060075376926042638835741119294174124878367670137759342179515564029333826669825/2990240884733586891805466086110034128106476136040329859563991181038574522112*t^34 - 259573749563028979417813224719398014512206423844294372800092489751766805223221234871635/5980481769467173783610932172220068256212952272080659719127982362077149044224*t^32 + 360547827632354176332942505413128826467963873513377896149726880061897178642573333573265/271840080430326081073224189646366738918770557821848169051271925548961320192*t^30 - 180686737462785097052861051865904484853770725909149988675975040504750798841463069551281325/5980481769467173783610932172220068256212952272080659719127982362077149044224*t^28 + 6206318690884347465911891484413974937155144445296058534252129474007228973716502636666345575/11960963538934347567221864344440136512425904544161319438255964724154298088448*t^26 - 161540928928425090744642261875998184240530507735278809090048119892103951314807497494746923125/23921927077868695134443728688880273024851809088322638876511929448308596176896*t^24 + 277071933041578574054074511199400881144873362034800657498878009496125358188095955480626191625/4160335143977164371207604989370482265191618971882198065480335556227581943808*t^22 - 374836192373764589872406770581405023171003978829514433626934527847339422415820647703059434125/756424571632211703855928179885542230034839813069490557360061010223196717056*t^20 + 219553837522534815884474972017378828302444272519820918317268696406359553540036764524831608125/79623639119180179353255597882688655793141032954683216564216948444547022848*t^18 - 1802867031738013394252727190248765040206620540744531613780078434189666042261916356253946314375/159247278238360358706511195765377311586282065909366433128433896889094045696*t^16 + 5359540618999275141430210033047357267884860837436242003176221995115018107112048275771988953125/159247278238360358706511195765377311586282065909366433128433896889094045696*t^14 - 22482154419892454931000840100689589383634455961578948317516369690535575255869287753051138061875/318494556476720717413022391530754623172564131818732866256867793778188091392*t^12 + 64175841125614442952694195080644895568136430466101324394949091960367727964827445116097673355625/636989112953441434826044783061509246345128263637465732513735587556376182784*t^10 - 118290644395928218235500388772577532697406733017158799511007080804410747368526242061643855071875/1273978225906882869652089566123018492690256527274931465027471175112752365568*t^8 + 519796128616516583179568234614320354159727963711016563950626264104035607903107017302242350146875/10191825807255062957216716528984147941522052218199451720219769400902018924544*t^6 - 298676285382693432669654619641981516874693532823339154834807060756894544596165858494904241578125/20383651614510125914433433057968295883044104436398903440439538801804037849088*t^4 + 70117914651742730189419949334386424875740744562614615560752631290100557783984650229459074734375/40767303229020251828866866115936591766088208872797806880879077603608075698176*t^2 - 3084528772947522571400972385646213792530185742408354826094849505259273182787353840683984953125/81534606458040503657733732231873183532176417745595613761758155207216151396352
-------------------------------------------------
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:
| (2.7962452403682858841 - 7.0325621055616212827e-962j)  +/-  (5.98e-247, 5.98e-247j)
| (-4.0502167631843838546 - 6.8919340618192902954e-965j)  +/-  (9.34e-246, 9.34e-246j)
| (-6.9363305081923849317 - 8.4212485096003769018e-972j)  +/-  (2.5e-247, 2.5e-247j)
| (4.8946494638808759564 - 1.2262186458449232299e-974j)  +/-  (8.03e-246, 8.03e-246j)
| (6.9363305081923849317 - 3.4646377320969986151e-990j)  +/-  (2.76e-247, 2.76e-247j)
| (5.8328017656289415687 + 1.1127368160554881161e-997j)  +/-  (3.42e-246, 3.42e-246j)
| (-5.3498206028561683149 + 3.538424919066211828e-1002j)  +/-  (6.14e-246, 6.14e-246j)
| (7.63576424380732723 - 4.9082650892725842439e-1006j)  +/-  (2.71e-248, 2.71e-248j)
| (-7.63576424380732723 + 4.8425570948380915455e-1008j)  +/-  (2.73e-248, 2.73e-248j)
| (5.3498206028561683149 - 1.5851321765695480654e-1004j)  +/-  (5.75e-246, 5.75e-246j)
| (0.99077372635897689188 - 2.4244018577121197526e-1014j)  +/-  (5.32e-251, 5.32e-251j)
| (6.354418176832210432 - 7.7963266266466881361e-1008j)  +/-  (1.18e-246, 1.18e-246j)
| (-6.354418176832210432 + 1.1466144659754993597e-1007j)  +/-  (1.17e-246, 1.17e-246j)
| (-5.8328017656289415687 + 8.7145041173263969919e-1015j)  +/-  (3.12e-246, 3.12e-246j)
| (-3.4280095055890347716 + 7.00480160303168736e-1021j)  +/-  (7.68e-246, 7.68e-246j)
| (2.0436541275856649452 + 2.6278980429869786461e-1031j)  +/-  (3.01e-248, 3.01e-248j)
| (-3.6783246397895513046 + 6.1712799945463144231e-1027j)  +/-  (1.04e-245, 1.04e-245j)
| (3.6783246397895513046 - 2.5293113251060327155e-1028j)  +/-  (9.7e-246, 9.7e-246j)
| (-1.6482908413469640681 + 1.0017246254499070227e-1040j)  +/-  (1.5e-248, 1.5e-248j)
| (0.16761481870756104368 - 1.9343436070621980898e-1047j)  +/-  (2.54e-254, 2.54e-254j)
| (4.0502167631843838546 + 4.3940201604290461792e-1036j)  +/-  (9.01e-246, 9.01e-246j)
| (1.6482908413469640681 + 5.031401582373628347e-1046j)  +/-  (1.43e-248, 1.43e-248j)
| (2.4202956065692988266 - 8.6153442308168663936e-1045j)  +/-  (1.32e-247, 1.32e-247j)
| (4.4616520277646766015 + 3.9403052619780434865e-1047j)  +/-  (9.51e-246, 9.51e-246j)
| (-0.99077372635897689188 - 8.0088594032134156571e-1059j)  +/-  (6.08e-251, 6.08e-251j)
| (-4.8946494638808759564 + 7.8941604818208923686e-1053j)  +/-  (8.09e-246, 8.09e-246j)
| (1.3532153932168790075 + 1.2376529458804834515e-1061j)  +/-  (1.59e-249, 1.59e-249j)
| (3.1585601909389327459 + 6.2601519547990804901e-1062j)  +/-  (3.31e-246, 3.31e-246j)
| (-4.4616520277646766015 + 9.9868242961718018131e-1071j)  +/-  (9.75e-246, 9.75e-246j)
| (-0.7071067811865475244 - 9.902377905630467488e-1082j)  +/-  (5.6e-252, 5.6e-252j)
| (-1.5275840294818693394 - 1.6039253870785042796e-1079j)  +/-  (9.65e-249, 9.65e-249j)
| (1.5275840294818693394 + 1.7022976948732624214e-1078j)  +/-  (1.01e-248, 1.01e-248j)
| (0.7071067811865475244 - 1.3873813400433505083e-1081j)  +/-  (5.1e-252, 5.1e-252j)
| (-2.0436541275856649452 + 3.6511336207588661264e-1075j)  +/-  (2.86e-248, 2.86e-248j)
| (-0.47502150955652660714 + 5.1869200936196475185e-1082j)  +/-  (4.89e-253, 4.89e-253j)
| (-2.4202956065692988266 - 1.2680308434733740119e-1074j)  +/-  (1.19e-247, 1.19e-247j)
| (3.4280095055890347716 + 3.2412088256401532488e-1076j)  +/-  (8.55e-246, 8.55e-246j)
| (0.47502150955652660714 + 1.8994924348007581499e-1087j)  +/-  (4.89e-253, 4.89e-253j)
| (-1.3532153932168790075 - 8.0365136824997300177e-1083j)  +/-  (1.83e-249, 1.83e-249j)
| (-3.1585601909389327459 - 3.619807960051427575e-1085j)  +/-  (3.24e-246, 3.24e-246j)
| (-0.16761481870756104368 - 8.6714943450735727127e-1096j)  +/-  (2.54e-254, 2.54e-254j)
| (-2.7962452403682858841 - 6.4779260118468137783e-1093j)  +/-  (6.27e-247, 6.27e-247j)
-------------------------------------------------
The weights are:
| (8.4797906901986920326e-05 + 1.96437601076368629e-965j)  +/-  (9.38e-77, 3.12e-198j)
| (1.6878729982859022634e-08 - 1.9912703262910557969e-969j)  +/-  (9.01e-84, 3e-205j)
| (4.4908901851906297996e-22 - 3.074384385620955039e-978j)  +/-  (2.29e-93, 7.64e-215j)
| (9.854949841407560546e-12 - 2.6936705403536032907e-971j)  +/-  (1.27e-87, 4.23e-209j)
| (4.4908901851906297996e-22 - 7.2291648901435678291e-978j)  +/-  (3.19e-94, 1.06e-215j)
| (4.7307358896806782435e-16 - 3.3855328781429713646e-974j)  +/-  (2.74e-91, 9.11e-213j)
| (9.810974221482512983e-14 + 3.4425026002955175539e-973j)  +/-  (1.14e-91, 3.79e-213j)
| (2.1689666876842021559e-26 + 2.2623661598693356432e-980j)  +/-  (1.18e-96, 3.94e-218j)
| (2.1689666876842021559e-26 + 1.0493111134405169533e-980j)  +/-  (4.54e-98, 1.51e-219j)
| (9.810974221482512983e-14 + 1.0987443860018600049e-972j)  +/-  (1.83e-90, 6.09e-212j)
| (0.069670553596810710037 + 1.6573892683688661997e-963j)  +/-  (1.07e-82, 3.56e-204j)
| (8.972832713952668752e-19 + 6.8577603508799241382e-976j)  +/-  (4.89e-93, 1.63e-214j)
| (8.972832713952668752e-19 + 2.6657641595361187202e-976j)  +/-  (2.47e-95, 8.22e-217j)
| (4.7307358896806782435e-16 - 1.1909043148243336228e-974j)  +/-  (4e-94, 1.33e-215j)
| (9.0997434466663838004e-07 - 1.2576109860166075027e-967j)  +/-  (9.09e-89, 3.03e-210j)
| (0.0032692032220368344192 + 1.5409654697009087483e-964j)  +/-  (1.13e-83, 3.75e-205j)
| (2.4633498720997490958e-07 + 2.7496168167097248972e-968j)  +/-  (2.27e-89, 7.57e-211j)
| (2.4633498720997490958e-07 + 2.01522683709588417e-967j)  +/-  (3.37e-90, 1.12e-211j)
| (0.018480320275669202397 + 4.2285357497260532089e-964j)  +/-  (8.51e-84, 2.83e-205j)
| (0.18192304765334124671 - 1.5571026764194039069e-963j)  +/-  (6.92e-83, 2.31e-204j)
| (1.6878729982859022634e-08 - 1.0828807874684887675e-968j)  +/-  (2.83e-91, 9.41e-213j)
| (0.018480320275669202397 - 1.6369313401977641981e-963j)  +/-  (4.44e-84, 1.48e-205j)
| (0.00060713468949095991365 - 6.1614777935842900939e-965j)  +/-  (6.44e-87, 2.15e-208j)
| (5.3984324903410582555e-10 + 5.5652159698976355893e-970j)  +/-  (1.75e-92, 5.83e-214j)
| (0.069670553596810710037 - 7.9022434921176887634e-964j)  +/-  (3.75e-85, 1.25e-206j)
| (9.854949841407560546e-12 - 7.3438958988088343093e-972j)  +/-  (1.57e-95, 5.23e-217j)
| (0.038543634309635253492 - 2.2487594459814582248e-963j)  +/-  (5.07e-85, 1.69e-206j)
| (8.8722196037973893388e-06 + 5.5561320669664300739e-966j)  +/-  (1.14e-89, 3.79e-211j)
| (5.3984324903410582555e-10 + 1.2750934717626813389e-970j)  +/-  (1.45e-94, 4.83e-216j)
| (0.079357731242263391588 + 1.3807059744028633809e-963j)  +/-  (3.19e-85, 1.06e-206j)
| (-0.012490420860611245754 - 9.0653990739893429621e-964j)  +/-  (1.73e-87, 5.75e-209j)
| (-0.012490420860611245754 + 3.0892602830241263889e-963j)  +/-  (1.13e-85, 3.76e-207j)
| (0.079357731242263391588 - 2.315235163786052457e-963j)  +/-  (1.73e-85, 5.75e-207j)
| (0.0032692032220368344192 - 2.3966289136284537117e-965j)  +/-  (3.31e-90, 1.1e-211j)
| (0.12054395200699922082 - 1.5765418015643768702e-963j)  +/-  (2.6e-87, 8.68e-209j)
| (0.00060713468949095991365 + 4.4416960367997759862e-966j)  +/-  (1.23e-91, 4.08e-213j)
| (9.0997434466663838004e-07 - 1.2379510405571400538e-966j)  +/-  (5.96e-92, 2e-213j)
| (0.12054395200699922082 + 2.221720853054121275e-963j)  +/-  (1.35e-87, 4.55e-209j)
| (0.038543634309635253492 + 7.8212103589991023074e-964j)  +/-  (5e-89, 1.68e-210j)
| (8.8722196037973893388e-06 + 3.3825287842031478772e-967j)  +/-  (2.04e-93, 6.83e-215j)
| (0.18192304765334124671 + 1.381001977950321857e-963j)  +/-  (7.74e-90, 3.69e-211j)
| (8.4797906901986920326e-05 - 1.0667418838747727863e-966j)  +/-  (6.33e-93, 2.09e-214j)
