Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 10 30
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P2 : t^12 - 8477/152*t^10 + 155745/152*t^8 - 563535/76*t^6 + 1500975/76*t^4 - 2132865/152*t^2 + 110565/152
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^42 - 61207353021989050186093439767945403405255979935645700964984353136634333843/92336983841822717755850607896184354252299781868834296552741822537011318*t^40 + 13420370807049796208295901872713657202189000795399043272735951035099306363972295/67960020107581520268306047411591684729692639455462042262817981387240330048*t^38 - 26214145493621980678309982576576547995642860370641859169536765486511102402132729195/747560221183396722951366521527508532026619034010082464890997795259643630528*t^36 + 3103346060075376926042638835741119294174124878367670137759342179515564029333826669825/747560221183396722951366521527508532026619034010082464890997795259643630528*t^34 - 259573749563028979417813224719398014512206423844294372800092489751766805223221234871635/747560221183396722951366521527508532026619034010082464890997795259643630528*t^32 + 360547827632354176332942505413128826467963873513377896149726880061897178642573333573265/16990005026895380067076511852897921182423159863865510565704495346810082512*t^30 - 180686737462785097052861051865904484853770725909149988675975040504750798841463069551281325/186890055295849180737841630381877133006654758502520616222749448814910907632*t^28 + 6206318690884347465911891484413974937155144445296058534252129474007228973716502636666345575/186890055295849180737841630381877133006654758502520616222749448814910907632*t^26 - 161540928928425090744642261875998184240530507735278809090048119892103951314807497494746923125/186890055295849180737841630381877133006654758502520616222749448814910907632*t^24 + 277071933041578574054074511199400881144873362034800657498878009496125358188095955480626191625/16251309156160798325029706989728446348404761608914836193282560766513991968*t^22 - 374836192373764589872406770581405023171003978829514433626934527847339422415820647703059434125/1477391741469163484093609726338949668036796509901348744843869160592181088*t^20 + 219553837522534815884474972017378828302444272519820918317268696406359553540036764524831608125/77757460077324393899663669807313140422989289994807828675993113715377952*t^18 - 1802867031738013394252727190248765040206620540744531613780078434189666042261916356253946314375/77757460077324393899663669807313140422989289994807828675993113715377952*t^16 + 5359540618999275141430210033047357267884860837436242003176221995115018107112048275771988953125/38878730038662196949831834903656570211494644997403914337996556857688976*t^14 - 22482154419892454931000840100689589383634455961578948317516369690535575255869287753051138061875/38878730038662196949831834903656570211494644997403914337996556857688976*t^12 + 64175841125614442952694195080644895568136430466101324394949091960367727964827445116097673355625/38878730038662196949831834903656570211494644997403914337996556857688976*t^10 - 118290644395928218235500388772577532697406733017158799511007080804410747368526242061643855071875/38878730038662196949831834903656570211494644997403914337996556857688976*t^8 + 519796128616516583179568234614320354159727963711016563950626264104035607903107017302242350146875/155514920154648787799327339614626280845978579989615657351986227430755904*t^6 - 298676285382693432669654619641981516874693532823339154834807060756894544596165858494904241578125/155514920154648787799327339614626280845978579989615657351986227430755904*t^4 + 70117914651742730189419949334386424875740744562614615560752631290100557783984650229459074734375/155514920154648787799327339614626280845978579989615657351986227430755904*t^2 - 3084528772947522571400972385646213792530185742408354826094849505259273182787353840683984953125/155514920154648787799327339614626280845978579989615657351986227430755904
-------------------------------------------------
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:
| (8.2488273635861840855 - 4.1826001494047328747e-515j)  +/-  (4.66e-246, 4.66e-246j)
| (10.798601352675862517 - 7.7413286828789644757e-528j)  +/-  (3.51e-248, 3.51e-248j)
| (-10.798601352675862517 + 3.5112670597638760943e-531j)  +/-  (3.77e-248, 3.77e-248j)
| (-7.5657888528222007451 - 9.0541178269344553516e-530j)  +/-  (9.07e-246, 9.07e-246j)
| (-9.809452677787933445 + 3.5781012221080456141e-532j)  +/-  (4.23e-247, 4.23e-247j)
| (-8.9865043666662281512 - 2.7291592301897788949e-535j)  +/-  (1.61e-246, 1.61e-246j)
| (-1.4011656410597947727 + 5.4371352516231267999e-540j)  +/-  (7.85e-251, 7.85e-251j)
| (-2.8901633840314029187 - 2.0685501844760759353e-540j)  +/-  (3.91e-248, 3.91e-248j)
| (7.5657888528222007451 + 7.3505538894216423841e-540j)  +/-  (9.26e-246, 9.26e-246j)
| (3.9544879426500450264 - 3.9281747326887826182e-547j)  +/-  (7.62e-247, 7.62e-247j)
| (6.3097288082542264754 + 8.8807275642159245649e-553j)  +/-  (1.49e-245, 1.49e-245j)
| (9.809452677787933445 + 4.2944930191544210012e-571j)  +/-  (3.81e-247, 3.81e-247j)
| (8.9865043666662281512 + 5.6593160828752314373e-582j)  +/-  (1.65e-246, 1.65e-246j)
| (-5.2019365924015129919 + 1.8602863933400878549e-586j)  +/-  (1.46e-245, 1.46e-245j)
| (-4.4668786595975913716 - 3.4752600346319407588e-589j)  +/-  (4.26e-246, 4.26e-246j)
| (2.8901633840314029187 - 4.5589893321593292563e-591j)  +/-  (3.98e-248, 3.98e-248j)
| (5.2019365924015129919 - 1.4572397427297642344e-588j)  +/-  (1.6e-245, 1.6e-245j)
| (-4.8479375347479011462 - 1.3832394574388069302e-594j)  +/-  (1.19e-245, 1.19e-245j)
| (-2.3310352625682360846 - 5.2272779375478268263e-602j)  +/-  (2.17e-248, 2.17e-248j)
| (-8.2488273635861840855 - 3.3488916621827198083e-597j)  +/-  (4.71e-246, 4.71e-246j)
| (4.4668786595975913716 + 4.3660443266264511369e-605j)  +/-  (4.5e-246, 4.5e-246j)
| (1.9137355618993510628 + 2.4076837741028033268e-617j)  +/-  (2.2e-249, 2.2e-249j)
| (5.7278714770462137747 - 3.024680042773669476e-630j)  +/-  (1.38e-245, 1.38e-245j)
| (-2.160330052157801491 - 1.6889322701353047134e-650j)  +/-  (1.52e-248, 1.52e-248j)
| (-1.9137355618993510628 + 2.1125089369170327357e-652j)  +/-  (2.68e-249, 2.68e-249j)
| (2.160330052157801491 - 8.2105015702289737754e-647j)  +/-  (1.35e-248, 1.35e-248j)
| (6.9220796548825334106 + 3.5102075833113101099e-653j)  +/-  (1.16e-245, 1.16e-245j)
| (-5.7278714770462137747 - 7.580091888634481269e-663j)  +/-  (1.34e-245, 1.34e-245j)
| (-3.9544879426500450264 + 2.6149505428069384568e-669j)  +/-  (7.89e-247, 7.89e-247j)
| (-1 + 7.4801668429918807422e-680j)  +/-  (7.31e-252, 7.31e-252j)
| (-6.3097288082542264754 + 1.3180403353807938155e-672j)  +/-  (1.49e-245, 1.49e-245j)
| (3.4228148717623190008 + 2.6483859075973660586e-679j)  +/-  (1.92e-247, 1.92e-247j)
| (0.67178186123378070672 + 2.6871954435911762759e-691j)  +/-  (8.32e-253, 8.32e-253j)
| (2.3310352625682360846 + 9.7695040559571610669e-685j)  +/-  (2.21e-248, 2.21e-248j)
| (-6.9220796548825334106 + 3.0684455808226552583e-689j)  +/-  (1.18e-245, 1.18e-245j)
| (-3.4228148717623190008 - 1.8898012427568473302e-704j)  +/-  (1.65e-247, 1.65e-247j)
| (0.23704314987094039888 + 1.0667457523347205224e-719j)  +/-  (3.23e-254, 3.23e-254j)
| (1.4011656410597947727 - 1.0563073185117563852e-711j)  +/-  (7.2e-251, 7.2e-251j)
| (1 - 4.2500167876725565888e-718j)  +/-  (8.11e-252, 8.11e-252j)
| (-0.23704314987094039888 - 3.8804001170013507448e-724j)  +/-  (3.23e-254, 3.23e-254j)
| (-0.67178186123378070672 + 1.0302149471162196411e-730j)  +/-  (8.41e-253, 8.41e-253j)
| (4.8479375347479011462 - 2.5558552145209128591e-737j)  +/-  (1.38e-245, 1.38e-245j)
-------------------------------------------------
The weights are:
| (4.7307358896806782435e-16 + 9.893592444704645758e-530j)  +/-  (3.93e-83, 6.62e-206j)
| (2.1689666876842021559e-26 + 8.264832024403721444e-537j)  +/-  (5.57e-88, 9.38e-211j)
| (2.1689666876842021559e-26 + 1.1063673755623609755e-537j)  +/-  (3.91e-89, 6.59e-212j)
| (9.810974221482512983e-14 + 3.4146957412169409538e-530j)  +/-  (1.47e-83, 2.48e-206j)
| (4.4908901851906297996e-22 - 3.1899969466265695706e-535j)  +/-  (8.07e-88, 1.36e-210j)
| (8.972832713952668752e-19 + 2.7249444136078272051e-533j)  +/-  (1.88e-86, 3.17e-209j)
| (0.069670553596810710037 - 5.9680170394136813819e-521j)  +/-  (7.69e-60, 1.3e-182j)
| (0.0032692032220368344192 - 2.0038110594702603087e-522j)  +/-  (8.2e-71, 1.38e-193j)
| (9.810974221482512983e-14 - 7.906157821586890184e-529j)  +/-  (9.34e-86, 1.57e-208j)
| (8.4797906901986920326e-05 + 2.6727451832375229566e-523j)  +/-  (1.64e-77, 2.77e-200j)
| (5.3984324903410582555e-10 - 9.1995156821606375632e-527j)  +/-  (8.29e-84, 1.4e-206j)
| (4.4908901851906297996e-22 - 3.6912036264622859644e-534j)  +/-  (1.23e-90, 2.07e-213j)
| (8.972832713952668752e-19 + 6.3666510842718481449e-532j)  +/-  (6.3e-89, 1.06e-211j)
| (2.4633498720997490958e-07 + 2.5435725348668708438e-525j)  +/-  (7.99e-84, 1.35e-206j)
| (8.8722196037973893388e-06 + 3.04702081460728839e-524j)  +/-  (3.87e-82, 6.52e-205j)
| (0.0032692032220368344192 + 4.1652980923181863099e-522j)  +/-  (6.1e-78, 1.03e-200j)
| (2.4633498720997490958e-07 - 1.1228821884588981715e-524j)  +/-  (3.78e-84, 6.38e-207j)
| (9.0997434466663838004e-07 - 1.1493514613655063664e-524j)  +/-  (2.89e-83, 4.88e-206j)
| (0.018480320275669202397 + 3.4183993052294094296e-521j)  +/-  (1.39e-76, 2.34e-199j)
| (4.7307358896806782435e-16 - 1.1993690597967782844e-531j)  +/-  (1.77e-90, 2.98e-213j)
| (8.8722196037973893388e-06 - 1.0244724071537145418e-523j)  +/-  (3.73e-83, 6.28e-206j)
| (0.038543634309635253492 - 9.8584963732827252074e-521j)  +/-  (4.61e-77, 7.77e-200j)
| (1.6878729982859022634e-08 + 1.0367261429731612371e-525j)  +/-  (1.37e-85, 2.31e-208j)
| (-0.012490420860611245754 - 7.2465507628183213546e-521j)  +/-  (1.89e-77, 3.19e-200j)
| (0.038543634309635253492 + 6.1455441908968775619e-521j)  +/-  (5.81e-77, 9.8e-200j)
| (-0.012490420860611245754 + 1.2389015507943276702e-520j)  +/-  (6.25e-79, 1.05e-201j)
| (9.854949841407560546e-12 + 8.199912620384440594e-528j)  +/-  (3.36e-88, 5.67e-211j)
| (1.6878729982859022634e-08 - 1.8699271570907634435e-526j)  +/-  (7.66e-88, 1.29e-210j)
| (8.4797906901986920326e-05 - 9.4053744531439784937e-524j)  +/-  (1.08e-84, 1.81e-207j)
| (0.079357731242263391588 + 1.0065017582955948081e-520j)  +/-  (1.07e-79, 1.8e-202j)
| (5.3984324903410582555e-10 + 1.2253115871155061299e-527j)  +/-  (1.61e-89, 2.72e-212j)
| (0.00060713468949095991365 - 9.2380256749198023143e-523j)  +/-  (5.15e-85, 8.76e-208j)
| (0.12054395200699922082 + 1.3099138347341233703e-520j)  +/-  (9.74e-82, 1.63e-204j)
| (0.018480320275669202397 - 6.1114338647429992956e-521j)  +/-  (9.88e-83, 1.67e-205j)
| (9.854949841407560546e-12 - 7.171104052919771985e-529j)  +/-  (6.53e-91, 1.1e-213j)
| (0.00060713468949095991365 + 3.8197561583860197358e-523j)  +/-  (6.13e-85, 1.02e-207j)
| (0.18192304765334124671 - 9.8321742381215015305e-521j)  +/-  (5.07e-82, 8.46e-205j)
| (0.069670553596810710037 + 8.4103632766343688583e-521j)  +/-  (6.77e-83, 1.14e-205j)
| (0.079357731242263391588 - 1.2842023318674546238e-520j)  +/-  (1.32e-82, 2.23e-205j)
| (0.18192304765334124671 + 9.2828730090281959569e-521j)  +/-  (8.82e-83, 1.42e-205j)
| (0.12054395200699922082 - 1.1126231942013611935e-520j)  +/-  (7.37e-83, 1.14e-205j)
| (9.0997434466663838004e-07 + 4.426131581040890765e-524j)  +/-  (2.05e-87, 3.69e-210j)
