Starting with polynomial:
P : 34461632205/262144*t^20 - 83945001525/131072*t^18 + 347123925225/262144*t^16 - 49589132175/32768*t^14 + 136745788725/131072*t^12 - 29113619535/65536*t^10 + 15058768725/131072*t^8 - 557732175/32768*t^6 + 334639305/262144*t^4 - 4849845/131072*t^2 + 46189/262144
Extension levels are: 20 21
-------------------------------------------------
Trying to find an order 21 Kronrod extension for:
P1 : 34461632205/262144*t^20 - 83945001525/131072*t^18 + 347123925225/262144*t^16 - 49589132175/32768*t^14 + 136745788725/131072*t^12 - 29113619535/65536*t^10 + 15058768725/131072*t^8 - 557732175/32768*t^6 + 334639305/262144*t^4 - 4849845/131072*t^2 + 46189/262144
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 34461632205/262144*t^41 - 15179907170505/11272192*t^39 + 1549324011602367/242352128*t^37 - 9140903435342360253/489793650688*t^35 + 7896308459244085183667/210611269795840*t^33 - 8460855361564525280207847/153956838220759040*t^31 + 626731592174338689406893702177/10306736757712601907200*t^29 - 68917880269506024435335452886519/1329569041744925646028800*t^27 + 249389123506817786811639166016101503/7241719380704028352036864000*t^25 - 9287258393976385286626256382576584631049/518097226341460582001114175897600*t^23 + 44333764918741170512738555232648885774632460733/6064399272695418063153066582080593920000*t^21 - 28266292786747463682403245967699053855386491/12159196536732667795795622219710464000*t^19 + 34022591747514081329019258424378239480953/59603904591826802920566775586816000*t^17 - 76225108295821168860264563632983810392221/715246855101921635046801307041792000*t^15 + 110213867577390279683508524590346458277/7450488073978350365070846948352000*t^13 - 16626174374040214341902162202041249649/11246019734306943947276750110720000*t^11 + 1370844965287099409531210651905516619/13495223681168332736732100132864000*t^9 - 7474732077970771145185413727060278471/1668909328571150481775869716430848000*t^7 + 121798498072143375389920085866404611/1072870282652882452570201960562688000*t^5 - 43681829000303649887373526634448413/32186108479586473577106058816880640000*t^3 + 259857126789906079897953704351423/53643514132644122628510098028134400000*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:
| (0.98150787745025025919 + 1.8884021482286292822e-879j)  +/-  (4.36e-241, 4.36e-241j)
| (-0.99885903158827766384 - 1.338512423456361147e-887j)  +/-  (1.59e-241, 1.59e-241j)
| (-0.96397192727791379127 + 1.3263603641955868647e-893j)  +/-  (3.48e-241, 3.48e-241j)
| (0.99885903158827766384 + 1.1011445577103513156e-900j)  +/-  (1.45e-241, 1.45e-241j)
| (0.94082263383175475352 + 2.5238709450558092902e-918j)  +/-  (2.37e-241, 2.37e-241j)
| (0.96397192727791379127 - 7.7514444045434546663e-928j)  +/-  (3.65e-241, 3.65e-241j)
| (-0.87827681125228197608 + 4.9994225775121636107e-935j)  +/-  (5.68e-242, 5.68e-242j)
| (-0.91223442825132590587 + 3.0041132139337509582e-934j)  +/-  (1.17e-241, 1.17e-241j)
| (-0.98150787745025025919 - 1.9393537842160904247e-933j)  +/-  (4.32e-241, 4.32e-241j)
| (0.79504142883755119835 + 2.488660297031738312e-940j)  +/-  (5.14e-243, 5.14e-243j)
| (0.91223442825132590587 + 3.895487715733980665e-939j)  +/-  (1.23e-241, 1.23e-241j)
| (-0.99312859918509492479 + 2.0529824910556600586e-941j)  +/-  (4e-241, 4e-241j)
| (-0.94082263383175475352 + 1.0461380394780123888e-950j)  +/-  (2.29e-241, 2.29e-241j)
| (-0.79504142883755119835 - 1.2511061915363776677e-960j)  +/-  (5.14e-243, 5.14e-243j)
| (0.99312859918509492479 + 1.3803654962927258137e-961j)  +/-  (3.67e-241, 3.67e-241j)
| (0.87827681125228197608 + 8.2674183508396912585e-977j)  +/-  (5.72e-242, 5.72e-242j)
| (0.83911697182221882339 - 6.241312574730916852e-987j)  +/-  (1.8e-242, 1.8e-242j)
| (-0.83911697182221882339 - 2.2125346311125449694e-992j)  +/-  (1.73e-242, 1.73e-242j)
| (-0.74633190646015079261 + 3.9859482887095137963e-994j)  +/-  (1.21e-243, 1.21e-243j)
| (-0.22778585114164507808 - 4.3577756805591387888e-1002j)  +/-  (8.67e-252, 8.67e-252j)
| (0.63605368072651502545 - 6.3143268026439125218e-994j)  +/-  (3.29e-245, 3.29e-245j)
| (0.74633190646015079261 - 1.3023633290466037763e-994j)  +/-  (1.09e-243, 1.09e-243j)
| (0.15260546524092267551 + 9.8339338682234803842e-1006j)  +/-  (4.32e-253, 4.32e-253j)
| (-0.69323765633475138481 - 1.3756478218409305976e-1000j)  +/-  (2.25e-244, 2.25e-244j)
| (-0.57514044681971031534 + 1.2379628859266621876e-1005j)  +/-  (4.08e-246, 4.08e-246j)
| (0.076526521133497333755 - 1.6418459340623655158e-1007j)  +/-  (2.01e-254, 2.01e-254j)
| (0.69323765633475138481 + 1.7117768495616535272e-1003j)  +/-  (2.42e-244, 2.42e-244j)
| (0.4435931752387251032 + 7.0806626099770109023e-1007j)  +/-  (3.87e-248, 3.87e-248j)
| (-0.15260546524092267551 + 8.6289100281800372236e-1013j)  +/-  (4.68e-253, 4.68e-253j)
| (-0.63605368072651502545 + 8.6906357997785664191e-1007j)  +/-  (3.62e-245, 3.62e-245j)
| (-0.076526521133497333755 + 3.5347907033384045258e-1014j)  +/-  (2.3e-254, 2.3e-254j)
| (0.37370608871541956067 - 3.5785032523793681307e-1009j)  +/-  (2.5e-249, 2.5e-249j)
| (0.57514044681971031534 - 5.202865800194698437e-1009j)  +/-  (4.01e-246, 4.01e-246j)
| (-5.2883075204126300105e-1017 + 1.0922527542405595981e-1017j)  +/-  (2.21e-1015, 2.21e-1015j)
| (-0.4435931752387251032 + 1.1687290298226850379e-1012j)  +/-  (4.11e-248, 4.11e-248j)
| (-0.37370608871541956067 - 8.8567741705301947128e-1015j)  +/-  (2.37e-249, 2.37e-249j)
| (0.22778585114164507808 - 2.8653889212150278105e-1015j)  +/-  (8.27e-252, 8.27e-252j)
| (0.510867001950827098 - 1.1205182717577564971e-1012j)  +/-  (4.62e-247, 4.62e-247j)
| (0.30162786811491300432 - 4.8916842829463235099e-1016j)  +/-  (1.66e-250, 1.66e-250j)
| (-0.30162786811491300432 - 3.6481264295939103603e-1018j)  +/-  (1.7e-250, 1.7e-250j)
| (-0.510867001950827098 + 7.2856447101851815751e-1019j)  +/-  (4.29e-247, 4.29e-247j)
-------------------------------------------------
The weights are:
| (0.014626169256971252984 - 3.3068425834767243306e-880j)  +/-  (2e-72, 3.24e-189j)
| (0.0030735837185205315012 - 2.9308660992182964766e-882j)  +/-  (5.67e-73, 9.17e-190j)
| (0.020388373461266523598 + 1.9620041291490384398e-881j)  +/-  (5.09e-73, 8.24e-190j)
| (0.0030735837185205315012 + 3.3451158639279095292e-880j)  +/-  (3.3e-73, 5.34e-190j)
| (0.025882133604951158835 - 1.2013170466890793753e-879j)  +/-  (1.9e-73, 3.08e-190j)
| (0.020388373461266523598 + 2.1766929445142620085e-879j)  +/-  (3.46e-73, 5.6e-190j)
| (0.036600169758200798031 - 3.7163359378458535774e-881j)  +/-  (1.6e-74, 2.58e-191j)
| (0.031287306777032798959 + 3.1296244680874406537e-881j)  +/-  (1.86e-74, 3e-191j)
| (0.014626169256971252984 - 1.4070244482223832761e-881j)  +/-  (1.26e-74, 2.05e-191j)
| (0.04643482186749767472 - 4.702594921724160081e-880j)  +/-  (8.15e-77, 1.32e-193j)
| (0.031287306777032798959 + 8.5555164465711119332e-880j)  +/-  (1.62e-75, 2.62e-192j)
| (0.0086002698556429421987 + 8.6201195134638360281e-882j)  +/-  (8.07e-75, 1.31e-191j)
| (0.025882133604951158835 - 2.5425330289688196244e-881j)  +/-  (3.48e-75, 5.64e-192j)
| (0.04643482186749767472 - 4.9358395218406036927e-881j)  +/-  (6.38e-78, 1.03e-194j)
| (0.0086002698556429421987 - 1.4647593529414207708e-879j)  +/-  (8.86e-76, 1.43e-192j)
| (0.036600169758200798031 - 6.695255776135790365e-880j)  +/-  (2.72e-77, 4.41e-194j)
| (0.041668873327973686264 + 5.5180762760592747105e-880j)  +/-  (7.36e-78, 1.19e-194j)
| (0.041668873327973686264 + 4.3156828361960558791e-881j)  +/-  (3.21e-78, 5.2e-195j)
| (0.050944573923728691933 + 5.5723464617455738926e-881j)  +/-  (6.08e-80, 9.83e-197j)
| (0.074582875400499188987 + 1.1647801044581788228e-880j)  +/-  (7.15e-83, 1.16e-199j)
| (0.059111400880639572375 + 3.2297396552844273876e-880j)  +/-  (3.26e-82, 5.27e-199j)
| (0.050944573923728691933 + 4.094007312079288363e-880j)  +/-  (8.13e-81, 1.32e-197j)
| (0.07570449768455667466 - 1.7246968362234247732e-880j)  +/-  (1.88e-84, 3.04e-201j)
| (0.055195105348285994745 - 6.2236654737804220603e-881j)  +/-  (6.38e-82, 1.03e-198j)
| (0.062653237554781168026 - 7.6005935077421819539e-881j)  +/-  (2.41e-83, 3.9e-200j)
| (0.076377867672080736706 + 1.5937090291571349258e-880j)  +/-  (8.66e-85, 1.4e-201j)
| (0.055195105348285994745 - 3.6157239979189718733e-880j)  +/-  (9.74e-83, 1.58e-199j)
| (0.068648672928521619346 - 2.4099787799246742926e-880j)  +/-  (3.95e-85, 6.39e-202j)
| (0.07570449768455667466 - 1.2605489419324954394e-880j)  +/-  (1.11e-85, 1.79e-202j)
| (0.059111400880639572375 + 6.8975869647207232666e-881j)  +/-  (1.55e-84, 2.51e-201j)
| (0.076377867672080736706 + 1.363166418630132535e-880j)  +/-  (6.37e-86, 1.03e-202j)
| (0.071054423553444068306 + 2.2072207571587344304e-880j)  +/-  (1.65e-86, 2.67e-203j)
| (0.062653237554781168026 - 2.911515532257495651e-880j)  +/-  (8.3e-86, 1.34e-202j)
| (0.076600711917999656445 - 1.4737828729920244924e-880j)  +/-  (1.75e-86, 2.83e-203j)
| (0.068648672928521619346 - 9.0966393958492940346e-881j)  +/-  (1.75e-87, 2.83e-204j)
| (0.071054423553444068306 + 9.8991950660926486108e-881j)  +/-  (1.36e-87, 2.2e-204j)
| (0.074582875400499188987 + 1.8688073544632802845e-880j)  +/-  (1.24e-87, 2.01e-204j)
| (0.065834597133618422112 + 2.6423313366621684556e-880j)  +/-  (1.31e-87, 2.13e-204j)
| (0.073030690332786667495 - 2.0284654810915571453e-880j)  +/-  (7.49e-88, 1.21e-204j)
| (0.073030690332786667495 - 1.0747990989003358014e-880j)  +/-  (1.19e-88, 1.94e-205j)
| (0.065834597133618422112 + 8.332954239717465961e-881j)  +/-  (9.25e-89, 1.47e-205j)
