Starting with polynomial:
P : 46189/256*t^10 - 109395/256*t^8 + 45045/128*t^6 - 15015/128*t^4 + 3465/256*t^2 - 63/256
Extension levels are: 10 31
-------------------------------------------------
Trying to find an order 31 Kronrod extension for:
P1 : 46189/256*t^10 - 109395/256*t^8 + 45045/128*t^6 - 15015/128*t^4 + 3465/256*t^2 - 63/256
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 46189/256*t^41 - 485744801018966872005680324261858886773010097250985/269876328992539857155697506407398442230832338688*t^39 + 51615984620059618713968189693153959781398885078335345/6207155566828416714581042647370164171309143789824*t^37 - 29457349694680006114193027739397931208235697902416803041/1247638268932511759630789572121402998433137901754624*t^35 + 412205833890364903018018299130185449771736468032152928495/8941407594016334277353991933536721488770821629241472*t^33 - 293414261846176136383896494661851402672635194084774433423/4470703797008167138676995966768360744385410814620736*t^31 + 172979115362557054804822416115130654982381971164289662786945/2454416384557483759133670785755830048667590537226784064*t^29 - 937373593140681452663402737994025354814820191056014022368355/16090062965432393532098508484399330319043093521820028864*t^27 + 1206826062191709454953356813047099856088158886381338654966169/32180125930864787064197016968798660638086187043640057728*t^25 - 6689443616202974051526276431949556997599987709123183968949125/353981385239512657706167186656785267018948057480040635008*t^23 + 552769691768355472635330473736602447774351718551781482484795/74154203231992770191410517362883870166024691883170567808*t^21 - 169864846724869955075326518611088421812728652186347485416675/74154203231992770191410517362883870166024691883170567808*t^19 + 5033902856615758907577329053431524865838603943883694693775/9269275403999096273926314670360483770753086485396320976*t^17 - 170455914119509745420312851343078667874973577115218295122345/1742623775951830099498147158027770948901580259254508343488*t^15 + 3396912681511424654102763194107915229012368392454931690475/259539711311974695669936810770093545581086421591096987328*t^13 - 1982726180301075145066919716189134312829674795402904684931765/1573589269684502579846826883699077166858126974106821034169664*t^11 + 174840921885121663349371770414698639535397418896630054051275/2098119026246003439795769178265436222477502632142428045559552*t^9 - 1058995009121446955654212140698273289560975270821937513175/299731289463714777113681311180776603211071804591775435079936*t^7 + 25764134631377243550721635505717497702193411691697605785/299731289463714777113681311180776603211071804591775435079936*t^5 - 294415919040899179517732199606619201149044897374205025/299731289463714777113681311180776603211071804591775435079936*t^3 + 5472636429176224517556988168512311256267619693374975/1648522092050431274125247211494271317660894925254764892939648*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:
| (0.97390652851717172008 + 1.3911697955278663491e-869j)  +/-  (1.21e-241, 1.21e-241j)
| (-0.99796335851602133935 - 1.6934899626828315104e-873j)  +/-  (2.57e-242, 2.57e-242j)
| (-0.95214288160745204474 + 2.6190650350349130065e-882j)  +/-  (1.27e-241, 1.27e-241j)
| (0.99796335851602133935 + 8.1571553825112759129e-893j)  +/-  (2.57e-242, 2.57e-242j)
| (0.92494080796092924165 - 9.5690162600384512446e-912j)  +/-  (1.06e-241, 1.06e-241j)
| (0.95214288160745204474 + 1.0839722658792801934e-924j)  +/-  (1.23e-241, 1.23e-241j)
| (-0.89479284776640817415 + 1.0298579520126496564e-932j)  +/-  (9.64e-242, 9.64e-242j)
| (-0.86506336668898451073 - 6.2589205246567983397e-940j)  +/-  (5.08e-242, 5.08e-242j)
| (-0.98930732004477920636 - 1.1394768439262153227e-944j)  +/-  (8.23e-242, 8.23e-242j)
| (0.49599179888091973177 + 2.4713532662664240616e-962j)  +/-  (3.28e-247, 3.28e-247j)
| (0.89479284776640817415 + 1.1530733537811412471e-955j)  +/-  (9.41e-242, 9.41e-242j)
| (-0.97390652851717172008 - 7.2218049071165605148e-959j)  +/-  (1.17e-241, 1.17e-241j)
| (-0.92494080796092924165 - 3.3970806214889635288e-964j)  +/-  (1.09e-241, 1.09e-241j)
| (-0.78665243882535449765 + 1.4704664310090988473e-969j)  +/-  (4.37e-243, 4.37e-243j)
| (0.98930732004477920636 - 8.9176604463013103766e-967j)  +/-  (8.82e-242, 8.82e-242j)
| (0.78665243882535449765 + 4.9425938148525104138e-973j)  +/-  (3.86e-243, 3.86e-243j)
| (0.83056913118909175115 + 7.1337850321720116887e-974j)  +/-  (1.8e-242, 1.8e-242j)
| (-0.83056913118909175115 + 1.8358191381638767127e-981j)  +/-  (1.81e-242, 1.81e-242j)
| (-0.73559437130606183486 + 2.0322554222245891414e-983j)  +/-  (7.69e-244, 7.69e-244j)
| (-0.22367436679155302337 + 1.6606968604877149799e-992j)  +/-  (8.55e-252, 8.55e-252j)
| (0.86506336668898451073 + 1.4381130891734259518e-983j)  +/-  (4.87e-242, 4.87e-242j)
| (0.73559437130606183486 + 2.231013824726028024e-993j)  +/-  (7.57e-244, 7.57e-244j)
| (0.14887433898163121088 - 1.124905736949578742e-1002j)  +/-  (4.26e-253, 4.26e-253j)
| (-0.55795190843102211023 + 3.811578956664631425e-999j)  +/-  (2.53e-246, 2.53e-246j)
| (-0.61962833094212869037 - 6.0552696713412728125e-997j)  +/-  (1.91e-245, 1.91e-245j)
| (0.074159887138375149369 - 4.5259478234378869649e-1002j)  +/-  (2.46e-254, 2.46e-254j)
| (0.67940956829902440623 - 5.1382713878270259796e-997j)  +/-  (1.29e-244, 1.29e-244j)
| (0.4333953941292471908 + 1.4740068999378363133e-1002j)  +/-  (3.62e-248, 3.62e-248j)
| (-0.14887433898163121088 - 1.3512482586123248856e-1005j)  +/-  (4.19e-253, 4.19e-253j)
| (-0.67940956829902440623 + 1.9216086580854059219e-999j)  +/-  (1.23e-244, 1.23e-244j)
| (-0.074159887138375149369 + 4.0910522128205475109e-1006j)  +/-  (1.85e-254, 1.85e-254j)
| (0.36749222036032573104 - 4.7874940217141591343e-1003j)  +/-  (2.66e-249, 2.66e-249j)
| (0.61962833094212869037 + 4.7400859777234248094e-1000j)  +/-  (1.97e-245, 1.97e-245j)
| (-1.0865425696031245366e-1010 - 2.1046341865377434728e-1010j)  +/-  (9.71e-1009, 9.71e-1009j)
| (-0.4333953941292471908 - 3.1724199185480985753e-1005j)  +/-  (3.88e-248, 3.88e-248j)
| (-0.36749222036032573104 + 4.0003000517204247685e-1007j)  +/-  (2.71e-249, 2.71e-249j)
| (0.22367436679155302337 + 1.5856819551537236082e-1008j)  +/-  (8.77e-252, 8.77e-252j)
| (0.55795190843102211023 + 1.8740329667339376042e-1005j)  +/-  (2.52e-246, 2.52e-246j)
| (0.29715510770640448885 - 1.483616761476322166e-1011j)  +/-  (1.71e-250, 1.71e-250j)
| (-0.29715510770640448885 + 6.7930719432584493726e-1010j)  +/-  (1.63e-250, 1.63e-250j)
| (-0.49599179888091973177 - 3.6814698123796347452e-1008j)  +/-  (3.45e-247, 3.45e-247j)
-------------------------------------------------
The weights are:
| (0.018673651085922242147 - 8.1665519300897072485e-870j)  +/-  (4.32e-74, 5.98e-191j)
| (0.0052224394575888838666 - 1.7011256848065615284e-872j)  +/-  (1.23e-74, 1.7e-191j)
| (0.024715140047638489168 + 2.826740096412323146e-871j)  +/-  (1.04e-74, 1.44e-191j)
| (0.0052224394575888838666 + 1.2085027510764826279e-870j)  +/-  (5.56e-75, 7.7e-192j)
| (0.029306555728307293837 - 2.248395833069203839e-869j)  +/-  (5.09e-75, 7.04e-192j)
| (0.024715140047638489168 + 2.4700451561617621992e-869j)  +/-  (7.96e-75, 1.1e-191j)
| (0.030157955312814409613 + 1.1556173434270031838e-870j)  +/-  (8.2e-76, 1.13e-192j)
| (0.030441649939006208666 - 1.7030915423574723488e-870j)  +/-  (4.69e-76, 6.49e-193j)
| (0.012068164691506406693 + 6.0703369462673487625e-872j)  +/-  (2.67e-76, 3.7e-193j)
| (0.061941719885462018887 + 1.4037373105441066208e-869j)  +/-  (3.36e-79, 4.65e-196j)
| (0.030157955312814409613 + 2.7146948912220151899e-869j)  +/-  (1.55e-77, 2.15e-194j)
| (0.018673651085922242147 - 1.3665624515481169419e-871j)  +/-  (2.19e-76, 3.03e-193j)
| (0.029306555728307293837 - 5.843774616206531914e-871j)  +/-  (1.19e-76, 1.64e-193j)
| (0.047914853603156535247 - 1.7340579927881441848e-870j)  +/-  (6.65e-79, 9.21e-196j)
| (0.012068164691506406693 - 7.2387023260347250051e-870j)  +/-  (3.28e-78, 4.54e-195j)
| (0.047914853603156535247 - 1.6262878040947061733e-869j)  +/-  (1.57e-80, 2.17e-197j)
| (0.039386655094522914573 + 2.2781542151916853319e-869j)  +/-  (4.31e-80, 5.96e-197j)
| (0.039386655094522914573 + 1.8155285967139107991e-870j)  +/-  (1.64e-79, 2.27e-196j)
| (0.053884932884232414676 + 1.811191700132582027e-870j)  +/-  (3.54e-81, 4.9e-198j)
| (0.07442695273168862437 + 6.084342907589419495e-870j)  +/-  (1.52e-84, 2.1e-201j)
| (0.030441649939006208666 - 2.8654636772374685583e-869j)  +/-  (2.37e-80, 3.29e-197j)
| (0.053884932884232414676 + 1.2967186411872780027e-869j)  +/-  (3.09e-82, 4.27e-199j)
| (0.074930239056522316238 - 9.0622982104275910724e-870j)  +/-  (2.7e-85, 3.73e-202j)
| (0.062010069054906258295 - 3.5424332523525853516e-870j)  +/-  (1.55e-84, 2.15e-201j)
| (0.061037541312973258326 + 2.6720936354007969474e-870j)  +/-  (4.64e-84, 6.43e-201j)
| (0.074415444244937743772 + 8.6361134823941066297e-870j)  +/-  (3.8e-86, 5.26e-203j)
| (0.058240683801180864684 - 1.1816258795413972076e-869j)  +/-  (1.53e-84, 2.12e-201j)
| (0.063798941754219078644 - 1.387768531950625334e-869j)  +/-  (6.33e-86, 8.77e-203j)
| (0.074930239056522316238 - 6.6603012291139941159e-870j)  +/-  (9.99e-87, 1.38e-203j)
| (0.058240683801180864684 - 2.1079818523661985829e-870j)  +/-  (4.02e-85, 5.57e-202j)
| (0.074415444244937743772 + 7.4146178271308835376e-870j)  +/-  (5.67e-87, 7.85e-204j)
| (0.068198648494949824619 + 1.2473754698910197574e-869j)  +/-  (1.94e-87, 2.69e-204j)
| (0.061037541312973258326 + 1.2004432671428767258e-869j)  +/-  (7.25e-87, 1e-203j)
| (0.074017802705621489747 - 8.1245856105225644609e-870j)  +/-  (2.81e-87, 3.89e-204j)
| (0.063798941754219078644 - 5.3335173493507703952e-870j)  +/-  (8.39e-89, 1.16e-205j)
| (0.068198648494949824619 + 5.6419738807352113413e-870j)  +/-  (6.96e-89, 9.63e-206j)
| (0.07442695273168862437 + 9.7095633184399250286e-870j)  +/-  (6.38e-89, 8.83e-206j)
| (0.062010069054906258295 - 1.3033167327872605986e-869j)  +/-  (6.97e-89, 9.65e-206j)
| (0.072218860465653468802 - 1.0851946153740601768e-869j)  +/-  (4.45e-89, 6.16e-206j)
| (0.072218860465653468802 - 5.7801714141522349766e-870j)  +/-  (6.92e-90, 9.65e-207j)
| (0.061941719885462018887 + 4.5676560781750714248e-870j)  +/-  (5.28e-90, 7.2e-207j)
