Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 3 4 32
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P2 : t^5 - 7*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Trying to find an order 32 Kronrod extension for:
P3 : t^9 - 71/3*t^7 + 1399/9*t^5 - 2965/9*t^3 + 590/3*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^41 - 20041075141830018175372523663011892468834990123001643323766876244686103/29244707524374122511034934906912935209344674454314263475326945859459*t^39 + 129415633377040605398195384614683189046207386183887171985235055291087635529/614138858011856572731733633045171639396238163540599532981865863048639*t^37 - 213044631207018688989069814934794267566016771400506562904122188009529271055555/5527249722106709154585602697406544754566143471865395796836792767437751*t^35 + 25910623366125810772157834210701115691101990579704017273868950153714689240278210/5527249722106709154585602697406544754566143471865395796836792767437751*t^33 - 739724802916301856502233695863932165648690275490621214795391493469231494364280740/1842416574035569718195200899135514918188714490621798598945597589145917*t^31 + 83679864012948300216343691595515228224973741061754889379014151034511559034358980/3343768736906660105617424499338502573845216861382574589737926659067*t^29 - 552816731313874482126716017179122259260378004358061820876979166914210636290915220/477681248129522872231060642762643224835030980197510655676846665581*t^27 + 40466278674053316653612035873785756249154896559828087143676555775513634545526555450/1008438190495659396932239134721135696873954291528078050873342960671*t^25 - 1056589312596232528953345919465447287464619506564242561348482654950353766825856404250/1008438190495659396932239134721135696873954291528078050873342960671*t^23 + 20759681238176470114494057095322975376588058015834805025023096945817954647980064270750/1008438190495659396932239134721135696873954291528078050873342960671*t^21 - 305339162869578934410894634417718977968185677282192964338645690796040988765088180960250/1008438190495659396932239134721135696873954291528078050873342960671*t^19 + 175252311723436412223198151228132609870700310563325984034596839983906042618315324908000/53075694236613652470117849195849247203892331133056739519649629509*t^17 - 1396716487033097854057589073481727546840447410934730750582098326217828743992968678632500/53075694236613652470117849195849247203892331133056739519649629509*t^15 + 7972786964268767995050370761006273199419069708860502876377641058791023827174942795707500/53075694236613652470117849195849247203892331133056739519649629509*t^13 - 31707827075173685152410304656819862598213467394946913382553357768940238210450421326122500/53075694236613652470117849195849247203892331133056739519649629509*t^11 + 84537444403092745956036447486519269725609452142091858430360661599485986246510141031923125/53075694236613652470117849195849247203892331133056739519649629509*t^9 - 142774270193978988620589571052160837132962420945333689703987839906329840007564777258925625/53075694236613652470117849195849247203892331133056739519649629509*t^7 + 139260873768401161875385398001801206071136765436129737916616693811246280820069296927246875/53075694236613652470117849195849247203892331133056739519649629509*t^5 - 65711645242755198784747544597407153585456180055463753625885990188387714297909981164690625/53075694236613652470117849195849247203892331133056739519649629509*t^3 + 9659132959185715036144239072041504598612480716467614111193838115790353720128539933781250/53075694236613652470117849195849247203892331133056739519649629509*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:
| (3.3288201088521846115 + 2.1634389498197971449e-530j)  +/-  (1.29e-247, 1.29e-247j)
| (10.980488857891455114 - 1.3415777625995156311e-537j)  +/-  (4.14e-248, 4.14e-248j)
| (-9.9974283305534118091 + 2.7924089853906434783e-548j)  +/-  (3.81e-247, 3.81e-247j)
| (7.1296099946997516464 - 2.100333776330510282e-569j)  +/-  (1.02e-245, 1.02e-245j)
| (7.7691549979601041779 - 2.8507293947630017558e-590j)  +/-  (8.26e-246, 8.26e-246j)
| (9.9974283305534118091 + 1.2426257596074062487e-601j)  +/-  (3.92e-247, 3.92e-247j)
| (-2.4494897427831780982 + 1.7080689783922977151e-609j)  +/-  (7.76e-249, 7.76e-249j)
| (-8.447376793246323686 + 4.2226067606288051085e-605j)  +/-  (4.72e-246, 4.72e-246j)
| (-1.5755966612135508857 - 1.7190680229111891941e-615j)  +/-  (1.16e-249, 1.16e-249j)
| (-10.980488857891455114 + 1.2132053604682656457e-610j)  +/-  (4.05e-248, 4.05e-248j)
| (8.447376793246323686 + 1.1909403700965621391e-620j)  +/-  (4.69e-246, 4.69e-246j)
| (5.9332530324860332285 + 2.0509994079433376368e-641j)  +/-  (7.75e-246, 7.75e-246j)
| (9.1799221762222989747 + 6.2225520455725526184e-652j)  +/-  (1.72e-246, 1.72e-246j)
| (-5.3672774764025336472 + 1.4116608751939894398e-651j)  +/-  (4.78e-246, 4.78e-246j)
| (2.8935441433921319331 - 3.2015476520317634344e-653j)  +/-  (3.67e-248, 3.67e-248j)
| (-9.1799221762222989747 + 5.7027013397933630326e-654j)  +/-  (1.68e-246, 1.68e-246j)
| (-4.820263409760250533 - 3.1162771610835605612e-657j)  +/-  (2.34e-246, 2.34e-246j)
| (-7.7691549979601041779 - 1.5851202911193568399e-660j)  +/-  (7.82e-246, 7.82e-246j)
| (-4.2936050585889444615 - 1.4922901092933241562e-666j)  +/-  (1.1e-246, 1.1e-246j)
| (2.4494897427831780982 - 4.1466013814405064028e-671j)  +/-  (7.94e-249, 7.94e-249j)
| (4.2936050585889444615 - 1.2916989620594785049e-695j)  +/-  (1.13e-246, 1.13e-246j)
| (0.50029242529061486056 + 1.7509836340321565955e-713j)  +/-  (1.79e-253, 1.79e-253j)
| (6.5195525777034150948 - 1.7310793070528078864e-723j)  +/-  (1.01e-245, 1.01e-245j)
| (-6.5195525777034150948 + 1.362034367657633476e-737j)  +/-  (9.91e-246, 9.91e-246j)
| (-2.8935441433921319331 + 7.8282496684386481422e-746j)  +/-  (3.81e-248, 3.81e-248j)
| (5.3672774764025336472 + 2.053321441509823063e-742j)  +/-  (5.22e-246, 5.22e-246j)
| (3.7932353000477464006 + 1.7752704731270274123e-753j)  +/-  (4.28e-247, 4.28e-247j)
| (1.9774178876257509876 + 5.5727350385265354567e-762j)  +/-  (1.72e-249, 1.72e-249j)
| (1.5093152835436173382 + 6.8657358788550445136e-763j)  +/-  (7.77e-250, 7.77e-250j)
| (-1.9774178876257509876 + 2.518268429428318466e-763j)  +/-  (1.77e-249, 1.77e-249j)
| (-5.9332530324860332285 + 2.8848504259281973661e-758j)  +/-  (7.86e-246, 7.86e-246j)
| (1.5755966612135508857 + 1.6158732061444262482e-764j)  +/-  (1.11e-249, 1.11e-249j)
| (-7.1296099946997516464 - 1.5177743794371186161e-760j)  +/-  (1.01e-245, 1.01e-245j)
| (-3.3288201088521846115 - 1.4830253934934086576e-769j)  +/-  (1.44e-247, 1.44e-247j)
| (-3.7932353000477464006 - 5.5482296460005595026e-769j)  +/-  (4.32e-247, 4.32e-247j)
| (-1 - 6.6575797294162739227e-774j)  +/-  (5.96e-252, 5.96e-252j)
| (1 + 2.8293929553418035671e-770j)  +/-  (5.14e-252, 5.14e-252j)
| (-1.5093152835436173382 + 4.2225263691995054731e-772j)  +/-  (8.85e-250, 8.85e-250j)
| (4.820263409760250533 - 2.0718880130455798798e-767j)  +/-  (2.56e-246, 2.56e-246j)
| (-6.975056680997122692e-782 - 8.8574385214158022195e-783j)  +/-  (2.88e-780, 2.88e-780j)
| (-0.50029242529061486056 + 6.362084251038180298e-785j)  +/-  (2.06e-253, 2.06e-253j)
-------------------------------------------------
The weights are:
| (0.00069738838733104312238 - 4.5021723803846986459e-533j)  +/-  (7.49e-67, 4.24e-190j)
| (2.9749804025283683067e-27 + 1.4980198406054898595e-548j)  +/-  (6.62e-88, 3.75e-211j)
| (6.9351585664914093503e-23 + 1.9488945884481944612e-546j)  +/-  (2.11e-87, 1.19e-210j)
| (2.2800409540232382563e-12 - 5.3645996289672391511e-540j)  +/-  (7.23e-81, 4.09e-204j)
| (2.0487667859650703636e-14 + 2.97533824912742892e-541j)  +/-  (2.27e-82, 1.28e-205j)
| (6.9351585664914093503e-23 - 3.8945837878669379059e-546j)  +/-  (7.72e-87, 4.37e-210j)
| (0.009100529850042942282 - 2.3618003760704042342e-533j)  +/-  (6.55e-68, 3.71e-191j)
| (8.9536652461906546108e-17 + 5.1498214532408486575e-543j)  +/-  (7.73e-87, 4.38e-210j)
| (-0.015149649154860131238 - 8.8166956701268887146e-532j)  +/-  (1.58e-62, 8.97e-186j)
| (2.9749804025283683067e-27 - 8.0104158953039070526e-549j)  +/-  (5.9e-91, 3.34e-214j)
| (8.9536652461906546108e-17 - 1.1848127349828039056e-542j)  +/-  (7.24e-85, 4.1e-208j)
| (5.2094199212700963895e-09 - 8.6713512430550956585e-538j)  +/-  (2.19e-81, 1.24e-204j)
| (1.5380422546032542483e-19 + 3.0042205541608728893e-544j)  +/-  (2.72e-86, 1.54e-209j)
| (1.2326385581924346667e-07 - 2.0387029478189090124e-537j)  +/-  (4.32e-83, 2.44e-206j)
| (0.0026257445527750792157 + 1.1105951635487022077e-532j)  +/-  (1.8e-74, 1.02e-197j)
| (1.5380422546032542483e-19 - 1.4052572748469414182e-544j)  +/-  (1.4e-89, 7.9e-213j)
| (1.9309969021092094238e-06 + 1.4669352494242509504e-536j)  +/-  (3.49e-82, 1.98e-205j)
| (2.0487667859650703636e-14 - 1.1904422299873565664e-541j)  +/-  (5.43e-88, 3.07e-211j)
| (2.0398051747722080053e-05 - 9.2631854481702993797e-536j)  +/-  (2.94e-81, 1.67e-204j)
| (0.009100529850042942282 - 1.5520008073476152255e-532j)  +/-  (2.81e-76, 1.59e-199j)
| (2.0398051747722080053e-05 + 7.3185156868453428664e-535j)  +/-  (7.63e-82, 4.32e-205j)
| (0.17603406149420642114 + 1.8856322038538290929e-532j)  +/-  (1.35e-74, 7.63e-198j)
| (1.4042745097000669473e-10 + 7.5121861676239976658e-539j)  +/-  (2.08e-85, 1.17e-208j)
| (1.4042745097000669473e-10 - 2.4338413136836827303e-539j)  +/-  (1.79e-87, 1.01e-210j)
| (0.0026257445527750792157 + 7.7689984458008149144e-534j)  +/-  (3.43e-80, 1.94e-203j)
| (1.2326385581924346667e-07 + 8.6971452353132414582e-537j)  +/-  (3.51e-84, 1.98e-207j)
| (0.00014492993445239073376 - 7.8002452470836584877e-534j)  +/-  (2.75e-81, 1.56e-204j)
| (0.027396248756863818548 + 3.6505857516785263568e-532j)  +/-  (2.24e-78, 1.27e-201j)
| (0.078469477155782124975 + 2.3927124216304063649e-531j)  +/-  (1.01e-77, 5.7e-201j)
| (0.027396248756863818548 + 9.2973773450616547732e-533j)  +/-  (1.01e-79, 5.72e-203j)
| (5.2094199212700963895e-09 + 2.4383258828965561587e-538j)  +/-  (2.07e-87, 1.17e-210j)
| (-0.015149649154860131238 - 2.4663570498886490937e-531j)  +/-  (1.13e-78, 6.38e-202j)
| (2.2800409540232382563e-12 + 1.9495962404984138755e-540j)  +/-  (1.8e-89, 1.02e-212j)
| (0.00069738838733104312238 - 2.2662041668935823561e-534j)  +/-  (3.88e-84, 2.2e-207j)
| (0.00014492993445239073376 + 5.0863861340783458763e-535j)  +/-  (8.02e-85, 4.54e-208j)
| (0.12084347328323869494 - 1.630266714666353621e-532j)  +/-  (2.89e-82, 1.62e-205j)
| (0.12084347328323869494 - 3.0303462729538076639e-532j)  +/-  (5.14e-82, 2.91e-205j)
| (0.078469477155782124975 + 8.9984083611526031234e-532j)  +/-  (7.53e-82, 4.27e-205j)
| (1.9309969021092094238e-06 - 8.0151741984938206376e-536j)  +/-  (8.87e-87, 5.08e-210j)
| (0.19963067615102795039 - 1.5036141893185295627e-532j)  +/-  (9.75e-83, 5.66e-206j)
| (0.17603406149420642114 + 1.3928979214004118329e-532j)  +/-  (6.72e-83, 3.56e-206j)
