Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 5 32
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Trying to find an order 32 Kronrod extension for:
P2 : t^9 - 21*t^7 + 108*t^5 - 135*t^3 + 45*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^41 - 22024992854302650810837451846489608801389437708401/32438330777928274825188044875952364404415805309*t^39 + 46896059474992255072654884544297564031555949687762348/227068315445497923776316314131666550830910637163*t^37 - 1209769863376173427258606939778990587884387771995641731/32438330777928274825188044875952364404415805309*t^35 + 1014372862444109274622251313680311153306611143187869747075/227068315445497923776316314131666550830910637163*t^33 - 85318286003173570763538827410680774845553747903874179134220/227068315445497923776316314131666550830910637163*t^31 + 179447265298064666796911259784885660456229010791022902558160/7829941911913721509528148763160915545893470247*t^29 - 1155026012248219195646387436131074769995616309868070416567420/1118563130273388787075449823308702220841924321*t^27 + 38809884085321226664571048661847381925246458773640581099349330/1118563130273388787075449823308702220841924321*t^25 - 975409792678696727187303211611565884889461901626374259299823750/1118563130273388787075449823308702220841924321*t^23 + 18292811206194013395038217054623739067483022581182177165028203000/1118563130273388787075449823308702220841924321*t^21 - 254105716981407670251184351300267094800885862999343469915366709250/1118563130273388787075449823308702220841924321*t^19 + 2582017269596425634500132840700204585609821023066397268548229618250/1118563130273388787075449823308702220841924321*t^17 - 18843657601795408557529204128404980683007709179408556607776734840500/1118563130273388787075449823308702220841924321*t^15 + 96285874487947109898882634905523051563816045182043297932614224150000/1118563130273388787075449823308702220841924321*t^13 - 332585804207631017632986407103027862899139385144553707894794769287500/1118563130273388787075449823308702220841924321*t^11 + 739562384406692726410916872909189054645134825979516541520518266438125/1118563130273388787075449823308702220841924321*t^9 - 987702250282296244969953762004619160717977154435061917520298480968125/1118563130273388787075449823308702220841924321*t^7 + 715891848152658202011762995146369437144768496200493113158869176022500/1118563130273388787075449823308702220841924321*t^5 - 240680240368651875561966582235537585048972107162411138863287136484375/1118563130273388787075449823308702220841924321*t^3 + 26802627074204618133600274930228771410752733081173302735020759478125/1118563130273388787075449823308702220841924321*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:
| (8.441139497575683765 - 4.1869966730061539526e-875j)  +/-  (3.68e-246, 3.68e-246j)
| (-7.1207441978383580306 - 3.1666250337182592521e-882j)  +/-  (8.15e-246, 8.15e-246j)
| (-8.441139497575683765 + 3.3117562740414593476e-903j)  +/-  (3.59e-246, 3.59e-246j)
| (10.976544974999706535 - 5.582527976225468413e-918j)  +/-  (3.39e-248, 3.39e-248j)
| (9.1745814189192514355 - 3.1261738049833871385e-916j)  +/-  (1.52e-246, 1.52e-246j)
| (-1.9277404473732421577 - 4.0795150340467711048e-921j)  +/-  (6.37e-250, 6.37e-250j)
| (-3.227502217995565342 + 7.494571819448716802e-920j)  +/-  (5.16e-248, 5.16e-248j)
| (-9.9928280619163162336 - 3.5973006115484686383e-917j)  +/-  (3.68e-247, 3.68e-247j)
| (-2.7567159842178125559 - 5.2320832603366941549e-927j)  +/-  (1.38e-248, 1.38e-248j)
| (5.919387666027616997 + 7.6931333246949371302e-923j)  +/-  (4.99e-246, 4.99e-246j)
| (4.2551896617484641959 + 7.7308654718071089558e-925j)  +/-  (4.46e-247, 4.46e-247j)
| (7.1207441978383580306 - 4.3914725439314240147e-922j)  +/-  (7.84e-246, 7.84e-246j)
| (2.7567159842178125559 + 8.1771525318752458765e-927j)  +/-  (1.22e-248, 1.22e-248j)
| (-10.976544974999706535 - 2.0479064520954904698e-924j)  +/-  (3.5e-248, 3.5e-248j)
| (-4.7946154296230636832 - 1.3031415721610480297e-926j)  +/-  (1.33e-246, 1.33e-246j)
| (6.5086366535204801926 + 2.1287249374879278003e-933j)  +/-  (6.95e-246, 6.95e-246j)
| (9.9928280619163162336 + 1.7302308061798353469e-936j)  +/-  (3.7e-247, 3.7e-247j)
| (-6.5086366535204801926 + 1.0129915155755153588e-947j)  +/-  (6.68e-246, 6.68e-246j)
| (-9.1745814189192514355 + 3.5769775628010562151e-967j)  +/-  (1.52e-246, 1.52e-246j)
| (3.227502217995565342 - 4.0489672490411287618e-980j)  +/-  (5.02e-248, 5.02e-248j)
| (7.7617830669190909562 - 2.2128914946271171052e-978j)  +/-  (6.55e-246, 6.55e-246j)
| (1.9277404473732421577 + 2.7536961136902478356e-983j)  +/-  (5.98e-250, 5.98e-250j)
| (-2.2530487063750952611e-994 + 1.0438465034010801273e-994j)  +/-  (1.02e-992, 1.02e-992j)
| (4.7946154296230636832 - 2.0792718317059315647e-978j)  +/-  (1.32e-246, 1.32e-246j)
| (-7.7617830669190909562 + 1.0931943491706070446e-982j)  +/-  (6.5e-246, 6.5e-246j)
| (5.3489250626371485649 - 1.006456960503100427e-987j)  +/-  (2.97e-246, 2.97e-246j)
| (1.4877749177963713948 - 3.2876386379384647172e-990j)  +/-  (7.17e-251, 7.17e-251j)
| (-2.3344142183389772393 + 3.0566713622150907382e-988j)  +/-  (3.12e-249, 3.12e-249j)
| (-4.2551896617484641959 + 1.0669128211395196783e-985j)  +/-  (4.34e-247, 4.34e-247j)
| (-5.3489250626371485649 - 2.6312321254667879029e-985j)  +/-  (2.89e-246, 2.89e-246j)
| (1.0379709584894152952 + 5.4012581312260125716e-1002j)  +/-  (9.57e-252, 9.57e-252j)
| (-5.919387666027616997 - 4.871839219581768096e-997j)  +/-  (4.68e-246, 4.68e-246j)
| (0.74196378430272585765 - 2.0356078886811175533e-1010j)  +/-  (1.99e-252, 1.99e-252j)
| (-1.0379709584894152952 + 1.6441018358722303408e-1009j)  +/-  (1.04e-251, 1.04e-251j)
| (-1.4877749177963713948 - 6.0491947740980430818e-1008j)  +/-  (7.88e-251, 7.88e-251j)
| (-3.7313022243357029508 + 7.6890952988211532485e-1004j)  +/-  (1.49e-247, 1.49e-247j)
| (2.3344142183389772393 + 4.6322355201749024082e-1005j)  +/-  (3.04e-249, 3.04e-249j)
| (0.4581139171416630049 - 2.6813411092761656611e-1010j)  +/-  (2.12e-253, 2.12e-253j)
| (3.7313022243357029508 + 2.4188093890146872901e-1007j)  +/-  (1.61e-247, 1.61e-247j)
| (-0.4581139171416630049 - 8.2296332870589035155e-1013j)  +/-  (2.12e-253, 2.12e-253j)
| (-0.74196378430272585765 + 8.102943310191804414e-1012j)  +/-  (2.03e-252, 2.03e-252j)
-------------------------------------------------
The weights are:
| (9.4513278785979227609e-17 + 1.8648048620562569759e-890j)  +/-  (1.07e-87, 1.82e-210j)
| (2.4354568761543435709e-12 + 8.310104895534060263e-890j)  +/-  (2.89e-85, 4.9e-208j)
| (9.4513278785979227609e-17 + 2.3442151749097324855e-892j)  +/-  (3.14e-88, 5.32e-211j)
| (3.1083943457741465119e-27 + 3.0358766303728682628e-897j)  +/-  (3.5e-93, 5.94e-216j)
| (1.6170022592594907406e-19 + 1.5807753996027329759e-892j)  +/-  (1.05e-89, 1.79e-212j)
| (0.026201426192731200064 + 3.0155360773522367534e-882j)  +/-  (7.82e-67, 1.33e-189j)
| (0.0010702746121257658474 - 8.4291433718709068153e-884j)  +/-  (7.21e-75, 1.22e-197j)
| (7.2671491329445348769e-23 + 9.3803142292020845262e-896j)  +/-  (1.11e-92, 1.89e-215j)
| (0.0039943484647062218957 + 3.6875506502292233716e-883j)  +/-  (1.15e-72, 1.94e-195j)
| (5.6906799934198153987e-09 + 5.4514141054971502785e-887j)  +/-  (3.5e-85, 5.94e-208j)
| (2.4831614829444715379e-05 - 9.449174185036295795e-885j)  +/-  (2.34e-81, 3.97e-204j)
| (2.4354568761543435709e-12 + 9.7978725862348304948e-889j)  +/-  (8.72e-88, 1.48e-210j)
| (0.0039943484647062218957 + 7.264263322178569464e-883j)  +/-  (7.96e-77, 1.35e-199j)
| (3.1083943457741465119e-27 - 3.9641198702157532417e-898j)  +/-  (3.69e-96, 6.27e-219j)
| (2.2226504950203328663e-06 + 5.1872368348129126546e-886j)  +/-  (2.58e-84, 4.37e-207j)
| (1.5138846345654348765e-10 - 7.7242452338793687333e-888j)  +/-  (7.26e-87, 1.23e-209j)
| (7.2671491329445348769e-23 - 1.1143336996364229666e-894j)  +/-  (1.6e-93, 2.72e-216j)
| (1.5138846345654348765e-10 - 9.9834037809725107715e-889j)  +/-  (9.59e-89, 1.63e-211j)
| (1.6170022592594907406e-19 - 6.5819952593934544015e-894j)  +/-  (3.96e-93, 6.72e-216j)
| (0.0010702746121257658474 - 1.8865546384072006368e-883j)  +/-  (8.75e-82, 1.49e-204j)
| (2.1737312615922585931e-14 - 1.2529397204069746106e-889j)  +/-  (8.45e-90, 1.43e-212j)
| (0.026201426192731200064 + 4.8005610160305004493e-882j)  +/-  (5.32e-79, 9.03e-202j)
| (0.18811494987237931992 - 3.1524769705043478925e-881j)  +/-  (7.51e-79, 1.28e-201j)
| (2.2226504950203328663e-06 + 1.8828670229739089516e-885j)  +/-  (1.35e-85, 2.28e-208j)
| (2.1737312615922585931e-14 - 5.2541209194410077387e-891j)  +/-  (2.4e-92, 4.08e-215j)
| (1.3736928446203805774e-07 - 3.3955043777472684946e-886j)  +/-  (1.56e-86, 2.65e-209j)
| (0.059919017325907034098 - 1.0297941328519887873e-881j)  +/-  (1.5e-79, 2.54e-202j)
| (0.010536930733881088354 - 1.2165579336742598864e-882j)  +/-  (1.08e-82, 1.83e-205j)
| (2.4831614829444715379e-05 - 3.1152950334602597648e-885j)  +/-  (1.47e-87, 2.49e-210j)
| (1.3736928446203805774e-07 - 7.6135655322644737113e-887j)  +/-  (1.16e-89, 1.96e-212j)
| (0.098777676671402692222 + 2.931165788868917907e-881j)  +/-  (8.11e-83, 1.38e-205j)
| (5.6906799934198153987e-09 + 9.5721762788443706753e-888j)  +/-  (1.4e-90, 2.37e-213j)
| (0.053925392096014738148 - 5.1998712936278355666e-881j)  +/-  (9.12e-84, 1.55e-206j)
| (0.098777676671402692222 + 2.2892264251140437605e-881j)  +/-  (8.78e-84, 1.49e-206j)
| (0.059919017325907034098 - 7.2117584930171980642e-882j)  +/-  (2.92e-84, 4.95e-207j)
| (0.00019478321521039066669 + 1.6921934157263959248e-884j)  +/-  (2.52e-87, 4.27e-210j)
| (0.010536930733881088354 - 2.1466842255141867485e-882j)  +/-  (2.27e-86, 3.85e-209j)
| (0.15129547827269653592 + 4.5913557223345215535e-881j)  +/-  (9.82e-85, 1.67e-207j)
| (0.00019478321521039066669 + 4.3735085175301034137e-884j)  +/-  (2.06e-88, 3.49e-211j)
| (0.15129547827269653592 + 4.1186430787587277338e-881j)  +/-  (1.65e-85, 2.81e-208j)
| (0.053925392096014738148 - 4.3595951891611140255e-881j)  +/-  (1.26e-85, 2.1e-208j)
