Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 35
-------------------------------------------------
Trying to find an order 35 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^39 - 74570538483901648336397/10040667672220953869*t^37 + 452150680760871770640376053/311260697838849569939*t^35 - 201896424599503669225725695265/1245042791355398279756*t^33 + 3635037636983303362528647455910/311260697838849569939*t^31 - 23223396593126305198522690313985/40162670688883815476*t^29 + 819688907475525769941674982510405/40162670688883815476*t^27 - 84220405027053039452476813510921455/160650682755535261904*t^25 + 99432348031473119158754127490495875/10040667672220953869*t^23 - 177286974289925000002910630728009378875/1285205462044282095232*t^21 + 1813938878779379552005976413888936916625/1285205462044282095232*t^19 - 53962012613927352795343251083211073802625/5140821848177128380928*t^17 + 71642462668336047327856125156692145876375/1285205462044282095232*t^15 - 2115656205255174747309211888917227139133125/10281643696354256761856*t^13 + 5217532831743250805397810078182216471683125/10281643696354256761856*t^11 - 32410245937386170870043735702641229699991875/41126574785417027047424*t^9 + 28872955598808046034711731794198423421606875/41126574785417027047424*t^7 - 200403569417496584380075261719940011432193125/658025196566672432758784*t^5 + 29316158507500929678552149856864829932196875/658025196566672432758784*t^3 - 64608886917423216872586725638685899584375/2632100786266689731035136*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:
| (-6.3121141184383663068 - 9.2622100024007147979e-859j)  +/-  (9.21e-247, 9.21e-247j)
| (-5.3086203408881164335 - 8.3844642444510438442e-873j)  +/-  (2.62e-246, 2.62e-246j)
| (-5.7915446141066570045 - 3.741474307727597657e-885j)  +/-  (1.9e-246, 1.9e-246j)
| (-7.5879288316781907385 - 3.1592940440729219368e-891j)  +/-  (2.86e-248, 2.86e-248j)
| (7.5879288316781907385 - 1.3584805026552753169e-895j)  +/-  (3.03e-248, 3.03e-248j)
| (-12.344790798978896656 + 3.3096147780391965884e-898j)  +/-  (5.12e-251, 5.12e-251j)
| (4.4154566214207021589 - 2.2554683665870647958e-894j)  +/-  (2.03e-246, 2.03e-246j)
| (-6.8919877674926407276 - 1.4387793885974192163e-892j)  +/-  (2.51e-247, 2.51e-247j)
| (3.9940221724304445839 + 6.5831367680437604419e-898j)  +/-  (1.25e-246, 1.25e-246j)
| (5.3086203408881164335 + 1.8823275987929735181e-897j)  +/-  (2.87e-246, 2.87e-246j)
| (-4.8521672648496794656 + 2.2505953115760416957e-902j)  +/-  (2.64e-246, 2.64e-246j)
| (6.8919877674926407276 + 1.2959843414511176577e-917j)  +/-  (2.38e-247, 2.38e-247j)
| (12.344790798978896656 - 2.1589346720671045629e-923j)  +/-  (5.32e-251, 5.32e-251j)
| (-1.2764183553022245596 - 1.6860627050795770028e-918j)  +/-  (3.86e-251, 3.86e-251j)
| (-3.584687965776744369 - 3.1877157544509916209e-923j)  +/-  (5.82e-247, 5.82e-247j)
| (6.3121141184383663068 - 6.9674266618742138808e-939j)  +/-  (9e-247, 9e-247j)
| (4.8521672648496794656 - 5.321264967006667046e-938j)  +/-  (2.64e-246, 2.64e-246j)
| (5.7915446141066570045 - 5.1303337084854045438e-940j)  +/-  (1.78e-246, 1.78e-246j)
| (-3.9940221724304445839 + 2.0484648403572121092e-943j)  +/-  (1.32e-246, 1.32e-246j)
| (-2.4078486993729140341 - 3.3993218108418524722e-954j)  +/-  (1.39e-248, 1.39e-248j)
| (2.0273846731556699311 - 1.7312915906176191004e-960j)  +/-  (2.41e-249, 2.41e-249j)
| (1.2764183553022245596 - 8.5607507946696174014e-962j)  +/-  (3.93e-251, 3.93e-251j)
| (2.7933031967689037798 - 1.0086610172000893219e-957j)  +/-  (6.59e-248, 6.59e-248j)
| (-2.0273846731556699311 - 3.2098167351172742982e-958j)  +/-  (2.45e-249, 2.45e-249j)
| (-0.90271131774531518925 + 1.824113838930393436e-964j)  +/-  (3.7e-252, 3.7e-252j)
| (-2.7933031967689037798 - 5.6858942845819563369e-959j)  +/-  (6e-248, 6e-248j)
| (0.52464762327529031788 + 2.626127698378489359e-976j)  +/-  (2.61e-253, 2.61e-253j)
| (3.1850716808522244079 - 4.4222775523292504146e-970j)  +/-  (2.05e-247, 2.05e-247j)
| (-7.8070162518509438774e-981 - 9.3329734918587020474e-981j)  +/-  (4.75e-979, 4.75e-979j)
| (-0.023517116302197881764 + 8.4026249915143610486e-978j)  +/-  (2.53e-255, 2.53e-255j)
| (0.023517116302197881764 + 2.0009261468521246849e-981j)  +/-  (2.53e-255, 2.53e-255j)
| (1.6506801238857845559 - 4.5355121077958459185e-974j)  +/-  (3.54e-250, 3.54e-250j)
| (0.90271131774531518925 - 7.5369096149075278147e-976j)  +/-  (3.75e-252, 3.75e-252j)
| (-4.4154566214207021589 + 5.6354534310753133807e-971j)  +/-  (2.11e-246, 2.11e-246j)
| (-0.52464762327529031788 + 7.2124430910947346148e-984j)  +/-  (2.61e-253, 2.61e-253j)
| (-1.6506801238857845559 - 2.239892482643839921e-980j)  +/-  (3.64e-250, 3.64e-250j)
| (-3.1850716808522244079 - 1.0268454667694408852e-979j)  +/-  (2.1e-247, 2.1e-247j)
| (3.584687965776744369 - 2.1475030704603012788e-988j)  +/-  (5.62e-247, 5.62e-247j)
| (2.4078486993729140341 - 4.373404413877459493e-991j)  +/-  (1.36e-248, 1.36e-248j)
-------------------------------------------------
The weights are:
| (1.5291078249935405033e-18 - 9.0857057208953831551e-876j)  +/-  (6.92e-86, 5.26e-209j)
| (1.5237129663419952102e-13 - 5.0454903633491404024e-874j)  +/-  (1.69e-83, 1.29e-206j)
| (7.6332477552681230277e-16 + 6.4491347305721843574e-875j)  +/-  (1.02e-84, 7.79e-208j)
| (4.4667798338679928921e-26 + 1.7176508479752972809e-880j)  +/-  (3.48e-90, 2.65e-213j)
| (4.4667798338679928921e-26 - 1.5765449300573809346e-881j)  +/-  (2.02e-93, 1.54e-216j)
| (7.8053257272474705235e-47 - 7.7956433780302801101e-891j)  +/-  (1.04e-99, 7.89e-223j)
| (8.2454784033215282187e-10 - 4.0370068605968223517e-873j)  +/-  (1.57e-85, 1.19e-208j)
| (8.2567502974076420272e-22 - 5.381979587082446361e-878j)  +/-  (1.02e-88, 7.76e-212j)
| (2.763407477670860983e-08 + 2.6545331879315215519e-872j)  +/-  (2.31e-84, 1.76e-207j)
| (1.5237129663419952102e-13 - 4.3569691760671327593e-875j)  +/-  (1.07e-88, 8.14e-212j)
| (1.4984329987711025773e-11 + 3.6950459154939595854e-873j)  +/-  (4.94e-86, 3.75e-209j)
| (8.2567502974076420272e-22 + 2.3635595735807249707e-879j)  +/-  (5.65e-93, 4.3e-216j)
| (7.8053257272474705235e-47 + 2.5207072783317518435e-891j)  +/-  (8.11e-104, 6.17e-227j)
| (0.041326381027957354378 - 1.9787243695270159059e-868j)  +/-  (3.18e-75, 2.42e-198j)
| (5.9877711700439662755e-07 - 5.1447856366297804695e-871j)  +/-  (1.74e-85, 1.32e-208j)
| (1.5291078249935405033e-18 - 1.1218838510913312189e-877j)  +/-  (6.07e-92, 4.62e-215j)
| (1.4984329987711025773e-11 + 4.8319909477001856201e-874j)  +/-  (5.94e-89, 4.52e-212j)
| (7.6332477552681230277e-16 + 2.7737256512806705514e-876j)  +/-  (6.5e-91, 4.95e-214j)
| (2.763407477670860983e-08 + 1.1801939466040700372e-871j)  +/-  (3.97e-88, 3.02e-211j)
| (0.00065526426061754054952 + 1.7273442118427177119e-869j)  +/-  (4.5e-85, 3.42e-208j)
| (0.0035016892448330708129 - 2.2077120479570010965e-869j)  +/-  (9.89e-85, 7.52e-208j)
| (0.041326381027957354378 - 1.3130673102499558768e-868j)  +/-  (6.91e-82, 5.26e-205j)
| (8.9552447070948719522e-05 - 2.3764041333734970729e-870j)  +/-  (5.65e-87, 4.3e-210j)
| (0.0035016892448330708129 - 4.2969368757700242562e-869j)  +/-  (8.44e-85, 6.42e-208j)
| (0.093531829048943608431 + 3.9081456687318592202e-868j)  +/-  (6.43e-81, 4.89e-204j)
| (8.9552447070948719522e-05 - 6.1492793519289736076e-870j)  +/-  (9.88e-87, 7.52e-210j)
| (0.1649233259718110411 - 7.0541173921388937989e-868j)  +/-  (2.42e-81, 1.84e-204j)
| (8.7638969445992484984e-06 + 6.3015192667948522762e-871j)  +/-  (8.42e-89, 6.4e-212j)
| (-14.996194914961520366 - 2.8272324536833750824e-865j)  +/-  (1.91e-81, 1.46e-204j)
| (7.6801798399569086366 + 1.4242940465299407781e-865j)  +/-  (9.61e-82, 7.31e-205j)
| (7.6801798399569086366 + 1.4137204233186892246e-865j)  +/-  (9.54e-82, 7.26e-205j)
| (0.013880184374796295769 + 5.6279830645356149956e-869j)  +/-  (1.12e-86, 8.55e-210j)
| (0.093531829048943608431 + 2.9301795743977838377e-868j)  +/-  (5e-85, 3.8e-208j)
| (8.2454784033215282187e-10 - 2.2833472433772238279e-872j)  +/-  (2.29e-92, 1.74e-215j)
| (0.1649233259718110411 - 8.3330624805246099484e-868j)  +/-  (1.17e-85, 8.92e-209j)
| (0.013880184374796295769 + 9.6138808775513224043e-869j)  +/-  (8.7e-88, 6.62e-211j)
| (8.7638969445992484984e-06 + 1.9138435275221628278e-870j)  +/-  (3.03e-90, 2.3e-213j)
| (5.9877711700439662755e-07 - 1.4178340413157977701e-871j)  +/-  (6.67e-92, 5.13e-215j)
| (0.00065526426061754054952 + 7.733989713054156492e-870j)  +/-  (4.32e-90, 3.23e-213j)
