Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 35
-------------------------------------------------
Trying to find an order 35 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^39 - 74570538483901648336397/80325341377767630952*t^37 + 452150680760871770640376053/1245042791355398279756*t^35 - 201896424599503669225725695265/2490085582710796559512*t^33 + 3635037636983303362528647455910/311260697838849569939*t^31 - 23223396593126305198522690313985/20081335344441907738*t^29 + 819688907475525769941674982510405/10040667672220953869*t^27 - 84220405027053039452476813510921455/20081335344441907738*t^25 + 1590917568503569906540066039847934000/10040667672220953869*t^23 - 177286974289925000002910630728009378875/40162670688883815476*t^21 + 1813938878779379552005976413888936916625/20081335344441907738*t^19 - 53962012613927352795343251083211073802625/40162670688883815476*t^17 + 143284925336672094655712250313384291752750/10040667672220953869*t^15 - 2115656205255174747309211888917227139133125/20081335344441907738*t^13 + 5217532831743250805397810078182216471683125/10040667672220953869*t^11 - 32410245937386170870043735702641229699991875/20081335344441907738*t^9 + 28872955598808046034711731794198423421606875/10040667672220953869*t^7 - 200403569417496584380075261719940011432193125/80325341377767630952*t^5 + 29316158507500929678552149856864829932196875/40162670688883815476*t^3 - 64608886917423216872586725638685899584375/80325341377767630952*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:
| (-6.2443986380832417043 - 2.7958298401970330375e-607j)  +/-  (3.1e-246, 3.1e-246j)
| (-9.7467425724975617647 - 3.8870633104422386043e-623j)  +/-  (3.66e-247, 3.66e-247j)
| (9.7467425724975617647 - 2.289366573078392572e-631j)  +/-  (3.99e-247, 3.99e-247j)
| (8.9266773935422304172 - 1.4964727490996702665e-630j)  +/-  (1.24e-246, 1.24e-246j)
| (-10.73095186408113124 - 1.5145264125261356114e-635j)  +/-  (4.89e-248, 4.89e-248j)
| (-17.458170572574551728 + 7.7232077661470356424e-650j)  +/-  (7.3e-251, 7.3e-251j)
| (-5.6484003246699871295 + 5.0677310574472093482e-650j)  +/-  (1.88e-246, 1.88e-246j)
| (17.458170572574551728 - 3.1051212486713463467e-669j)  +/-  (6.31e-251, 6.31e-251j)
| (-4.5043715681916859497 + 6.700767812375952542e-665j)  +/-  (3.24e-247, 3.24e-247j)
| (10.73095186408113124 - 1.7040187591333335237e-672j)  +/-  (4.65e-248, 4.65e-248j)
| (1.8051281493303659494 + 6.7802719338214311084e-678j)  +/-  (5.52e-251, 5.52e-251j)
| (3.4052122867955923505 + 2.0630227254263050063e-678j)  +/-  (2.23e-248, 2.23e-248j)
| (-1.8051281493303659494 + 1.1377388152852873089e-689j)  +/-  (5.51e-251, 5.51e-251j)
| (-8.1904809403584874706 + 1.3412899954533221464e-720j)  +/-  (2.7e-246, 2.7e-246j)
| (7.50752288357365735 + 1.2821820381841565489e-742j)  +/-  (3.7e-246, 3.7e-246j)
| (-8.9266773935422304172 - 1.7441789943293092024e-766j)  +/-  (1.29e-246, 1.29e-246j)
| (-5.0695143380770930823 - 8.8417451217029595344e-789j)  +/-  (9.01e-247, 9.01e-247j)
| (-7.50752288357365735 + 1.790077308180685658e-803j)  +/-  (3.8e-246, 3.8e-246j)
| (-1.3723400716209562536e-830 - 1.5402298677561529304e-829j)  +/-  (6.03e-828, 6.03e-828j)
| (-3.9503272646907058977 - 9.8544503292636574953e-817j)  +/-  (8.55e-248, 8.55e-248j)
| (5.6484003246699871295 + 3.2873760743552283661e-813j)  +/-  (2.01e-246, 2.01e-246j)
| (3.9503272646907058977 - 1.7930147003982036365e-822j)  +/-  (8.88e-248, 8.88e-248j)
| (0.74196378430272585765 + 9.0506769048072852589e-832j)  +/-  (3.64e-253, 3.64e-253j)
| (-3.4052122867955923505 - 9.8857461487530796443e-828j)  +/-  (1.96e-248, 1.96e-248j)
| (-2.3344142183389772393 + 4.3742791919824414641e-829j)  +/-  (5.11e-250, 5.11e-250j)
| (6.8620007528531821741 - 2.9000587140689789458e-824j)  +/-  (3.83e-246, 3.83e-246j)
| (-6.8620007528531821741 - 2.4273581336106053877e-836j)  +/-  (3.98e-246, 3.98e-246j)
| (2.3344142183389772393 - 5.4354819757398208036e-850j)  +/-  (4.91e-250, 4.91e-250j)
| (0.033258224822473654452 - 1.4867949921355510007e-853j)  +/-  (3.23e-255, 3.23e-255j)
| (-0.033258224822473654452 + 1.4889804157070771691e-853j)  +/-  (3.23e-255, 3.23e-255j)
| (4.5043715681916859497 - 3.9762046835221076907e-846j)  +/-  (3.31e-247, 3.31e-247j)
| (-2.8671549009240929373 + 1.0753753658732282043e-847j)  +/-  (3.59e-249, 3.59e-249j)
| (1.2766265884631131257 + 2.0138131261146331574e-850j)  +/-  (5.49e-252, 5.49e-252j)
| (6.2443986380832417043 - 7.1873960333136285998e-845j)  +/-  (3.02e-246, 3.02e-246j)
| (-0.74196378430272585765 - 7.2377608673292801485e-855j)  +/-  (3.64e-253, 3.64e-253j)
| (-1.2766265884631131257 + 4.5710157001709546434e-854j)  +/-  (5.64e-252, 5.64e-252j)
| (8.1904809403584874706 + 1.9160467396644742989e-847j)  +/-  (2.64e-246, 2.64e-246j)
| (2.8671549009240929373 - 3.1798170372928010573e-853j)  +/-  (3.73e-249, 3.73e-249j)
| (5.0695143380770930823 + 1.9748819935118290609e-850j)  +/-  (8.42e-247, 8.42e-247j)
-------------------------------------------------
The weights are:
| (8.2454784033215282187e-10 - 7.5131707553835386589e-616j)  +/-  (8.91e-87, 3.26e-209j)
| (8.2567502974076420272e-22 - 4.743319160752771124e-623j)  +/-  (2.96e-94, 1.08e-216j)
| (8.2567502974076420272e-22 + 1.0388711395195234561e-623j)  +/-  (2.65e-95, 9.7e-218j)
| (1.5291078249935405033e-18 - 4.9693784152673002597e-622j)  +/-  (6.19e-94, 2.27e-216j)
| (4.4667798338679928921e-26 + 2.6000122247647106923e-625j)  +/-  (1.1e-96, 4.04e-219j)
| (7.8053257272474705235e-47 - 2.2324205634043177806e-635j)  +/-  (1.44e-105, 5.27e-228j)
| (2.763407477670860983e-08 + 2.4434571642144059142e-615j)  +/-  (1.65e-87, 6.02e-210j)
| (7.8053257272474705235e-47 + 1.0561663099639095014e-635j)  +/-  (9.63e-107, 3.52e-229j)
| (8.7638969445992484984e-06 + 1.830838000713123971e-614j)  +/-  (1.73e-85, 6.35e-208j)
| (4.4667798338679928921e-26 - 6.8717834327867058767e-626j)  +/-  (3.89e-98, 1.42e-220j)
| (0.041326381027957354378 - 6.5893132836644615509e-613j)  +/-  (2.23e-76, 8.18e-199j)
| (0.00065526426061754054952 + 3.7202672596590555803e-614j)  +/-  (2.75e-84, 1.01e-206j)
| (0.041326381027957354378 - 1.1948101365280440498e-612j)  +/-  (6.91e-77, 2.53e-199j)
| (7.6332477552681230277e-16 - 9.1830022266656000665e-620j)  +/-  (7.28e-94, 2.66e-216j)
| (1.5237129663419952102e-13 - 1.9598390169209997499e-619j)  +/-  (5.63e-95, 2.06e-217j)
| (1.5291078249935405033e-18 + 2.8107003276412974397e-621j)  +/-  (4.8e-95, 1.76e-217j)
| (5.9877711700439662755e-07 - 6.3575663908779408221e-615j)  +/-  (8.64e-89, 3.16e-211j)
| (1.5237129663419952102e-13 + 2.1337214016753112379e-618j)  +/-  (3.89e-93, 1.42e-215j)
| (-14.996194914961520366 - 1.5212880680109088596e-609j)  +/-  (4.57e-82, 1.67e-204j)
| (8.9552447070948719522e-05 - 5.0208696707510285654e-614j)  +/-  (1.59e-87, 5.81e-210j)
| (2.763407477670860983e-08 + 1.2245194367871341907e-616j)  +/-  (1.45e-94, 5.32e-217j)
| (8.9552447070948719522e-05 - 1.1298227623825248726e-614j)  +/-  (3.94e-91, 1.44e-213j)
| (0.1649233259718110411 - 3.6745802509647718308e-612j)  +/-  (1.21e-83, 4.43e-206j)
| (0.00065526426061754054952 + 1.2644161795154382184e-613j)  +/-  (7.05e-88, 2.58e-210j)
| (0.013880184374796295769 + 6.1011115942387556822e-613j)  +/-  (4.48e-86, 1.64e-208j)
| (1.4984329987711025773e-11 + 2.1909840079898034024e-618j)  +/-  (1.23e-96, 4.49e-219j)
| (1.4984329987711025773e-11 - 4.6495811431225116053e-617j)  +/-  (3.18e-93, 1.16e-215j)
| (0.013880184374796295769 + 2.7807170614214123637e-613j)  +/-  (4.85e-89, 1.78e-211j)
| (7.6801798399569086366 + 7.5948914257232841538e-610j)  +/-  (1.71e-83, 6.27e-206j)
| (7.6801798399569086366 + 7.6762267650434830397e-610j)  +/-  (1.49e-83, 5.46e-206j)
| (8.7638969445992484984e-06 + 2.9637880619749556106e-615j)  +/-  (2.16e-93, 7.91e-216j)
| (0.0035016892448330708129 - 2.9019217171537613687e-613j)  +/-  (5.24e-89, 1.92e-211j)
| (0.093531829048943608431 + 1.4962657636908178662e-612j)  +/-  (1.27e-87, 4.65e-210j)
| (8.2454784033215282187e-10 - 1.8458906856227526125e-617j)  +/-  (3.68e-96, 1.35e-218j)
| (0.1649233259718110411 - 4.6655617132374861203e-612j)  +/-  (4.52e-88, 1.65e-210j)
| (0.093531829048943608431 + 2.2652916522602536933e-612j)  +/-  (1.03e-88, 3.78e-211j)
| (7.6332477552681230277e-16 + 1.2380344441361312833e-620j)  +/-  (2.75e-99, 1e-221j)
| (0.0035016892448330708129 - 1.0756120680218695341e-613j)  +/-  (2.34e-92, 8.46e-215j)
| (5.9877711700439662755e-07 - 6.6019642847068984803e-616j)  +/-  (8.89e-95, 3.26e-217j)
