Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 10 25
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Trying to find an order 25 Kronrod extension for:
P2 : t^14 - 477/7*t^12 + 11241/7*t^10 - 112815/7*t^8 + 68715*t^6 - 108945*t^4 + 46845*t^2 - 2835
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^39 - 17013651128611322459249057766501897729807477/31953937920019321059559451508016970375107*t^37 + 1241262770894434517458510704744418018388014107/9850462065569865890540883547584178837439*t^35 - 391206503039340529035806997814687924653868050514005/22271894730253466778512937701087828351449579*t^33 + 2110996793586087228755617176622671948871383453163530/1310111454720792163441937511828695785379387*t^31 - 2293360292421304682429663202012850311190344844882530030/22271894730253466778512937701087828351449579*t^29 + 80630677623169529255426595482312665004059492936971611070/17031448911370298124745187653773045209932031*t^27 - 46178284975498279919050144725335569867377858214963889245170/289534631493295068120668190114141768568844527*t^25 + 1150422018277957383364709158983357692122752048666848102982000/289534631493295068120668190114141768568844527*t^23 - 3034234681189706654888578674958012027070154504088229736087000/41362090213327866874381170016305966938406361*t^21 + 1008570900387246639814994230818786216794945216380289517199500/1008831468617752850594662683324535778985521*t^19 - 21675503416636886111450942983545687236228982212478527735020500/2176952116490940361809535264016103523074019*t^17 + 9125863598519827703036803619444211213632580332229412505715750/128056006852408256577031486118594324886707*t^15 - 45790696484004459767862184096418027934807339593920115672501250/128056006852408256577031486118594324886707*t^13 + 11960283409063160329211320465549670243638155183413800952711250/9850462065569865890540883547584178837439*t^11 - 26130908423522790268374546670106053385544781001955843243078750/9850462065569865890540883547584178837439*t^9 + 34085073498241368907951010743537937692511276969577753356900625/9850462065569865890540883547584178837439*t^7 - 23488796508238121512286769755164174390988520706906161175989375/9850462065569865890540883547584178837439*t^5 + 6699307328947459913648224063952737677502852871353954934990625/9850462065569865890540883547584178837439*t^3 - 372829467881574034182337011699076919358056582095430286496875/9850462065569865890540883547584178837439*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:
| (6.160261254487276916 - 7.7397291359637502223e-933j)  +/-  (1.8e-246, 1.8e-246j)
| (8.2699608769663253159 - 2.2553225086855812261e-933j)  +/-  (3.39e-247, 3.39e-247j)
| (-8.2699608769663253159 + 4.4644214064318052831e-933j)  +/-  (3.58e-247, 3.58e-247j)
| (9.109444369990656991 - 3.0199581115337143561e-934j)  +/-  (8.86e-248, 8.86e-248j)
| (7.5168411865889094511 - 9.1499894713660806227e-934j)  +/-  (9.06e-247, 9.06e-247j)
| (1.8842179690720350942 + 8.4954142676552994702e-936j)  +/-  (5.28e-250, 5.28e-250j)
| (-2.3344142183389772393 - 1.1873687886270542668e-934j)  +/-  (3.3e-249, 3.3e-249j)
| (-2.7894946639437866192 - 2.6641695087007661492e-932j)  +/-  (1.87e-248, 1.87e-248j)
| (-6.160261254487276916 - 4.0797967624593681959e-932j)  +/-  (1.86e-246, 1.86e-246j)
| (5.5317060638607199116 - 1.5049128098323766145e-937j)  +/-  (1.88e-246, 1.88e-246j)
| (-10.11754004044569887 - 1.2914667226439586362e-939j)  +/-  (1.09e-248, 1.09e-248j)
| (-4.9270564906324137689 - 1.4994576414816637111e-935j)  +/-  (2.22e-246, 2.22e-246j)
| (-9.109444369990656991 - 1.6737881768352936746e-947j)  +/-  (9.55e-248, 9.55e-248j)
| (-6.8188909261559596618 + 7.1843538971127354579e-946j)  +/-  (1.41e-246, 1.41e-246j)
| (10.11754004044569887 + 1.091125306347394933e-957j)  +/-  (1.02e-248, 1.02e-248j)
| (2.3344142183389772393 - 6.9964134302996482359e-954j)  +/-  (3.58e-249, 3.58e-249j)
| (4.9270564906324137689 + 1.1817668184295557128e-955j)  +/-  (2.18e-246, 2.18e-246j)
| (-3.8051950067440668328 + 6.6064357985994946594e-966j)  +/-  (6.73e-247, 6.73e-247j)
| (-4.2688150167168727359 - 2.2886694050909523307e-988j)  +/-  (1.53e-245, 1.53e-245j)
| (-7.5168411865889094511 + 4.1338391836324083931e-1003j)  +/-  (8.57e-247, 8.57e-247j)
| (-5.5317060638607199116 - 3.5537182777435995737e-1003j)  +/-  (1.96e-246, 1.96e-246j)
| (4.2688150167168727359 + 1.416467026556717525e-998j)  +/-  (1.53e-245, 1.53e-245j)
| (2.7894946639437866192 - 5.3398752500733331473e-1011j)  +/-  (1.84e-248, 1.84e-248j)
| (4.3114957943342286437 - 1.4193518298492369602e-1009j)  +/-  (1.62e-245, 1.62e-245j)
| (-1.4656205133845524345 + 4.8166142105437599412e-1027j)  +/-  (8.92e-251, 8.92e-251j)
| (1.4656205133845524345 - 1.0804465198904848741e-1026j)  +/-  (1.02e-250, 1.02e-250j)
| (-0.26842728825432580984 + 3.6589399728809899214e-1030j)  +/-  (3.49e-254, 3.49e-254j)
| (-3.2762772292662860982 - 9.297156569941662646e-1024j)  +/-  (8.2e-248, 8.2e-248j)
| (6.8188909261559596618 - 1.3791940882225958809e-1034j)  +/-  (1.4e-246, 1.4e-246j)
| (-4.3114957943342286437 - 2.4769601213285261165e-1046j)  +/-  (1.66e-245, 1.66e-245j)
| (-0.74196378430272585765 - 2.6391161705205351487e-1065j)  +/-  (9.43e-253, 9.43e-253j)
| (1.1413091178544209714 - 1.4440800660562110476e-1063j)  +/-  (1.54e-251, 1.54e-251j)
| (0.26842728825432580984 - 2.6864603761419142957e-1066j)  +/-  (4.23e-254, 4.23e-254j)
| (4.8437459452722728788e-1075 + 1.375556011948960961e-1074j)  +/-  (5.69e-1073, 5.69e-1073j)
| (-1.1413091178544209714 + 7.5209550942972297486e-1064j)  +/-  (1.3e-251, 1.3e-251j)
| (-1.8842179690720350942 + 4.1738812956089047534e-1063j)  +/-  (5.07e-250, 5.07e-250j)
| (3.8051950067440668328 - 2.7216882579677562673e-1061j)  +/-  (6.13e-247, 6.13e-247j)
| (0.74196378430272585765 + 2.2471787601958649631e-1069j)  +/-  (9.15e-253, 9.15e-253j)
| (3.2762772292662860982 - 1.5297327840068083116e-1064j)  +/-  (9.72e-248, 9.72e-248j)
-------------------------------------------------
The weights are:
| (1.4731079143028757384e-09 + 9.1612659734752110214e-941j)  +/-  (3.38e-83, 1.69e-206j)
| (4.4338524657948327458e-16 - 1.2043501982298321886e-945j)  +/-  (2.31e-88, 1.15e-211j)
| (4.4338524657948327458e-16 + 2.0036306491537913167e-945j)  +/-  (1.62e-90, 8.09e-214j)
| (3.4399628981357199914e-19 + 1.54200458629791727e-947j)  +/-  (2.45e-90, 1.22e-213j)
| (1.5489649528702826154e-13 + 4.8383460146677195786e-944j)  +/-  (5.15e-87, 2.57e-210j)
| (0.030261499946285487052 - 1.8125733508715636036e-934j)  +/-  (9.55e-69, 4.77e-192j)
| (0.01175828837929458259 + 6.5986127513423145426e-934j)  +/-  (7.08e-73, 3.53e-196j)
| (0.0038042664485364612323 - 2.5741774729739576661e-934j)  +/-  (1.55e-75, 7.76e-199j)
| (1.4731079143028757384e-09 - 3.9146430354979361661e-940j)  +/-  (1.1e-87, 5.49e-211j)
| (5.5668236669358118159e-08 - 1.0553958927714422069e-939j)  +/-  (6.65e-85, 3.32e-208j)
| (2.7389136088818206683e-23 + 9.260797644438357788e-950j)  +/-  (8.05e-96, 4.02e-219j)
| (1.2701991700596579725e-06 - 7.332056516551143751e-938j)  +/-  (1.43e-85, 7.16e-209j)
| (3.4399628981357199914e-19 - 2.5171179511330445622e-947j)  +/-  (5.48e-94, 2.74e-217j)
| (2.1593756445207352674e-11 + 3.256885575806317084e-943j)  +/-  (9.19e-90, 4.59e-213j)
| (2.7389136088818206683e-23 - 5.842937167680573753e-950j)  +/-  (1.49e-96, 7.47e-220j)
| (0.01175828837929458259 + 5.6239885314481735676e-935j)  +/-  (1.18e-79, 5.87e-203j)
| (1.2701991700596579725e-06 + 1.7319069457739659001e-938j)  +/-  (6.46e-87, 3.23e-210j)
| (0.00015779837105192167709 + 1.1684050030418254023e-935j)  +/-  (1.4e-84, 7e-208j)
| (-2.5855086571300987087e-05 - 1.7533095958247891983e-935j)  +/-  (1.07e-85, 5.34e-209j)
| (1.5489649528702826154e-13 - 7.2388693984980596437e-944j)  +/-  (2.5e-92, 1.25e-215j)
| (5.5668236669358118159e-08 + 4.1623445392533214808e-939j)  +/-  (1.77e-88, 8.84e-212j)
| (-2.5855086571300987087e-05 + 3.3063170285006855078e-936j)  +/-  (9.84e-89, 4.91e-212j)
| (0.0038042664485364612323 - 1.719929302853261173e-935j)  +/-  (6.74e-87, 3.36e-210j)
| (4.1549403570042083144e-05 - 2.7487235337854469423e-936j)  +/-  (8.63e-89, 4.31e-212j)
| (0.050076328016055492339 + 1.8375756570314708636e-933j)  +/-  (4.42e-84, 2.21e-207j)
| (0.050076328016055492339 + 5.6216576321027029791e-934j)  +/-  (4.19e-84, 2.1e-207j)
| (0.18007262532971739669 - 4.3740921405691776209e-933j)  +/-  (1.39e-83, 6.96e-207j)
| (0.00094610834465046493107 - 6.4212098610662648603e-935j)  +/-  (1.13e-87, 5.67e-211j)
| (2.1593756445207352674e-11 - 9.6327055512199047795e-943j)  +/-  (6.39e-95, 3.19e-218j)
| (4.1549403570042083144e-05 + 1.4289438402533347954e-935j)  +/-  (4.05e-88, 2.02e-211j)
| (0.13836014239146626467 + 2.5395185809312468654e-933j)  +/-  (4.48e-84, 2.24e-207j)
| (0.068633260631689634103 - 1.0207259813268638908e-933j)  +/-  (6.23e-85, 3.12e-208j)
| (0.18007262532971739669 - 3.5940955010439185978e-933j)  +/-  (1.31e-84, 6.56e-208j)
| (0.031825320923979627256 + 5.8070082536882936175e-933j)  +/-  (2.07e-84, 1.04e-207j)
| (0.068633260631689634103 - 2.4685521943921950647e-933j)  +/-  (1.8e-85, 8.99e-209j)
| (0.030261499946285487052 - 9.558103706149744124e-934j)  +/-  (1.01e-86, 5.05e-210j)
| (0.00015779837105192167709 - 1.65620418745021649e-936j)  +/-  (2.15e-90, 1.08e-213j)
| (0.13836014239146626467 + 1.458876408550111295e-933j)  +/-  (2.37e-87, 1.76e-210j)
| (0.00094610834465046493107 + 4.8282513883048851971e-936j)  +/-  (6.28e-90, 3.09e-213j)
