Starting with polynomial:
P : 1048576*t^20 - 99614720*t^18 + 3810263040*t^16 - 76205260800*t^14 + 866834841600*t^12 - 5721109954560*t^10 + 21454162329600*t^8 - 42908324659200*t^6 + 40226554368000*t^4 - 13408851456000*t^2 + 670442572800
Extension levels are: 20 35
-------------------------------------------------
Trying to find an order 35 Kronrod extension for:
P1 : 1048576*t^20 - 99614720*t^18 + 3810263040*t^16 - 76205260800*t^14 + 866834841600*t^12 - 5721109954560*t^10 + 21454162329600*t^8 - 42908324659200*t^6 + 40226554368000*t^4 - 13408851456000*t^2 + 670442572800
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1048576*t^55 - 424004861224152240619612152388648960/719676700547021253036700269*t^53 + 2533342344381053124811862770993250959360/16552564112581488819844106187*t^51 - 1483283490473812683322475067728100519116800/60692735079465459006095056019*t^49 + 163288939563059024513656838845797684527104000/60692735079465459006095056019*t^47 - 13174346565636769911881446566572452885902295040/60692735079465459006095056019*t^45 + 808480900877080537244927000451797133512225587200/60692735079465459006095056019*t^43 - 38659503520725443420359497743970624954822058598400/60692735079465459006095056019*t^41 + 63647170183696104579852343229216317552355507712000/2638814568672411261134567653*t^39 - 4033908040187693996725770844524145873488668059008000/5517521370860496273281368729*t^37 + 1084193211643649942703850315469435132556249562381363200/60692735079465459006095056019*t^35 - 1948893430580340937153407562879524469130800540344864000/5517521370860496273281368729*t^33 + 31230286126290154326017055389919521623868580757400448000/5517521370860496273281368729*t^31 - 17620590387581114520423292817241142873732038827101920000/239892233515673751012233423*t^29 + 4246916008998816079348876483355191260007611951230328960000/5517521370860496273281368729*t^27 - 35761526946255420035344306058144204802628488026342809080000/5517521370860496273281368729*t^25 + 240257681140217354845162297042393162796645110961152794150000/5517521370860496273281368729*t^23 - 55456291971079822387245385406127838217338570428582558412500/239892233515673751012233423*t^21 + 229740613105316570649636500935387566755220644570285638875000/239892233515673751012233423*t^19 - 730764101697366605018505203633836194519293057643132147984375/239892233515673751012233423*t^17 + 1747806276517156098042662907120883510998470372377928440443750/239892233515673751012233423*t^15 - 6117473506340718840308388013001127194412665668651164946640625/479784467031347502024466846*t^13 + 3776882054730346556982346888744350662902130976412692812812500/239892233515673751012233423*t^11 - 25037541456114778088123192160974200278311805698116148137734375/1919137868125390008097867384*t^9 + 25895722170111905470748617607703816783467729776453937816484375/3838275736250780016195734768*t^7 - 29840586116328757156238987596946094053035661541468939677109375/15353102945003120064782939072*t^5 + 1957513691382290227864264235757107246321303934253030904296875/7676551472501560032391469536*t^3 - 590723060430682154443963092740687252745393152679878698828125/61412411780012480259131756288*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
Positive weights:   55 out of 55
Indefinite weights: 0 out of 55
Negative weights:   0 out of 55
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (8.0658852416672224796 - 2.5978862680925905077e-913j)  +/-  (3.19e-245, 3.19e-245j)
| (7.5151372088734658681 + 8.6794145078358245225e-912j)  +/-  (2.31e-244, 2.31e-244j)
| (8.7308635792758172984 + 1.4641413011724092178e-913j)  +/-  (1.81e-246, 1.81e-246j)
| (-8.0658852416672224796 - 3.3484332463588385089e-911j)  +/-  (3.28e-245, 3.28e-245j)
| (6.5712537047378230758 + 2.3348179616155011334e-910j)  +/-  (3.61e-243, 3.61e-243j)
| (-6.1476372048032242411 + 1.0039733927419369699e-907j)  +/-  (9.44e-243, 9.44e-243j)
| (5.1717982810552820184 - 3.6016887775991091452e-910j)  +/-  (8.16e-242, 8.16e-242j)
| (5.7491382651107542272 + 1.2549129988949852731e-911j)  +/-  (2.16e-242, 2.16e-242j)
| (-3.0661266731711900313 + 8.1777570924471226258e-913j)  +/-  (2.79e-244, 2.79e-244j)
| (4.6036824495507442731 - 2.2806566115956530883e-910j)  +/-  (2.18e-242, 2.18e-242j)
| (-6.5712537047378230758 + 1.1599036624646013172e-910j)  +/-  (3.54e-243, 3.54e-243j)
| (1.4837129335319649771 - 2.763867052314288315e-919j)  +/-  (1.92e-248, 1.92e-248j)
| (3.0661266731711900313 - 1.8155548037863660428e-915j)  +/-  (2.67e-244, 2.67e-244j)
| (-1.4837129335319649771 + 4.5272178054114923877e-919j)  +/-  (2.04e-248, 2.04e-248j)
| (-8.7308635792758172984 - 1.2276173644756930253e-916j)  +/-  (1.85e-246, 1.85e-246j)
| (6.1476372048032242411 + 1.5653513423040464984e-913j)  +/-  (9.37e-243, 9.37e-243j)
| (1.9964716557046272516 - 2.6103905510956941643e-917j)  +/-  (8.51e-247, 8.51e-247j)
| (-5.387480890011232862 + 1.5030344146390499412e-911j)  +/-  (6.14e-242, 6.14e-242j)
| (-3.9447640401156252104 - 4.0944424570264881992e-925j)  +/-  (4.72e-243, 4.72e-243j)
| (-7.5151372088734658681 - 1.2375390210193055814e-937j)  +/-  (2.32e-244, 2.32e-244j)
| (2.2549740020892755231 - 6.1773765943727126468e-939j)  +/-  (4.47e-246, 4.47e-246j)
| (1.2340762153953230079 - 3.8953091483085426553e-942j)  +/-  (2.47e-249, 2.47e-249j)
| (3.6386047651754048873 - 4.5490588356258250294e-936j)  +/-  (2.1e-243, 2.1e-243j)
| (5.387480890011232862 + 7.9014672125916335017e-934j)  +/-  (6.1e-242, 6.1e-242j)
| (-2.5177616016975487327 - 5.0988348046412666112e-939j)  +/-  (2.25e-245, 2.25e-245j)
| (-4.2675838194471376745 - 2.7375333505047123538e-936j)  +/-  (9.88e-243, 9.88e-243j)
| (7.0237848462045913587 - 3.6795284003765272907e-946j)  +/-  (1.1e-243, 1.1e-243j)
| (-5.7491382651107542272 + 1.2428851312476773262e-942j)  +/-  (2.51e-242, 2.51e-242j)
| (-1.7385377121165862068 + 3.0553956342474004577e-963j)  +/-  (1.34e-247, 1.34e-247j)
| (-0.73747372854539435871 - 4.7689468993903091837e-967j)  +/-  (1.98e-251, 1.98e-251j)
| (-3.6386047651754048873 - 1.0157240064153460495e-957j)  +/-  (2.05e-243, 2.05e-243j)
| (-5.1717982810552820184 + 1.0099516773568241526e-971j)  +/-  (8.33e-242, 8.33e-242j)
| (4.9398906103746333756 - 4.7829140768985465664e-985j)  +/-  (5.25e-242, 5.25e-242j)
| (-7.0237848462045913587 - 4.1230372617263881314e-993j)  +/-  (1.14e-243, 1.14e-243j)
| (4.2675838194471376745 - 7.859730803974927698e-996j)  +/-  (1e-242, 1e-242j)
| (-1.2340762153953230079 + 2.3011112664075968766e-1015j)  +/-  (2.29e-249, 2.29e-249j)
| (-4.9398906103746333756 + 1.2102187379136982741e-1006j)  +/-  (5.68e-242, 5.68e-242j)
| (0.98608889035692977853 + 7.8822230160183578208e-1034j)  +/-  (2.36e-250, 2.36e-250j)
| (0.73747372854539435871 + 3.0588387565833996491e-1034j)  +/-  (2.16e-251, 2.16e-251j)
| (-4.6036824495507442731 + 4.2803865196666300326e-1026j)  +/-  (2.03e-242, 2.03e-242j)
| (-1.9964716557046272516 + 2.7149504785856002477e-1034j)  +/-  (9.46e-247, 9.46e-247j)
| (2.5177616016975487327 - 1.1782315854155888066e-1033j)  +/-  (2.25e-245, 2.25e-245j)
| (3.4390391131401043759e-1064 + 1.0767565236096752891e-1063j)  +/-  (6.22e-1062, 6.22e-1062j)
| (1.7385377121165862068 - 6.8404634651565062979e-1036j)  +/-  (1.49e-247, 1.49e-247j)
| (-2.2549740020892755231 - 3.2547940460439148708e-1033j)  +/-  (4.33e-246, 4.33e-246j)
| (-0.98608889035692977853 + 1.8163869103794450734e-1038j)  +/-  (2.48e-250, 2.48e-250j)
| (-2.7888060584281304805 - 1.3008381317798042147e-1031j)  +/-  (8.09e-245, 8.09e-245j)
| (-3.3478545673832163269 + 1.0754583810426145251e-1031j)  +/-  (9.03e-244, 9.03e-244j)
| (0.49045240768675091417 + 1.0497734316680952441e-1040j)  +/-  (1.19e-252, 1.19e-252j)
| (2.7888060584281304805 + 3.6753502357058078103e-1032j)  +/-  (8.23e-245, 8.23e-245j)
| (-0.2453407083009012499 + 1.9271840391612993436e-1042j)  +/-  (6.99e-254, 6.99e-254j)
| (-0.49045240768675091417 - 5.7971231987433454299e-1042j)  +/-  (1.15e-252, 1.15e-252j)
| (3.9447640401156252104 + 3.6461971360445381409e-1032j)  +/-  (4.9e-243, 4.9e-243j)
| (0.2453407083009012499 - 1.7160972277119467138e-1043j)  +/-  (8.44e-254, 8.44e-254j)
| (3.3478545673832163269 - 1.0304161419410389146e-1040j)  +/-  (8e-244, 8e-244j)
-------------------------------------------------
The weights are:
| (1.861673664813588246e-29 + 5.7023507354014007389e-933j)  +/-  (1.08e-75, 2.24e-198j)
| (8.6387586395733569428e-26 - 1.0298608324470585743e-930j)  +/-  (2.88e-74, 5.99e-197j)
| (3.3991258405713110724e-34 - 8.5833888638466653828e-936j)  +/-  (5.24e-78, 1.09e-200j)
| (1.861673664813588246e-29 - 1.9389537393459908846e-932j)  +/-  (2.13e-79, 4.42e-202j)
| (4.3493993153775138142e-20 - 5.6970857179536624849e-927j)  +/-  (3.98e-72, 8.27e-195j)
| (8.9483673696741866396e-18 + 7.7871285963746272882e-924j)  +/-  (8.44e-74, 1.76e-196j)
| (1.97330709582227766e-13 - 3.0676394686414806415e-921j)  +/-  (2.95e-68, 6.13e-191j)
| (9.6042195657692018625e-16 - 1.0978178411002020286e-923j)  +/-  (3.64e-70, 7.56e-193j)
| (1.3023014861877955531e-05 + 1.4774611929853192523e-916j)  +/-  (2.13e-61, 4.44e-184j)
| (1.1995779416518863874e-10 + 1.3355933338348382628e-919j)  +/-  (1.01e-66, 2.09e-189j)
| (4.3493993153775138142e-20 + 5.5994154146241585147e-926j)  +/-  (1.82e-76, 3.79e-199j)
| (0.015735024071325612539 + 4.3936866040433704274e-915j)  +/-  (2.5e-48, 5.19e-171j)
| (1.3023014861877955531e-05 - 2.8579407172447085486e-917j)  +/-  (7.22e-61, 1.5e-183j)
| (0.015735024071325612539 + 2.0121749383742147397e-914j)  +/-  (8.75e-50, 1.82e-172j)
| (3.3991258405713110724e-34 + 2.467987454038636153e-935j)  +/-  (1.7e-83, 3.54e-206j)
| (8.9483673696741866396e-18 + 2.5936294579439912082e-925j)  +/-  (3.71e-72, 7.71e-195j)
| (0.0027056014553009849006 + 3.0833052787044954087e-916j)  +/-  (3.58e-55, 7.44e-178j)
| (4.4921869099452936958e-14 + 1.1784916649862834155e-921j)  +/-  (7.57e-74, 1.57e-196j)
| (3.0992918503522336964e-08 - 1.2988198671815283802e-918j)  +/-  (5.43e-69, 1.13e-191j)
| (8.6387586395733569428e-26 + 4.3165548479320553415e-930j)  +/-  (6.13e-80, 1.27e-202j)
| (0.00090656549651635935687 + 5.0232547204343666769e-917j)  +/-  (7.13e-59, 1.48e-181j)
| (0.030510172033862897523 - 1.0064758398827803617e-914j)  +/-  (1.59e-51, 3.3e-174j)
| (2.9883453174911193781e-07 - 3.8231059796248412174e-918j)  +/-  (2.77e-66, 5.76e-189j)
| (4.4921869099452936958e-14 + 4.845768150757856804e-922j)  +/-  (5.38e-71, 1.12e-193j)
| (0.00026578092261612675746 + 1.1059905685084383499e-915j)  +/-  (4e-64, 8.31e-187j)
| (2.2955372049984693974e-09 + 2.6454779838396442701e-919j)  +/-  (1.47e-71, 3.06e-194j)
| (9.9528830968128129488e-23 + 9.3622248158151357435e-929j)  +/-  (1.44e-77, 2.99e-200j)
| (9.6042195657692018625e-16 - 7.2948211035748130428e-923j)  +/-  (4.2e-76, 8.73e-199j)
| (0.007061467576438205613 - 1.1182878564242260955e-914j)  +/-  (8.11e-62, 1.69e-184j)
| (0.081304815222204388598 - 6.0311354802093593706e-914j)  +/-  (4.43e-58, 9.21e-181j)
| (2.9883453174911193781e-07 + 5.6749773783079286532e-918j)  +/-  (3.98e-70, 8.28e-193j)
| (1.97330709582227766e-13 - 5.6548144625108263115e-921j)  +/-  (7.44e-75, 1.55e-197j)
| (4.5468149975508194277e-12 + 1.7934709042084748101e-920j)  +/-  (9.69e-74, 2.02e-196j)
| (9.9528830968128129488e-23 - 5.3302583992850382723e-928j)  +/-  (2.97e-81, 6.18e-204j)
| (2.2955372049984693974e-09 - 4.4379757248107678032e-919j)  +/-  (3.64e-73, 7.58e-196j)
| (0.030510172033862897523 - 3.2433086563754463588e-914j)  +/-  (1.6e-63, 3.33e-186j)
| (4.5468149975508194277e-12 + 1.5216343808247328975e-920j)  +/-  (9.57e-75, 1.99e-197j)
| (0.053009622551052080687 + 1.9169353394294395813e-914j)  +/-  (5.01e-64, 1.04e-186j)
| (0.081304815222204388598 - 3.1858066825916363095e-914j)  +/-  (5.19e-64, 1.08e-186j)
| (1.1995779416518863874e-10 - 5.5105199454724285562e-920j)  +/-  (3.48e-74, 7.25e-197j)
| (0.0027056014553009849006 + 5.6967098030609770913e-915j)  +/-  (2.37e-68, 4.93e-191j)
| (0.00026578092261612675746 - 9.4907045258999250135e-917j)  +/-  (1.17e-70, 2.44e-193j)
| (0.1385573949408836191 + 7.202107173280115679e-914j)  +/-  (4.63e-66, 9.63e-189j)
| (0.007061467576438205613 - 1.489559222381508513e-915j)  +/-  (9.13e-68, 1.9e-190j)
| (0.00090656549651635935687 - 2.6466124878522573238e-915j)  +/-  (1.59e-69, 3.31e-192j)
| (0.053009622551052080687 + 4.6490748985990042009e-914j)  +/-  (3.72e-67, 7.74e-190j)
| (6.498331618765030841e-05 - 4.4558272973754096802e-916j)  +/-  (3.08e-71, 6.41e-194j)
| (2.1808243347899378731e-06 - 1.7864725769558400932e-917j)  +/-  (1.47e-72, 3.05e-195j)
| (0.10899845651206244812 + 4.7064050413066167037e-914j)  +/-  (4.12e-69, 8.66e-192j)
| (6.498331618765030841e-05 + 6.0551376015719332516e-917j)  +/-  (1.68e-73, 3.51e-196j)
| (0.13014327728505947936 - 7.5629277955915748805e-914j)  +/-  (8.27e-70, 1.76e-192j)
| (0.10899845651206244812 + 7.1212720091086982632e-914j)  +/-  (5.75e-70, 1.22e-192j)
| (3.0992918503522336964e-08 + 1.2017786182218248578e-918j)  +/-  (6.93e-77, 1.44e-199j)
| (0.13014327728505947936 - 6.1653388625641674925e-914j)  +/-  (5.11e-71, 1.64e-193j)
| (2.1808243347899378731e-06 + 1.1295757234580914889e-917j)  +/-  (1.94e-75, 3.94e-198j)
