Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 39
-------------------------------------------------
Trying to find an order 39 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^41 - 633097315998243674179/298132551856770427*t^39 + 378549460575093139139769/298132551856770427*t^37 - 3135218193437021981977311/8057636536669471*t^35 + 594872018984243412956006190/8057636536669471*t^33 - 76388963026963467523408906140/8057636536669471*t^31 + 6971856665812289374496425792740/8057636536669471*t^29 - 465366984428024780923862358858540/8057636536669471*t^27 + 23094320633233351140319142453761770/8057636536669471*t^25 - 859022160822903833920127463753503250/8057636536669471*t^23 + 23990310936945474534689306196588171750/8057636536669471*t^21 - 501085986642273748631988307967697215250/8057636536669471*t^19 + 7754495575776680695551871432234815729000/8057636536669471*t^17 - 87547550346040817257024283748190205779500/8057636536669471*t^15 + 704783602321980388896678959232121391032500/8057636536669471*t^13 - 3915395000653004171501514109834644441337500/8057636536669471*t^11 + 14320333737984004227544773108839010669489375/8057636536669471*t^9 - 32149052812002296362347723102610089328689375/8057636536669471*t^7 + 39634808502789975185269365441115397759968125/8057636536669471*t^5 - 21980204592058212954982309085536328756034375/8057636536669471*t^3 + 3464997548449834266605005980309683014181250/8057636536669471*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:
| (-10.30535773065872288 + 1.5484954091757207123e-636j)  +/-  (6.88e-247, 6.88e-247j)
| (-11.280903994371072078 - 3.0746017279030220161e-637j)  +/-  (6.95e-248, 6.95e-248j)
| (37.197800963343769479 - 1.7931409486265514605e-641j)  +/-  (6.04e-252, 6.04e-252j)
| (-8.7667235436212849594 - 7.0751705681918116092e-634j)  +/-  (7.84e-246, 7.84e-246j)
| (-9.4939974104232291899 + 2.2084438574423696088e-636j)  +/-  (2.81e-246, 2.81e-246j)
| (-37.197800963343769479 - 1.1144566272564687192e-646j)  +/-  (6.04e-252, 6.04e-252j)
| (9.4939974104232291899 + 8.0978084535378851904e-639j)  +/-  (3.07e-246, 3.07e-246j)
| (-5.1420998736825360118 + 1.8455568208763316446e-655j)  +/-  (2.63e-246, 2.63e-246j)
| (5.1420998736825360118 - 1.7352110967783401631e-676j)  +/-  (2.88e-246, 2.88e-246j)
| (-3.026353236711750199 + 5.0774528807056984863e-695j)  +/-  (1.29e-248, 1.29e-248j)
| (-2.5142401743703562283 - 3.2324239859222698122e-696j)  +/-  (2.06e-249, 2.06e-249j)
| (-6.263761394250182667 + 3.6350722179393921906e-695j)  +/-  (1.13e-245, 1.13e-245j)
| (10.30535773065872288 - 6.1625665451826431424e-697j)  +/-  (7.59e-247, 7.59e-247j)
| (4.600192437884120745 - 1.2703604435980920708e-711j)  +/-  (9.28e-247, 9.28e-247j)
| (-7.457016382566035285 + 5.730791960521295308e-727j)  +/-  (1.49e-245, 1.49e-245j)
| (-2.0064474672230281095 + 3.114872928745558494e-731j)  +/-  (2.17e-250, 2.17e-250j)
| (6.263761394250182667 - 4.4675801840647183479e-726j)  +/-  (1.12e-245, 1.12e-245j)
| (5.6957721053788043481 - 1.2144578444196538014e-736j)  +/-  (6.11e-246, 6.11e-246j)
| (8.0929799251590938245 + 2.798485095336399676e-741j)  +/-  (1.3e-245, 1.3e-245j)
| (-6.8493652377425953371 + 7.7607518994010744501e-748j)  +/-  (1.4e-245, 1.4e-245j)
| (7.457016382566035285 - 1.9801795397237101764e-746j)  +/-  (1.43e-245, 1.43e-245j)
| (6.8493652377425953371 + 9.6374689267988162465e-765j)  +/-  (1.53e-245, 1.53e-245j)
| (3.5438678060650370127 + 1.8323218017345958607e-787j)  +/-  (6.36e-248, 6.36e-248j)
| (11.280903994371072078 - 8.7510059046422025401e-804j)  +/-  (6.64e-248, 6.64e-248j)
| (-5.6957721053788043481 + 2.821368396203178196e-802j)  +/-  (6.75e-246, 6.75e-246j)
| (-4.600192437884120745 + 9.6656039203395044099e-804j)  +/-  (9.2e-247, 9.2e-247j)
| (2.5142401743703562283 + 2.7346803375692721027e-805j)  +/-  (2.01e-249, 2.01e-249j)
| (8.7667235436212849594 - 5.7242183499436489987e-819j)  +/-  (7.36e-246, 7.36e-246j)
| (-8.0929799251590938245 - 2.4208207370160895141e-829j)  +/-  (1.22e-245, 1.22e-245j)
| (-1 - 6.5259065797908830601e-840j)  +/-  (2.02e-252, 2.02e-252j)
| (-4.0680083451908172131 + 3.52531668144268838e-835j)  +/-  (2.81e-247, 2.81e-247j)
| (4.0680083451908172131 + 4.3022089634186193925e-853j)  +/-  (2.62e-247, 2.62e-247j)
| (0.49960330067126164005 + 4.6720885106564406128e-874j)  +/-  (1.34e-253, 1.34e-253j)
| (1 + 7.2810490679554481637e-871j)  +/-  (2.02e-252, 2.02e-252j)
| (-3.5438678060650370127 - 7.5370885903051429902e-869j)  +/-  (6.37e-248, 6.37e-248j)
| (-1.5020000394036501653 - 2.924477817693436156e-872j)  +/-  (2.29e-251, 2.29e-251j)
| (2.0064474672230281095 + 2.1975760917093397918e-867j)  +/-  (2.18e-250, 2.18e-250j)
| (1.5020000394036501653 + 7.6904312386443465488e-871j)  +/-  (2.44e-251, 2.44e-251j)
| (3.026353236711750199 + 1.5608778172230750093e-871j)  +/-  (1.3e-248, 1.3e-248j)
| (9.3649354498209127418e-888 - 6.9524899220873854476e-889j)  +/-  (3.85e-886, 3.85e-886j)
| (-0.49960330067126164005 - 3.1399322863531604688e-891j)  +/-  (1.34e-253, 1.34e-253j)
-------------------------------------------------
The weights are:
| (3.0211571379007141922e-24 + 1.9290418878810216162e-654j)  +/-  (4.29e-81, 2.76e-205j)
| (1.0421776813831594489e-28 - 6.9909474334970067584e-657j)  +/-  (6.89e-83, 4.44e-207j)
| (9.6870289498921975859e-77 - 8.9720163302677754682e-681j)  +/-  (1.37e-105, 8.84e-230j)
| (5.6918781109886697686e-18 - 1.7625913960577429027e-650j)  +/-  (2.69e-79, 1.74e-203j)
| (8.1315684523905257817e-21 - 2.1027768102057902449e-652j)  +/-  (3.37e-80, 2.17e-204j)
| (9.6870289498921975859e-77 + 1.4505121918908207146e-680j)  +/-  (3.28e-106, 2.11e-230j)
| (8.1315684523905257817e-21 + 8.3787761996159416286e-654j)  +/-  (1.08e-84, 6.95e-209j)
| (3.95907327184893747e-07 - 2.8756370250497787214e-646j)  +/-  (1.08e-73, 6.99e-198j)
| (3.95907327184893747e-07 - 7.4939690273866777609e-647j)  +/-  (7.49e-76, 4.82e-200j)
| (0.0021066295249063319758 - 1.3161753625924397231e-644j)  +/-  (2.79e-67, 1.8e-191j)
| (0.0086222323179294902828 + 2.4421379572191392477e-644j)  +/-  (3.98e-65, 2.57e-189j)
| (6.9462690816700301173e-10 - 1.752557180970767561e-647j)  +/-  (1.72e-76, 1.11e-200j)
| (3.0211571379007141922e-24 - 1.556072089673521763e-655j)  +/-  (1.03e-86, 6.61e-211j)
| (5.4381809549003120605e-06 + 2.8844260250410637397e-646j)  +/-  (1.08e-75, 6.93e-200j)
| (2.0833691720150457216e-13 - 5.8359207532249218735e-649j)  +/-  (1.69e-79, 1.09e-203j)
| (0.026966973958882474863 - 3.9912032336323823623e-644j)  +/-  (7.09e-66, 4.57e-190j)
| (6.9462690816700301173e-10 - 2.9185125985982384704e-648j)  +/-  (3.59e-80, 2.31e-204j)
| (2.017065926590452881e-08 + 1.6303579832300251345e-647j)  +/-  (7.96e-79, 5.13e-203j)
| (1.5610303635176785868e-15 + 3.9390378529514778085e-651j)  +/-  (1.73e-84, 1.11e-208j)
| (1.5444828865465103358e-11 + 3.4211989848743465104e-648j)  +/-  (7.29e-81, 4.69e-205j)
| (2.0833691720150457216e-13 - 4.7113659543072983109e-650j)  +/-  (1.84e-83, 1.19e-207j)
| (1.5444828865465103358e-11 + 4.2006816341397184243e-649j)  +/-  (2.37e-82, 1.53e-206j)
| (0.00038928709305674169048 + 2.6415278072846273697e-645j)  +/-  (1.49e-78, 9.58e-203j)
| (1.0421776813831594489e-28 + 8.7669828735991150725e-658j)  +/-  (2.82e-91, 1.82e-215j)
| (2.017065926590452881e-08 + 7.6779765980044514708e-647j)  +/-  (1.28e-81, 8.28e-206j)
| (5.4381809549003120605e-06 + 9.2536191167022067802e-646j)  +/-  (1.18e-80, 7.58e-205j)
| (0.0086222323179294902828 + 1.3535630886123537087e-644j)  +/-  (6.31e-79, 4.06e-203j)
| (5.6918781109886697686e-18 - 2.2970423750973099004e-652j)  +/-  (8.78e-87, 5.65e-211j)
| (1.5610303635176785868e-15 + 9.8565227889363726237e-650j)  +/-  (1.19e-85, 7.69e-210j)
| (0.12124212939719662322 - 7.3581163373856552723e-644j)  +/-  (9.51e-78, 6.13e-202j)
| (5.3698805591245819219e-05 - 2.5741302287643943306e-645j)  +/-  (1.04e-80, 6.68e-205j)
| (5.3698805591245819219e-05 - 9.4238086978397124342e-646j)  +/-  (1.41e-81, 9.06e-206j)
| (0.17602071716180923663 + 7.4290784844658433978e-644j)  +/-  (2.67e-78, 1.72e-202j)
| (0.12124212939719662322 - 5.8513535143883891846e-644j)  +/-  (1.77e-78, 1.14e-202j)
| (0.00038928709305674169048 + 6.2262001351457156897e-645j)  +/-  (2.51e-80, 1.62e-204j)
| (0.064962304850576388818 + 5.7608441925428600163e-644j)  +/-  (5.33e-79, 3.43e-203j)
| (0.026966973958882474863 - 2.5045300573866328759e-644j)  +/-  (1.42e-80, 9.13e-205j)
| (0.064962304850576388818 + 4.0755842538375141598e-644j)  +/-  (3.14e-80, 2.02e-204j)
| (0.0021066295249063319758 - 6.4066203694289689244e-645j)  +/-  (2.23e-81, 1.44e-205j)
| (0.19926034384165694982 - 8.3540007308040118604e-644j)  +/-  (1.37e-80, 9.09e-205j)
| (0.17602071716180923663 + 8.3269880727936095078e-644j)  +/-  (1.03e-80, 6.34e-205j)
