Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 63
-------------------------------------------------
Trying to find an order 63 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^65 - 1108195160285199591026688614062076721785278/274662905080377442409531016691131991427*t^63 + 524279254251641169810714793009925908396115727/274662905080377442409531016691131991427*t^61 - 5074822214940336393026488702040428573805694705/9005341150176309587197738252168262014*t^59 + 2098905894820062680368828557495628571726386797885/18010682300352619174395476504336524028*t^57 - 647036462634047352783688042003753651665558149277435/36021364600705238348790953008673048056*t^55 + 14042298681934440704857035190235309922811206735074505/6549339018310043336143809637940554192*t^53 - 204826479598271213291513640021561892059088520258444655/1007590618201545128637509175067777568*t^51 + 31398857035101812428430181579010314949764205292284245375/2015181236403090257275018350135555136*t^49 - 3940056534205942297833982565865669238074527215334839517625/4030362472806180514550036700271110272*t^47 + 408329273817375950785968820591198389918630066588191185505625/8060724945612361029100073400542220544*t^45 - 35166459265838058525847571323108614168126336707881759724038875/16121449891224722058200146801084441088*t^43 + 2527142112580449181442085646673955336579091548567680034631005375/32242899782449444116400293602168882176*t^41 - 151889745817953788940584313234836131903498041007011636386386925625/64485799564898888232800587204337764352*t^39 + 7641570068585522890667347792034748217805525556595562878998016610625/128971599129797776465601174408675528704*t^37 - 321626179711179658572631902564728307878427315972322723528832131606875/257943198259595552931202348817351057408*t^35 + 11303759736525715623486373130128294247333883240807653803871289612043125/515886396519191105862404697634702114816*t^33 - 330684720184831947195763683444531670587744726657430925905850760365679375/1031772793038382211724809395269404229632*t^31 + 8015772338596076422505390537088061792113820637813358747205952600760009375/2063545586076764423449618790538808459264*t^29 - 160025029757970262222954860504637359834138232446268032009931690535882128125/4127091172153528846899237581077616918528*t^27 + 2610837352704828660168996698769952030844114790937085550839835281693920865625/8254182344307057693798475162155233837056*t^25 - 34474791902246845976073365652621691379987194320602387712933848492615862609375/16508364688614115387596950324310467674112*t^23 + 363996934378741320421923666640949639529600896577048005473791290480449269234375/33016729377228230775193900648620935348224*t^21 - 3027047391093270501956120084265976692163621838178495477054656430092234125078125/66033458754456461550387801297241870696448*t^19 + 19455842146375117666731090061158824465672248519982339757152322894841631104453125/132066917508912923100775602594483741392896*t^17 - 94351205673786115558215045399258753598252081449609371867178789865501951728421875/264133835017825846201551205188967482785792*t^15 + 334637544518677579076475418881169912340036490377079062416236116700841160619421875/528267670035651692403102410377934965571584*t^13 - 832697302135965775373793557210962923762825438599903022176722792507337268969515625/1056535340071303384806204820755869931143168*t^11 + 1372375557352766585478951478725318729678353186407464018649753641666908875373203125/2113070680142606769612409641511739862286336*t^9 - 1376808454918676356016570120483418682242814846514334332128069227137882389399921875/4226141360285213539224819283023479724572672*t^7 + 734984800841673865524247228543060914178061464517720021187097201785928322421796875/8452282720570427078449638566046959449145344*t^5 - 163291510722669123173192055725073790576178237572711616091789014379141603956015625/16904565441140854156899277132093918898290688*t^3 + 4194897665910403701858016889401158075517796498484254010816451925878270495546875/16904565441140854156899277132093918898290688*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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: 0
  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:
| (-9.3743163446374657129 + 3.4420263410599292771e-717j)  +/-  (4.27e-242, 4.27e-242j)
| (9.8963833635281543406 - 2.811837284970069722e-719j)  +/-  (4.72e-243, 4.72e-243j)
| (-3.5174578082374115506 - 1.0443113800232087261e-718j)  +/-  (9.13e-243, 9.13e-243j)
| (9.3743163446374657129 + 6.0323871047116721864e-719j)  +/-  (4.29e-242, 4.29e-242j)
| (-7.6909501145650960139 + 4.234871875932885826e-715j)  +/-  (4.43e-240, 4.43e-240j)
| (8.4788080394983189581 - 8.8888068833819206347e-719j)  +/-  (8.35e-241, 8.35e-241j)
| (-8.0750301834251241841 + 5.4554965122816219814e-717j)  +/-  (2.18e-240, 2.18e-240j)
| (-7.3224939167037091608 + 7.8630269493154565867e-719j)  +/-  (7.74e-240, 7.74e-240j)
| (-10.527153293681838476 - 1.2355837469344657556e-732j)  +/-  (2.14e-244, 2.14e-244j)
| (5.3203632150463832312 + 2.1243396861273590293e-727j)  +/-  (4.02e-240, 4.02e-240j)
| (-8.4788080394983189581 + 1.2410444702268883363e-728j)  +/-  (8.2e-241, 8.2e-241j)
| (-2.9410360725695640965 - 9.9676585127147288602e-741j)  +/-  (3.66e-244, 3.66e-244j)
| (-1.2558083233103057787 - 4.8081915958113042998e-746j)  +/-  (1.81e-249, 1.81e-249j)
| (10.527153293681838476 - 1.0735565113085726951e-741j)  +/-  (2.16e-244, 2.16e-244j)
| (8.9084663796579088308 - 5.632453396434425582e-738j)  +/-  (2.15e-241, 2.15e-241j)
| (-6.285736308839245587 + 1.8054729069377282404e-736j)  +/-  (1.13e-239, 1.13e-239j)
| (4.4023799174239598537 - 1.1184234936917275769e-749j)  +/-  (3.32e-241, 3.32e-241j)
| (3.809417358345849241 - 4.7733779261691227777e-751j)  +/-  (3.41e-242, 3.41e-242j)
| (-8.9084663796579088308 - 4.1268610587142834208e-748j)  +/-  (2.24e-241, 2.24e-241j)
| (-2.3729207172555657021 + 2.8314264700371824268e-768j)  +/-  (1.13e-245, 1.13e-245j)
| (2.9410360725695640965 + 5.2869865962523117102e-767j)  +/-  (4.01e-244, 4.01e-244j)
| (-6.9667975970073654493 + 6.781321099538379117e-761j)  +/-  (1.05e-239, 1.05e-239j)
| (5.9574864301956492621 + 9.1396961066667540488e-774j)  +/-  (8.68e-240, 8.68e-240j)
| (-9.8963833635281543406 - 1.2027012075136921274e-775j)  +/-  (4.32e-243, 4.32e-243j)
| (7.6909501145650960139 + 1.627601885242802398e-777j)  +/-  (4.56e-240, 4.56e-240j)
| (-5.3203632150463832312 + 8.5009378398566758752e-780j)  +/-  (3.97e-240, 3.97e-240j)
| (1.53294843575074438 - 7.3841974316286522216e-808j)  +/-  (2.02e-248, 2.02e-248j)
| (-5.9574864301956492621 - 3.6819115813474206886e-797j)  +/-  (9e-240, 9e-240j)
| (5.6359760653589015552 + 4.0670647927414366383e-810j)  +/-  (6.48e-240, 6.48e-240j)
| (-1.8114946213260856679 + 6.7640968287845998572e-819j)  +/-  (2.03e-247, 2.03e-247j)
| (8.0750301834251241841 - 4.4061743796993261995e-811j)  +/-  (2.05e-240, 2.05e-240j)
| (7.3224939167037091608 + 2.8092551117416061264e-810j)  +/-  (7.76e-240, 7.76e-240j)
| (4.1042759957544032575 - 3.0508956160449782155e-812j)  +/-  (1.18e-241, 1.18e-241j)
| (6.6217498261095293621 - 7.764229647705434772e-810j)  +/-  (1.12e-239, 1.12e-239j)
| (2.6560525585790567956 + 1.3165191470988335137e-817j)  +/-  (6.69e-245, 6.69e-245j)
| (4.7041205009288102186 - 2.7581024015958154235e-813j)  +/-  (8.65e-241, 8.65e-241j)
| (1.2558083233103057787 + 1.3797191699703401386e-821j)  +/-  (1.74e-249, 1.74e-249j)
| (6.285736308839245587 + 7.6605391102082317726e-812j)  +/-  (1.15e-239, 1.15e-239j)
| (-5.009943818452004986 + 3.4357034064337375515e-812j)  +/-  (2.06e-240, 2.06e-240j)
| (-0.98027474946545138438 + 4.7720299244517134187e-831j)  +/-  (1.46e-250, 1.46e-250j)
| (-0.7071067811865475244 - 3.3844191086559917774e-832j)  +/-  (1.09e-251, 1.09e-251j)
| (-3.809417358345849241 + 3.0701285303099741958e-822j)  +/-  (3.24e-242, 3.24e-242j)
| (2.3729207172555657021 - 1.8820048371098878351e-827j)  +/-  (1.15e-245, 1.15e-245j)
| (0.18912751542128262451 - 3.7825913772688175381e-834j)  +/-  (4.75e-254, 4.75e-254j)
| (-6.6217498261095293621 - 6.8135040126216574219e-819j)  +/-  (1.16e-239, 1.16e-239j)
| (-3.6809274687444205733e-877 + 2.169814779447187495e-877j)  +/-  (2.78e-875, 2.78e-875j)
| (6.9667975970073654493 - 1.8246018431648561901e-824j)  +/-  (1.12e-239, 1.12e-239j)
| (3.228089169317419618 - 1.0450424227278846566e-829j)  +/-  (2.11e-243, 2.11e-243j)
| (0.98027474946545138438 - 1.5630260254570724166e-835j)  +/-  (1.64e-250, 1.64e-250j)
| (2.0914521870301096441 + 7.9391392960301957704e-833j)  +/-  (1.61e-246, 1.61e-246j)
| (-4.1042759957544032575 + 1.3758167777122072721e-825j)  +/-  (1.15e-241, 1.15e-241j)
| (-1.53294843575074438 - 7.9130156770372639498e-835j)  +/-  (2.14e-248, 2.14e-248j)
| (3.5174578082374115506 + 2.1560690473968912215e-828j)  +/-  (9.05e-243, 9.05e-243j)
| (-4.7041205009288102186 + 1.4439521064413945981e-824j)  +/-  (8.43e-241, 8.43e-241j)
| (-5.6359760653589015552 - 1.6738948864807089977e-832j)  +/-  (6.92e-240, 6.92e-240j)
| (-4.4023799174239598537 + 1.1355877044058698975e-835j)  +/-  (3.28e-241, 3.28e-241j)
| (-0.43906931015994746321 + 6.2392034378610336373e-849j)  +/-  (6.99e-253, 6.99e-253j)
| (-3.228089169317419618 + 1.1547146070892969278e-838j)  +/-  (2.06e-243, 2.06e-243j)
| (1.8114946213260856679 - 6.8910442069528018348e-843j)  +/-  (2.02e-247, 2.02e-247j)
| (0.43906931015994746321 - 2.6568022477364964953e-849j)  +/-  (6.9e-253, 6.9e-253j)
| (5.009943818452004986 - 1.714266639686059257e-845j)  +/-  (1.84e-240, 1.84e-240j)
| (-2.0914521870301096441 + 1.209435662484807192e-850j)  +/-  (1.51e-246, 1.51e-246j)
| (-0.18912751542128262451 - 1.0814959896686176044e-859j)  +/-  (4.75e-254, 4.75e-254j)
| (-2.6560525585790567956 + 1.0601770746575700826e-851j)  +/-  (6.92e-245, 6.92e-245j)
| (0.7071067811865475244 + 1.2935337757839693573e-858j)  +/-  (1.12e-251, 1.12e-251j)
-------------------------------------------------
The weights are:
| (1.8885284723815430713e-39 - 2.4245155735178998133e-742j)  +/-  (1.45e-61, 7.75e-180j)
| (9.2726199563873986052e-44 - 7.0265944358164089004e-745j)  +/-  (1.91e-63, 1.02e-181j)
| (6.9411499550525195675e-07 - 2.7553534457888942687e-724j)  +/-  (4.95e-36, 2.65e-154j)
| (1.8885284723815430713e-39 + 1.1014789394349144933e-742j)  +/-  (5.11e-62, 2.73e-180j)
| (4.3395964311253350847e-27 - 6.2859425115493091379e-736j)  +/-  (3.51e-57, 1.88e-175j)
| (1.4074199515778371058e-32 + 3.5725917689213602171e-739j)  +/-  (2.29e-60, 1.23e-178j)
| (1.064854471904948408e-29 + 2.7159086737666829979e-737j)  +/-  (1.26e-58, 6.72e-177j)
| (1.0552144782253522853e-24 + 1.1292104396616585937e-734j)  +/-  (1.38e-56, 7.4e-175j)
| (3.0558839674056271139e-49 - 2.2947685069407699703e-747j)  +/-  (1.22e-67, 6.51e-186j)
| (8.9864447233208697079e-14 - 1.9522658156761662894e-729j)  +/-  (5.61e-53, 3e-171j)
| (1.4074199515778371058e-32 - 8.638359495856348441e-739j)  +/-  (2.17e-60, 1.16e-178j)
| (2.8264817453489680454e-05 - 9.5931451690125715981e-724j)  +/-  (3.82e-38, 2.04e-156j)
| (0.032214651774958500861 - 1.9202409957949936927e-722j)  +/-  (2.79e-20, 1.5e-138j)
| (3.0558839674056271139e-49 + 1.1453225171956449261e-747j)  +/-  (3.26e-69, 1.74e-187j)
| (8.5969592863695769841e-36 - 8.1133575136257639351e-741j)  +/-  (4.12e-64, 2.2e-182j)
| (1.2980899460051823561e-18 - 2.0052738384265763695e-731j)  +/-  (8.71e-56, 4.66e-174j)
| (6.4758090422882054651e-10 + 2.2345129504576194832e-727j)  +/-  (1.37e-50, 7.34e-169j)
| (8.2505725443601417132e-08 + 3.1499719761850289989e-726j)  +/-  (7.95e-48, 4.25e-166j)
| (8.5969592863695769841e-36 + 1.8700809522677432114e-740j)  +/-  (5.66e-63, 3.03e-181j)
| (0.00057106717438415837597 - 2.6894302464829516692e-723j)  +/-  (2.16e-38, 1.15e-156j)
| (2.8264817453489680454e-05 - 8.5619021513679806596e-725j)  +/-  (3.53e-44, 1.89e-162j)
| (1.6464316835945051219e-22 - 1.6353685823928698728e-733j)  +/-  (8.49e-58, 4.54e-176j)
| (7.0650820938728003891e-17 - 4.5602719395607423444e-731j)  +/-  (2.87e-58, 1.54e-176j)
| (9.2726199563873986052e-44 + 1.4775805283183259914e-744j)  +/-  (5.42e-67, 2.9e-185j)
| (4.3395964311253350847e-27 + 2.3406487818092989022e-736j)  +/-  (8.94e-64, 4.79e-182j)
| (8.9864447233208697079e-14 + 9.569974367548906311e-729j)  +/-  (1.77e-55, 9.45e-174j)
| (0.014951310701836155553 + 4.8120011979193764273e-723j)  +/-  (2.19e-37, 1.17e-155j)
| (7.0650820938728003891e-17 + 1.7708095134693471505e-730j)  +/-  (1.35e-56, 7.24e-175j)
| (2.8801580114762973169e-15 + 3.1857241006953790125e-730j)  +/-  (7.69e-58, 4.11e-176j)
| (0.005919179556995048779 - 7.5969633117185499239e-723j)  +/-  (8.42e-41, 4.51e-159j)
| (1.064854471904948408e-29 - 1.0677478162209885656e-737j)  +/-  (5.48e-65, 2.93e-183j)
| (1.0552144782253522853e-24 - 3.9637810284144105887e-735j)  +/-  (1.19e-63, 6.35e-182j)
| (8.0836365024899779617e-09 - 8.7985051328672177538e-727j)  +/-  (9.81e-55, 5.25e-173j)
| (1.7398891190158224127e-20 - 6.0170854585847765234e-733j)  +/-  (1.93e-62, 1.03e-180j)
| (0.00013835638628771919453 + 2.1936247405869770481e-724j)  +/-  (2.41e-51, 1.29e-169j)
| (4.2022270976759440768e-11 - 5.1319443593817819937e-728j)  +/-  (2.39e-57, 1.28e-175j)
| (0.032214651774958500861 - 9.0984087024924493629e-723j)  +/-  (2.37e-44, 1.27e-162j)
| (1.2980899460051823561e-18 + 5.6626103025750741211e-732j)  +/-  (1.87e-61, 1e-179j)
| (2.1848762469468789008e-12 - 6.0530732270925106084e-728j)  +/-  (4.58e-62, 2.45e-180j)
| (0.059255921466533098229 + 2.958666231509295595e-722j)  +/-  (1.4e-45, 7.49e-164j)
| (0.092872312593614353269 - 4.5805035090528135586e-722j)  +/-  (1.22e-45, 6.55e-164j)
| (8.2505725443601417132e-08 - 7.9050128565141236188e-725j)  +/-  (5.77e-59, 3.09e-177j)
| (0.00057106717438415837597 - 5.2257311692633249391e-724j)  +/-  (1.03e-52, 5.54e-171j)
| (0.12415127601449244274 - 1.1716118223585543372e-721j)  +/-  (5.41e-47, 2.89e-165j)
| (1.7398891190158224127e-20 + 1.965289502424483761e-732j)  +/-  (4.32e-65, 2.31e-183j)
| (0.091004748412142677676 + 1.6289149259899355462e-721j)  +/-  (1.23e-47, 6.59e-166j)
| (1.6464316835945051219e-22 + 5.3804139896420293355e-734j)  +/-  (2.35e-64, 1.26e-182j)
| (4.8470611889476255745e-06 + 3.0936133012933588337e-725j)  +/-  (1.04e-55, 5.55e-174j)
| (0.059255921466533098229 + 1.6689917596739132267e-722j)  +/-  (1.62e-49, 8.65e-168j)
| (0.001995147697106713665 + 1.163065795716995025e-723j)  +/-  (5.33e-53, 2.85e-171j)
| (8.0836365024899779617e-09 + 1.1427700694381078102e-725j)  +/-  (5.15e-61, 2.75e-179j)
| (0.014951310701836155553 + 1.2246128645786841459e-722j)  +/-  (1.84e-53, 9.85e-172j)
| (6.9411499550525195675e-07 - 1.0303926101754940332e-725j)  +/-  (5.53e-57, 2.96e-175j)
| (4.2022270976759440768e-11 + 3.555572400947582318e-727j)  +/-  (9.41e-63, 5.03e-181j)
| (2.8801580114762973169e-15 - 1.3764469501835082108e-729j)  +/-  (1.07e-64, 5.72e-183j)
| (6.4758090422882054651e-10 - 1.9998334730163219151e-726j)  +/-  (2.87e-62, 1.54e-180j)
| (0.12239450515283971382 + 7.4432922893809849917e-722j)  +/-  (1.67e-55, 8.9e-174j)
| (4.8470611889476255745e-06 + 7.2115989753732158656e-724j)  +/-  (9.89e-61, 5.29e-179j)
| (0.005919179556995048779 - 2.4320243728956103206e-723j)  +/-  (6.24e-58, 3.32e-176j)
| (0.12239450515283971382 + 5.791277471405703712e-722j)  +/-  (5.97e-57, 3.18e-175j)
| (2.1848762469468789008e-12 + 1.0594241071023373687e-728j)  +/-  (1.17e-63, 6.25e-182j)
| (0.001995147697106713665 + 4.5746873773643297548e-723j)  +/-  (2.09e-59, 1.12e-177j)
| (0.12415127601449244274 - 1.3047620646886858264e-721j)  +/-  (4.54e-57, 2.44e-175j)
| (0.00013835638628771919453 + 1.5721242770684190771e-723j)  +/-  (2.6e-60, 1.4e-178j)
| (0.092872312593614353269 - 3.04713618952462628e-722j)  +/-  (9.45e-58, 4.9e-176j)
