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 31
-------------------------------------------------
Trying to find an order 31 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^51 - 1531697772666304700042372749970636800/3006477738722676008953699127*t^49 + 339800872082618399517137684036281958400/3006477738722676008953699127*t^47 - 45741788657278151297140188368231340441600/3006477738722676008953699127*t^45 + 4188170463607782176064460226315472273408000/3006477738722676008953699127*t^43 - 277124625240510746160501814850280090450001920/3006477738722676008953699127*t^41 + 13744181423553050897220741221291258478853324800/3006477738722676008953699127*t^39 - 523030467105451350539853829533120586085790105600/3006477738722676008953699127*t^37 + 15508618260709669141324551513079922341672637952000/3006477738722676008953699127*t^35 - 361875647837523571179448660286964691794805921536000/3006477738722676008953699127*t^33 + 6684047841643787336354575413271326541303629743001600/3006477738722676008953699127*t^31 - 97988009688246254048612955542631993776232079742208000/3006477738722676008953699127*t^29 + 1140031387806325278151279882790975558115316779991296000/3006477738722676008953699127*t^27 - 10498087340598674585523610668911364956474892505157760000/3006477738722676008953699127*t^25 + 76115334151373752964026572843704538576332359298498400000/3006477738722676008953699127*t^23 - 431043063007145967010394014880338874372555674557948720000/3006477738722676008953699127*t^21 + 1885395472589831883130282198183488562782622928936389650000/3006477738722676008953699127*t^19 - 6274923214287921194125536549654588827958344040516542925000/3006477738722676008953699127*t^17 + 15578393802408745156135446061596887980388022996313864125000/3006477738722676008953699127*t^15 - 28100429651802130821778854340912623586575670247372591062500/3006477738722676008953699127*t^13 + 35546357840873536391205342822398160918061147103365452900000/3006477738722676008953699127*t^11 - 30029857955290809610632835871792796225881145361254580875000/3006477738722676008953699127*t^9 + 31593490247275261949368870191500104826337379348029320296875/6012955477445352017907398254*t^7 - 18577642747992838603527114009649007565659569206787414921875/12025910954890704035814796508*t^5 + 10048369615026694281722716635370944013410801035429741953125/48103643819562816143259186032*t^3 - 769679417750370574915694903165493979565123437643879765625/96207287639125632286518372064*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:
| (-6.7499454078772146272 + 5.9454865595922193245e-966j)  +/-  (6.4e-245, 6.4e-245j)
| (7.9040161923322071705 - 7.5082258210168486107e-967j)  +/-  (2.49e-246, 2.49e-246j)
| (-7.9040161923322071705 - 5.8659161500192729218e-969j)  +/-  (2.41e-246, 2.41e-246j)
| (-3.6548891028376575873 + 3.1393928264671579398e-964j)  +/-  (3.12e-244, 3.12e-244j)
| (7.2842236682350117605 + 2.1538370880019778612e-965j)  +/-  (1.67e-245, 1.67e-245j)
| (-7.2842236682350117605 - 4.1919745003031736346e-972j)  +/-  (1.66e-245, 1.66e-245j)
| (5.387480890011232862 + 4.7822320929699567809e-969j)  +/-  (4.51e-244, 4.51e-244j)
| (-8.79542987068111741 + 5.3105430609736667934e-981j)  +/-  (1.22e-247, 1.22e-247j)
| (6.7499454078772146272 + 2.0981273514458287023e-976j)  +/-  (6.38e-245, 6.38e-245j)
| (4.2536377799665558018 + 2.2295968184869667567e-983j)  +/-  (6.53e-244, 6.53e-244j)
| (0.94415820833891919795 + 2.7013457964966903964e-1006j)  +/-  (1.42e-250, 1.42e-250j)
| (-0.73747372854539435871 + 4.0604896841161342412e-1008j)  +/-  (2.32e-251, 2.32e-251j)
| (-0.94415820833891919795 - 1.182100891712172369e-1006j)  +/-  (1.58e-250, 1.58e-250j)
| (5.8131785813407813725 - 2.0538913913851085582e-999j)  +/-  (2.96e-244, 2.96e-244j)
| (-5.8131785813407813725 - 2.3827335718515523496e-1008j)  +/-  (3.24e-244, 3.24e-244j)
| (2.5511324482970145245 + 4.1395716476868902139e-1007j)  +/-  (1.05e-245, 1.05e-245j)
| (2.2549740020892755231 - 8.0419380357754286855e-1012j)  +/-  (1.75e-246, 1.75e-246j)
| (-4.9840969819839663148 + 3.2832655055826757213e-1009j)  +/-  (6.29e-244, 6.29e-244j)
| (-3.3478545673832163269 + 9.5502243369121675997e-1011j)  +/-  (1.58e-244, 1.58e-244j)
| (-4.6036824495507442731 + 6.3474446102188914506e-1011j)  +/-  (6.36e-244, 6.36e-244j)
| (-6.2647318691015834025 - 3.5719101286370773739e-1010j)  +/-  (1.65e-244, 1.65e-244j)
| (4.6036824495507442731 - 1.4594215801214318994e-1010j)  +/-  (6.64e-244, 6.64e-244j)
| (3.3478545673832163269 - 4.6511159055516122389e-1017j)  +/-  (1.52e-244, 1.52e-244j)
| (6.2647318691015834025 - 2.3188395973857077845e-1019j)  +/-  (1.79e-244, 1.79e-244j)
| (-2.7888060584281304805 - 1.6305708098492129891e-1022j)  +/-  (3.36e-245, 3.36e-245j)
| (-1.9517076052415437387 - 1.0884312827955939684e-1024j)  +/-  (3.9e-247, 3.9e-247j)
| (0.73747372854539435871 - 8.4723430427652520902e-1029j)  +/-  (2.16e-251, 2.16e-251j)
| (0.2453407083009012499 + 1.0279119343995794188e-1032j)  +/-  (6e-254, 6e-254j)
| (-2.2549740020892755231 + 2.2595877563471736825e-1024j)  +/-  (1.79e-246, 1.79e-246j)
| (-4.2536377799665558018 + 1.0704861836757291398e-1021j)  +/-  (6.22e-244, 6.22e-244j)
| (-5.387480890011232862 - 5.399998463481103296e-1022j)  +/-  (4.57e-244, 4.57e-244j)
| (-1.2340762153953230079 - 2.5588147745155622734e-1027j)  +/-  (1.49e-249, 1.49e-249j)
| (1.5322972587022766315 + 4.4592901493025130883e-1026j)  +/-  (2.11e-248, 2.11e-248j)
| (2.7888060584281304805 + 5.8535512825981688066e-1022j)  +/-  (3.3e-245, 3.3e-245j)
| (-1.7385377121165862068 - 1.9970915309204507594e-1025j)  +/-  (1.15e-247, 1.15e-247j)
| (-1.5322972587022766315 + 2.2254244315591392487e-1027j)  +/-  (2.11e-248, 2.11e-248j)
| (3.0418816928666674015 + 2.6583901318179281897e-1021j)  +/-  (7.04e-245, 7.04e-245j)
| (1.2340762153953230079 - 9.2302085058670096182e-1036j)  +/-  (1.41e-249, 1.41e-249j)
| (4.9840969819839663148 + 1.232865104037334084e-1028j)  +/-  (6.22e-244, 6.22e-244j)
| (-3.0418816928666674015 - 8.5875179601938791926e-1044j)  +/-  (6.77e-245, 6.77e-245j)
| (-0.2453407083009012499 - 2.0440131212970825414e-1054j)  +/-  (7.9e-254, 7.9e-254j)
| (-2.5511324482970145245 - 1.6379646596092476222e-1045j)  +/-  (1.08e-245, 1.08e-245j)
| (3.6548891028376575873 - 2.0113135584714706993e-1051j)  +/-  (3.32e-244, 3.32e-244j)
| (1.7385377121165862068 - 1.0353805464833661246e-1071j)  +/-  (1.17e-247, 1.17e-247j)
| (-3.9447640401156252104 - 6.2085917253578943308e-1076j)  +/-  (4.82e-244, 4.82e-244j)
| (3.9447640401156252104 + 2.9091144637121090444e-1082j)  +/-  (5.23e-244, 5.23e-244j)
| (1.9517076052415437387 + 4.5898448852858830782e-1096j)  +/-  (3.93e-247, 3.93e-247j)
| (8.79542987068111741 + 6.7299614979562548072e-1100j)  +/-  (1.24e-247, 1.24e-247j)
| (0.51685236863615187749 - 2.473331254716777621e-1102j)  +/-  (1.85e-252, 1.85e-252j)
| (3.7373868149406857363e-1117 - 3.2112768682870173342e-1117j)  +/-  (2.51e-1115, 2.51e-1115j)
| (-0.51685236863615187749 + 1.9438128588423202006e-1102j)  +/-  (2.03e-252, 2.03e-252j)
-------------------------------------------------
The weights are:
| (4.661468172683653062e-21 - 3.5432976946375982313e-981j)  +/-  (1.91e-83, 8.9e-206j)
| (2.870501947397658287e-28 + 6.3028630084130834874e-986j)  +/-  (7.68e-88, 3.58e-210j)
| (2.870501947397658287e-28 - 1.7146004052012041927e-985j)  +/-  (2.81e-87, 1.31e-209j)
| (2.645215675564187692e-07 + 4.6988309267468003787e-970j)  +/-  (3.98e-72, 1.86e-194j)
| (2.8966259512290639594e-24 - 1.2691060904267427759e-983j)  +/-  (1.68e-86, 7.85e-209j)
| (2.8966259512290639594e-24 + 3.8251038568348385666e-983j)  +/-  (1.7e-85, 7.93e-208j)
| (5.7985785742659332883e-14 - 4.3051370630637663781e-977j)  +/-  (1.7e-81, 7.95e-204j)
| (2.1150819532675394949e-34 + 7.8060685539209189685e-989j)  +/-  (1.24e-90, 5.78e-213j)
| (4.661468172683653062e-21 + 1.054073808382614626e-981j)  +/-  (1.28e-85, 5.97e-208j)
| (2.5851870110382675202e-09 + 2.039206363149415435e-973j)  +/-  (1.59e-78, 7.42e-201j)
| (0.059928187779396892631 + 9.8196764667682175567e-967j)  +/-  (1.17e-66, 5.45e-189j)
| (0.058306996660842202848 - 2.5821006998691783313e-966j)  +/-  (6.17e-67, 2.88e-189j)
| (0.059928187779396892631 + 1.6660124487111624201e-966j)  +/-  (5.48e-67, 2.55e-189j)
| (5.2058689038981148646e-16 + 1.7022511316612851567e-978j)  +/-  (4.62e-83, 2.16e-205j)
| (5.2058689038981148646e-16 - 7.4675384710320751784e-978j)  +/-  (2.64e-84, 1.23e-206j)
| (0.0002278660902011166433 + 4.9865741604513233662e-969j)  +/-  (3.47e-71, 1.62e-193j)
| (0.0010829681979160227955 - 1.4682877347425303964e-968j)  +/-  (2.51e-69, 1.17e-191j)
| (3.60410603490021283e-12 - 5.7253065236559744751e-975j)  +/-  (1.23e-82, 5.76e-205j)
| (2.3978640189833300961e-06 - 1.5488685038752523421e-969j)  +/-  (3.1e-77, 1.45e-199j)
| (1.2940397998548653033e-10 + 1.3093157877443446519e-973j)  +/-  (1.09e-81, 5.08e-204j)
| (2.3752344048898965622e-18 + 1.9412937237205665133e-979j)  +/-  (3.56e-86, 1.66e-208j)
| (1.2940397998548653033e-10 - 1.5042370772208648553e-974j)  +/-  (4.58e-83, 2.14e-205j)
| (2.3978640189833300961e-06 - 6.7910292644889823789e-971j)  +/-  (2.58e-79, 1.21e-201j)
| (2.3752344048898965622e-18 - 5.1075868915108921117e-980j)  +/-  (9.04e-88, 4.22e-210j)
| (5.2497419571368781985e-05 - 1.3824525458444284051e-968j)  +/-  (7.59e-78, 3.54e-200j)
| (0.0035169475079444010459 + 2.0935354010994417575e-967j)  +/-  (1.11e-74, 5.18e-197j)
| (0.058306996660842202848 - 1.7150372255092146537e-966j)  +/-  (7.11e-72, 3.32e-194j)
| (0.14028924750904567754 - 2.1467517071608666441e-966j)  +/-  (4.68e-72, 2.18e-194j)
| (0.0010829681979160227955 - 6.1984883241349347663e-968j)  +/-  (4.09e-76, 1.91e-198j)
| (2.5851870110382675202e-09 - 2.6934471422181152568e-972j)  +/-  (6.26e-83, 2.92e-205j)
| (5.7985785742659332883e-14 + 2.2467195883543653618e-976j)  +/-  (5.17e-86, 2.41e-208j)
| (0.037584558073270017359 - 7.9281006007031688129e-967j)  +/-  (1.22e-72, 5.7e-195j)
| (0.014801226632806757857 + 2.4876894416547169538e-967j)  +/-  (1.24e-75, 5.77e-198j)
| (5.2497419571368781985e-05 - 1.8581307962011614282e-969j)  +/-  (8.45e-81, 3.94e-203j)
| (0.0042858198282112229289 - 4.7343503373904203115e-967j)  +/-  (1.18e-75, 5.52e-198j)
| (0.014801226632806757857 + 6.0794015755177958718e-967j)  +/-  (4.96e-75, 2.32e-197j)
| (1.5608484845096455208e-05 + 4.3484838179722508814e-970j)  +/-  (4.33e-82, 2.02e-204j)
| (0.037584558073270017359 - 3.9256715658384703442e-967j)  +/-  (1.97e-76, 9.18e-199j)
| (3.60410603490021283e-12 + 8.809229603276442506e-976j)  +/-  (2.33e-88, 1.09e-210j)
| (1.5608484845096455208e-05 + 4.7504619340926756373e-969j)  +/-  (2.83e-81, 1.32e-203j)
| (0.14028924750904567754 - 2.4556985369774902163e-966j)  +/-  (3e-76, 1.4e-198j)
| (0.0002278660902011166433 + 2.8037605119635155136e-968j)  +/-  (8.44e-80, 3.94e-202j)
| (2.645215675564187692e-07 + 1.1360698101959269265e-971j)  +/-  (2.63e-85, 1.23e-207j)
| (0.0042858198282112229289 - 1.6821764493499687778e-967j)  +/-  (1.35e-80, 6.28e-203j)
| (2.86590343476020497e-08 + 4.7980277562316000579e-971j)  +/-  (3.27e-85, 1.53e-207j)
| (2.86590343476020497e-08 - 1.8301329266158453723e-972j)  +/-  (2.59e-86, 1.21e-208j)
| (0.0035169475079444010459 + 6.3597909715971670532e-968j)  +/-  (1.17e-81, 5.45e-204j)
| (2.1150819532675394949e-34 - 3.2229698743023018858e-989j)  +/-  (2.58e-103, 1.2e-225j)
| (0.11419952802434886227 + 1.9406192688457123031e-966j)  +/-  (3.28e-80, 1.53e-202j)
| (0.13141170805745173536 + 2.4837109749003514428e-966j)  +/-  (1.57e-80, 7.57e-203j)
| (0.11419952802434886227 + 2.5798798645819747139e-966j)  +/-  (9.71e-81, 4.15e-203j)
