Starting with polynomial:
P : t
Extension levels are: 1 20 36
-------------------------------------------------
Trying to find an order 20 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 36 Kronrod extension for:
P2 : t^21 - 210*t^19 + 17955*t^17 - 813960*t^15 + 21366450*t^13 - 333316620*t^11 + 3055402350*t^9 - 15713497800*t^7 + 41247931725*t^5 - 45831035250*t^3 + 13749310575*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^57 - 411287889662130948830614956/343303287907604831431525*t^55 + 456602185512307029270930226443/686606575815209662863050*t^53 - 359183344222952161495206411922161/1579195124374982224585015*t^51 + 1868078708065313720227478277168698187/34742292736249608940870330*t^49 - 32459987023876327598438383631644412940/3474229273624960894087033*t^47 + 21519984755444280436122050814165857761137/17371146368124804470435165*t^45 - 2231418723268570049243015714812442190977718/17371146368124804470435165*t^43 + 36794039193304667069530838349107173172420952/3474229273624960894087033*t^41 - 2439445842043945035992360410868603998812403848/3474229273624960894087033*t^39 + 262092661436349985122502190520982956603125770869/6948458547249921788174066*t^37 - 5730417550047815127907866494260172246061470177649/3474229273624960894087033*t^35 + 408864614088280072764891076945267146007627719727497/6948458547249921788174066*t^33 - 541001649252312406657964355283768669589897827341480/315839024874996444917003*t^31 + 12828267099018162532921111994262392746478375371854570/315839024874996444917003*t^29 - 246891092009644708430049202749939136835142937098944940/315839024874996444917003*t^27 + 3835438843651576555253050390252851716824483050217829175/315839024874996444917003*t^25 - 2075210789906061433463733256939398546791295029724042300/13732131516304193257261*t^23 + 40962236383265312658053651905993701356725724914310677125/27464263032608386514522*t^21 - 158258156591001580942901529339480693717945331526737981125/13732131516304193257261*t^19 + 1883554064605383073125954233400323381683561353087006199125/27464263032608386514522*t^17 - 4225935961086012916046843408472497994692689332411412555500/13732131516304193257261*t^15 + 13911046884005759060345008389438453321085391957338317647625/13732131516304193257261*t^13 - 32389028069824624358032245584122335988196147142514421193750/13732131516304193257261*t^11 + 50727844873917410161171356469117061273534026064746437506250/13732131516304193257261*t^9 - 49721606966365901323370667920059386801967385386129379610000/13732131516304193257261*t^7 + 54584908442380668654488506443791846519411910125964612309375/27464263032608386514522*t^5 - 6931255637463360129590431469199120113045897370906599596875/13732131516304193257261*t^3 + 1067583015073643668378398532684940793829042330432387321875/27464263032608386514522*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:   57 out of 57
Indefinite weights: 0 out of 57
Negative weights:   0 out of 57
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (12.604614863307852997 - 1.642533958148203999e-616j)  +/-  (4.21e-246, 4.21e-246j)
| (-7.849382895113821993 + 1.2623950015603605007e-612j)  +/-  (1.08e-241, 1.08e-241j)
| (-10.890693182654115922 - 4.2895292567857208283e-614j)  +/-  (5.81e-244, 5.81e-244j)
| (-12.604614863307852997 - 3.5759953012342447388e-616j)  +/-  (4.18e-246, 4.18e-246j)
| (5.3975234421842323043 - 3.1531353984706002048e-611j)  +/-  (1.25e-242, 1.25e-242j)
| (10.19721145324634822 - 2.2313260857955032864e-613j)  +/-  (2.88e-243, 2.88e-243j)
| (-11.667366733816217142 - 2.3030170008644843471e-624j)  +/-  (8.16e-245, 8.16e-245j)
| (-10.19721145324634822 + 1.7758164173391526354e-622j)  +/-  (2.6e-243, 2.6e-243j)
| (2.0491024682571626618 - 1.8226026405048817363e-633j)  +/-  (3.07e-248, 3.07e-248j)
| (7.849382895113821993 - 8.6117286049158880275e-626j)  +/-  (1.07e-241, 1.07e-241j)
| (8.3886587903574837001 + 3.1996424322632409983e-643j)  +/-  (5.11e-242, 5.11e-242j)
| (-4.9949639447820251929 - 5.1840239490587407701e-653j)  +/-  (5.31e-243, 5.31e-243j)
| (-6.7514447187174607668 - 3.7999549699306882175e-651j)  +/-  (1.61e-241, 1.61e-241j)
| (-9.5576650830087819746 - 1.0605501018203797881e-656j)  +/-  (8.33e-243, 8.33e-243j)
| (3.1180265632373337591 - 4.0205026618180645606e-664j)  +/-  (9.1e-246, 9.1e-246j)
| (11.667366733816217142 + 5.1183996708859554383e-659j)  +/-  (8.5e-245, 8.5e-245j)
| (-2.0491024682571626618 + 4.4173198517439121332e-669j)  +/-  (3.16e-248, 3.16e-248j)
| (-7.0889139785647254369 - 3.5630850083901089461e-665j)  +/-  (2.98e-241, 2.98e-241j)
| (-2.3845302775673255413 - 5.4247545174607518341e-679j)  +/-  (2.1e-247, 2.1e-247j)
| (-4.6058036083258650489 - 1.0062163801330581794e-673j)  +/-  (2.11e-243, 2.11e-243j)
| (3.8302546836304001098 + 7.9826029185412347733e-677j)  +/-  (1.82e-244, 1.82e-244j)
| (3.4698466904753762952 + 5.7879608718477664266e-686j)  +/-  (4.32e-245, 4.32e-245j)
| (6.2870118564701213137 - 8.0465516663371182593e-709j)  +/-  (5.56e-242, 5.56e-242j)
| (-4.21434398168842135 + 2.1831554750956544112e-726j)  +/-  (6.31e-244, 6.31e-244j)
| (10.890693182654115922 + 9.794973248586648705e-731j)  +/-  (6.01e-244, 6.01e-244j)
| (2.3845302775673255413 + 6.1997557414651896333e-750j)  +/-  (2.17e-247, 2.17e-247j)
| (6.7514447187174607668 - 2.0801079532697975506e-743j)  +/-  (1.6e-241, 1.6e-241j)
| (9.5576650830087819746 + 3.6912383681487939362e-762j)  +/-  (8.66e-243, 8.66e-243j)
| (8.9574232147725472928 + 4.9096021674228621265e-794j)  +/-  (2.11e-242, 2.11e-242j)
| (-0.67804569244064402621 - 4.6121201513150895293e-821j)  +/-  (2.21e-252, 2.21e-252j)
| (-3.4698466904753762952 - 8.0089639131306082594e-811j)  +/-  (4.66e-245, 4.66e-245j)
| (7.0889139785647254369 + 3.162162764883174474e-821j)  +/-  (2.91e-241, 2.91e-241j)
| (0.67804569244064402621 - 2.9697964677784573491e-854j)  +/-  (2.08e-252, 2.08e-252j)
| (7.3616208113663700344 + 9.9517965833939197526e-842j)  +/-  (2.44e-241, 2.44e-241j)
| (-1.3597658232112302657 + 5.7857037449292458185e-860j)  +/-  (3.08e-250, 3.08e-250j)
| (-5.3975234421842323043 - 5.1754154828436583444e-853j)  +/-  (1.19e-242, 1.19e-242j)
| (4.21434398168842135 + 4.7552282005018546332e-853j)  +/-  (6.13e-244, 6.13e-244j)
| (1.3597658232112302657 + 1.3595254098735068354e-859j)  +/-  (2.83e-250, 2.83e-250j)
| (-5.8293820073044713717 - 2.1431473217826563742e-851j)  +/-  (2.83e-242, 2.83e-242j)
| (-3.1180265632373337591 - 3.3440701947960170123e-855j)  +/-  (8.54e-246, 8.54e-246j)
| (-0.9991703987669885786 + 9.0537822921296718083e-861j)  +/-  (2.76e-251, 2.76e-251j)
| (0.9991703987669885786 - 1.1302765442886677025e-860j)  +/-  (2.53e-251, 2.53e-251j)
| (-8.9574232147725472928 + 2.7056329156948833447e-852j)  +/-  (2.31e-242, 2.31e-242j)
| (5.8293820073044713717 + 3.9995150881137030232e-850j)  +/-  (2.61e-242, 2.61e-242j)
| (2.7505929810523730936 - 9.1528264592824975013e-861j)  +/-  (1.49e-246, 1.49e-246j)
| (-1.719594270031742883 - 1.0916086554285825e-862j)  +/-  (4.2e-249, 4.2e-249j)
| (-6.2870118564701213137 - 1.2843001989010690072e-855j)  +/-  (5.65e-242, 5.65e-242j)
| (1.719594270031742883 - 1.0306465311415016518e-862j)  +/-  (4.11e-249, 4.11e-249j)
| (0.3592000161452291901 - 4.9099407585054885335e-887j)  +/-  (1.65e-253, 1.65e-253j)
| (4.9949639447820251929 - 6.7303421774595733369e-857j)  +/-  (5.5e-243, 5.5e-243j)
| (-3.8302546836304001098 - 4.1003092490644664445e-859j)  +/-  (1.72e-244, 1.72e-244j)
| (-2.7505929810523730936 + 2.8870448018040667672e-860j)  +/-  (1.55e-246, 1.55e-246j)
| (4.6058036083258650489 - 6.2499991518460226063e-856j)  +/-  (1.95e-243, 1.95e-243j)
| (-7.3616208113663700344 + 6.6019406055713273246e-855j)  +/-  (2.36e-241, 2.36e-241j)
| (5.8617970079754334659e-884 - 4.0298363391199468264e-884j)  +/-  (4.05e-882, 4.05e-882j)
| (-8.3886587903574837001 - 3.1539107659676115386e-856j)  +/-  (4.91e-242, 4.91e-242j)
| (-0.3592000161452291901 - 3.6337221915042842346e-867j)  +/-  (1.41e-253, 1.41e-253j)
-------------------------------------------------
The weights are:
| (1.3666205686196882208e-35 + 2.5361187368900244114e-637j)  +/-  (7.42e-74, 1.05e-193j)
| (8.7063871547914068407e-15 + 2.4330685721764531973e-624j)  +/-  (1.1e-62, 1.55e-182j)
| (5.1041831453043359049e-27 - 1.2178648156927156984e-632j)  +/-  (7.78e-71, 1.1e-190j)
| (1.3666205686196882208e-35 - 1.0141008048100803658e-637j)  +/-  (7.04e-75, 9.96e-195j)
| (7.8370880420068144389e-08 + 1.0249394528315543285e-617j)  +/-  (4.08e-57, 5.77e-177j)
| (6.9656295539997935373e-24 - 3.4776348205571292422e-630j)  +/-  (1.61e-71, 2.28e-191j)
| (9.1916590611313630988e-31 + 6.8181775571037673149e-635j)  +/-  (6.66e-73, 9.41e-193j)
| (6.9656295539997935373e-24 + 1.0679381522571603966e-630j)  +/-  (4.67e-70, 6.6e-190j)
| (0.015745609191231479077 - 1.4957274551373666333e-614j)  +/-  (9.86e-39, 1.4e-158j)
| (8.7063871547914068407e-15 - 1.2757324488477668025e-623j)  +/-  (7.9e-67, 1.12e-186j)
| (1.159124739321132802e-16 + 3.6206816575697797476e-625j)  +/-  (3.21e-68, 4.54e-188j)
| (5.9736432055733178668e-07 - 1.163915334555398008e-618j)  +/-  (5.56e-59, 7.87e-179j)
| (2.2629725709190284589e-11 - 1.2112529173056147143e-621j)  +/-  (1.74e-64, 2.46e-184j)
| (3.5960371222482020332e-21 - 5.9075275114798009721e-629j)  +/-  (8.34e-71, 1.18e-190j)
| (0.0011084559936726233891 + 2.1113562568202194616e-615j)  +/-  (3.06e-52, 4.32e-172j)
| (9.1916590611313630988e-31 - 1.8584411716333693656e-634j)  +/-  (9.79e-78, 1.38e-197j)
| (0.015745609191231479077 - 6.7278645087456672751e-615j)  +/-  (7.95e-46, 1.12e-165j)
| (9.7277553912787685335e-13 + 3.596374056848129492e-622j)  +/-  (1.78e-65, 2.52e-185j)
| (0.0082140871186210557627 + 3.2732653554128355684e-615j)  +/-  (8.31e-49, 1.18e-168j)
| (3.8481470530696591627e-06 + 4.9442216140649459259e-618j)  +/-  (3.68e-59, 5.21e-179j)
| (9.7149904192476607592e-05 + 4.185774117892459396e-616j)  +/-  (4.41e-58, 6.24e-178j)
| (0.00033945244053444271211 - 1.0167145379610029952e-615j)  +/-  (2.94e-56, 4.15e-176j)
| (4.8584998398930693206e-10 - 7.9113477770158002446e-620j)  +/-  (2.3e-67, 3.26e-187j)
| (2.1705181247982230308e-05 - 1.9333080170561878463e-617j)  +/-  (2.87e-60, 4.07e-180j)
| (5.1041831453043359049e-27 + 3.6176214549568304429e-632j)  +/-  (3.38e-78, 4.79e-198j)
| (0.0082140871186210557627 + 8.4509389164534841245e-615j)  +/-  (1.48e-53, 2.09e-173j)
| (2.2629725709190284589e-11 + 1.0826333431361393355e-620j)  +/-  (4.49e-69, 6.36e-189j)
| (3.5960371222482020332e-21 + 2.1300544586982311157e-628j)  +/-  (7.35e-76, 1.04e-195j)
| (8.7930585961622805778e-19 - 9.6442927764170809255e-627j)  +/-  (1.43e-74, 2.02e-194j)
| (0.096788196948057060527 - 4.0152882319198539764e-614j)  +/-  (5.07e-56, 7.18e-176j)
| (0.00033945244053444271211 - 2.2116748924176737984e-616j)  +/-  (9.57e-64, 1.35e-183j)
| (9.7277553912787685335e-13 - 2.6396349324140112481e-621j)  +/-  (8.51e-71, 1.2e-190j)
| (0.096788196948057060527 - 5.1685049102732781384e-614j)  +/-  (1e-56, 1.42e-176j)
| (2.8766025649151689143e-13 + 4.55451475179339795e-622j)  +/-  (2.07e-71, 2.93e-191j)
| (0.058286584596755699589 - 1.6971273880313833652e-614j)  +/-  (1.82e-56, 2.57e-176j)
| (7.8370880420068144389e-08 + 2.2926838153272702207e-619j)  +/-  (1.03e-70, 1.45e-190j)
| (2.1705181247982230308e-05 - 1.569169439419003421e-616j)  +/-  (5.81e-67, 8.22e-187j)
| (0.058286584596755699589 - 2.8395841458945932856e-614j)  +/-  (4.36e-58, 6.17e-178j)
| (7.4419352076693854537e-09 - 3.7878568497030225605e-620j)  +/-  (2.99e-72, 4.23e-192j)
| (0.0011084559936726233891 + 5.6549747619108287759e-616j)  +/-  (4.71e-66, 6.66e-186j)
| (0.083416084601191154637 + 2.79591006897899927e-614j)  +/-  (5.75e-59, 8.14e-179j)
| (0.083416084601191154637 + 4.065575665257672944e-614j)  +/-  (2.14e-59, 3.02e-179j)
| (8.7930585961622805778e-19 + 2.380990345198488904e-627j)  +/-  (2.98e-80, 4.22e-200j)
| (7.4419352076693854537e-09 + 9.8278826386532853825e-619j)  +/-  (2.43e-71, 3.43e-191j)
| (0.0033810482934625535454 - 4.1807024636947350351e-615j)  +/-  (4.59e-65, 6.48e-185j)
| (0.031382609092297685342 + 1.1000249077876204056e-614j)  +/-  (1.51e-63, 2.13e-183j)
| (4.8584998398930693206e-10 + 6.0384945880037981309e-621j)  +/-  (7.87e-74, 1.11e-193j)
| (0.031382609092297685342 + 2.1280646122652036402e-614j)  +/-  (6.61e-64, 9.3e-184j)
| (0.12776104646666279793 + 5.0889261666221272563e-614j)  +/-  (2.03e-63, 2.86e-183j)
| (5.9736432055733178668e-07 - 3.0009610537160671033e-617j)  +/-  (1.19e-70, 1.68e-190j)
| (9.7149904192476607592e-05 + 7.114622681456872471e-617j)  +/-  (2.25e-69, 3.19e-189j)
| (0.0033810482934625535454 - 1.3587521990883800661e-615j)  +/-  (1.04e-67, 1.48e-187j)
| (3.8481470530696591627e-06 + 6.240367939414667666e-617j)  +/-  (2.48e-70, 3.46e-190j)
| (2.8766025649151689143e-13 - 7.0758196674662101456e-623j)  +/-  (6.53e-77, 9.23e-197j)
| (0.1469068766762695305 - 4.5420604784607799046e-614j)  +/-  (8.85e-67, 7.56e-187j)
| (1.159124739321132802e-16 - 7.7855987251054295433e-626j)  +/-  (6.53e-80, 9.45e-200j)
| (0.12776104646666279793 + 4.4541048884931255845e-614j)  +/-  (7.61e-67, 6.21e-187j)
