Starting with polynomial:
P : 2*t
Extension levels are: 1 2 50
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 50 Kronrod extension for:
P2 : 2*t^3 - 3*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^53 - 9056318089372798804507319/6464577632329223032848*t^51 + 1955945242796634757321894975/4309718421552815355232*t^49 - 194767443376951877331226496925/2154859210776407677616*t^47 + 53469571362395016467236194122575/4309718421552815355232*t^45 - 21504083496258840081940537270662825/17238873686211261420928*t^43 + 3286049618317892673249759021152285475/34477747372422522841856*t^41 - 195378744983431466401237363579803496125/34477747372422522841856*t^39 + 18366506534231411774757627170725100332875/68955494744845045683712*t^37 - 5516272817054255256333790487801786943802875/551643957958760365469696*t^35 + 332965552148572751326689738317602179249947625/1103287915917520730939392*t^33 - 2026277230094503889409113655665988212061745125/275821978979380182734848*t^31 + 79621994457780886745750944155271579759172424375/551643957958760365469696*t^29 - 5042254304193276553449367087125440495105631294375/2206575831835041461878784*t^27 + 128144993932235141393400856821563222351718352618125/4413151663670082923757568*t^25 - 1298734692379102777681782959587671865761455206415625/4413151663670082923757568*t^23 + 20809557480954443611354875612050438220340556395153125/8826303327340165847515136*t^21 - 2083483884291533249707989278531939370964188937016671875/141220853237442653560242176*t^19 + 20049691601772489389320983658675966048517514505278890625/282441706474885307120484352*t^17 - 36337564962861265200955071148639435498829366300135765625/141220853237442653560242176*t^15 + 193182855746022792189302163741047760124004328299200171875/282441706474885307120484352*t^13 - 1452980251817892141118098657927200165959433306168536265625/1129766825899541228481937408*t^11 + 3677219652377608850646310248730828141779943291000392421875/2259533651799082456963874816*t^9 - 2912860702338642272737075189025469810256672160801304140625/2259533651799082456963874816*t^7 + 2579410162790565742608169127859331157817258592999839609375/4519067303598164913927749632*t^5 - 4176107537655711194514235944514201970655886472477660953125/36152538428785319311421997056*t^3 + 487518324789982753944853994360016241015864522633335984375/72305076857570638622843994112*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:   53 out of 53
Indefinite weights: 0 out of 53
Negative weights:   0 out of 53
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-7.4201893722610168162 + 1.7098442032540069197e-846j)  +/-  (6.48e-243, 6.48e-243j)
| (-1.5329875655643069854 - 2.9218803916733042886e-853j)  +/-  (3.38e-249, 3.38e-249j)
| (9.5958369769376509729 + 2.955488274396574458e-847j)  +/-  (4.14e-246, 4.14e-246j)
| (7.8739258968264592252 + 2.7971153907198287575e-855j)  +/-  (2.26e-243, 2.26e-243j)
| (-5.4593679068862078002 - 1.1291238013215103636e-864j)  +/-  (2.02e-242, 2.02e-242j)
| (6.9940547914537423377 + 2.693956158158128872e-864j)  +/-  (1.25e-242, 1.25e-242j)
| (-8.9207519387641804094 - 2.106969302813030449e-872j)  +/-  (7.01e-245, 7.01e-245j)
| (8.3666592286886577811 - 8.4615735641889591256e-870j)  +/-  (5.33e-244, 5.33e-244j)
| (8.9207519387641804094 + 5.7077730721074170364e-874j)  +/-  (7.31e-245, 7.31e-245j)
| (-3.1020407565889390658 + 5.5264102412061543851e-877j)  +/-  (3.29e-245, 3.29e-245j)
| (-7.8739258968264592252 - 1.4043620617908658986e-875j)  +/-  (2.12e-243, 2.12e-243j)
| (5.1038456704433472274 - 8.5788133442692838987e-874j)  +/-  (1.37e-242, 1.37e-242j)
| (-2.7833261566142877168 - 4.5819367173167181816e-887j)  +/-  (6.95e-246, 6.95e-246j)
| (-6.9940547914537423377 - 2.5649031193041328612e-883j)  +/-  (1.24e-242, 1.24e-242j)
| (6.1997918656001904832 + 3.4627046247950761276e-882j)  +/-  (2.47e-242, 2.47e-242j)
| (4.7561529730803031738 + 1.6390465514517200496e-891j)  +/-  (7.72e-243, 7.72e-243j)
| (-9.5958369769376509729 + 8.4026084589400910584e-899j)  +/-  (4.26e-246, 4.26e-246j)
| (-5.1038456704433472274 - 2.6550916069189506333e-894j)  +/-  (1.35e-242, 1.35e-242j)
| (-6.5887382286614141362 - 2.2557382305467231441e-895j)  +/-  (1.9e-242, 1.9e-242j)
| (6.5887382286614141362 - 3.224682784227450906e-895j)  +/-  (1.9e-242, 1.9e-242j)
| (1.8426367804753540375 + 1.6241680194408818159e-908j)  +/-  (2.77e-248, 2.77e-248j)
| (-3.4240432585795618644 + 2.09931480343482763e-905j)  +/-  (1.33e-244, 1.33e-244j)
| (-8.3666592286886577811 + 3.2085667108620055119e-905j)  +/-  (5.39e-244, 5.39e-244j)
| (4.4151756312682962123 - 8.024359011230902363e-903j)  +/-  (3.48e-243, 3.48e-243j)
| (-4.0799944775984052202 - 1.8657925459755270381e-912j)  +/-  (1.32e-243, 1.32e-243j)
| (-5.8240993613307964187 + 2.2155527606522890185e-912j)  +/-  (2.57e-242, 2.57e-242j)
| (5.4593679068862078002 - 2.3099393409286474884e-915j)  +/-  (1.99e-242, 1.99e-242j)
| (-2.1540109696010218557 - 8.1748363752530274668e-933j)  +/-  (2.03e-247, 2.03e-247j)
| (-6.1997918656001904832 - 1.1350859431452937436e-928j)  +/-  (2.44e-242, 2.44e-242j)
| (-0.91760781481511996727 + 2.2107368138404653086e-936j)  +/-  (2.55e-251, 2.55e-251j)
| (2.7833261566142877168 + 3.2140172296712762618e-930j)  +/-  (6.77e-246, 6.77e-246j)
| (1.5329875655643069854 + 6.9076131229373284306e-934j)  +/-  (3.29e-249, 3.29e-249j)
| (1.2247448713915890491 + 2.4727514389152161735e-935j)  +/-  (3.25e-250, 3.25e-250j)
| (-4.7561529730803031738 - 1.2342333276802028096e-927j)  +/-  (7.83e-243, 7.83e-243j)
| (-1.8426367804753540375 - 2.1459717602040630783e-934j)  +/-  (2.71e-248, 2.71e-248j)
| (3.4240432585795618644 + 1.2271248812766104205e-927j)  +/-  (1.24e-244, 1.24e-244j)
| (-4.4151756312682962123 + 1.6311429581900858894e-938j)  +/-  (3.26e-243, 3.26e-243j)
| (0.91760781481511996727 - 1.3031672229087464243e-948j)  +/-  (2.71e-251, 2.71e-251j)
| (0.61128887097545684217 + 3.321356320810111114e-950j)  +/-  (1.81e-252, 1.81e-252j)
| (7.4201893722610168162 - 1.2872053050144083602e-940j)  +/-  (6.42e-243, 6.42e-243j)
| (-0.30551014807992675243 + 1.2715155126294437179e-960j)  +/-  (1.06e-253, 1.06e-253j)
| (-1.2247448713915890491 + 3.2233368068883094955e-957j)  +/-  (3.39e-250, 3.39e-250j)
| (4.0799944775984052202 - 2.5156676785719933885e-950j)  +/-  (1.4e-243, 1.4e-243j)
| (2.4674510414260927251 + 8.9949520001210688086e-959j)  +/-  (1.36e-246, 1.36e-246j)
| (2.1540109696010218557 - 3.0144121841513833556e-959j)  +/-  (1.86e-247, 1.86e-247j)
| (5.8240993613307964187 + 2.5470334402817900845e-957j)  +/-  (2.34e-242, 2.34e-242j)
| (-3.7498370250656753818 + 6.2108151713511294292e-967j)  +/-  (4.76e-244, 4.76e-244j)
| (1.3177039692526459426e-995 + 2.0870051581736281035e-995j)  +/-  (1.31e-993, 1.31e-993j)
| (0.30551014807992675243 - 1.8777978408207387283e-976j)  +/-  (1.06e-253, 1.06e-253j)
| (3.1020407565889390658 + 3.5995056664273384442e-968j)  +/-  (3.28e-245, 3.28e-245j)
| (-2.4674510414260927251 - 3.4256852757686620305e-971j)  +/-  (1.26e-246, 1.26e-246j)
| (-0.61128887097545684217 + 6.6100704432508188154e-977j)  +/-  (1.58e-252, 1.58e-252j)
| (3.7498370250656753818 + 1.1441587955389648148e-975j)  +/-  (4.68e-244, 4.68e-244j)
-------------------------------------------------
The weights are:
| (3.0304986611205675344e-25 - 4.6736689736536973209e-867j)  +/-  (9.13e-73, 9.8e-193j)
| (0.016619620476216269268 - 7.3831397885025556744e-855j)  +/-  (1.21e-37, 1.29e-157j)
| (4.5393303087773923214e-41 + 4.4470907219692554904e-875j)  +/-  (5.02e-79, 5.39e-199j)
| (3.1515441477692866586e-28 - 9.9537288267284144448e-869j)  +/-  (5.64e-75, 6.05e-195j)
| (2.3096976665669909268e-14 + 1.6566622113485065933e-861j)  +/-  (3.47e-68, 3.73e-188j)
| (1.3335330750526692855e-22 - 6.4917412718517184674e-866j)  +/-  (5.24e-73, 5.62e-193j)
| (9.2742772411680927171e-36 + 2.5681044651608887792e-872j)  +/-  (1.71e-79, 1.84e-199j)
| (1.1610116720331860097e-31 + 1.9450391909100745519e-870j)  +/-  (1.55e-76, 1.66e-196j)
| (9.2742772411680927171e-36 - 1.8147593527819064892e-872j)  +/-  (4.36e-78, 4.68e-198j)
| (1.1964309271021991781e-05 - 8.5635018139387134044e-857j)  +/-  (5.13e-60, 5.5e-180j)
| (3.1515441477692866586e-28 + 1.4770275229878020465e-868j)  +/-  (2.25e-77, 2.41e-197j)
| (9.6424724777978777201e-13 + 6.2104323299620289019e-861j)  +/-  (3.39e-70, 3.64e-190j)
| (7.7330955405228481723e-05 + 2.7099775892061354683e-856j)  +/-  (4.65e-59, 4.99e-179j)
| (1.3335330750526692855e-22 + 1.0133804560413004948e-865j)  +/-  (3.02e-75, 3.24e-195j)
| (4.3671061817061454519e-18 - 1.2136171761771359055e-863j)  +/-  (1.51e-73, 1.62e-193j)
| (2.9108731872617183923e-11 - 3.5395311663899721857e-860j)  +/-  (1.52e-69, 1.63e-189j)
| (4.5393303087773923214e-41 - 6.1384917407174056923e-875j)  +/-  (2.48e-83, 2.66e-203j)
| (9.6424724777978777201e-13 - 1.1542322837794928033e-860j)  +/-  (2.59e-71, 2.78e-191j)
| (3.135678069348325991e-20 - 1.6204540814916469586e-864j)  +/-  (3.96e-75, 4.25e-195j)
| (3.135678069348325991e-20 + 1.0088543855599653382e-864j)  +/-  (6.58e-76, 7.06e-196j)
| (0.0058730256055361658555 + 8.5886559266285245242e-856j)  +/-  (2.37e-60, 2.55e-180j)
| (1.4791565004473502241e-06 + 2.5215663870770023527e-857j)  +/-  (1.27e-66, 1.36e-186j)
| (1.1610116720331860097e-31 - 2.8180443487382199886e-870j)  +/-  (4.82e-80, 5.17e-200j)
| (6.5196589249004053919e-10 + 1.7444713831399665408e-859j)  +/-  (4.06e-72, 4.36e-192j)
| (1.1062749548900824842e-08 + 1.6557442578837678777e-858j)  +/-  (6.99e-70, 7.5e-190j)
| (3.8740163597632778982e-16 - 2.0074505200209080461e-862j)  +/-  (5.06e-74, 5.43e-194j)
| (2.3096976665669909268e-14 - 9.3030131562394557479e-862j)  +/-  (1.04e-75, 1.11e-195j)
| (0.0017023170479103959047 + 2.5264294176661480778e-855j)  +/-  (4.64e-65, 4.97e-185j)
| (4.3671061817061454519e-18 + 2.0107674966899221316e-863j)  +/-  (6.6e-75, 7.08e-195j)
| (0.074547691416729318015 - 1.661018167614630651e-854j)  +/-  (1.55e-62, 1.66e-182j)
| (7.7330955405228481723e-05 - 7.8502952833378644191e-857j)  +/-  (1.49e-70, 1.6e-190j)
| (0.016619620476216269268 - 1.5838633395545788809e-855j)  +/-  (1.98e-64, 2.12e-184j)
| (0.03872821818447153839 + 2.6787138034148982889e-855j)  +/-  (1.09e-62, 1.17e-182j)
| (2.9108731872617183923e-11 + 6.9062188848557933901e-860j)  +/-  (8.94e-73, 9.59e-193j)
| (0.0058730256055361658555 - 9.3628033117756230283e-855j)  +/-  (5.13e-66, 5.51e-186j)
| (1.4791565004473502241e-06 - 9.6196818580743571502e-858j)  +/-  (1.45e-73, 1.56e-193j)
| (6.5196589249004053919e-10 - 3.6000825911026465405e-859j)  +/-  (2.6e-72, 2.78e-192j)
| (0.074547691416729318015 - 4.1710711897219869823e-855j)  +/-  (1.24e-65, 1.33e-185j)
| (0.11881365718201649723 + 6.0066283168226877322e-855j)  +/-  (1.25e-65, 1.34e-185j)
| (3.0304986611205675344e-25 + 3.0757186050731629532e-867j)  +/-  (3.99e-82, 4.28e-202j)
| (0.1570515498552151416 - 1.2050184777061528409e-854j)  +/-  (2.31e-66, 2.47e-186j)
| (0.03872821818447153839 + 2.3965332052485369029e-854j)  +/-  (2.33e-67, 2.5e-187j)
| (1.1062749548900824842e-08 - 7.5134594779470804464e-859j)  +/-  (5.6e-75, 6.01e-195j)
| (0.00040276636657113074137 + 1.9194087494148246467e-856j)  +/-  (5.43e-72, 5.81e-192j)
| (0.0017023170479103959047 - 4.2554577472316737644e-856j)  +/-  (3.13e-71, 3.34e-191j)
| (3.8740163597632778982e-16 + 1.1709417805533452539e-862j)  +/-  (9.1e-79, 9.64e-199j)
| (1.4467590594321471478e-07 - 6.7981789471827930341e-858j)  +/-  (5.56e-74, 5.81e-194j)
| (0.17234044604687798534 + 1.0103642480157481333e-854j)  +/-  (3.21e-70, 3.34e-190j)
| (0.1570515498552151416 - 8.045344737487776359e-855j)  +/-  (3.71e-70, 3.91e-190j)
| (1.1964309271021991781e-05 + 2.8989667723544357227e-857j)  +/-  (3.59e-74, 3.88e-194j)
| (0.00040276636657113074137 - 8.2168980852715086403e-856j)  +/-  (3.38e-73, 3.2e-193j)
| (0.11881365718201649723 + 1.3974023983814062409e-854j)  +/-  (1.7e-71, 1.32e-191j)
| (1.4467590594321471478e-07 + 2.8528005180224119338e-858j)  +/-  (2.82e-75, 3.09e-195j)
