Starting with polynomial:
P : t
Extension levels are: 1 2 50
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 50 Kronrod extension for:
P2 : t^3 - 3*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^53 - 9056318089372798804507319/6464577632329223032848*t^51 + 1955945242796634757321894975/2154859210776407677616*t^49 - 194767443376951877331226496925/538714802694101919404*t^47 + 53469571362395016467236194122575/538714802694101919404*t^45 - 21504083496258840081940537270662825/1077429605388203838808*t^43 + 3286049618317892673249759021152285475/1077429605388203838808*t^41 - 195378744983431466401237363579803496125/538714802694101919404*t^39 + 18366506534231411774757627170725100332875/538714802694101919404*t^37 - 5516272817054255256333790487801786943802875/2154859210776407677616*t^35 + 332965552148572751326689738317602179249947625/2154859210776407677616*t^33 - 2026277230094503889409113655665988212061745125/269357401347050959702*t^31 + 79621994457780886745750944155271579759172424375/269357401347050959702*t^29 - 5042254304193276553449367087125440495105631294375/538714802694101919404*t^27 + 128144993932235141393400856821563222351718352618125/538714802694101919404*t^25 - 1298734692379102777681782959587671865761455206415625/269357401347050959702*t^23 + 20809557480954443611354875612050438220340556395153125/269357401347050959702*t^21 - 2083483884291533249707989278531939370964188937016671875/2154859210776407677616*t^19 + 20049691601772489389320983658675966048517514505278890625/2154859210776407677616*t^17 - 36337564962861265200955071148639435498829366300135765625/538714802694101919404*t^15 + 193182855746022792189302163741047760124004328299200171875/538714802694101919404*t^13 - 1452980251817892141118098657927200165959433306168536265625/1077429605388203838808*t^11 + 3677219652377608850646310248730828141779943291000392421875/1077429605388203838808*t^9 - 2912860702338642272737075189025469810256672160801304140625/538714802694101919404*t^7 + 2579410162790565742608169127859331157817258592999839609375/538714802694101919404*t^5 - 4176107537655711194514235944514201970655886472477660953125/2154859210776407677616*t^3 + 487518324789982753944853994360016241015864522633335984375/2154859210776407677616*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:
| (-8.7678297402221822997 + 1.6690196220972785118e-639j)  +/-  (3.35e-242, 3.35e-242j)
| (-11.135412792412714163 - 1.183746884607152875e-662j)  +/-  (3.17e-243, 3.17e-243j)
| (13.570562795106466499 + 1.0764283156774920381e-674j)  +/-  (5.79e-246, 5.79e-246j)
| (7.7207121359028913975 - 2.8653698834360989138e-673j)  +/-  (2.82e-242, 2.82e-242j)
| (11.135412792412714163 - 5.3431408758396567956e-675j)  +/-  (3.24e-243, 3.24e-243j)
| (-13.570562795106466499 - 8.1634539445251165259e-684j)  +/-  (6.32e-246, 6.32e-246j)
| (10.493732445628232501 - 7.9208715779782910083e-700j)  +/-  (8.35e-243, 8.35e-243j)
| (-2.1679718061703571924 - 2.3419316577377218922e-710j)  +/-  (4.76e-249, 4.76e-249j)
| (-9.8910871420544113234 - 1.8241236332267594772e-719j)  +/-  (1.75e-242, 1.75e-242j)
| (4.3869481090021745335 - 2.172676054723402877e-738j)  +/-  (4.7e-245, 4.7e-245j)
| (3.9362175991917069003 - 1.6326288957803405017e-739j)  +/-  (1.06e-245, 1.06e-245j)
| (2.1679718061703571924 - 2.208028175152298657e-742j)  +/-  (4.86e-249, 4.86e-249j)
| (-11.832242952965518443 + 6.4320822192573346892e-735j)  +/-  (7.47e-244, 7.47e-244j)
| (-2.6058819254757411461 + 7.3188198126990321971e-749j)  +/-  (3.94e-248, 3.94e-248j)
| (-4.3869481090021745335 - 7.4506376071574658712e-741j)  +/-  (4.88e-245, 4.88e-245j)
| (2.6058819254757411461 - 1.0327082219203664152e-748j)  +/-  (4.31e-248, 4.31e-248j)
| (7.2179277674001837512 + 7.9704958442521698178e-743j)  +/-  (1.78e-242, 1.78e-242j)
| (-4.8423284144353828313 + 8.5678762410947721494e-741j)  +/-  (1.81e-244, 1.81e-244j)
| (-3.9362175991917069003 + 8.2142156647115290505e-745j)  +/-  (9.65e-246, 9.65e-246j)
| (6.7262160392512827891 + 4.7647830559270747378e-743j)  +/-  (1.17e-242, 1.17e-242j)
| (12.615848378366385835 + 2.8523791241552377295e-744j)  +/-  (1.05e-244, 1.05e-244j)
| (4.8423284144353828313 + 1.6158065249663562475e-744j)  +/-  (1.83e-244, 1.83e-244j)
| (8.236520305402493299 + 1.670725183747546615e-741j)  +/-  (3.76e-242, 3.76e-242j)
| (-8.236520305402493299 + 1.7227674144559405549e-747j)  +/-  (3.6e-242, 3.6e-242j)
| (-5.7699835246269955907 + 1.1104830824029835173e-755j)  +/-  (1.91e-243, 1.91e-243j)
| (8.7678297402221822997 + 6.3196343456158566897e-759j)  +/-  (3.5e-242, 3.5e-242j)
| (-12.615848378366385835 - 9.1775198712155113422e-763j)  +/-  (1e-244, 1e-244j)
| (5.7699835246269955907 + 1.7958916486794442371e-774j)  +/-  (1.99e-243, 1.99e-243j)
| (-9.3178829618990545885 - 2.0223702436960008066e-773j)  +/-  (2.69e-242, 2.69e-242j)
| (-3.4895027272763979192 + 3.5355042957303996383e-789j)  +/-  (1.8e-246, 1.8e-246j)
| (-6.2440012579988159316 + 2.6964276733663966121e-784j)  +/-  (4.8e-243, 4.8e-243j)
| (1.2976934166510821128 + 2.4191869784567708245e-805j)  +/-  (3.63e-251, 3.63e-251j)
| (6.2440012579988159316 - 1.1303031828993326754e-795j)  +/-  (5.22e-243, 5.22e-243j)
| (-7.7207121359028913975 - 1.3390567138579215601e-798j)  +/-  (2.88e-242, 2.88e-242j)
| (-1.7320508075688772935 - 1.9860885446811195705e-815j)  +/-  (5.06e-250, 5.06e-250j)
| (9.3178829618990545885 - 3.6620543653209541483e-807j)  +/-  (2.75e-242, 2.75e-242j)
| (-1.2976934166510821128 - 1.2430206308397124411e-821j)  +/-  (3.72e-251, 3.72e-251j)
| (0.86449301186122808649 - 4.4446786809442018502e-822j)  +/-  (2.63e-252, 2.63e-252j)
| (11.832242952965518443 - 2.1089915151548810624e-812j)  +/-  (7.29e-244, 7.29e-244j)
| (1.7320508075688772935 + 1.1520888436930890405e-826j)  +/-  (4.58e-250, 4.58e-250j)
| (-0.86449301186122808649 - 2.0740408951498555341e-828j)  +/-  (2.63e-252, 2.63e-252j)
| (-7.2179277674001837512 + 1.1887959898181340427e-817j)  +/-  (1.83e-242, 1.83e-242j)
| (3.0462315267101856652 - 4.4612288862555316501e-837j)  +/-  (2.65e-247, 2.65e-247j)
| (3.4895027272763979192 - 1.046488613049149923e-835j)  +/-  (1.92e-246, 1.92e-246j)
| (-5.3030703775366576935 + 5.2044043654031066763e-831j)  +/-  (6.92e-244, 6.92e-244j)
| (-3.6622264323269128963e-862 - 1.9819503649910948135e-862j)  +/-  (2.21e-860, 2.21e-860j)
| (-3.0462315267101856652 + 5.0896781485339702824e-839j)  +/-  (2.8e-247, 2.8e-247j)
| (5.3030703775366576935 - 1.9164699244613993884e-839j)  +/-  (6.77e-244, 6.77e-244j)
| (0.43205659485724499686 - 3.2810812209637197223e-855j)  +/-  (1.29e-253, 1.29e-253j)
| (-10.493732445628232501 - 2.7167074269315768664e-843j)  +/-  (9.16e-243, 9.16e-243j)
| (-6.7262160392512827891 - 2.5354371919926805384e-854j)  +/-  (1.01e-242, 1.01e-242j)
| (-0.43205659485724499686 + 5.6815214813180642684e-888j)  +/-  (1.29e-253, 1.29e-253j)
| (9.8910871420544113234 + 4.1333967336857293774e-864j)  +/-  (1.8e-242, 1.8e-242j)
-------------------------------------------------
The weights are:
| (4.3671061817061454519e-18 + 3.1580378760738425045e-656j)  +/-  (5.98e-74, 4.79e-193j)
| (3.1515441477692866586e-28 - 3.0716038386174818167e-662j)  +/-  (2.11e-79, 1.69e-198j)
| (4.5393303087773923214e-41 - 1.7207212362213403006e-669j)  +/-  (4.94e-85, 3.96e-204j)
| (2.3096976665669909268e-14 + 3.0641000525443529084e-656j)  +/-  (3.89e-73, 3.11e-192j)
| (3.1515441477692866586e-28 + 3.6538152913676970428e-663j)  +/-  (5.4e-81, 4.33e-200j)
| (4.5393303087773923214e-41 + 8.0033901487607021379e-669j)  +/-  (2.87e-86, 2.3e-205j)
| (3.0304986611205675344e-25 - 1.110375387134406935e-661j)  +/-  (7.55e-80, 6.05e-199j)
| (0.016619620476216269268 + 5.7146738030470578588e-650j)  +/-  (2.29e-50, 1.83e-169j)
| (1.3335330750526692855e-22 - 3.8275246502921153235e-659j)  +/-  (6.09e-79, 4.87e-198j)
| (1.1964309271021991781e-05 - 7.93324758979363035e-652j)  +/-  (2.18e-64, 1.75e-183j)
| (7.7330955405228481723e-05 + 2.0715524421907974176e-651j)  +/-  (1.86e-62, 1.49e-181j)
| (0.016619620476216269268 + 3.4488587854815144879e-650j)  +/-  (1.56e-52, 1.25e-171j)
| (1.1610116720331860097e-31 + 4.8802054132198331283e-664j)  +/-  (2.56e-83, 2.05e-202j)
| (0.0058730256055361658555 - 3.6542715592258706445e-650j)  +/-  (8.58e-57, 6.87e-176j)
| (1.1964309271021991781e-05 - 2.3821714086707037808e-651j)  +/-  (1.5e-66, 1.2e-185j)
| (0.0058730256055361658555 - 1.9797785727918916735e-650j)  +/-  (2.9e-57, 2.32e-176j)
| (9.6424724777978777201e-13 - 2.0025699025787922102e-655j)  +/-  (5.3e-75, 4.25e-194j)
| (1.4791565004473502241e-06 + 9.4346536499196436211e-652j)  +/-  (7.7e-69, 6.17e-188j)
| (7.7330955405228481723e-05 + 5.4468569751663659677e-651j)  +/-  (2.63e-65, 2.1e-184j)
| (2.9108731872617183923e-11 + 1.1158619828199646409e-654j)  +/-  (2.39e-74, 1.91e-193j)
| (9.2742772411680927171e-36 + 6.8904181390914368179e-667j)  +/-  (2.12e-87, 1.7e-206j)
| (1.4791565004473502241e-06 + 2.7211840590129171766e-652j)  +/-  (8.1e-70, 6.49e-189j)
| (3.8740163597632778982e-16 - 3.9347678164883096021e-657j)  +/-  (3.07e-78, 2.46e-197j)
| (3.8740163597632778982e-16 - 1.2593070048253930031e-655j)  +/-  (1.29e-80, 1.03e-199j)
| (1.1062749548900824842e-08 + 1.0926039318306402654e-652j)  +/-  (1.66e-75, 1.33e-194j)
| (4.3671061817061454519e-18 + 4.1565507799568524613e-658j)  +/-  (2.02e-80, 1.62e-199j)
| (9.2742772411680927171e-36 - 3.8290480749821590587e-666j)  +/-  (3.49e-89, 2.79e-208j)
| (1.1062749548900824842e-08 + 2.2530613803539506574e-653j)  +/-  (8.65e-75, 6.93e-194j)
| (3.135678069348325991e-20 + 1.1569373858967146556e-657j)  +/-  (1.21e-82, 9.66e-202j)
| (0.00040276636657113074137 - 1.129842683358815549e-650j)  +/-  (1.27e-70, 1.02e-189j)
| (6.5196589249004053919e-10 - 3.1931938018618837989e-653j)  +/-  (8.07e-78, 6.46e-197j)
| (0.074547691416729318015 + 7.8872018473121825196e-650j)  +/-  (5.49e-64, 4.41e-183j)
| (6.5196589249004053919e-10 - 5.3684813447161727605e-654j)  +/-  (9.07e-77, 7.28e-196j)
| (2.3096976665669909268e-14 + 4.8249157325416414855e-655j)  +/-  (7.89e-81, 6.32e-200j)
| (0.03872821818447153839 - 8.1546654333854245194e-650j)  +/-  (1.17e-67, 9.43e-187j)
| (3.135678069348325991e-20 - 3.5186732581252788055e-659j)  +/-  (9.59e-84, 7.7e-203j)
| (0.074547691416729318015 + 1.0627491841956442918e-649j)  +/-  (1.91e-67, 1.53e-186j)
| (0.11881365718201649723 - 1.0385342437210388795e-649j)  +/-  (1.28e-67, 1.02e-186j)
| (1.1610116720331860097e-31 - 7.2596665904571838238e-665j)  +/-  (4.32e-89, 3.45e-208j)
| (0.03872821818447153839 - 5.4642929505630995501e-650j)  +/-  (5.01e-70, 4.01e-189j)
| (0.11881365718201649723 - 1.2657308385601952305e-649j)  +/-  (6.26e-69, 4.99e-188j)
| (9.6424724777978777201e-13 - 2.0654594558906381601e-654j)  +/-  (7.84e-81, 6.26e-200j)
| (0.0017023170479103959047 + 1.0314765970761557293e-650j)  +/-  (1.25e-73, 1e-192j)
| (0.00040276636657113074137 - 4.8653972401949758428e-651j)  +/-  (2.08e-74, 1.67e-193j)
| (1.4467590594321471478e-07 - 3.3783384049406565546e-652j)  +/-  (4.2e-78, 3.36e-197j)
| (0.17234044604687798534 - 1.372035356808395623e-649j)  +/-  (1.11e-72, 8.93e-192j)
| (0.0017023170479103959047 + 2.1298118564995712827e-650j)  +/-  (6.09e-75, 4.92e-194j)
| (1.4467590594321471478e-07 - 8.3186786352532008049e-653j)  +/-  (5.62e-78, 4.57e-197j)
| (0.1570515498552151416 + 1.248722228371802043e-649j)  +/-  (4.17e-73, 3.31e-192j)
| (3.0304986611205675344e-25 + 1.239210327554083749e-660j)  +/-  (8e-88, 6.4e-207j)
| (2.9108731872617183923e-11 + 8.4684074353363678538e-654j)  +/-  (1.05e-80, 8.21e-200j)
| (0.1570515498552151416 + 1.3781688110713008537e-649j)  +/-  (9.68e-75, 4.87e-194j)
| (1.3335330750526692855e-22 + 2.304150568471459423e-660j)  +/-  (1.4e-86, 1.23e-205j)
