Starting with polynomial:
P : t
Extension levels are: 1 66
-------------------------------------------------
Trying to find an order 66 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^67 - 67/4*t^65 + 134*t^63 - 43617/64*t^61 + 633485/256*t^59 - 6992857/1024*t^57 + 15246721/1024*t^55 - 215632197/8192*t^53 + 2518145487/65536*t^51 - 12301285425/262144*t^49 + 6344873535/131072*t^47 - 89075432355/2097152*t^45 + 267226297065/8388608*t^43 - 687479618945/33554432*t^41 + 379874182975/33554432*t^39 - 1443521895305/268435456*t^37 + 9425348845815/4294967296*t^35 - 13195488384141/17179869184*t^33 + 987417498133/4294967296*t^31 - 8055248011085/137438953472*t^29 + 6958363175533/549755813888*t^27 - 5056698705201/2199023255552*t^25 + 766166470485/2199023255552*t^23 - 766166470485/17592186044416*t^21 + 623623871325/140737488355328*t^19 - 203123203803/562949953421312*t^17 + 6478601247/281474976710656*t^15 - 5038912081/4503599627370496*t^13 + 719844583/18014398509481984*t^11 - 71853815/72057594037927936*t^9 + 1165197/72057594037927936*t^7 - 87703/576460752303423488*t^5 + 12529/18446744073709551616*t^3 - 67/73786976294838206464*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:
| (0.99752757218401010076 - 3.34851412561305689e-861j)  +/-  (1.24e-231, 1.24e-231j)
| (-0.99313717716255418008 - 2.5715940551930031719e-871j)  +/-  (1.53e-231, 1.53e-231j)
| (-0.93879848160038637306 - 2.4159805893172631615e-874j)  +/-  (3.51e-232, 3.51e-232j)
| (-0.99972518510981592489 - 1.6458891460723055366e-872j)  +/-  (4.79e-232, 4.79e-232j)
| (0.93879848160038637306 + 7.2090034675920976255e-873j)  +/-  (3.55e-232, 3.55e-232j)
| (0.95391258081477900892 + 2.3641027175720325937e-877j)  +/-  (6.53e-232, 6.53e-232j)
| (0.99972518510981592489 + 6.6348707340420754796e-883j)  +/-  (4.47e-232, 4.47e-232j)
| (-0.90241699523858837602 + 5.7369704102902945838e-896j)  +/-  (7.14e-233, 7.14e-233j)
| (-0.99752757218401010076 - 1.3695121994586105523e-894j)  +/-  (1.26e-231, 1.26e-231j)
| (0.98656365108654650751 - 1.1832543771270521676e-892j)  +/-  (1.67e-231, 1.67e-231j)
| (0.88122958249402846594 + 2.6556990767887126115e-903j)  +/-  (2.73e-233, 2.73e-233j)
| (-0.95391258081477900892 + 8.2416094861447271677e-903j)  +/-  (5.85e-232, 5.85e-232j)
| (-0.9216206995773374113 - 8.3850654996531167197e-904j)  +/-  (1.77e-232, 1.77e-232j)
| (-0.88122958249402846594 - 1.4350016140964031333e-904j)  +/-  (2.68e-233, 2.68e-233j)
| (0.71534696952012749945 - 4.9516294339200306173e-908j)  +/-  (6.8e-237, 6.8e-237j)
| (0.90241699523858837602 - 4.3047219559688787379e-903j)  +/-  (7.78e-233, 7.78e-233j)
| (0.9216206995773374113 + 1.5161010861928800282e-901j)  +/-  (1.62e-232, 1.62e-232j)
| (-0.97782144399294515896 + 1.0760325362898139774e-907j)  +/-  (1.32e-231, 1.32e-231j)
| (-0.80625201860222982825 - 4.9824823632248162526e-912j)  +/-  (7.57e-235, 7.57e-235j)
| (-0.68180782155043771162 + 1.5382499989911978772e-914j)  +/-  (1.11e-237, 1.11e-237j)
| (-0.36638003816824614738 - 3.2942960406581919758e-923j)  +/-  (1.11e-245, 1.11e-245j)
| (0.80625201860222982825 + 1.0927456616994326774e-910j)  +/-  (7.95e-235, 7.95e-235j)
| (-0.32236433316115374202 + 3.2407726591255298078e-923j)  +/-  (8.25e-247, 8.25e-247j)
| (-0.85810503587514426482 + 2.3761374955126925913e-910j)  +/-  (8.95e-234, 8.95e-234j)
| (-0.77763753213375201754 - 3.3506888081268927943e-913j)  +/-  (1.57e-235, 1.57e-235j)
| (0.96692977315025063671 + 7.5328296415861084393e-906j)  +/-  (1.1e-231, 1.1e-231j)
| (0.77763753213375201754 + 6.237229502266237162e-928j)  +/-  (1.76e-235, 1.76e-235j)
| (0.74731362960007709544 - 3.3215076914256381553e-931j)  +/-  (3.22e-236, 3.22e-236j)
| (0.99313717716255418008 - 6.3050958896930979552e-927j)  +/-  (1.94e-231, 1.94e-231j)
| (-0.64676991201719867224 + 4.4254081423086812666e-955j)  +/-  (1.7e-238, 1.7e-238j)
| (-0.093641489534350766117 + 4.3022248881675722645e-970j)  +/-  (2.86e-253, 2.86e-253j)
| (0.53344927362357033992 + 1.1354010771276700624e-956j)  +/-  (2.7e-241, 2.7e-241j)
| (0.68180782155043771162 - 3.1786789769242068641e-953j)  +/-  (1.07e-237, 1.07e-237j)
| (0.85810503587514426482 - 2.0750104530941635812e-946j)  +/-  (8.51e-234, 8.51e-234j)
| (-0.74731362960007709544 - 2.018704491425619675e-955j)  +/-  (3.91e-236, 3.91e-236j)
| (-0.83309418815409152968 - 2.2753091406374713356e-952j)  +/-  (2.65e-234, 2.65e-234j)
| (-0.98656365108654650751 + 8.280851788805685428e-952j)  +/-  (1.51e-231, 1.51e-231j)
| (0.64676991201719867224 + 2.9107544393950643071e-967j)  +/-  (1.52e-238, 1.52e-238j)
| (0.97782144399294515896 + 1.2442273594311217889e-966j)  +/-  (1.54e-231, 1.54e-231j)
| (-0.96692977315025063671 + 2.2138686586116020312e-983j)  +/-  (9.66e-232, 9.66e-232j)
| (-0.57250901727207193052 - 6.7013483709490418444e-993j)  +/-  (2.22e-240, 2.22e-240j)
| (-0.71534696952012749945 - 1.4344667083628853335e-990j)  +/-  (6.51e-237, 6.51e-237j)
| (0.83309418815409152968 - 9.4215594239005580176e-993j)  +/-  (2.5e-234, 2.5e-234j)
| (0.61031026184979209245 - 4.8702785001090642417e-996j)  +/-  (2.09e-239, 2.09e-239j)
| (-0.18646005429168117523 + 2.7098627733964357302e-1008j)  +/-  (1.22e-250, 1.22e-250j)
| (-0.61031026184979209245 - 2.0406402728032187174e-998j)  +/-  (2.3e-239, 2.3e-239j)
| (0.093641489534350766117 + 4.3120922077395598999e-1013j)  +/-  (2.79e-253, 2.79e-253j)
| (0.57250901727207193052 + 6.3187938021935625255e-1001j)  +/-  (2.4e-240, 2.4e-240j)
| (0.4932168926979073144 + 4.2170343023560545494e-1004j)  +/-  (2.09e-242, 2.09e-242j)
| (0.046872262469940062623 + 1.103707179190127414e-1015j)  +/-  (1.21e-254, 1.21e-254j)
| (-0.14020487228188573234 - 1.2435233078135413414e-1012j)  +/-  (5.54e-252, 5.54e-252j)
| (-0.45190031399993384825 - 1.9089258484492841075e-1002j)  +/-  (2.01e-243, 2.01e-243j)
| (-0.23230535663498322777 - 2.5354892882464443373e-1010j)  +/-  (2.43e-249, 2.43e-249j)
| (0.27764000138750057624 - 7.9450562232021459625e-1009j)  +/-  (4.42e-248, 4.42e-248j)
| (0.36638003816824614738 + 2.6530338522799183229e-1006j)  +/-  (1e-245, 1e-245j)
| (-0.046872262469940062623 - 1.4453671752369266517e-1015j)  +/-  (1.21e-254, 1.21e-254j)
| (-0.40959036033650637399 - 1.9126643615998192808e-1004j)  +/-  (1.77e-244, 1.77e-244j)
| (0.45190031399993384825 - 2.8695878021678255974e-1004j)  +/-  (2.1e-243, 2.1e-243j)
| (0.18646005429168117523 + 3.5495460241615764005e-1012j)  +/-  (1.09e-250, 1.09e-250j)
| (0.40959036033650637399 + 2.4167749876185257629e-1005j)  +/-  (1.54e-244, 1.54e-244j)
| (0.14020487228188573234 + 5.2836380946229684132e-1013j)  +/-  (5.37e-252, 5.37e-252j)
| (-0.27764000138750057624 - 6.4982498040896579019e-1009j)  +/-  (3.63e-248, 3.63e-248j)
| (-0.53344927362357033992 + 1.5400311294187993387e-1002j)  +/-  (2.42e-241, 2.42e-241j)
| (1.1096076826988993815e-1041 + 3.6396160737861848293e-1041j)  +/-  (2.55e-1039, 2.55e-1039j)
| (0.32236433316115374202 - 1.1229277520976529701e-1010j)  +/-  (7.37e-247, 7.37e-247j)
| (0.23230535663498322777 - 2.991352215915551871e-1013j)  +/-  (2.12e-249, 2.12e-249j)
| (-0.4932168926979073144 - 3.3963447396942357018e-1006j)  +/-  (2.19e-242, 2.19e-242j)
-------------------------------------------------
The weights are:
| (0.014925373134328358209 + 5.0472619156014337994e-861j)  +/-  (8.45e-36, 4.4e-145j)
| (0.014925373134328358209 - 4.1782170506963488191e-863j)  +/-  (4.05e-36, 2.11e-145j)
| (0.014925373134328358209 + 1.2651385132131027981e-862j)  +/-  (1.24e-36, 6.43e-146j)
| (0.014925373134328358209 - 8.3472110678455708293e-864j)  +/-  (2.67e-36, 1.39e-145j)
| (0.014925373134328358209 + 4.1712218514989555414e-861j)  +/-  (1.19e-37, 6.19e-147j)
| (0.014925373134328358209 - 4.8930212188125400502e-861j)  +/-  (1.15e-37, 5.98e-147j)
| (0.014925373134328358209 + 7.5861813116228691588e-861j)  +/-  (8.09e-38, 4.21e-147j)
| (0.014925373134328358209 + 1.6127540940448568858e-862j)  +/-  (6.57e-39, 3.42e-148j)
| (0.014925373134328358209 + 2.5050847607879891491e-863j)  +/-  (1.47e-37, 7.63e-147j)
| (0.014925373134328358209 + 1.0597297053882482163e-860j)  +/-  (1.35e-38, 7.03e-148j)
| (0.014925373134328358209 - 2.8904932828284975302e-861j)  +/-  (6.83e-40, 3.56e-149j)
| (0.014925373134328358209 - 1.0935978668045120319e-862j)  +/-  (5.52e-39, 2.88e-148j)
| (0.014925373134328358209 - 1.4381200057814279311e-862j)  +/-  (4.44e-39, 2.31e-148j)
| (0.014925373134328358209 - 1.7892602963933343188e-862j)  +/-  (3.32e-40, 1.73e-149j)
| (0.014925373134328358209 - 1.7610669625849905696e-861j)  +/-  (3.74e-43, 1.95e-152j)
| (0.014925373134328358209 + 3.2216641662200302871e-861j)  +/-  (3.13e-41, 1.63e-150j)
| (0.014925373134328358209 - 3.6359889750328754186e-861j)  +/-  (5.96e-41, 3.1e-150j)
| (0.014925373134328358209 - 7.5402451789381865669e-863j)  +/-  (1.34e-40, 7e-150j)
| (0.014925373134328358209 + 2.332348419399478812e-862j)  +/-  (9.75e-44, 5.08e-153j)
| (0.014925373134328358209 + 3.0978802337254608882e-862j)  +/-  (2.39e-45, 1.24e-154j)
| (0.014925373134328358209 + 4.8515929694170660407e-862j)  +/-  (5e-47, 2.6e-156j)
| (0.014925373134328358209 + 2.1994668928207404823e-861j)  +/-  (9.41e-46, 4.9e-155j)
| (0.014925373134328358209 - 5.1004025857932168343e-862j)  +/-  (3.57e-47, 1.86e-156j)
| (0.014925373134328358209 + 1.9678670642297700722e-862j)  +/-  (1.38e-43, 7.2e-153j)
| (0.014925373134328358209 - 2.5187364505991234147e-862j)  +/-  (5.98e-45, 3.11e-154j)
| (0.014925373134328358209 + 5.9277783615908929024e-861j)  +/-  (5.88e-45, 3.06e-154j)
| (0.014925373134328358209 - 2.033367700902879683e-861j)  +/-  (3.04e-47, 1.58e-156j)
| (0.014925373134328358209 + 1.8885738225212529793e-861j)  +/-  (1.02e-47, 5.29e-157j)
| (0.014925373134328358209 - 1.8944603600640289785e-860j)  +/-  (2.14e-45, 1.11e-154j)
| (0.014925373134328358209 - 3.2986333470368219214e-862j)  +/-  (2.35e-49, 1.22e-158j)
| (0.014925373134328358209 + 6.4888029290097127473e-862j)  +/-  (2.49e-52, 1.29e-161j)
| (0.014925373134328358209 + 1.2961701408580857995e-861j)  +/-  (6.14e-52, 3.2e-161j)
| (0.014925373134328358209 + 1.6477841218249427739e-861j)  +/-  (1.42e-49, 7.38e-159j)
| (0.014925373134328358209 + 2.6191162392979061905e-861j)  +/-  (1.53e-47, 7.95e-157j)
| (0.014925373134328358209 + 2.7082550647557543971e-862j)  +/-  (4.71e-49, 2.45e-158j)
| (0.014925373134328358209 - 2.1488130392673546273e-862j)  +/-  (6.69e-48, 3.48e-157j)
| (0.014925373134328358209 + 5.8559772483644742892e-863j)  +/-  (1.27e-47, 6.64e-157j)
| (0.014925373134328358209 - 1.546348128153617071e-861j)  +/-  (4.89e-52, 2.55e-161j)
| (0.014925373134328358209 - 7.558367449506530979e-861j)  +/-  (8.42e-48, 4.39e-157j)
| (0.014925373134328358209 + 9.2329300120838938436e-863j)  +/-  (9.21e-48, 4.8e-157j)
| (0.014925373134328358209 - 3.7138076687014255119e-862j)  +/-  (6.98e-54, 3.63e-163j)
| (0.014925373134328358209 - 2.9011986862726616016e-862j)  +/-  (4.6e-51, 2.39e-160j)
| (0.014925373134328358209 - 2.3922538170070518838e-861j)  +/-  (4.32e-50, 2.25e-159j)
| (0.014925373134328358209 + 1.4548848847218428725e-861j)  +/-  (8.17e-54, 4.25e-163j)
| (0.014925373134328358209 + 5.9011678638286654069e-862j)  +/-  (1.75e-57, 9.1e-167j)
| (0.014925373134328358209 + 3.5038148755942118403e-862j)  +/-  (1.4e-53, 7.28e-163j)
| (0.014925373134328358209 + 7.8332669785150290828e-862j)  +/-  (4.34e-59, 2.26e-168j)
| (0.014925373134328358209 - 1.3718963225142400019e-861j)  +/-  (5.1e-55, 2.66e-164j)
| (0.014925373134328358209 - 1.2267144414273167917e-861j)  +/-  (7.43e-57, 3.87e-166j)
| (0.014925373134328358209 - 7.4725435252749178438e-862j)  +/-  (2.32e-59, 1.21e-168j)
| (0.014925373134328358209 - 6.1889635372142952528e-862j)  +/-  (1.34e-58, 6.96e-168j)
| (0.014925373134328358209 + 4.3769410200118141325e-862j)  +/-  (1.63e-58, 8.48e-168j)
| (0.014925373134328358209 - 5.6244030755052515132e-862j)  +/-  (9.8e-59, 5.1e-168j)
| (0.014925373134328358209 + 9.4904225660411638476e-862j)  +/-  (1.68e-61, 8.76e-171j)
| (0.014925373134328358209 + 1.0484275412643087761e-861j)  +/-  (3.26e-61, 1.7e-170j)
| (0.014925373134328358209 - 6.8018137726033579503e-862j)  +/-  (1.24e-60, 6.44e-170j)
| (0.014925373134328358209 - 4.6106463671582788771e-862j)  +/-  (7.16e-60, 3.73e-169j)
| (0.014925373134328358209 + 1.1627095740809967298e-861j)  +/-  (1.23e-60, 6.4e-170j)
| (0.014925373134328358209 + 8.6144612847455166282e-862j)  +/-  (1.86e-62, 9.66e-172j)
| (0.014925373134328358209 - 1.1034721144062014376e-861j)  +/-  (2.14e-61, 1.12e-170j)
| (0.014925373134328358209 - 8.2132254452868885885e-862j)  +/-  (2.37e-62, 1.23e-171j)
| (0.014925373134328358209 + 5.3577564149226141567e-862j)  +/-  (3.82e-62, 1.96e-171j)
| (0.014925373134328358209 + 3.9290237169288601751e-862j)  +/-  (9.93e-63, 5.14e-172j)
| (0.014925373134328358209 + 7.1292562034348633939e-862j)  +/-  (1.24e-62, 6.54e-172j)
| (0.014925373134328358209 - 9.9708925150287204891e-862j)  +/-  (2.88e-63, 1.52e-172j)
| (0.014925373134328358209 - 9.0393038338905171376e-862j)  +/-  (2.49e-63, 1.32e-172j)
| (0.014925373134328358209 - 4.1499077015846544773e-862j)  +/-  (1.66e-63, 7.78e-173j)
