Starting with polynomial:
P : 2097152*t^22 - 11534336*t^20 + 27394048*t^18 - 36765696*t^16 + 30638080*t^14 - 16400384*t^12 + 5637632*t^10 - 1208064*t^8 + 151008*t^6 - 9680*t^4 + 242*t^2 - 1
Extension levels are: 22 44
-------------------------------------------------
Trying to find an order 44 Kronrod extension for:
P1 : 2097152*t^22 - 11534336*t^20 + 27394048*t^18 - 36765696*t^16 + 30638080*t^14 - 16400384*t^12 + 5637632*t^10 - 1208064*t^8 + 151008*t^6 - 9680*t^4 + 242*t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2097152*t^66 - 34603008*t^64 + 272498688*t^62 - 1363214336*t^60 + 4864696320*t^58 - 13182529536*t^56 + 28195965952*t^54 - 48847974912*t^52 + 69797860704*t^50 - 83335652400*t^48 + 83930907060*t^46 - 71792139510*t^44 + 209615320915/4*t^42 - 261943093335/8*t^40 + 561306628575/32*t^38 - 515815110965/64*t^36 + 6499270398159/2048*t^34 - 4377059655903/4096*t^32 + 5025512938259/16384*t^30 - 2448038217405/32768*t^28 + 4023297592083/262144*t^26 - 1383673775055/524288*t^24 + 789037111395/2097152*t^22 - 184294815705/4194304*t^20 + 277904880825/67108864*t^18 - 41482387089/134217728*t^16 + 9572858559/536870912*t^14 - 827284073/1073741824*t^12 + 205265973/8589934592*t^10 - 8608545/17179869184*t^8 + 446369/68719476736*t^6 - 6171/137438953472*t^4 + 1089/8796093022208*t^2 - 1/17592186044416
-------------------------------------------------
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
Positive weights:   66 out of 66
Indefinite weights: 0 out of 66
Negative weights:   0 out of 66
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.99745211461025354136 + 2.6718959408071426464e-882j)  +/-  (4.9e-232, 4.9e-232j)
| (-0.99745211461025354136 - 7.2020722757826243917e-890j)  +/-  (5.41e-232, 5.41e-232j)
| (-0.93694972499976173582 + 7.9368209198645676734e-904j)  +/-  (1.73e-232, 1.73e-232j)
| (-0.99292788467328826634 + 9.3774279403130282572e-911j)  +/-  (7.23e-232, 7.23e-232j)
| (0.95251665393586051141 - 2.6635603224633746673e-925j)  +/-  (3.27e-232, 3.27e-232j)
| (0.96592582628906828675 - 7.0209111926890478749e-925j)  +/-  (4.99e-232, 4.99e-232j)
| (0.99292788467328826634 + 1.9205195905057226038e-925j)  +/-  (7.45e-232, 7.45e-232j)
| (-0.91926030358166559679 + 1.3211222708042868865e-925j)  +/-  (6.98e-233, 6.98e-233j)
| (0.99971679469312907424 + 1.2921587005631130009e-926j)  +/-  (1.95e-232, 1.95e-232j)
| (-0.98615435371818657489 - 1.255656046584650902e-926j)  +/-  (7.71e-232, 7.71e-232j)
| (0.89948846191060316825 + 1.7001129330864377966e-944j)  +/-  (3.13e-233, 3.13e-233j)
| (0.97714686597115951949 + 2.4911566773939899055e-942j)  +/-  (7.4e-232, 7.4e-232j)
| (-0.7071067811865475244 - 2.2598882431515686105e-947j)  +/-  (2.42e-237, 2.42e-237j)
| (-0.85388129202114809963 + 9.9596613655881727711e-945j)  +/-  (3.69e-234, 3.69e-234j)
| (0.87767898956725561521 - 2.0933302524936348801e-945j)  +/-  (1.15e-233, 1.15e-233j)
| (0.82814927871137082792 - 1.270210772156483443e-945j)  +/-  (1.17e-234, 1.17e-234j)
| (0.67266037370125250168 - 3.0257485143235584726e-949j)  +/-  (3.62e-238, 3.62e-238j)
| (-0.97714686597115951949 + 9.1943393239220332634e-942j)  +/-  (6.4e-232, 6.4e-232j)
| (-0.77111971974538759153 - 3.75935000694928e-962j)  +/-  (6.29e-236, 6.29e-236j)
| (-0.96592582628906828675 + 2.4534900841228874145e-956j)  +/-  (4.16e-232, 4.16e-232j)
| (0.98615435371818657489 + 2.0108490923599546041e-969j)  +/-  (7.2e-232, 7.2e-232j)
| (0.80054124092436040397 - 1.0357710597268714142e-974j)  +/-  (2.88e-235, 2.88e-235j)
| (-0.87767898956725561521 - 3.5819137138216478438e-971j)  +/-  (1.14e-233, 1.14e-233j)
| (-0.82814927871137082792 + 1.7633189625686689422e-975j)  +/-  (1.07e-234, 1.07e-234j)
| (-0.80054124092436040397 - 5.4931241225470570922e-976j)  +/-  (2.72e-235, 2.72e-235j)
| (0.73995136438288383753 + 1.9015692512306680041e-979j)  +/-  (1.36e-236, 1.36e-236j)
| (0.7071067811865475244 + 4.4312791912827624929e-980j)  +/-  (2.19e-237, 2.19e-237j)
| (0.21256528955297667388 + 4.6334852171489696349e-992j)  +/-  (4.73e-250, 4.73e-250j)
| (-0.99971679469312907424 - 2.9161391448144322725e-971j)  +/-  (2.03e-232, 2.03e-232j)
| (-0.67266037370125250168 - 1.5813592472214480071e-995j)  +/-  (4.12e-238, 4.12e-238j)
| (-0.30448649226990701781 - 7.5361539900863591071e-1006j)  +/-  (1.72e-247, 1.72e-247j)
| (0.91926030358166559679 - 1.8683557642645013155e-988j)  +/-  (7.03e-233, 7.03e-233j)
| (0.59927766651134693453 + 5.0318125925752280906e-1000j)  +/-  (7.24e-240, 7.24e-240j)
| (-0.16583000525437414429 - 8.6245965625098444721e-1010j)  +/-  (2.43e-251, 2.43e-251j)
| (-0.63669017411908823818 + 9.9778390345622113853e-997j)  +/-  (5.72e-239, 5.72e-239j)
| (-0.73995136438288383753 - 2.1464242607908571952e-994j)  +/-  (1.22e-236, 1.22e-236j)
| (0.77111971974538759153 + 1.3414740710428381075e-993j)  +/-  (6.62e-236, 6.62e-236j)
| (0.56050760224089399983 - 6.6216546164326765068e-1000j)  +/-  (9.11e-241, 9.11e-241j)
| (0.93694972499976173582 - 6.967938048391996632e-990j)  +/-  (1.46e-232, 1.46e-232j)
| (-0.95251665393586051141 - 4.4272694634023969845e-992j)  +/-  (2.83e-232, 2.83e-232j)
| (-0.52046780797307224304 - 6.2948109135529528129e-1008j)  +/-  (9.29e-242, 9.29e-242j)
| (-0.89948846191060316825 + 7.4740445841840933083e-1001j)  +/-  (2.97e-233, 2.97e-233j)
| (0.63669017411908823818 - 5.3581037499405503434e-1004j)  +/-  (4.77e-239, 4.77e-239j)
| (0.52046780797307224304 + 9.0653095091408023398e-1007j)  +/-  (8.17e-242, 8.17e-242j)
| (0.85388129202114809963 - 8.6459170071422279059e-1013j)  +/-  (3.42e-234, 3.42e-234j)
| (-0.56050760224089399983 - 1.079789708631779989e-1020j)  +/-  (8.35e-241, 8.35e-241j)
| (-0.59927766651134693453 - 7.2227152587269711735e-1025j)  +/-  (7.59e-240, 7.59e-240j)
| (0.071339183199232340327 + 5.5833648357171255165e-1037j)  +/-  (4.38e-254, 4.38e-254j)
| (0.4792489867200568312 - 9.1530555195938921842e-1026j)  +/-  (8.15e-243, 8.15e-243j)
| (0.11871906265730519282 - 1.1881020859408450439e-1036j)  +/-  (1.41e-252, 1.41e-252j)
| (-0.34946417959909833671 + 1.3544081159568403953e-1030j)  +/-  (2.82e-246, 2.82e-246j)
| (-0.4792489867200568312 - 6.0088006695086819378e-1027j)  +/-  (8.1e-243, 8.1e-243j)
| (-0.11871906265730519282 + 3.0733180735221506327e-1037j)  +/-  (1.5e-252, 1.5e-252j)
| (0.43694451236935954153 - 1.0305503617488465612e-1028j)  +/-  (5.85e-244, 5.85e-244j)
| (0.34946417959909833671 - 2.7160006661054595077e-1030j)  +/-  (3.11e-246, 3.11e-246j)
| (-0.071339183199232340327 - 8.5282673132080858039e-1038j)  +/-  (4.06e-254, 4.06e-254j)
| (-0.43694451236935954153 - 7.3713202375827503634e-1028j)  +/-  (6.5e-244, 6.5e-244j)
| (-0.21256528955297667388 - 4.995984194807818451e-1034j)  +/-  (5.33e-250, 5.33e-250j)
| (0.16583000525437414429 + 1.8638137219861737915e-1034j)  +/-  (2.23e-251, 2.23e-251j)
| (0.39365021816194133181 + 2.2091373267886566511e-1029j)  +/-  (4.56e-245, 4.56e-245j)
| (0.023797697546107515581 - 1.325772185773583219e-1038j)  +/-  (3.64e-255, 3.64e-255j)
| (-0.25881904510252076235 + 4.9969319784299300844e-1033j)  +/-  (1e-248, 1e-248j)
| (-0.39365021816194133181 + 1.1557536545388141555e-1029j)  +/-  (4.68e-245, 4.68e-245j)
| (-0.023797697546107515581 + 1.191294897241720145e-1038j)  +/-  (3.64e-255, 3.64e-255j)
| (0.30448649226990701781 - 6.6019654384391674299e-1031j)  +/-  (1.7e-247, 1.7e-247j)
| (0.25881904510252076235 + 1.0858669095808787005e-1031j)  +/-  (9.83e-249, 9.83e-249j)
-------------------------------------------------
The weights are:
| (0.015151515151515151515 - 3.9671753715660859507e-882j)  +/-  (4.59e-35, 1.07e-144j)
| (0.015151515151515151515 + 2.0293234087438299184e-884j)  +/-  (1.87e-35, 4.34e-145j)
| (0.015151515151515151515 + 1.0251869471615690656e-883j)  +/-  (8.03e-36, 1.86e-145j)
| (0.015151515151515151515 - 3.3847514426559877913e-884j)  +/-  (1.08e-35, 2.51e-145j)
| (0.015151515151515151515 + 3.8452652613060930405e-882j)  +/-  (3.1e-36, 7.19e-146j)
| (0.015151515151515151515 - 4.6587655935804586468e-882j)  +/-  (2.42e-36, 5.61e-146j)
| (0.015151515151515151515 + 1.489097936740408577e-881j)  +/-  (1.34e-36, 3.1e-146j)
| (0.015151515151515151515 - 1.1654689963585030207e-883j)  +/-  (7.67e-39, 1.78e-148j)
| (0.015151515151515151515 - 5.9631475028148812251e-882j)  +/-  (1.15e-36, 2.67e-146j)
| (0.015151515151515151515 + 4.7440910485352571034e-884j)  +/-  (9.28e-39, 2.15e-148j)
| (0.015151515151515151515 - 2.5310970104010261811e-882j)  +/-  (2.73e-39, 6.34e-149j)
| (0.015151515151515151515 + 5.9406163860118433328e-882j)  +/-  (3.35e-37, 7.77e-147j)
| (0.015151515151515151515 - 2.3540755354550032716e-883j)  +/-  (1.18e-41, 2.74e-151j)
| (0.015151515151515151515 + 1.5953521277111807419e-883j)  +/-  (5.21e-41, 1.21e-150j)
| (0.015151515151515151515 + 2.2706452775826468866e-882j)  +/-  (4.36e-40, 1.01e-149j)
| (0.015151515151515151515 + 1.8787316231546859195e-882j)  +/-  (3.16e-41, 7.33e-151j)
| (0.015151515151515151515 - 1.2928426418782874255e-882j)  +/-  (2.88e-43, 6.67e-153j)
| (0.015151515151515151515 - 6.1088543961064311942e-884j)  +/-  (2.16e-40, 5.02e-150j)
| (0.015151515151515151515 - 2.0429268852056921612e-883j)  +/-  (6.7e-43, 1.55e-152j)
| (0.015151515151515151515 + 7.4806453599026055229e-884j)  +/-  (6.66e-41, 1.54e-150j)
| (0.015151515151515151515 - 8.3294860943842835426e-882j)  +/-  (4.7e-39, 1.09e-148j)
| (0.015151515151515151515 - 1.7270537921781357744e-882j)  +/-  (8.71e-43, 2.02e-152j)
| (0.015151515151515151515 - 1.4503634751461858233e-883j)  +/-  (4.48e-42, 1.04e-151j)
| (0.015151515151515151515 - 1.7422998317229145857e-883j)  +/-  (7.26e-43, 1.68e-152j)
| (0.015151515151515151515 + 1.8914173813611574908e-883j)  +/-  (2.74e-43, 6.35e-153j)
| (0.015151515151515151515 - 1.4823979846323074866e-882j)  +/-  (1.1e-45, 2.54e-155j)
| (0.015151515151515151515 + 1.3820304823184988084e-882j)  +/-  (5.4e-46, 1.25e-155j)
| (0.015151515151515151515 + 7.0648064580129521151e-883j)  +/-  (1.13e-50, 2.63e-160j)
| (0.015151515151515151515 - 6.7620431775887829566e-885j)  +/-  (6.52e-44, 1.51e-153j)
| (0.015151515151515151515 + 2.5142291870522917534e-883j)  +/-  (1.03e-47, 2.38e-157j)
| (0.015151515151515151515 - 4.1517340154804274652e-883j)  +/-  (1.15e-51, 2.66e-161j)
| (0.015151515151515151515 + 2.8569108996371171495e-882j)  +/-  (1.47e-45, 3.4e-155j)
| (0.015151515151515151515 - 1.1409268283160801659e-882j)  +/-  (1.63e-49, 3.77e-159j)
| (0.015151515151515151515 + 4.8106891947174997085e-883j)  +/-  (3.59e-52, 8.33e-162j)
| (0.015151515151515151515 - 2.6778075367430007336e-883j)  +/-  (3.21e-49, 7.44e-159j)
| (0.015151515151515151515 + 2.197063203197487945e-883j)  +/-  (2.82e-47, 6.53e-157j)
| (0.015151515151515151515 + 1.5963528771588491559e-882j)  +/-  (1.4e-47, 3.25e-157j)
| (0.015151515151515151515 + 1.0755480255930825679e-882j)  +/-  (4.78e-51, 1.11e-160j)
| (0.015151515151515151515 - 3.2777634680351807083e-882j)  +/-  (4.01e-46, 9.29e-156j)
| (0.015151515151515151515 - 8.861093916713509563e-884j)  +/-  (4.4e-47, 1.02e-156j)
| (0.015151515151515151515 + 3.1922439480260183583e-883j)  +/-  (2.23e-53, 5.18e-163j)
| (0.015151515151515151515 + 1.3071330882502530225e-883j)  +/-  (1.67e-47, 3.87e-157j)
| (0.015151515151515151515 + 1.2129658242667078791e-882j)  +/-  (4.31e-51, 1e-160j)
| (0.015151515151515151515 - 1.0158764122081527693e-882j)  +/-  (1.66e-53, 3.84e-163j)
| (0.015151515151515151515 - 2.0571935554362795389e-882j)  +/-  (5.18e-49, 1.2e-158j)
| (0.015151515151515151515 - 3.0164757206168511839e-883j)  +/-  (9.06e-54, 2.1e-163j)
| (0.015151515151515151515 + 2.8451142422815752025e-883j)  +/-  (4.39e-53, 1.02e-162j)
| (0.015151515151515151515 - 6.1118905577357337415e-883j)  +/-  (8.36e-59, 1.94e-168j)
| (0.015151515151515151515 + 9.6113222802717841155e-883j)  +/-  (3.65e-56, 8.46e-166j)
| (0.015151515151515151515 + 6.4122169565643959024e-883j)  +/-  (9.79e-59, 2.27e-168j)
| (0.015151515151515151515 + 3.9475090016657482757e-883j)  +/-  (2.88e-58, 6.68e-168j)
| (0.015151515151515151515 - 3.3727996334870631666e-883j)  +/-  (6.1e-57, 1.41e-166j)
| (0.015151515151515151515 - 5.0481745250510671993e-883j)  +/-  (1.08e-59, 2.5e-169j)
| (0.015151515151515151515 - 9.1067110515292818566e-883j)  +/-  (1.29e-58, 2.99e-168j)
| (0.015151515151515151515 - 8.2053447873909823016e-883j)  +/-  (5.92e-60, 1.37e-169j)
| (0.015151515151515151515 + 5.2959832743918846127e-883j)  +/-  (1.34e-60, 3.1e-170j)
| (0.015151515151515151515 + 3.5585558285950109049e-883j)  +/-  (2.77e-59, 6.42e-169j)
| (0.015151515151515151515 - 4.5826393553705067299e-883j)  +/-  (1.84e-60, 4.27e-170j)
| (0.015151515151515151515 - 6.7292448873692796893e-883j)  +/-  (2.62e-61, 6.08e-171j)
| (0.015151515151515151515 + 8.6395575246406208068e-883j)  +/-  (9.19e-61, 2.13e-170j)
| (0.015151515151515151515 + 5.8266591133659136365e-883j)  +/-  (1.13e-61, 2.63e-171j)
| (0.015151515151515151515 + 4.3632273259880757814e-883j)  +/-  (2.33e-61, 5.41e-171j)
| (0.015151515151515151515 - 3.7499620495431475717e-883j)  +/-  (3.44e-61, 7.97e-171j)
| (0.015151515151515151515 - 5.5551073795303406489e-883j)  +/-  (5.2e-62, 1.21e-171j)
| (0.015151515151515151515 + 7.8002469706734225625e-883j)  +/-  (3.52e-63, 8.18e-173j)
| (0.015151515151515151515 - 7.4210010946120603708e-883j)  +/-  (3.64e-63, 8.43e-173j)
