Starting with polynomial:
P : 64*t^6 - 480*t^4 + 720*t^2 - 120
Extension levels are: 6 38
-------------------------------------------------
Trying to find an order 38 Kronrod extension for:
P1 : 64*t^6 - 480*t^4 + 720*t^2 - 120
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 64*t^44 - 130714750632718428248780557692100336/3118634737581259774746335498441*t^42 + 379394011174937701810324622432488268568/34304982113393857522209690482851*t^40 - 112919110130118498011861054921283033822309/68609964226787715044419380965702*t^38 + 21719724782242313079815979517210438689793227/137219928453575430088838761931404*t^36 - 2899101136241919599566065986725829073661126065/274439856907150860177677523862808*t^34 + 1497026984888819981502970609165505867307125745/2935185635370597435055374586768*t^32 - 26817773327604436570445694419172064303915812615/1467592817685298717527687293384*t^30 + 1448023092304841997526823050146410854081242170985/2935185635370597435055374586768*t^28 - 59404678947089084184562248874557264221400922944555/5870371270741194870110749173536*t^26 + 1856888449049577745126270705067093149373484829706625/11740742541482389740221498347072*t^24 - 88288990938356695854548792106339979372329214487990625/46962970165929558960885993388288*t^22 + 1586417664455318552426825593593651870741174231733785375/93925940331859117921771986776576*t^20 - 21313604803439128081776466656955682464438296257363125125/187851880663718235843543973553152*t^18 + 210707853844910341423611722495707760957769378454732740375/375703761327436471687087947106304*t^16 - 749474841562407784531744906046338205925851033873299546875/375703761327436471687087947106304*t^14 + 3720665384520214581219915081511578539655734624931530960625/751407522654872943374175894212608*t^12 - 12354238245653042049691566864397781765023219063457308640625/1502815045309745886748351788425216*t^10 + 25832844190032984712176786706137598740806263301939527516875/3005630090619491773496703576850432*t^8 - 124346529587485208295090812328417378694838066300050546524375/24045040724955934187973628614803456*t^6 + 74322223122432879869658948736530461266170614855574167465625/48090081449911868375947257229606912*t^4 - 16576034493817407424360705889253055399644218443533254596875/96180162899823736751894514459213824*t^2 + 583926872127114303989168714956303789022526093085681115625/192360325799647473503789028918427648
-------------------------------------------------
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:   44 out of 44
Indefinite weights: 0 out of 44
Negative weights:   0 out of 44
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-7.4130897815661190625 - 1.037115459352450135e-886j)  +/-  (1.23e-246, 1.23e-246j)
| (-6.844974650528435701 - 2.3195257038260177472e-892j)  +/-  (5.56e-246, 5.56e-246j)
| (8.0965459182509213158 - 9.0657195417101823061e-905j)  +/-  (1.32e-247, 1.32e-247j)
| (6.336058617890358527 + 1.9491846826227557982e-903j)  +/-  (1.39e-245, 1.39e-245j)
| (2.7044454172407986204 + 5.1726963217779844797e-905j)  +/-  (2.28e-247, 2.28e-247j)
| (-8.0965459182509213158 - 2.5592277701201782725e-902j)  +/-  (1.27e-247, 1.27e-247j)
| (3.8083038331539897564 - 2.7833591634447247632e-909j)  +/-  (7.05e-246, 7.05e-246j)
| (-16.160195461439988122 - 7.1509262475130135185e-918j)  +/-  (2.25e-251, 2.25e-251j)
| (-1.6646257769195461004 + 5.706715201583285804e-909j)  +/-  (1.69e-249, 1.69e-249j)
| (1.3358490740136969497 - 5.5852966020174444702e-918j)  +/-  (2.49e-250, 2.49e-250j)
| (16.160195461439988122 - 4.4306182103705501925e-920j)  +/-  (2.12e-251, 2.12e-251j)
| (3.0650229231566870242 - 7.5062505600886281934e-913j)  +/-  (8.99e-247, 8.99e-247j)
| (7.4130897815661190625 + 2.3518085341568726246e-916j)  +/-  (1.16e-246, 1.16e-246j)
| (-4.9965287077855300256 - 6.8815983707759148686e-922j)  +/-  (3.17e-245, 3.17e-245j)
| (-5.4206315676258488325 + 3.0816557998580812396e-939j)  +/-  (3.16e-245, 3.16e-245j)
| (3.4327136000550930358 - 8.4365038668958719797e-948j)  +/-  (2.83e-246, 2.83e-246j)
| (5.4206315676258488325 + 2.562234608956997899e-946j)  +/-  (3.02e-245, 3.02e-245j)
| (-3.0650229231566870242 + 8.0699821097214403228e-948j)  +/-  (7.99e-247, 7.99e-247j)
| (-1.3358490740136969497 + 2.3753291034873563452e-953j)  +/-  (2.45e-250, 2.45e-250j)
| (-5.8649458150721838707 + 3.5635358197837093705e-947j)  +/-  (2.43e-245, 2.43e-245j)
| (2.3506049736744922228 - 2.6644423631687926872e-951j)  +/-  (5.53e-248, 5.53e-248j)
| (-6.336058617890358527 - 1.378710209483801889e-948j)  +/-  (1.36e-245, 1.36e-245j)
| (-2.3506049736744922228 - 1.8380005988093316326e-952j)  +/-  (5.36e-248, 5.36e-248j)
| (-2.0036645985046844415 - 4.402827644370711646e-954j)  +/-  (9.59e-249, 9.59e-249j)
| (4.9965287077855300256 + 1.3551112344872980347e-952j)  +/-  (3.39e-245, 3.39e-245j)
| (6.844974650528435701 - 1.5922065337658098308e-952j)  +/-  (5.26e-246, 5.26e-246j)
| (0.1464776322074105859 + 2.9468746030938828616e-961j)  +/-  (2.39e-254, 2.39e-254j)
| (5.8649458150721838707 + 6.0138071771400455712e-952j)  +/-  (2.6e-245, 2.6e-245j)
| (4.1929661534212249257 + 6.897178733420630998e-953j)  +/-  (1.5e-245, 1.5e-245j)
| (-3.4327136000550930358 - 1.2955070196290193192e-951j)  +/-  (2.64e-246, 2.64e-246j)
| (-0.43607741192761650868 - 3.5172654544584128921e-971j)  +/-  (3.34e-253, 3.34e-253j)
| (0.43607741192761650868 + 1.5458986312120606896e-971j)  +/-  (3.17e-253, 3.17e-253j)
| (1.6646257769195461004 + 2.7835899359062680797e-967j)  +/-  (1.73e-249, 1.73e-249j)
| (4.5883123951090223659 + 3.9587256010797031662e-964j)  +/-  (2.57e-245, 2.57e-245j)
| (-3.8083038331539897564 - 3.1015248255726823132e-962j)  +/-  (7.43e-246, 7.43e-246j)
| (-2.7044454172407986204 - 4.9566895481629424024e-972j)  +/-  (2.28e-247, 2.28e-247j)
| (-1.0212951320142950479 + 4.9327791687707807783e-982j)  +/-  (2.86e-251, 2.86e-251j)
| (0.72358946360449537613 + 7.851160771870787333e-986j)  +/-  (3.86e-252, 3.86e-252j)
| (-0.1464776322074105859 + 6.455927424445274997e-985j)  +/-  (2.39e-254, 2.39e-254j)
| (-4.1929661534212249257 - 6.083818000031834954e-983j)  +/-  (1.53e-245, 1.53e-245j)
| (-0.72358946360449537613 - 4.5988936082763379977e-1006j)  +/-  (3.38e-252, 3.38e-252j)
| (-4.5883123951090223659 + 6.9202443235950125617e-1009j)  +/-  (2.33e-245, 2.33e-245j)
| (1.0212951320142950479 - 1.9545679067085751041e-1020j)  +/-  (2.86e-251, 2.86e-251j)
| (2.0036645985046844415 - 1.1327422794722119866e-1019j)  +/-  (9.81e-249, 9.81e-249j)
-------------------------------------------------
The weights are:
| (4.6879214535171736347e-25 - 3.7177627395702442482e-910j)  +/-  (4.44e-87, 3.02e-209j)
| (1.3497887012864753281e-21 + 5.2794932399464269194e-909j)  +/-  (1.26e-85, 8.57e-208j)
| (1.5071478680321217012e-29 - 1.5300223682741224067e-914j)  +/-  (1.99e-90, 1.36e-212j)
| (1.0103772246071118575e-18 + 6.8587649722267280636e-909j)  +/-  (3.75e-86, 2.56e-208j)
| (0.00013423853346299591147 - 5.4040355056362485916e-901j)  +/-  (5.35e-72, 3.64e-194j)
| (1.5071478680321217012e-29 - 3.4722503094427046129e-913j)  +/-  (4.32e-90, 2.94e-212j)
| (1.0775588397881488946e-07 + 7.1475240345906826594e-903j)  +/-  (4e-78, 2.72e-200j)
| (1.567920062562580651e-60 + 2.8133124584220151832e-929j)  +/-  (2.45e-104, 1.67e-226j)
| (0.011812144475183004326 - 2.2054629031173465411e-899j)  +/-  (9.15e-67, 6.23e-189j)
| (0.03053840292928089264 - 3.3770521120407389841e-899j)  +/-  (2.67e-63, 1.82e-185j)
| (1.567920062562580651e-60 + 1.0438986787391517187e-929j)  +/-  (7.62e-105, 5.19e-227j)
| (1.708626303188660191e-05 + 1.4636577710992832837e-901j)  +/-  (2.06e-75, 1.4e-197j)
| (4.6879214535171736347e-25 + 3.278921763295549443e-912j)  +/-  (2.07e-89, 1.41e-211j)
| (3.3711381981731450705e-12 + 1.1066754876361617512e-904j)  +/-  (1.02e-84, 6.97e-207j)
| (4.2391130263838078933e-14 - 1.2919673034548677245e-905j)  +/-  (8.1e-86, 5.51e-208j)
| (1.5989652410563840592e-06 - 3.4780488600994993467e-902j)  +/-  (1.08e-78, 7.37e-201j)
| (4.2391130263838078933e-14 + 2.0058761477072956465e-906j)  +/-  (4.57e-86, 3.11e-208j)
| (1.708626303188660191e-05 - 3.5271359388185137661e-901j)  +/-  (2.59e-80, 1.76e-202j)
| (0.03053840292928089264 + 4.8616666419151216103e-899j)  +/-  (1.01e-70, 6.89e-193j)
| (2.9651154304875376294e-16 + 1.2016869630595822456e-906j)  +/-  (2.52e-87, 1.72e-209j)
| (0.00078786951523292518183 + 1.7730788081391397079e-900j)  +/-  (3.7e-77, 2.52e-199j)
| (1.0103772246071118575e-18 - 8.7547714411240162992e-908j)  +/-  (1.92e-88, 1.31e-210j)
| (0.00078786951523292518183 - 3.4196019516239461925e-900j)  +/-  (9.19e-79, 6.26e-201j)
| (0.0034953021507671888167 + 9.1010571031839377912e-900j)  +/-  (4.4e-77, 3e-199j)
| (3.3711381981731450705e-12 - 2.1551196542567821364e-905j)  +/-  (2.64e-87, 1.8e-209j)
| (1.3497887012864753281e-21 - 2.1042811285256983698e-910j)  +/-  (4.61e-92, 3.14e-214j)
| (0.16137838328547055011 - 2.2592188100053581358e-898j)  +/-  (6.43e-78, 4.38e-200j)
| (2.9651154304875376294e-16 - 1.4011773536023010126e-907j)  +/-  (1.4e-89, 9.54e-212j)
| (5.0913444571483701315e-09 - 1.2492650491251817433e-903j)  +/-  (4.41e-86, 3e-208j)
| (1.5989652410563840592e-06 + 9.4769427118663126156e-902j)  +/-  (5.75e-87, 3.92e-209j)
| (0.13390631893207550461 - 2.1158417250072840079e-898j)  +/-  (5.42e-80, 3.69e-202j)
| (0.13390631893207550461 + 1.8807435112618145524e-898j)  +/-  (8.56e-80, 5.83e-202j)
| (0.011812144475183004326 + 1.3966158020219362366e-899j)  +/-  (1.07e-81, 7.27e-204j)
| (1.6290160065070843076e-10 + 1.8200907465944258752e-904j)  +/-  (3.44e-87, 2.35e-209j)
| (1.0775588397881488946e-07 - 2.2249327231006521544e-902j)  +/-  (1.94e-88, 1.32e-210j)
| (0.00013423853346299591147 + 1.161163797166046956e-900j)  +/-  (7.56e-86, 5.15e-208j)
| (0.060850612688005098532 - 9.5283444273414947569e-899j)  +/-  (2.71e-83, 1.85e-205j)
| (0.097077929248705033423 - 1.2957146805909962252e-898j)  +/-  (2.55e-83, 1.74e-205j)
| (0.16137838328547055011 + 2.3502989017774325819e-898j)  +/-  (4.05e-83, 2.76e-205j)
| (5.0913444571483701315e-09 + 4.5025581687513673509e-903j)  +/-  (9.55e-90, 6.5e-212j)
| (0.097077929248705033423 + 1.5760213313224893143e-898j)  +/-  (1.13e-83, 7.66e-206j)
| (1.6290160065070843076e-10 - 7.7327086932118469697e-904j)  +/-  (1.21e-90, 8.25e-213j)
| (0.060850612688005098532 + 7.2208445307357007518e-899j)  +/-  (2.54e-85, 1.85e-207j)
| (0.0034953021507671888167 - 5.2281029418532559494e-900j)  +/-  (1.54e-86, 1.01e-208j)
