Starting with polynomial:
P : 64*t^6 - 480*t^4 + 720*t^2 - 120
Extension levels are: 6 37
-------------------------------------------------
Trying to find an order 37 Kronrod extension for:
P1 : 64*t^6 - 480*t^4 + 720*t^2 - 120
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 64*t^43 - 16020097344530635922584031800157856/633555602248846271995200121823*t^41 + 2856294859798422574093855738255509234/633555602248846271995200121823*t^39 - 9447238503211931565163187290123606328121/19640223669714234431851203776513*t^37 + 1348938273215293097223572548040474123974875/39280447339428468863702407553026*t^35 - 136545541584284561335808746579931518022457945/78560894678856937727404815106052*t^33 + 230209240537209734673056333120947886885769165/3570949758129860805791127959366*t^31 - 411672812296294326614228178243035462856881685/230383855363216826180072771572*t^29 + 17238777767451141201783555871800551932741311855/460767710726433652360145543144*t^27 - 547681058522804108968370983808330261742320564925/921535421452867304720291086288*t^25 + 26381337001738247476732570531973005733488746883125/3686141685811469218881164345152*t^23 - 479019206410314470108577303022976223329013408262875/7372283371622938437762328690304*t^21 + 6490063002553164836736048314922880233111376856777625/14744566743245876875524657380608*t^19 - 64594465328386720134304794731009933281412216009737875/29489133486491753751049314761216*t^17 + 230978060217913937566766862737450786681139734515044375/29489133486491753751049314761216*t^15 - 1151275992276772858466397255812886934481336727935810625/58978266972983507502098629522432*t^13 + 3833294671183049837049540910907222786757925375259765625/117956533945967015004197259044864*t^11 - 8024592213005651585366385420320566704227974362549166875/235913067891934030008394518089728*t^9 + 38546627736150367394424098513592145052450063205107611875/1887304543135472240067156144717824*t^7 - 22769400061845720248084829083083016489502261733695028125/3774609086270944480134312289435648*t^5 + 4805707350953199409530973969331730776387051741416284375/7549218172541888960268624578871296*t^3 - 92259956188554875026725760882872843244660313439178125/15098436345083777920537249157742592*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:
| (-7.4284517726059643051 + 5.0045285385169000522e-881j)  +/-  (6.12e-247, 6.12e-247j)
| (3.4359994282550688435 + 1.8045761472467309688e-884j)  +/-  (2.3e-246, 2.3e-246j)
| (-5.8755165832768278676 - 2.5580471458809948401e-888j)  +/-  (1.58e-245, 1.58e-245j)
| (7.4284517726059643051 + 4.158795350629786888e-891j)  +/-  (7.12e-247, 7.12e-247j)
| (8.1141863597984029938 + 3.8607752850831672577e-897j)  +/-  (6.66e-248, 6.66e-248j)
| (6.3480491788110595054 - 1.1088332617834216101e-896j)  +/-  (9.05e-246, 9.05e-246j)
| (-5.4298799606192470341 + 9.2027693179544433478e-907j)  +/-  (2.25e-245, 2.25e-245j)
| (-6.3480491788110595054 + 4.890821987548658765e-925j)  +/-  (7.99e-246, 7.99e-246j)
| (-2.3506049736744922228 - 1.407942301307275729e-936j)  +/-  (5.1e-248, 5.1e-248j)
| (5.4298799606192470341 - 3.8586839882965749734e-947j)  +/-  (2.28e-245, 2.28e-245j)
| (1.0244635820904966455 + 2.0870346160709975675e-963j)  +/-  (3.14e-251, 3.14e-251j)
| (5.0045213455869544175 - 1.7659800992694261084e-958j)  +/-  (2.34e-245, 2.34e-245j)
| (-3.4359994282550688435 - 9.5482833821075680382e-958j)  +/-  (2.48e-246, 2.48e-246j)
| (6.8585315604190511156 - 4.589709379254920208e-961j)  +/-  (2.97e-246, 2.97e-246j)
| (-4.1985672200837085005 - 2.2534382389984452577e-962j)  +/-  (1.22e-245, 1.22e-245j)
| (-4.5950945103212017978 + 2.2343137008363340312e-970j)  +/-  (1.81e-245, 1.81e-245j)
| (-6.8585315604190511156 + 2.8131613658275637988e-974j)  +/-  (3.47e-246, 3.47e-246j)
| (5.8755165832768278676 - 1.012108688453082182e-971j)  +/-  (1.56e-245, 1.56e-245j)
| (3.8127417833017694176 - 4.2905011008540951758e-977j)  +/-  (6.19e-246, 6.19e-246j)
| (-8.1141863597984029938 - 1.2647051775285032537e-981j)  +/-  (6.87e-248, 6.87e-248j)
| (2.0028514630985536091 + 2.4667946950660576702e-981j)  +/-  (9.17e-249, 9.17e-249j)
| (0.10311323438868651733 - 4.0482713380629004694e-987j)  +/-  (1.46e-254, 1.46e-254j)
| (1.0138925666387060522e-991 + 5.8150130812413895256e-993j)  +/-  (4.37e-990, 4.37e-990j)
| (-0.10311323438868651733 + 4.1998184075023868176e-987j)  +/-  (1.06e-254, 1.06e-254j)
| (-3.0671682111338066865 + 1.591261857903617611e-979j)  +/-  (7.73e-247, 7.73e-247j)
| (1.6635643382797310511 + 2.1637966712625838663e-982j)  +/-  (1.59e-249, 1.59e-249j)
| (2.3506049736744922228 - 1.5296923233485827017e-980j)  +/-  (4.76e-248, 4.76e-248j)
| (3.0671682111338066865 - 5.1333192750267960514e-980j)  +/-  (7.49e-247, 7.49e-247j)
| (4.1985672200837085005 + 1.4363568644208429826e-979j)  +/-  (1.22e-245, 1.22e-245j)
| (-0.43607741192761650868 + 7.9899109304888195708e-988j)  +/-  (2.86e-253, 2.86e-253j)
| (4.5950945103212017978 - 3.05156275471626499e-980j)  +/-  (1.89e-245, 1.89e-245j)
| (-3.8127417833017694176 + 1.0834162814788996199e-984j)  +/-  (6.63e-246, 6.63e-246j)
| (2.7054779810176048595 + 5.4061785562239869467e-995j)  +/-  (2.12e-247, 2.12e-247j)
| (-5.0045213455869544175 - 2.566404038561336487e-1000j)  +/-  (2.58e-245, 2.58e-245j)
| (-1.6635643382797310511 + 1.7991736683229409943e-1010j)  +/-  (1.5e-249, 1.5e-249j)
| (-1.3358490740136969497 - 2.6741121855335985186e-1012j)  +/-  (2.31e-250, 2.31e-250j)
| (-1.0244635820904966455 - 3.2216293250374354207e-1012j)  +/-  (2.94e-251, 2.94e-251j)
| (0.72957435456952164897 + 2.1231839693272358725e-1014j)  +/-  (3.84e-252, 3.84e-252j)
| (0.43607741192761650868 - 7.962572679414563138e-1015j)  +/-  (2.6e-253, 2.6e-253j)
| (-2.7054779810176048595 - 8.3235685312598166562e-1012j)  +/-  (1.96e-247, 1.96e-247j)
| (-0.72957435456952164897 - 3.6472214690732432067e-1017j)  +/-  (3.34e-252, 3.34e-252j)
| (-2.0028514630985536091 - 7.7226669914988691373e-1014j)  +/-  (9.86e-249, 9.86e-249j)
| (1.3358490740136969497 + 8.5696433480615579695e-1016j)  +/-  (2.41e-250, 2.41e-250j)
-------------------------------------------------
The weights are:
| (3.7442796614356909618e-25 + 1.2562115747093207723e-901j)  +/-  (5.2e-91, 1.57e-213j)
| (1.5681100212151938695e-06 - 1.2197853909299780523e-889j)  +/-  (1.13e-77, 3.42e-200j)
| (2.6268793706633047521e-16 - 7.8442169567997414439e-897j)  +/-  (5.68e-87, 1.72e-209j)
| (3.7442796614356909618e-25 - 3.4144562441175706102e-901j)  +/-  (5.7e-92, 1.72e-214j)
| (1.1361949158849651122e-29 + 1.2313348803874387563e-903j)  +/-  (9.62e-94, 2.91e-216j)
| (8.7046300083438102705e-19 - 1.1443700169342305643e-897j)  +/-  (1.18e-89, 3.57e-212j)
| (3.8457358089822245495e-14 + 1.2633812683527275261e-895j)  +/-  (1.1e-87, 3.33e-210j)
| (8.7046300083438102705e-19 + 3.4064490471463343563e-898j)  +/-  (4.56e-90, 1.38e-212j)
| (0.00079002228630468870144 + 3.424479995378039558e-889j)  +/-  (1.27e-76, 3.83e-199j)
| (3.8457358089822245495e-14 - 5.6173260413655230863e-895j)  +/-  (1.68e-88, 5.07e-211j)
| (0.059672052144322342179 + 6.8550981039146249625e-887j)  +/-  (3.2e-67, 9.68e-190j)
| (3.1213680300058240667e-12 + 8.2202459416923893115e-894j)  +/-  (1.52e-87, 4.6e-210j)
| (1.5681100212151938695e-06 - 4.1179299138201950555e-891j)  +/-  (1.32e-83, 3.98e-206j)
| (1.12444065468715927e-21 + 2.7740440788144977688e-899j)  +/-  (4.65e-92, 1.4e-214j)
| (4.8721705030429578896e-09 - 1.1311345783756057146e-892j)  +/-  (2e-86, 6.05e-209j)
| (1.5352028728285871088e-10 + 1.4552524488109804018e-893j)  +/-  (1.45e-87, 4.39e-210j)
| (1.12444065468715927e-21 - 9.224939654558784664e-900j)  +/-  (1.29e-93, 3.89e-216j)
| (2.6268793706633047521e-16 + 2.9938427702264080364e-896j)  +/-  (3.97e-91, 1.2e-213j)
| (1.0448957189549765639e-07 - 1.4182583079288585233e-890j)  +/-  (2.77e-87, 8.38e-210j)
| (1.1361949158849651122e-29 - 4.9861575667474533315e-904j)  +/-  (2.98e-98, 9e-221j)
| (0.0035129897910028447039 - 4.6874252033681851019e-888j)  +/-  (3.55e-82, 1.07e-204j)
| (0.27703372181718880677 - 1.7194796356846066696e-885j)  +/-  (3.14e-74, 9.47e-197j)
| (-0.23957435265980506448 + 2.9895946615767181518e-885j)  +/-  (2.14e-74, 6.47e-197j)
| (0.27703372181718880677 - 1.6192853086860382616e-885j)  +/-  (9.73e-75, 2.94e-197j)
| (1.6915366497736466644e-05 + 2.0101157206631159406e-890j)  +/-  (1.83e-85, 5.52e-208j)
| (0.011845381826187070481 + 1.1939008094017517865e-887j)  +/-  (6.04e-81, 1.82e-203j)
| (0.00079002228630468870144 + 1.8256801006382683965e-888j)  +/-  (4.96e-84, 1.5e-206j)
| (1.6915366497736466644e-05 + 3.5441299470139543999e-889j)  +/-  (2.76e-86, 8.33e-209j)
| (4.8721705030429578896e-09 + 1.1324152017168697154e-891j)  +/-  (2.81e-89, 8.48e-212j)
| (0.1402108103202109317 + 2.2229001462237820622e-886j)  +/-  (3.45e-81, 1.04e-203j)
| (1.5352028728285871088e-10 - 1.0082691046226690907e-892j)  +/-  (3.2e-90, 9.66e-213j)
| (1.0448957189549765639e-07 + 7.3713896994478722516e-892j)  +/-  (3.79e-90, 1.15e-212j)
| (0.00013389667660600153727 - 7.335022588381676125e-889j)  +/-  (5.56e-87, 1.68e-209j)
| (3.1213680300058240667e-12 - 1.527663630166770908e-894j)  +/-  (1.35e-92, 4.07e-215j)
| (0.011845381826187070481 + 4.1496329185654341019e-888j)  +/-  (6.01e-87, 1.81e-209j)
| (0.03034290191584049398 - 1.3011365755567033019e-887j)  +/-  (3.14e-86, 9.48e-209j)
| (0.059672052144322342179 + 3.7062090412890025798e-887j)  +/-  (1.26e-85, 3.79e-208j)
| (0.096226806557297625756 - 1.4234098422573695438e-886j)  +/-  (2.57e-85, 7.75e-208j)
| (0.1402108103202109317 + 2.8691478387106798307e-886j)  +/-  (9.55e-85, 2.88e-207j)
| (0.00013389667660600153727 - 8.7250697481350863511e-890j)  +/-  (1.08e-89, 3.27e-212j)
| (0.096226806557297625756 - 9.2481076149235895845e-887j)  +/-  (1.73e-86, 5.22e-209j)
| (0.0035129897910028447039 - 1.2351602638513245282e-888j)  +/-  (1.18e-88, 3.57e-211j)
| (0.03034290191584049398 - 2.95635032548821885e-887j)  +/-  (9.84e-88, 2.78e-210j)
