Starting with polynomial:
P : t^6 - 15*t^4 + 45*t^2 - 15
Extension levels are: 6 37
-------------------------------------------------
Trying to find an order 37 Kronrod extension for:
P1 : t^6 - 15*t^4 + 45*t^2 - 15
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^43 - 500628042016582372580750993754933/633555602248846271995200121823*t^41 + 1428147429899211287046927869127754617/5068444817990770175961600974584*t^39 - 9447238503211931565163187290123606328121/157121789357713875454809630212104*t^37 + 1348938273215293097223572548040474123974875/157121789357713875454809630212104*t^35 - 136545541584284561335808746579931518022457945/157121789357713875454809630212104*t^33 + 230209240537209734673056333120947886885769165/3570949758129860805791127959366*t^31 - 411672812296294326614228178243035462856881685/115191927681608413090036385786*t^29 + 17238777767451141201783555871800551932741311855/115191927681608413090036385786*t^27 - 547681058522804108968370983808330261742320564925/115191927681608413090036385786*t^25 + 26381337001738247476732570531973005733488746883125/230383855363216826180072771572*t^23 - 479019206410314470108577303022976223329013408262875/230383855363216826180072771572*t^21 + 6490063002553164836736048314922880233111376856777625/230383855363216826180072771572*t^19 - 64594465328386720134304794731009933281412216009737875/230383855363216826180072771572*t^17 + 230978060217913937566766862737450786681139734515044375/115191927681608413090036385786*t^15 - 1151275992276772858466397255812886934481336727935810625/115191927681608413090036385786*t^13 + 3833294671183049837049540910907222786757925375259765625/115191927681608413090036385786*t^11 - 8024592213005651585366385420320566704227974362549166875/115191927681608413090036385786*t^9 + 38546627736150367394424098513592145052450063205107611875/460767710726433652360145543144*t^7 - 22769400061845720248084829083083016489502261733695028125/460767710726433652360145543144*t^5 + 4805707350953199409530973969331730776387051741416284375/460767710726433652360145543144*t^3 - 92259956188554875026725760882872843244660313439178125/460767710726433652360145543144*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:
| (-8.9774972432859891063 - 1.5943999439876676798e-536j)  +/-  (1.29e-245, 1.29e-245j)
| (-9.6994283507085286581 - 1.4547081724416791639e-538j)  +/-  (4.38e-246, 4.38e-246j)
| (-10.505417244253813379 + 3.9057880692445906075e-545j)  +/-  (9.56e-247, 9.56e-247j)
| (7.0774619601147219231 - 4.8941686363535730178e-566j)  +/-  (3.75e-245, 3.75e-245j)
| (10.505417244253813379 - 1.3838889592740578852e-604j)  +/-  (9.58e-247, 9.58e-247j)
| (8.309235238018118517 + 6.145336460716874246e-639j)  +/-  (2.22e-245, 2.22e-245j)
| (-3.3242574335521189524 - 3.2417728908378650397e-655j)  +/-  (6.84e-248, 6.84e-248j)
| (-1.8891758777537106755 - 4.7172234312916147591e-657j)  +/-  (3.39e-250, 3.39e-250j)
| (-7.6790098823656264028 - 1.6424777453534750372e-651j)  +/-  (3e-245, 3e-245j)
| (3.8261236534568757925 - 3.6677698406095425718e-651j)  +/-  (2.97e-247, 2.97e-247j)
| (1.4488102919497029576 - 2.6062569630201955564e-669j)  +/-  (4.36e-251, 4.36e-251j)
| (4.3376308822650540861 - 8.4041331160746517487e-663j)  +/-  (9.93e-247, 9.93e-247j)
| (8.9774972432859891063 + 6.7315678806033535199e-682j)  +/-  (1.23e-245, 1.23e-245j)
| (0.14582413453263628939 + 3.7570204457448311981e-704j)  +/-  (2.15e-254, 2.15e-254j)
| (-5.3920311397719425307 - 1.100843637763792967e-694j)  +/-  (8.63e-246, 8.63e-246j)
| (-11.475192397649675856 + 2.9912746748257702143e-699j)  +/-  (8.76e-248, 8.76e-248j)
| (11.475192397649675856 - 2.1596683765469014185e-698j)  +/-  (9.37e-248, 9.37e-248j)
| (7.6790098823656264028 + 3.818053567809872843e-713j)  +/-  (3.04e-245, 3.04e-245j)
| (5.3920311397719425307 - 7.9408466806681233766e-728j)  +/-  (8.37e-246, 8.37e-246j)
| (6.4984449768823995691 + 1.251488217671149158e-739j)  +/-  (2.71e-245, 2.71e-245j)
| (2.832459702532771021 + 2.104452456101557094e-749j)  +/-  (1.25e-248, 1.25e-248j)
| (-8.309235238018118517 - 3.0416237545082311632e-746j)  +/-  (2.2e-245, 2.2e-245j)
| (9.6994283507085286581 + 1.3864677657882706401e-745j)  +/-  (4.47e-246, 4.47e-246j)
| (-3.8261236534568757925 + 1.3113701010561309851e-753j)  +/-  (2.91e-247, 2.91e-247j)
| (-4.3376308822650540861 + 1.9967883997935356595e-752j)  +/-  (1.09e-246, 1.09e-246j)
| (-6.4984449768823995691 - 3.2031041442103984412e-751j)  +/-  (2.95e-245, 2.95e-245j)
| (-1.8272264384493294389e-764 - 6.7957686845608987881e-765j)  +/-  (8.38e-763, 8.38e-763j)
| (-7.0774619601147219231 + 1.9815162845836880978e-751j)  +/-  (3.45e-245, 3.45e-245j)
| (1.0317739469918147672 - 4.3078743303328885641e-758j)  +/-  (5.18e-252, 5.18e-252j)
| (-1.4488102919497029576 - 3.0913188362945719979e-757j)  +/-  (4.32e-251, 4.32e-251j)
| (-1.0317739469918147672 - 1.1527676679221394741e-758j)  +/-  (4.97e-252, 4.97e-252j)
| (-0.14582413453263628939 + 6.1840892103417819033e-760j)  +/-  (2.15e-254, 2.15e-254j)
| (3.3242574335521189524 - 5.0503004436602836273e-751j)  +/-  (7.15e-248, 7.15e-248j)
| (-4.8592369917445187281 + 2.1736849029958775141e-752j)  +/-  (3.5e-246, 3.5e-246j)
| (-5.9376707051774839785 + 3.5255512895704899691e-751j)  +/-  (1.7e-245, 1.7e-245j)
| (-2.832459702532771021 + 1.0166770164274055216e-757j)  +/-  (1.25e-248, 1.25e-248j)
| (2.3526352490754190202 - 9.1710885670298247896e-756j)  +/-  (2.41e-249, 2.41e-249j)
| (0.61670659019259415219 - 1.0389011418073816652e-761j)  +/-  (3.75e-253, 3.75e-253j)
| (4.8592369917445187281 + 2.4636807722011881325e-755j)  +/-  (3.66e-246, 3.66e-246j)
| (-2.3526352490754190202 - 3.921748770973271714e-771j)  +/-  (2.62e-249, 2.62e-249j)
| (-0.61670659019259415219 - 9.0922702424337183173e-782j)  +/-  (3.75e-253, 3.75e-253j)
| (5.9376707051774839785 - 2.2418931863896632381e-772j)  +/-  (1.61e-245, 1.61e-245j)
| (1.8891758777537106755 + 7.5607931665151758128e-790j)  +/-  (3.16e-250, 3.16e-250j)
-------------------------------------------------
The weights are:
| (8.7046300083438102705e-19 - 6.6933769754024619979e-554j)  +/-  (2.67e-81, 4.78e-204j)
| (1.12444065468715927e-21 - 5.4855010130730234332e-556j)  +/-  (6.93e-83, 1.24e-205j)
| (3.7442796614356909618e-25 + 3.7128091583264057691e-558j)  +/-  (1.2e-84, 2.15e-207j)
| (3.1213680300058240667e-12 + 3.3433053965408651574e-552j)  +/-  (1.85e-80, 3.31e-203j)
| (3.7442796614356909618e-25 - 2.9128408760252970917e-559j)  +/-  (7.24e-88, 1.3e-210j)
| (2.6268793706633047521e-16 + 1.7588533052053637647e-554j)  +/-  (1.62e-83, 2.89e-206j)
| (0.00079002228630468870144 - 1.4592709143307031818e-546j)  +/-  (1.37e-69, 2.45e-192j)
| (0.03034290191584049398 + 3.6465269840522626903e-545j)  +/-  (3.68e-61, 6.6e-184j)
| (3.8457358089822245495e-14 - 3.5913484734343539081e-552j)  +/-  (6.54e-82, 1.17e-204j)
| (0.00013389667660600153727 + 1.7422567159488366322e-547j)  +/-  (4.87e-73, 8.73e-196j)
| (0.059672052144322342179 - 6.6006721896984295434e-545j)  +/-  (6.45e-60, 1.16e-182j)
| (1.6915366497736466644e-05 - 4.0869785430380465407e-548j)  +/-  (6.43e-75, 1.15e-197j)
| (8.7046300083438102705e-19 - 7.7266201051451775124e-556j)  +/-  (8.58e-86, 1.54e-208j)
| (0.27703372181718880677 + 2.6150286282863716144e-543j)  +/-  (5.68e-62, 1.02e-184j)
| (1.0448957189549765639e-07 - 6.2042008877434831711e-549j)  +/-  (1.54e-79, 2.76e-202j)
| (1.1361949158849651122e-29 - 9.5994070611282575442e-561j)  +/-  (1.68e-90, 3.01e-213j)
| (1.1361949158849651122e-29 + 1.1724993647868518805e-561j)  +/-  (3.36e-91, 6.01e-214j)
| (3.8457358089822245495e-14 - 2.7993331540857984823e-553j)  +/-  (1.06e-83, 1.9e-206j)
| (1.0448957189549765639e-07 - 1.5479874412459741696e-549j)  +/-  (1.6e-80, 2.87e-203j)
| (1.5352028728285871088e-10 - 3.1437526949468893402e-551j)  +/-  (2.69e-82, 4.81e-205j)
| (0.0035129897910028447039 + 2.3680337007586367717e-546j)  +/-  (4.58e-75, 8.21e-198j)
| (2.6268793706633047521e-16 + 4.5507385245085555787e-553j)  +/-  (1.19e-87, 2.13e-210j)
| (1.12444065468715927e-21 + 2.1162403363475021541e-557j)  +/-  (3.3e-88, 5.91e-211j)
| (0.00013389667660600153727 + 4.3304637299793761901e-547j)  +/-  (2.65e-80, 4.74e-203j)
| (1.6915366497736466644e-05 - 1.1728897505486290309e-547j)  +/-  (9.04e-82, 1.62e-204j)
| (1.5352028728285871088e-10 - 1.9626927353970893372e-550j)  +/-  (2.25e-86, 4.04e-209j)
| (-0.23957435265980506448 - 4.763455260275214248e-543j)  +/-  (8.08e-74, 1.45e-196j)
| (3.1213680300058240667e-12 + 2.8253050199503974588e-551j)  +/-  (3.34e-87, 5.99e-210j)
| (0.096226806557297625756 + 1.6022673784718976418e-544j)  +/-  (3.48e-75, 6.22e-198j)
| (0.059672052144322342179 - 9.1412070090488300446e-545j)  +/-  (8.76e-77, 1.57e-199j)
| (0.096226806557297625756 + 2.0183983776814811135e-544j)  +/-  (1.29e-75, 2.31e-198j)
| (0.27703372181718880677 + 2.7013871999094385796e-543j)  +/-  (2.04e-74, 3.65e-197j)
| (0.00079002228630468870144 - 6.7058816274951912647e-547j)  +/-  (5.46e-82, 9.78e-205j)
| (1.5681100212151938695e-06 + 2.8606592319281738202e-548j)  +/-  (3.77e-84, 6.75e-207j)
| (4.8721705030429578896e-09 + 1.1826918273080256911e-549j)  +/-  (8.94e-86, 1.6e-208j)
| (0.0035129897910028447039 + 4.5511399876429247046e-546j)  +/-  (5.67e-82, 1.02e-204j)
| (0.011845381826187070481 - 7.7752536165270946374e-546j)  +/-  (7.56e-82, 1.35e-204j)
| (0.1402108103202109317 - 3.7347850749901378243e-544j)  +/-  (2.06e-78, 3.69e-201j)
| (1.5681100212151938695e-06 + 8.5138975677029511578e-549j)  +/-  (8.23e-86, 1.47e-208j)
| (0.011845381826187070481 - 1.329779433332451372e-545j)  +/-  (4.08e-82, 7.3e-205j)
| (0.1402108103202109317 - 4.2857705321780498917e-544j)  +/-  (6.66e-80, 1.19e-202j)
| (4.8721705030429578896e-09 + 2.4102719998987577581e-550j)  +/-  (1.66e-87, 2.99e-210j)
| (0.03034290191584049398 + 2.3785966938967020108e-545j)  +/-  (3.16e-82, 5.53e-205j)
