Starting with polynomial:
P : 256*t^8 - 3584*t^6 + 13440*t^4 - 13440*t^2 + 1680
Extension levels are: 8 44
-------------------------------------------------
Trying to find an order 44 Kronrod extension for:
P1 : 256*t^8 - 3584*t^6 + 13440*t^4 - 13440*t^2 + 1680
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 256*t^52 - 14748961046415140680722505104276938864674798289072896/96463059700968922754665093508150590981130145789*t^50 + 3348047648568943405709680729157200127290946729239721920/79686875405148240536462468550211357767020555217*t^48 - 159531571650496850701862913500166464931011051023254828780800/22604510323260384232176520245409955153244830829889*t^46 + 55072448697803368072398317303361908379299065330193882587099040/67813530969781152696529560736229865459734492489667*t^44 - 354714092140733631066130167384179833246426315060844706633723040/5216425459213934822809966210479220419979576345359*t^42 + 97103783456031657885157944364712431650859201369643576452774016360/22604510323260384232176520245409955153244830829889*t^40 - 364342883263895416312181441451366409198431461456414743885920640400/1738808486404644940936655403493073473326525448453*t^38 + 19814295124022451031281895361015854909360071327900900849707458825/2473411787204331352683720346362835666182824251*t^36 - 599446874113649559988740660853629324930657653980617253613849885475/2473411787204331352683720346362835666182824251*t^34 + 57718816390549484217613344471506469256565877316485796880038193356575/9893647148817325410734881385451342664731297004*t^32 - 277005115533613314919279551706539496805130238022242689299795238739950/2473411787204331352683720346362835666182824251*t^30 + 16954851881084099824806110176783011630535087725537068757673158428124375/9893647148817325410734881385451342664731297004*t^28 - 206180405592701208174638843966773417606451243925480985754677162796862375/9893647148817325410734881385451342664731297004*t^26 + 7926389030793746927557735013019473133280546507749840341919161374156648125/39574588595269301642939525541805370658925188016*t^24 - 1298288830201894337298088611466638268825006192593802436340137610673438125/860317143375419600933467946560986318672286696*t^22 + 242700615335770043078164873449080812154894313735079048675367602262491576875/27530148588013427229870974289951562197513174272*t^20 - 1083557801268346726594798149042409312774697214617743422750309894687070978125/27530148588013427229870974289951562197513174272*t^18 + 14516117195517555526899294246948703395260283277237680915763660054383019003125/110120594352053708919483897159806248790052697088*t^16 - 8901729389369426954728059278783912279129212176044365173257715998297808253125/27530148588013427229870974289951562197513174272*t^14 + 123991281108521042512162249019133885273589043530079820340452985532107639996875/220241188704107417838967794319612497580105394176*t^12 - 146926346693802499523672947387840963611680987433573960323315597097963316659375/220241188704107417838967794319612497580105394176*t^10 + 446783720175406579145274061460099760085457220171081882420466963484660582390625/880964754816429671355871177278449990320421576704*t^8 - 99668596295593413358324595940440560123034846140447972283777889868481337703125/440482377408214835677935588639224995160210788352*t^6 + 359536782402768037026341710124257477019255355903710296381842369480696379265625/7047718038531437370846969418227599922563372613632*t^4 - 30335359591520212189801596960524336827884249437665394774015294237900646796875/7047718038531437370846969418227599922563372613632*t^2 + 1543883273673835963592062164167340794728377833051342048147041636825187109375/28190872154125749483387877672910399690253490454528
-------------------------------------------------
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:
| (-6.1201805327310735477 + 1.6236020537223683402e-923j)  +/-  (3.08e-243, 3.08e-243j)
| (7.4095681848210223624 + 7.2592015004795220049e-929j)  +/-  (4.96e-244, 4.96e-244j)
| (-7.9012926121292800031 - 9.3019163665249802131e-943j)  +/-  (1.37e-244, 1.37e-244j)
| (-4.2727631126170102852 - 2.4813818362307802166e-946j)  +/-  (7.75e-244, 7.75e-244j)
| (-8.4513904676572778016 - 1.6726014459004732158e-956j)  +/-  (2.05e-245, 2.05e-245j)
| (5.3501128230004757998 + 1.1821161480550802447e-953j)  +/-  (3.1e-243, 3.1e-243j)
| (6.1201805327310735477 + 1.7330650665425021237e-969j)  +/-  (3.23e-243, 3.23e-243j)
| (-9.1147790655447366248 - 5.0420264098771745004e-983j)  +/-  (1.38e-246, 1.38e-246j)
| (8.4513904676572778016 + 2.0966534418971768543e-979j)  +/-  (2.07e-245, 2.07e-245j)
| (6.527631552315805435 + 1.2108288065074791598e-977j)  +/-  (2.21e-243, 2.21e-243j)
| (1.1571937124467801947 + 3.8273792451177149171e-991j)  +/-  (5.03e-250, 5.03e-250j)
| (9.1147790655447366248 - 6.4638910544258755155e-988j)  +/-  (1.42e-246, 1.42e-246j)
| (-3.2580959734704169154 - 4.1953254984408658868e-986j)  +/-  (3.69e-245, 3.69e-245j)
| (-2.9306374202572440192 + 1.034392659456068365e-986j)  +/-  (1.02e-245, 1.02e-245j)
| (-6.9552741825275744848 + 1.7832433111443152591e-984j)  +/-  (1.27e-243, 1.27e-243j)
| (5.7286687941616197643 - 2.0222549171508664588e-983j)  +/-  (3.64e-243, 3.64e-243j)
| (-1.9816567566958429259 - 1.8693993748549251106e-993j)  +/-  (8.93e-248, 8.93e-248j)
| (-4.6236346536728669855 + 1.1949607188129022982e-989j)  +/-  (1.59e-243, 1.59e-243j)
| (-3.5906684164216699908 - 9.0465137554348387059e-990j)  +/-  (1.25e-244, 1.25e-244j)
| (4.2727631126170102852 + 7.0985912736056882507e-988j)  +/-  (7.9e-244, 7.9e-244j)
| (1.9816567566958429259 - 1.8986667610774827771e-1000j)  +/-  (8.32e-248, 8.32e-248j)
| (2.2914067078560275968 - 1.985558267580589581e-997j)  +/-  (4.9e-247, 4.9e-247j)
| (-4.9823219902791439547 + 3.6142435779938019619e-995j)  +/-  (2.47e-243, 2.47e-243j)
| (3.9287005761714112393 + 6.4193526117133833754e-997j)  +/-  (3.44e-244, 3.44e-244j)
| (4.9823219902791439547 + 6.8894436306783706652e-1005j)  +/-  (2.41e-243, 2.41e-243j)
| (7.9012926121292800031 + 4.4871260468627131266e-1014j)  +/-  (1.29e-244, 1.29e-244j)
| (0.65006414625209309634 - 3.203791767250941455e-1025j)  +/-  (4.28e-252, 4.28e-252j)
| (1.4054949192137777283 + 1.0423968585147342336e-1021j)  +/-  (3.42e-249, 3.42e-249j)
| (-2.2914067078560275968 - 1.2533291697959252519e-1019j)  +/-  (4.52e-247, 4.52e-247j)
| (4.6236346536728669855 - 3.1285912689148171108e-1017j)  +/-  (1.61e-243, 1.61e-243j)
| (6.9552741825275744848 + 1.3844504483955396651e-1024j)  +/-  (1.5e-243, 1.5e-243j)
| (-7.4095681848210223624 - 5.291498386212967136e-1029j)  +/-  (5.27e-244, 5.27e-244j)
| (3.2580959734704169154 + 1.2464694285212291762e-1029j)  +/-  (3.67e-245, 3.67e-245j)
| (2.9306374202572440192 - 2.6489583814696927849e-1033j)  +/-  (1.07e-245, 1.07e-245j)
| (-0.91333920899679258459 - 3.0437593890977438276e-1039j)  +/-  (6.2e-251, 6.2e-251j)
| (-1.1571937124467801947 - 1.6645455346817621669e-1038j)  +/-  (5.39e-250, 5.39e-250j)
| (-2.6082500277726571147 - 2.6005684975515339356e-1034j)  +/-  (2.34e-246, 2.34e-246j)
| (-6.527631552315805435 + 1.6124636673663830582e-1030j)  +/-  (2.42e-243, 2.42e-243j)
| (-1.6831336019665544848 - 1.4023735692285856585e-1038j)  +/-  (1.6e-248, 1.6e-248j)
| (-3.9287005761714112393 - 3.4494508055347817699e-1032j)  +/-  (3.43e-244, 3.43e-244j)
| (-0.38118699020732211685 + 2.2477373214857205632e-1042j)  +/-  (3.04e-253, 3.04e-253j)
| (3.5906684164216699908 - 1.6839233276616391642e-1032j)  +/-  (1.17e-244, 1.17e-244j)
| (0.38118699020732211685 - 7.4157523574337501832e-1049j)  +/-  (3.04e-253, 3.04e-253j)
| (1.6831336019665544848 - 4.9598479091147797384e-1043j)  +/-  (1.64e-248, 1.64e-248j)
| (-0.12378909617297220692 - 5.5108546888689110309e-1050j)  +/-  (2.09e-254, 2.09e-254j)
| (-1.4054949192137777283 + 5.2055725387026700185e-1044j)  +/-  (3.08e-249, 3.08e-249j)
| (-5.3501128230004757998 - 6.4100993959484623506e-1039j)  +/-  (3.06e-243, 3.06e-243j)
| (0.12378909617297220692 + 1.0762596484221675688e-1053j)  +/-  (2.09e-254, 2.09e-254j)
| (0.91333920899679258459 + 7.9914626541112281398e-1050j)  +/-  (7.04e-251, 7.04e-251j)
| (-5.7286687941616197643 - 2.0961389302947594199e-1048j)  +/-  (3.53e-243, 3.53e-243j)
| (2.6082500277726571147 + 1.7671462924448121461e-1056j)  +/-  (2.32e-246, 2.32e-246j)
| (-0.65006414625209309634 + 1.0894930079887679541e-1064j)  +/-  (4.46e-252, 4.46e-252j)
-------------------------------------------------
The weights are:
| (1.2164365276946802752e-17 + 1.3021051429134999762e-939j)  +/-  (4.32e-74, 3.39e-194j)
| (3.8074784520247755569e-25 + 1.5006759023495206435e-945j)  +/-  (3.11e-79, 2.44e-199j)
| (2.243304259125175216e-28 - 2.3183150236484270825e-946j)  +/-  (4.63e-80, 3.64e-200j)
| (2.3091649695354606894e-09 - 4.2852633387070536006e-936j)  +/-  (6.34e-68, 4.98e-188j)
| (3.1895065215868745821e-32 + 1.7615790241250159286e-948j)  +/-  (1.09e-81, 8.58e-202j)
| (7.7956347142935141052e-14 - 2.0425845922125661622e-939j)  +/-  (2.83e-74, 2.22e-194j)
| (1.2164365276946802752e-17 - 1.6135216996481297261e-941j)  +/-  (5.12e-77, 4.02e-197j)
| (3.5868142860352101021e-37 - 3.7731462355032271522e-951j)  +/-  (8.95e-85, 7.02e-205j)
| (3.1895065215868745821e-32 + 2.8182346292350954181e-949j)  +/-  (1.37e-84, 1.07e-204j)
| (7.3446165172080550517e-20 + 1.0080333121862053252e-942j)  +/-  (7.11e-79, 5.58e-199j)
| (0.035311937291844305446 + 2.6861178651098049285e-931j)  +/-  (2.46e-50, 1.93e-170j)
| (3.5868142860352101021e-37 - 7.4165331668108172732e-952j)  +/-  (1.3e-86, 1.02e-206j)
| (4.5687067649120417317e-06 + 2.8535469533136159648e-934j)  +/-  (7.78e-69, 6.11e-189j)
| (3.413832649897968401e-05 - 9.8172889454246610163e-934j)  +/-  (2.43e-67, 1.9e-187j)
| (2.427483592436574065e-22 - 7.3292251752508955534e-943j)  +/-  (3.34e-82, 2.62e-202j)
| (1.2131862529036080619e-15 + 2.017595355165013484e-940j)  +/-  (3.77e-78, 2.96e-198j)
| (0.0033924475360978049269 + 2.809581244058519627e-932j)  +/-  (5.51e-63, 4.32e-183j)
| (1.0394555655659256404e-10 + 8.8367937985920905209e-937j)  +/-  (2.86e-75, 2.25e-195j)
| (4.7582338456961772205e-07 - 7.6778210724721686931e-935j)  +/-  (5.33e-71, 4.19e-191j)
| (2.3091649695354606894e-09 + 7.6173511353976734346e-937j)  +/-  (2.35e-76, 1.84e-196j)
| (0.0033924475360978049269 - 1.4351706097285373695e-932j)  +/-  (1.73e-66, 1.36e-186j)
| (0.00092821727060842069296 + 4.3778452574157865517e-933j)  +/-  (1.38e-68, 1.08e-188j)
| (3.3931668633249807455e-12 - 1.678369469888110304e-937j)  +/-  (5.27e-78, 4.13e-198j)
| (3.8097526979784468894e-08 - 4.138045744800432401e-936j)  +/-  (5.72e-76, 4.49e-196j)
| (3.3931668633249807455e-12 + 1.7201050151459369257e-938j)  +/-  (1.1e-78, 8.66e-199j)
| (2.243304259125175216e-28 - 2.9448967376244530331e-947j)  +/-  (1.92e-87, 1.5e-207j)
| (0.099671454979258490807 + 5.8604537304997576254e-931j)  +/-  (6.2e-65, 4.86e-185j)
| (0.020557963800139121903 - 1.2591880878285493833e-931j)  +/-  (1.13e-66, 8.83e-187j)
| (0.00092821727060842069296 - 9.6178643752470974369e-933j)  +/-  (4.79e-72, 3.76e-192j)
| (1.0394555655659256404e-10 - 1.230909788258325173e-937j)  +/-  (2.53e-78, 1.98e-198j)
| (2.427483592436574065e-22 - 4.6809761455915760491e-944j)  +/-  (1.64e-84, 1.29e-204j)
| (3.8074784520247755569e-25 + 1.5746832029779220037e-944j)  +/-  (9.25e-89, 7.26e-209j)
| (4.5687067649120417317e-06 - 8.7085219194285565009e-935j)  +/-  (1.13e-76, 8.89e-197j)
| (3.413832649897968401e-05 + 3.4596504347674730833e-934j)  +/-  (6.16e-76, 4.83e-196j)
| (0.062166401597662357787 + 5.7606716956540765307e-931j)  +/-  (7.59e-71, 5.96e-191j)
| (0.035311937291844305446 - 3.9387340112861746473e-931j)  +/-  (6.91e-71, 5.42e-191j)
| (0.00020033272976268151998 + 3.1581511902858766538e-933j)  +/-  (1.7e-75, 1.34e-195j)
| (7.3446165172080550517e-20 + 3.129067187117590398e-941j)  +/-  (6.9e-87, 5.42e-207j)
| (0.0096363234230398311481 - 7.8928565139365993293e-932j)  +/-  (3.43e-74, 2.69e-194j)
| (3.8097526979784468894e-08 + 1.8974725158085983695e-935j)  +/-  (9.94e-80, 7.8e-200j)
| (0.12933565816941122441 + 8.9086740926118992439e-931j)  +/-  (8.38e-73, 6.58e-193j)
| (4.7582338456961772205e-07 + 1.9999426898943700714e-935j)  +/-  (1.07e-78, 8.4e-199j)
| (0.12933565816941122441 - 7.8640105941480743717e-931j)  +/-  (3.15e-73, 2.47e-193j)
| (0.0096363234230398311481 + 4.4879616690945750582e-932j)  +/-  (6.5e-75, 5.1e-195j)
| (0.1387600398314174455 - 1.0204256098058088671e-930j)  +/-  (3.02e-73, 2.37e-193j)
| (0.020557963800139121903 + 2.0099412066953882757e-931j)  +/-  (8.01e-75, 6.28e-195j)
| (7.7956347142935141052e-14 + 3.0424655333855207262e-938j)  +/-  (1.16e-84, 9.13e-205j)
| (0.1387600398314174455 + 9.7996495041404976326e-931j)  +/-  (4.58e-75, 3.57e-195j)
| (0.062166401597662357787 - 4.2645651850214533247e-931j)  +/-  (6.77e-76, 5.25e-196j)
| (1.2131862529036080619e-15 - 6.1061217938880698563e-939j)  +/-  (1.05e-85, 8.25e-206j)
| (0.00020033272976268151998 - 1.2706989424271734138e-933j)  +/-  (7.55e-79, 6.07e-199j)
| (0.099671454979258490807 - 7.2533567660196761998e-931j)  +/-  (6.21e-76, 4.62e-196j)
