Starting with polynomial:
P : t
Extension levels are: 1 26 44
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 44 Kronrod extension for:
P2 : t^27 - 351*t^25 + 52650*t^23 - 4440150*t^21 + 233107875*t^19 - 7972289325*t^17 + 180705224700*t^15 - 2710578370500*t^13 + 26428139112375*t^11 - 161505294575625*t^9 + 581419060472250*t^7 - 1109981842719750*t^5 + 924984868933125*t^3 - 213458046676875*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^71 - 4123964009500291191467339877579250750572776110737902471/2240758616243123085684006629009389718779104141555315*t^69 + 34514262837776522421562868222626572476723230787851278255509/21660666623683523161612064080424100614864673368368045*t^67 - 18710719957878528493623522133643707173833469137439908003111421/21660666623683523161612064080424100614864673368368045*t^65 + 12838209301807615934473375915717648658379516107588801631523733008/38989199922630341690901715344763381106756412063062481*t^63 - 407044923925804776417985041172795281241751399267136971128366053808/4332133324736704632322412816084820122972934673673609*t^61 + 90384633668591656742320829471237080852973550660468715915996397821440/4332133324736704632322412816084820122972934673673609*t^59 - 16028582397140446373687793616773406029952216747120516722543644271680480/4332133324736704632322412816084820122972934673673609*t^57 + 2311916470748906146748325099809539984484902576856328388483248659429609460/4332133324736704632322412816084820122972934673673609*t^55 - 274829207072733725614722796939341817591141541685617786365695523874036655300/4332133324736704632322412816084820122972934673673609*t^53 + 27187950100296078161249906112792334065754802875380155885335254473325168279300/4332133324736704632322412816084820122972934673673609*t^51 - 2254233106087730440945742337822937991373960067923366992368998084134662885357380/4332133324736704632322412816084820122972934673673609*t^49 + 157453244771730433843976954963786225401783322038613087840535883418036233009943040/4332133324736704632322412816084820122972934673673609*t^47 - 9297426481741861778842199683555269079121393316199958638071094740712071456385976160/4332133324736704632322412816084820122972934673673609*t^45 + 465136465982543801443204286991112241894160394371057667760749084381842690865928890800/4332133324736704632322412816084820122972934673673609*t^43 - 19735519169719483597586902347738266588255208739080662086749242150244272176296676285200/4332133324736704632322412816084820122972934673673609*t^41 + 7979308925396850156564933492479818939423108858249673213321870674551797184310042905150/48675655334120276767667559731290113741268928917681*t^39 - 21650085208211454017648540651770639051305810694751606654350953236676335414267230400810550/4332133324736704632322412816084820122972934673673609*t^37 + 558085886563640018492183961980901012262705839073958491029344648997280769506019190802843950/4332133324736704632322412816084820122972934673673609*t^35 - 12128112375119393737605047137574470187275254466887182724563640575331624399735997959223506750/4332133324736704632322412816084820122972934673673609*t^33 + 221310385758720526754558933750039943225971705027055619465963410037543648264245307516966122000/4332133324736704632322412816084820122972934673673609*t^31 - 116334174610393105298593454470369854042654895180321660087706430007570143911024700400234254000/149383907749541539045600441933959314585273609437021*t^29 + 1472101988820776017968337966727388311096356114553461352388335118175401266231959797750829932000/149383907749541539045600441933959314585273609437021*t^27 - 15342527934682164393236066871107409603590663129191995055731284026977603195365911910555688768000/149383907749541539045600441933959314585273609437021*t^25 + 130447974532112432627352129312910736533617070654296092590531260339671243872072180117528017112500/149383907749541539045600441933959314585273609437021*t^23 - 894334712279164654497106010300332537842975358030007534846373093111653948663883442349718079762500/149383907749541539045600441933959314585273609437021*t^21 + 4873985380719908048108809849010843369194298687727522536169860366324692908051910551159536826262500/149383907749541539045600441933959314585273609437021*t^19 - 20745200878386462060239564073386225314902326576427237767077255099881565400746082998136510288662500/149383907749541539045600441933959314585273609437021*t^17 + 67448403248926258458950443543574760909157150763463276732512597213308934807832621126983071551900000/149383907749541539045600441933959314585273609437021*t^15 - 162823102363085784062261081149164667225076625647560258014779597528582801291801184210064849194000000/149383907749541539045600441933959314585273609437021*t^13 + 281129482361872152330769821872370603455148317094298814224819080950518819088113913841708759234750000/149383907749541539045600441933959314585273609437021*t^11 - 329782524860073298907026655626025396261929597637207706019901821517251721139773398520900051885250000/149383907749541539045600441933959314585273609437021*t^9 + 243734256325537179260809527851432366121649351663547109413691906594921650236014583162728743806453125/149383907749541539045600441933959314585273609437021*t^7 - 100273154854445507169319688790360148108481168327445002320009670519331115914909285988167113044640625/149383907749541539045600441933959314585273609437021*t^5 + 201833253874725784362905665900184266125232413344988491373312343815555575094758059701198079453125/1678470873590354371298881370044486680733411341989*t^3 - 698702956871074888834996210496515643563832302762889908059187431739722314206534208591870404453125/149383907749541539045600441933959314585273609437021*t
-------------------------------------------------
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
  current precision for roots: 848
  current precision for roots: 1696
 current precision for weights: 848
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   71 out of 71
Indefinite weights: 0 out of 71
Negative weights:   0 out of 71
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (13.246952573787508943 + 2.8517281567474992257e-1799j)  +/-  (4.23e-498, 4.23e-498j)
| (10.645310900314863743 - 1.1409751570113271094e-1795j)  +/-  (3.95e-495, 3.95e-495j)
| (-11.220241488596528538 - 1.9261189268030009297e-1794j)  +/-  (1.13e-495, 1.13e-495j)
| (-12.499785620710159689 + 6.1054415665073699717e-1801j)  +/-  (4.27e-497, 4.27e-497j)
| (-10.101337057107179481 + 2.3825408972538624913e-1806j)  +/-  (1.24e-494, 1.24e-494j)
| (9.5867424107933855284 + 4.6334721327682892601e-1814j)  +/-  (3.6e-494, 3.6e-494j)
| (3.9762470746861553347 + 1.0251251721266614174e-1822j)  +/-  (1.25e-497, 1.25e-497j)
| (14.150136705026530543 + 3.4466891650798330746e-1826j)  +/-  (1.67e-499, 1.67e-499j)
| (-4.6599938778445346808 - 4.2632500417533113835e-1822j)  +/-  (1.78e-496, 1.78e-496j)
| (6.4161549345621731946 + 1.7513697488297386739e-1819j)  +/-  (1.16e-494, 1.16e-494j)
| (8.5230510906052109115 + 7.3861052389908589849e-1829j)  +/-  (1.16e-493, 1.16e-493j)
| (-8.5230510906052109115 + 7.0379537460453356671e-1854j)  +/-  (1.18e-493, 1.18e-493j)
| (-10.645310900314863743 + 2.4568748262009016868e-1871j)  +/-  (3.99e-495, 3.99e-495j)
| (-1.4459446453555826206 - 1.2117478763456855562e-1887j)  +/-  (2.3e-504, 2.3e-504j)
| (-2.6927334418055497035 + 2.6062810591026241353e-1884j)  +/-  (1.65e-500, 1.65e-500j)
| (2.1546237674199220206 - 1.5648181894338932701e-1885j)  +/-  (4.38e-502, 4.38e-502j)
| (7.6331224083930074584 - 4.8870311794824057322e-1876j)  +/-  (3.97e-494, 3.97e-494j)
| (-14.150136705026530543 + 7.2912652405579601891e-1886j)  +/-  (1.6e-499, 1.6e-499j)
| (-8.0783492745341676988 - 1.5171840460043283077e-1889j)  +/-  (6.1e-494, 6.1e-494j)
| (2.6927334418055497035 - 1.2454459626237568624e-1908j)  +/-  (1.47e-500, 1.47e-500j)
| (11.833670148180757562 + 5.468362571868485323e-1904j)  +/-  (2.63e-496, 2.63e-496j)
| (10.101337057107179481 + 2.3711741613400542114e-1901j)  +/-  (1.17e-494, 1.17e-494j)
| (12.499785620710159689 + 5.2129236345571241924e-1907j)  +/-  (4.06e-497, 4.06e-497j)
| (-11.833670148180757562 - 7.0697511913266989889e-1904j)  +/-  (2.74e-496, 2.74e-496j)
| (-5.324045352108998622 - 1.882140850151316942e-1903j)  +/-  (1.21e-495, 1.21e-495j)
| (9.1244212506729358783 - 9.6242156759452905337e-1903j)  +/-  (1.06e-493, 1.06e-493j)
| (6.048728392526296704 - 2.3462498411408886582e-1906j)  +/-  (6.49e-495, 6.49e-495j)
| (4.9869064106798010371 - 1.6221763137233266255e-1911j)  +/-  (4.74e-496, 4.74e-496j)
| (-9.5867424107933855284 + 1.168111499944409153e-1909j)  +/-  (3.47e-494, 3.47e-494j)
| (-7.6331224083930074584 - 1.1009445044341414021e-1924j)  +/-  (4.08e-494, 4.08e-494j)
| (8.0783492745341676988 + 6.599600568213040953e-1933j)  +/-  (6.16e-494, 6.16e-494j)
| (-6.048728392526296704 + 3.4950557051637708942e-1933j)  +/-  (6.43e-495, 6.43e-495j)
| (3.6704729864924044791 - 1.0718723801504541415e-1942j)  +/-  (3.33e-498, 3.33e-498j)
| (11.220241488596528538 + 2.1053558704449947212e-1941j)  +/-  (1.2e-495, 1.2e-495j)
| (-5.6827607616290614623 - 3.7329645714964402653e-1938j)  +/-  (3e-495, 3e-495j)
| (-1.8060452131386712366 + 5.5149832041991744784e-1948j)  +/-  (2.69e-503, 2.69e-503j)
| (-6.7975966363076879068 + 6.0610131398059942133e-1938j)  +/-  (2.06e-494, 2.06e-494j)
| (4.3184176719366875248 - 2.5005508784506035893e-1953j)  +/-  (4.93e-497, 4.93e-497j)
| (-4.9869064106798010371 + 4.9231974698481962113e-1951j)  +/-  (5.53e-496, 5.53e-496j)
| (-7.2038766119106394825 - 2.3629769695191988954e-1949j)  +/-  (2.92e-494, 2.92e-494j)
| (-13.246952573787508943 - 3.41354457128369608e-1962j)  +/-  (4.04e-498, 4.04e-498j)
| (-6.4161549345621731946 + 1.5985274795110223566e-1961j)  +/-  (1.1e-494, 1.1e-494j)
| (8.8515706346301230453 + 1.4627825761574094818e-1970j)  +/-  (1.67e-493, 1.67e-493j)
| (4.6599938778445346808 + 2.4871624609148376344e-1982j)  +/-  (1.73e-496, 1.73e-496j)
| (5.324045352108998622 - 9.598842434718891502e-1981j)  +/-  (1.19e-495, 1.19e-495j)
| (-3.9762470746861553347 - 4.7852287128508405652e-1983j)  +/-  (1.34e-497, 1.34e-497j)
| (-2.4176839831625435769 + 1.4878485066409686517e-1997j)  +/-  (2.96e-501, 2.96e-501j)
| (1.4459446453555826206 + 4.6617999008164278839e-2002j)  +/-  (2.27e-504, 2.27e-504j)
| (1.2006833545499806979 + 6.5573836932043341327e-2003j)  +/-  (3.65e-505, 3.65e-505j)
| (-3.0381502518710366553 - 7.2967215790541737183e-1992j)  +/-  (9.97e-500, 9.97e-500j)
| (-8.8515706346301230453 + 5.163126963277976839e-1994j)  +/-  (1.71e-493, 1.71e-493j)
| (7.2038766119106394825 - 4.9537070184025615294e-2012j)  +/-  (3.07e-494, 3.07e-494j)
| (3.0381502518710366553 - 1.1739060918079094258e-2022j)  +/-  (1.01e-499, 1.01e-499j)
| (0.96383958925799246023 + 1.0039691411104414385e-2028j)  +/-  (3.57e-506, 3.57e-506j)
| (-0.96383958925799246023 + 1.0860344897177638545e-2029j)  +/-  (3.67e-506, 3.67e-506j)
| (6.7975966363076879068 - 4.5559007260571764117e-2017j)  +/-  (1.93e-494, 1.93e-494j)
| (-4.3184176719366875248 - 6.3642720358664579245e-2021j)  +/-  (5.17e-497, 5.17e-497j)
| (-3.6704729864924044791 + 5.8077285491246902171e-2022j)  +/-  (3.53e-498, 3.53e-498j)
| (5.6827607616290614623 - 3.1704231301461924973e-2023j)  +/-  (2.92e-495, 2.92e-495j)
| (0.59935488078998477575 + 8.3240837199666760396e-2040j)  +/-  (8.3e-508, 8.3e-508j)
| (1.8060452131386712366 - 2.2111801016154249475e-2035j)  +/-  (2.63e-503, 2.63e-503j)
| (-1.2006833545499806979 + 2.6051128336148332894e-2037j)  +/-  (4.26e-505, 4.26e-505j)
| (-3.375773401238072737 - 2.8045639311801320308e-2031j)  +/-  (7.29e-499, 7.29e-499j)
| (-9.1244212506729358783 + 1.3182808352642191777e-2039j)  +/-  (1.14e-493, 1.14e-493j)
| (-0.22892693224107493006 - 1.59657394703012468e-2063j)  +/-  (3.72e-509, 3.72e-509j)
| (2.4176839831625435769 + 1.2906155120479927998e-2055j)  +/-  (3.18e-501, 3.18e-501j)
| (-2.1546237674199220206 - 4.7527039915383588365e-2057j)  +/-  (4.8e-502, 4.8e-502j)
| (-0.59935488078998477575 - 3.7525596500489633966e-2062j)  +/-  (8.63e-508, 8.63e-508j)
| (3.8623482756133560525e-2093 + 1.5682429170154416214e-2091j)  +/-  (1.11e-2089, 1.11e-2089j)
| (3.375773401238072737 - 1.8636547423462817919e-2057j)  +/-  (7.55e-499, 7.55e-499j)
| (0.22892693224107493006 - 1.1894309136812290182e-2066j)  +/-  (2.91e-509, 2.91e-509j)
-------------------------------------------------
The weights are:
| (2.5190487503878494076e-39 - 9.5569855265370344237e-1830j)  +/-  (1.5e-183, 2.24e-430j)
| (5.4995138193328032404e-26 + 4.541147880642145747e-1820j)  +/-  (5.91e-177, 8.83e-424j)
| (1.086651747580477608e-28 - 1.5143518663475560612e-1821j)  +/-  (8.2e-180, 1.23e-426j)
| (3.2952723011274121237e-35 + 1.3900848561516031181e-1826j)  +/-  (2.57e-183, 3.84e-430j)
| (1.4719744950923565439e-23 - 5.5197339124402047496e-1819j)  +/-  (5.12e-177, 7.65e-424j)
| (2.1907361259294111108e-21 + 1.3356431013723790259e-1817j)  +/-  (5.98e-176, 8.93e-423j)
| (4.843212401428029878e-05 - 4.284041477627890407e-1806j)  +/-  (9.83e-153, 1.47e-399j)
| (1.3832863553192683137e-44 + 5.5056762198591117817e-1833j)  +/-  (1.17e-187, 1.75e-434j)
| (2.5555616445254239506e-06 - 4.6967665234645132887e-1807j)  +/-  (1.42e-158, 2.12e-405j)
| (1.7047480523948158652e-10 + 1.800288979363566915e-1810j)  +/-  (2.69e-166, 4.02e-413j)
| (2.8584979679956462728e-17 - 8.372965233396939017e-1815j)  +/-  (2.6e-173, 3.89e-420j)
| (2.8584979679956462728e-17 - 1.1608764657283795408e-1814j)  +/-  (3.44e-175, 5.14e-422j)
| (5.4995138193328032404e-26 + 2.2124960806095618157e-1820j)  +/-  (3.4e-180, 5.07e-427j)
| (0.047171510003564886746 - 1.6275913647279894541e-1803j)  +/-  (4.27e-132, 6.38e-379j)
| (0.0034555781177128993524 - 1.816830824518983003e-1804j)  +/-  (1.87e-147, 2.8e-394j)
| (0.012364282699326593069 - 4.7017299676614911038e-1804j)  +/-  (1.05e-142, 1.57e-389j)
| (3.8993256749580877621e-14 - 4.1262629763564303391e-1813j)  +/-  (3.08e-172, 4.61e-419j)
| (1.3832863553192683137e-44 + 1.7128010498300753108e-1832j)  +/-  (1.31e-190, 1.96e-437j)
| (1.2107695452685224286e-15 + 7.1827487831492041851e-1814j)  +/-  (2.09e-174, 3.12e-421j)
| (0.0034555781177128993524 - 1.5819199213342171611e-1804j)  +/-  (1.28e-149, 1.91e-396j)
| (9.9180320924307222936e-32 - 9.4169072199312662634e-1825j)  +/-  (1.31e-184, 1.96e-431j)
| (1.4719744950923565439e-23 - 5.8092523169897863172e-1819j)  +/-  (7.38e-180, 1.1e-426j)
| (3.2952723011274121237e-35 + 4.1602743533752456001e-1827j)  +/-  (2.43e-186, 3.63e-433j)
| (9.9180320924307222936e-32 - 4.0128923135396155406e-1824j)  +/-  (2.85e-186, 4.25e-433j)
| (9.752625198450785774e-08 - 3.3796544733097176059e-1808j)  +/-  (2.02e-169, 3.02e-416j)
| (1.3282549926230348833e-19 - 3.7043344696876719475e-1816j)  +/-  (1.05e-177, 1.57e-424j)
| (1.657410114767693126e-09 - 1.0145176357406223572e-1809j)  +/-  (1.09e-170, 1.62e-417j)
| (5.1862346028768780271e-07 + 1.0828457347901117536e-1807j)  +/-  (1.16e-167, 1.74e-414j)
| (2.1907361259294111108e-21 + 1.634790482127577416e-1817j)  +/-  (4.95e-182, 7.39e-429j)
| (3.8993256749580877621e-14 - 5.7674217937218867869e-1813j)  +/-  (5.92e-178, 8.85e-425j)
| (1.2107695452685224286e-15 + 5.1339818351593498872e-1814j)  +/-  (9.93e-177, 1.48e-423j)
| (1.657410114767693126e-09 - 1.359289916462070499e-1809j)  +/-  (1.35e-174, 2.01e-421j)
| (0.00013552770907513562153 + 1.227383122452176377e-1805j)  +/-  (4.75e-165, 7.1e-412j)
| (1.086651747580477608e-28 + 1.7267857074224107154e-1822j)  +/-  (5.97e-185, 8.91e-432j)
| (1.4144519366029079262e-08 + 6.9759756046629512728e-1809j)  +/-  (1.42e-173, 2.12e-420j)
| (0.028596352631651867875 + 7.1757666477437574301e-1804j)  +/-  (1.33e-157, 1.98e-404j)
| (1.4515458673450920112e-11 - 3.7279692561067288265e-1811j)  +/-  (2.51e-177, 3.75e-424j)
| (1.2372154338403625237e-05 + 1.232801913373428401e-1806j)  +/-  (2.66e-170, 3.98e-417j)
| (5.1862346028768780271e-07 + 1.3884781142196087522e-1807j)  +/-  (1.19e-172, 1.78e-419j)
| (8.9911284752761203736e-13 + 4.8180189867880010954e-1812j)  +/-  (1.65e-178, 2.47e-425j)
| (2.5190487503878494076e-39 - 2.9845669071686938773e-1829j)  +/-  (9.77e-196, 1.46e-442j)
| (1.7047480523948158652e-10 + 2.4440005196845017663e-1810j)  +/-  (1.86e-176, 2.78e-423j)
| (8.2279095412414385696e-19 + 2.1150619825745923322e-1815j)  +/-  (7.27e-183, 1.09e-429j)
| (2.5555616445254239506e-06 - 3.717373311950218732e-1807j)  +/-  (2.54e-174, 3.8e-421j)
| (9.752625198450785774e-08 - 2.5972555319329888098e-1808j)  +/-  (2.06e-176, 3.07e-423j)
| (4.843212401428029878e-05 - 5.241697702819229791e-1806j)  +/-  (9.21e-175, 1.38e-421j)
| (0.0049871314254789840684 + 3.8545869097749054966e-1804j)  +/-  (5.22e-170, 7.8e-417j)
| (0.047171510003564886746 - 1.5102077056168326234e-1803j)  +/-  (3.61e-166, 5.39e-413j)
| (0.032040300554836178222 + 2.6096513254274160817e-1803j)  +/-  (9.93e-165, 1.48e-411j)
| (0.0013885460717841200731 + 6.7050582208625567858e-1805j)  +/-  (1.51e-172, 2.26e-419j)
| (8.2279095412414385696e-19 + 2.8829562684942193036e-1815j)  +/-  (2.8e-185, 4.18e-432j)
| (8.9911284752761203736e-13 + 3.4710064438051252752e-1812j)  +/-  (3.61e-182, 5.39e-429j)
| (0.0013885460717841200731 + 5.7378772420893561563e-1805j)  +/-  (2.21e-174, 3.3e-421j)
| (0.083413215790777066472 - 2.4831690592435079527e-1803j)  +/-  (5.42e-169, 8.1e-416j)
| (0.083413215790777066472 - 2.6103982241315801144e-1803j)  +/-  (9.21e-170, 1.38e-416j)
| (1.4515458673450920112e-11 - 2.7133977094953083461e-1811j)  +/-  (2.24e-181, 3.35e-428j)
| (1.2372154338403625237e-05 + 1.5330980816442342551e-1806j)  +/-  (3.19e-177, 4.76e-424j)
| (0.00013552770907513562153 + 1.4797142735373756816e-1805j)  +/-  (1.22e-176, 1.82e-423j)
| (1.4144519366029079262e-08 + 5.2815493977525395213e-1809j)  +/-  (4.39e-180, 6.57e-427j)
| (0.12593573166226323326 + 2.1358234162721296144e-1803j)  +/-  (3.04e-172, 4.53e-419j)
| (0.028596352631651867875 + 6.5361686785408946082e-1804j)  +/-  (6.29e-174, 9.37e-421j)
| (0.032040300554836178222 + 2.777145302273167944e-1803j)  +/-  (3.69e-173, 5.46e-420j)
| (0.00042261810704884475037 - 3.1341183263767334233e-1805j)  +/-  (2e-176, 2.98e-423j)
| (1.3282549926230348833e-19 - 4.9253438060183560884e-1816j)  +/-  (2.77e-188, 4.18e-435j)
| (0.13446799548390881431 - 3.8740316005673972333e-1803j)  +/-  (3.29e-174, 4.82e-421j)
| (0.0049871314254789840684 + 3.4031836057322428759e-1804j)  +/-  (6.27e-176, 9.46e-423j)
| (0.012364282699326593069 - 5.2546270108460212342e-1804j)  +/-  (3.87e-175, 5.62e-422j)
| (0.12593573166226323326 + 2.2032754837191041465e-1803j)  +/-  (1.17e-174, 1.7e-421j)
| (0.051114435530005607035 + 5.3599408242686722737e-1803j)  +/-  (8.05e-175, 1.17e-421j)
| (0.00042261810704884475037 - 2.6374895808076391145e-1805j)  +/-  (7.63e-178, 1.3e-424j)
| (0.13446799548390881431 - 3.8282788201894766918e-1803j)  +/-  (4.38e-175, 6.06e-422j)
