Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 11 26
-------------------------------------------------
Trying to find an order 11 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P2 : t^15 - 641/6*t^13 + 29116/7*t^11 - 1045605/14*t^9 + 4515555/7*t^7 - 5082165/2*t^5 + 3863970*t^3 - 2916045/2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^41 - 81565308699484619085528345650708918680856936140982019584978741/132950653289254862646262641431500852295769369208005485227806*t^39 + 497747372175492561609692039078534135554268311327998301331875625404/2947072814578482788658821885064935559222887684110788255883033*t^37 - 23295922296700774368241548116711123022534294088252858783462690584585/842020804165280796759663395732838731206539338317368073109438*t^35 + 151060574776309772365769233588648365756616585625514070934173478559894240/50100237847834207407199972046103904506789090629883400350011561*t^33 - 11602098522581959730682495029168914211170751182098587575278402893503734345/50100237847834207407199972046103904506789090629883400350011561*t^31 + 649020848436876815797981410118453660251848738536211294904084324046383237420/50100237847834207407199972046103904506789090629883400350011561*t^29 - 26954513112757326021841275322456041263574699799636818690186467780707524110685/50100237847834207407199972046103904506789090629883400350011561*t^27 + 839624448001761946773006189607509238889920852423886236146994059238944153522000/50100237847834207407199972046103904506789090629883400350011561*t^25 - 19687673082608000965419295934364353763431493815385658862927201566348699766457000/50100237847834207407199972046103904506789090629883400350011561*t^23 + 346876660444093575128692815286789057802425852753475193880181230578743990736927000/50100237847834207407199972046103904506789090629883400350011561*t^21 - 34293294593487554547463919419052390018252690000688468766779867957443624853294000/376693517652888777497744150722585748171346546089348874812117*t^19 + 19558618085196545375044633009072886995538087797984549540837670439644290239602250/22158442214875810441043773571916808715961561534667580871301*t^17 - 137352796435956291832111593775508664966284005869180708309440798223134602955431875/22158442214875810441043773571916808715961561534667580871301*t^15 + 35854038060978187509385183771036224143425696584013151089207195845965586097342500/1166233800782937391633882819574568879787450607087767414279*t^13 - 2303331797050782858212793939778490233867467902210925633544315678188313305524199375/22158442214875810441043773571916808715961561534667580871301*t^11 + 5046687050932010287900564880071772352558612029946329759747119438006998984060511875/22158442214875810441043773571916808715961561534667580871301*t^9 - 13253860512262349030574541077921420945120111259887550351661271735986697871392605625/44316884429751620882087547143833617431923123069335161742602*t^7 + 4537117322486721691444338985561930770425471857358764301492064010898198992079212500/22158442214875810441043773571916808715961561534667580871301*t^5 - 2329284645744138046761340249564982729481691704347195340502901540001631536171928125/44316884429751620882087547143833617431923123069335161742602*t^3 + 7677806118320347904471325094494563560600144434642240891761869697798015728218750/22158442214875810441043773571916808715961561534667580871301*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:
| (8.6497973426709447971 - 1.5703621676320428329e-930j)  +/-  (1.19e-246, 1.19e-246j)
| (-4.1533469233083435108 - 1.3665941285621957914e-937j)  +/-  (9.78e-247, 9.78e-247j)
| (-7.9114056053046457659 + 2.6802923988493456592e-937j)  +/-  (3.77e-246, 3.77e-246j)
| (10.471932175551820392 - 3.2112840451976582184e-937j)  +/-  (2.46e-248, 2.46e-248j)
| (-10.471932175551820392 - 4.7339485378794190075e-947j)  +/-  (2.54e-248, 2.54e-248j)
| (7.9114056053046457659 + 1.6937819745506821778e-942j)  +/-  (3.72e-246, 3.72e-246j)
| (-4.6879979717656610888 + 1.5723982773770333454e-949j)  +/-  (2.78e-246, 2.78e-246j)
| (-5.2223117617903654322 - 6.3769070769569306431e-949j)  +/-  (8.08e-246, 8.08e-246j)
| (-3.2073341618684212087 - 1.8556802200820525775e-957j)  +/-  (1.08e-247, 1.08e-247j)
| (9.476557875867585899 + 1.8968589763183600984e-955j)  +/-  (2.65e-247, 2.65e-247j)
| (2.3344142183389772393 - 1.8796183719306977629e-965j)  +/-  (4.17e-249, 4.17e-249j)
| (5.2223117617903654322 - 1.1291850981075555119e-966j)  +/-  (7.29e-246, 7.29e-246j)
| (6.0855310803322803494 + 1.8895733314303962396e-980j)  +/-  (1.94e-245, 1.94e-245j)
| (-5.6874369521203121531 - 6.1031790226754335637e-990j)  +/-  (1.8e-245, 1.8e-245j)
| (-8.6497973426709447971 - 4.7892695881774726518e-992j)  +/-  (1.25e-246, 1.25e-246j)
| (1.8463440350640540229 - 1.3050645561203910302e-995j)  +/-  (6.43e-250, 6.43e-250j)
| (-3.6489380961230149524 + 4.6011061097005350527e-993j)  +/-  (3.28e-247, 3.28e-247j)
| (-9.476557875867585899 + 7.4904196797895832426e-993j)  +/-  (2.56e-247, 2.56e-247j)
| (-7.2337996626725418641 - 1.2634267997915359384e-990j)  +/-  (7.78e-246, 7.78e-246j)
| (-6.612633292961629502 - 3.8219783207406049147e-992j)  +/-  (1.43e-245, 1.43e-245j)
| (3.2073341618684212087 - 2.9257725391461920571e-992j)  +/-  (1.15e-247, 1.15e-247j)
| (7.2337996626725418641 - 1.3101252921558884417e-992j)  +/-  (7.57e-246, 7.57e-246j)
| (-6.0855310803322803494 + 1.6452678437385707917e-1005j)  +/-  (1.9e-245, 1.9e-245j)
| (-1.5154507704216881063 - 1.1624902221892566233e-1010j)  +/-  (1.79e-250, 1.79e-250j)
| (-2.7960625606468181694 + 8.7238310096083306013e-1009j)  +/-  (2.81e-248, 2.81e-248j)
| (6.612633292961629502 - 6.8762647272488161692e-1005j)  +/-  (1.55e-245, 1.55e-245j)
| (1.2478638457137761474 + 2.3526600368235283702e-1024j)  +/-  (2.79e-251, 2.79e-251j)
| (4.6879979717656610888 + 1.3802444824822061034e-1019j)  +/-  (2.99e-246, 2.99e-246j)
| (3.6489380961230149524 - 6.7381010634033319966e-1034j)  +/-  (3.53e-247, 3.53e-247j)
| (-2.3344142183389772393 - 3.3411957872685289523e-1046j)  +/-  (3.82e-249, 3.82e-249j)
| (5.6874369521203121531 - 1.0305586896770712389e-1044j)  +/-  (1.81e-245, 1.81e-245j)
| (0.082274952397505301878 - 1.9444124214884062141e-1059j)  +/-  (1.02e-254, 1.02e-254j)
| (2.7960625606468181694 - 5.2596897868843929536e-1054j)  +/-  (2.84e-248, 2.84e-248j)
| (1.5154507704216881063 + 9.9156753880207808359e-1057j)  +/-  (1.75e-250, 1.75e-250j)
| (-1.8463440350640540229 - 2.6964235352550816471e-1057j)  +/-  (6.37e-250, 6.37e-250j)
| (-1.2478638457137761474 + 4.2604434064026252425e-1059j)  +/-  (2.94e-251, 2.94e-251j)
| (4.1533469233083435108 - 5.0557291296835034695e-1060j)  +/-  (9.92e-247, 9.92e-247j)
| (0.74196378430272585765 - 2.9583858117814169619e-1066j)  +/-  (4.92e-253, 4.92e-253j)
| (-0.082274952397505301878 + 2.0279371895475149382e-1068j)  +/-  (8.62e-255, 8.62e-255j)
| (5.724974770230078169e-1077 - 2.1723902023380431038e-1077j)  +/-  (2.51e-1075, 2.51e-1075j)
| (-0.74196378430272585765 + 2.1373713418840363774e-1066j)  +/-  (5.2e-253, 5.2e-253j)
-------------------------------------------------
The weights are:
| (1.753149077662454026e-17 + 1.4750058999901654086e-946j)  +/-  (1.55e-86, 1.12e-209j)
| (3.7569940671571502991e-05 + 5.5607287734564855084e-940j)  +/-  (2.04e-74, 1.48e-197j)
| (7.2119197096915811912e-15 - 7.7261804038553285828e-947j)  +/-  (1.08e-85, 7.86e-209j)
| (7.0469926265505642987e-25 - 6.0054132219546923e-952j)  +/-  (1.62e-90, 1.18e-213j)
| (7.0469926265505642987e-25 + 5.7343239075325487712e-953j)  +/-  (6.42e-91, 4.66e-214j)
| (7.2119197096915811912e-15 - 1.727706005687382814e-945j)  +/-  (9.43e-86, 6.85e-209j)
| (3.6423071125325777697e-06 - 1.0512367444084549383e-940j)  +/-  (1.27e-77, 9.23e-201j)
| (2.470174584759377812e-07 + 2.1012359789935180831e-941j)  +/-  (1.61e-79, 1.17e-202j)
| (0.00095338511449799013315 + 1.2700108720057617393e-938j)  +/-  (3.01e-73, 2.18e-196j)
| (1.1192090918693288516e-20 + 3.8094202711551193985e-949j)  +/-  (2.01e-89, 1.46e-212j)
| (0.012678490771994217168 + 1.7720369139969408768e-937j)  +/-  (5.97e-72, 4.33e-195j)
| (2.470174584759377812e-07 + 8.4257090971740998614e-941j)  +/-  (1.53e-82, 1.11e-205j)
| (1.6309625331511297196e-09 + 5.1667453475372032314e-942j)  +/-  (2.39e-84, 1.74e-207j)
| (1.5104676003528410374e-08 - 4.8909140202353470862e-942j)  +/-  (5.6e-83, 4.07e-206j)
| (1.753149077662454026e-17 + 1.5957548070044234838e-948j)  +/-  (2.98e-90, 2.17e-213j)
| (0.03439633600094567917 - 6.3789316341589261104e-937j)  +/-  (3.82e-73, 2.77e-196j)
| (0.00024483564172599308379 - 3.0680682156480232524e-939j)  +/-  (1.19e-78, 8.61e-202j)
| (1.1192090918693288516e-20 - 1.7416112172720106602e-950j)  +/-  (3.88e-92, 2.82e-215j)
| (1.125796744772847285e-12 + 2.5025190493813039146e-945j)  +/-  (7.24e-88, 5.25e-211j)
| (7.4821438074125983266e-11 - 6.0770593780722610768e-944j)  +/-  (8.78e-87, 6.38e-210j)
| (0.00095338511449799013315 + 2.789942201426280459e-938j)  +/-  (1.9e-83, 1.38e-206j)
| (1.125796744772847285e-12 + 2.7968973176069533345e-944j)  +/-  (2.06e-91, 1.49e-214j)
| (1.6309625331511297196e-09 + 9.0407314439652366156e-943j)  +/-  (5.38e-86, 3.91e-209j)
| (0.019867670444707179534 + 1.0769347138239093821e-936j)  +/-  (1e-78, 7.28e-202j)
| (0.0034568782279986214419 - 3.6366145840101468821e-938j)  +/-  (1.75e-81, 1.27e-204j)
| (7.4821438074125983266e-11 - 4.5327179362350049847e-943j)  +/-  (1.45e-90, 1.05e-213j)
| (0.082926008167029845509 - 1.6375733958097369903e-936j)  +/-  (1.52e-79, 1.1e-202j)
| (3.6423071125325777697e-06 - 3.477282059681249173e-940j)  +/-  (2.27e-88, 1.65e-211j)
| (0.00024483564172599308379 - 7.6729771503098703937e-939j)  +/-  (6.14e-87, 4.46e-210j)
| (0.012678490771994217168 + 1.0152172800956011468e-937j)  +/-  (3.68e-84, 2.67e-207j)
| (1.5104676003528410374e-08 - 2.3512466389672953367e-941j)  +/-  (9.26e-90, 6.72e-213j)
| (1.3071504521974172974 - 2.8688482854188776501e-935j)  +/-  (3.24e-83, 2.36e-206j)
| (0.0034568782279986214419 - 7.1487293447055622456e-938j)  +/-  (7.41e-86, 5.38e-209j)
| (0.019867670444707179534 + 1.5372482653559984535e-936j)  +/-  (6.25e-84, 4.53e-207j)
| (0.03439633600094567917 - 4.1248346541668400847e-937j)  +/-  (7.93e-85, 5.75e-208j)
| (0.082926008167029845509 - 1.2229055023796569709e-936j)  +/-  (1.22e-84, 8.87e-208j)
| (3.7569940671571502991e-05 + 1.6306205210570789322e-939j)  +/-  (3.95e-88, 2.87e-211j)
| (0.16206389477953789319 + 1.4162888826564461711e-936j)  +/-  (2.66e-84, 1.93e-207j)
| (1.3071504521974172974 - 2.8145455544043029391e-935j)  +/-  (2.02e-84, 1.47e-207j)
| (-2.2475588548453805952 + 5.5320215950080026998e-935j)  +/-  (3.97e-84, 2.89e-207j)
| (0.16206389477953789319 + 1.1915593546665020317e-936j)  +/-  (6.01e-86, 4.24e-209j)
