Starting with polynomial:
P : 5/2*t^3 - 3/2*t
Extension levels are: 3 4 44
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 5/2*t^3 - 3/2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 44 Kronrod extension for:
P2 : 5/2*t^7 - 77/18*t^5 + 3745/1782*t^3 - 155/594*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 5/2*t^51 - 87157768709928771194357939184929783610143786534267915126581749199354139/2690727698521596296935171052557073291089951689799433655268138047981726*t^49 + 43267204038346311571647579019817530963520159893546384094953455286976197245169/218832847629213644435292058947887935154409136003853240032474765235281802991*t^47 - 32254554130744025923439259821001714782454802675081033356644577889772318027359363/42672405287696660664881951494838147355109781520751381806332579220879951583245*t^45 + 15571441737448625434794346201765954963375263236063292914842930365310283427679166/7672412263848490503382815521294131544656102132013884809623433435673365032139*t^43 - 7359302217867218133121574426394387966089926209021165004717099630041362994085946/1808942728874847354456110976565283047114040340068314304707963980768516958797*t^41 + 3546553875491207850863028171877051766588247707449289702542365180148503128734453/561396019305987110003620647899570600828495277952235473874885373341953538937*t^39 - 14192910512446349295969423454870673329588580235487087446802157615806179362325527/1823590038420392677164257624148807606199983986546600250495073000855711428099*t^37 + 1268471029082309045353506992530806553219635026721248771918608772315274175984500247/164123103457835340944783186173392684557998558789194022544556570077014028528910*t^35 - 3740702705370324148531084593005615739868063705028667947887807854242272629893809163/598418084915491935444824848047601019080702437431368974508613955511574227097718*t^33 + 5373083201101975705561816241973815997582596213144411555928462991425246933545947198/1296572517316899193463787170769802208008188614434632778101996903608410825378389*t^31 - 1417278446093272873149120108146613810640474505772937287577398461018629829246721982/627373798701725416192155082630549455487833200532886828113869469487940721957285*t^29 + 4799751532702715393098438106301104475040187307526532060754511552689927110828362888/4737753859161305729175240106761735543166740376438007426101290131650310969263635*t^27 - 19658568705338217890536882387459028077056106865860370232601964206436238655015980232/52709198917449854337405449051010191726684105897408601136539994199699328589670925*t^25 + 1025031479584503678543521489183322060305320139942293071613523123318956389218571086/9136261145691308085150277835508433232625245022217490863666932327947883622209627*t^23 - 13710359233365252366378039708417414068863587710953877402460198106844741665493660846/500833224622896252304147048619235021752092977127013362799196381250233984017491371*t^21 + 23271377079655981912440393006389403331774951210116874615802286512670252757211776883/4340554613398434186635941088033370188518139135100782477593035304168694528151591882*t^19 - 3606589257185133176097220949018082877795876377285020906759294767126476548529246755/4340554613398434186635941088033370188518139135100782477593035304168694528151591882*t^17 + 198543610937890716967931816624744863712501779513662268587288052277734059569283066869/1985803735629783640385943047775266861247048654308607983498813651657177746629353286015*t^15 - 71125757156588933150984482496431809800691441247881434364255326897370770860092350633/7810828026810482318851375987916049654238391373613858068428667029851565803408789591659*t^13 + 292511554677141866221212020799161428617757984562640069104798265361061867865112414/482358827224482656743801117346928310175068589703130996641857010510876761423944752681*t^11 - 2890779432750129104819915259917384709511883105566212976397164074008457644300643550/102742430198814805886429637994895730067289609606766902284715543238816750183300232321053*t^9 + 39437595548340037728534014189422904662463831808635840326070841896721884303310757/46541442739634057367357015501961313620225207770586716419571998219293057775341130880477*t^7 - 4979948976621184528563777067019762877364265697520823746570317926635234836928189/336132642008468192097578445291942820590515389454237396363575542694894306155241500803445*t^5 + 4919343983943102954468925253149049590545009521558149302125725159088398397675803/39932557870606021221192319300682807086153228267163402687992774472153443571242690295449266*t^3 - 4099417174662853911847807282507809633367099946261884062700565068421535260777/13310852623535340407064106433560935695384409422387800895997591490717814523747563431816422*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: 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:
| (0.99905441308740210245 - 1.398523717730821889e-879j)  +/-  (1.13e-237, 1.13e-237j)
| (-0.9949208746921766185 + 3.3421208683775074895e-889j)  +/-  (2.92e-237, 2.92e-237j)
| (-0.91899265143257804311 + 2.3275536600428290839e-901j)  +/-  (1.23e-237, 1.23e-237j)
| (-0.49089683734372844131 - 3.1771698411526217431e-915j)  +/-  (1.76e-245, 1.76e-245j)
| (0.91899265143257804311 + 2.3929016550202393495e-906j)  +/-  (1.15e-237, 1.15e-237j)
| (0.94150076402621432443 + 1.1456232208845801669e-906j)  +/-  (1.96e-237, 1.96e-237j)
| (-0.99905441308740210245 + 9.4266474862348610276e-904j)  +/-  (1.05e-237, 1.05e-237j)
| (-0.89339912240291804607 - 7.0521026954768443047e-917j)  +/-  (6.95e-238, 6.95e-238j)
| (-0.77459666924148337704 - 1.4940167510339782886e-923j)  +/-  (9.64e-240, 9.64e-240j)
| (-0.97575567907989692765 - 3.5861138489519779149e-923j)  +/-  (3.82e-237, 3.82e-237j)
| (0.89339912240291804607 - 1.0228680386675335524e-932j)  +/-  (6.67e-238, 6.67e-238j)
| (0.96049126870802028342 - 2.7847108669161511059e-933j)  +/-  (3.37e-237, 3.37e-237j)
| (-0.064203956686681625733 + 5.8256630686899025772e-954j)  +/-  (2.6e-254, 2.6e-254j)
| (-0.86562390118846295555 - 7.8366183421794497934e-936j)  +/-  (3.25e-238, 3.25e-238j)
| (0.98721689144822372738 - 7.6206770971308040641e-937j)  +/-  (4.13e-237, 4.13e-237j)
| (0.80785683693812518704 - 2.2686116265881009204e-943j)  +/-  (4.57e-239, 4.57e-239j)
| (0.83713809943853406076 + 8.756300714210504345e-943j)  +/-  (1.36e-238, 1.36e-238j)
| (0.9949208746921766185 - 1.1515021520349519861e-941j)  +/-  (3.14e-237, 3.14e-237j)
| (-0.80785683693812518704 - 3.6056078919591426748e-940j)  +/-  (4.72e-239, 4.72e-239j)
| (-0.98721689144822372738 - 6.2434504396791491362e-943j)  +/-  (3.99e-237, 3.99e-237j)
| (0.86562390118846295555 - 1.7708737825402947127e-960j)  +/-  (3.28e-238, 3.28e-238j)
| (0.77459666924148337704 + 4.4201192674498055573e-965j)  +/-  (9.57e-240, 9.57e-240j)
| (-0.94150076402621432443 - 1.1284417003371801467e-960j)  +/-  (2.11e-237, 2.11e-237j)
| (-0.73612040435187543268 - 7.5886231664383092402e-980j)  +/-  (1.6e-240, 1.6e-240j)
| (-0.96049126870802028342 - 2.4523986573012880378e-984j)  +/-  (3.02e-237, 3.02e-237j)
| (0.25409192597105399968 + 6.6185836549960275224e-1007j)  +/-  (2.64e-250, 2.64e-250j)
| (0.73612040435187543268 - 1.5670500860084589146e-996j)  +/-  (1.6e-240, 1.6e-240j)
| (0.54541424387442191976 - 2.0831982590911765502e-1001j)  +/-  (2.35e-244, 2.35e-244j)
| (-0.83713809943853406076 + 4.3928877201466999814e-997j)  +/-  (1.42e-238, 1.42e-238j)
| (-0.5975258816308875806 - 4.0198902040762182778e-1000j)  +/-  (2.62e-243, 2.62e-243j)
| (-0.37571742755949298204 - 2.8993618797301261532e-1005j)  +/-  (8.66e-248, 8.66e-248j)
| (0.64693896816340327722 + 2.0717401515901563038e-998j)  +/-  (2.54e-242, 2.54e-242j)
| (0.69330223855507760787 + 1.3530048685519509313e-998j)  +/-  (2.31e-241, 2.31e-241j)
| (0.19152115560738434758 + 5.1823999062853297592e-1011j)  +/-  (1e-251, 1e-251j)
| (-0.64693896816340327722 + 1.2015312733198656658e-999j)  +/-  (2.52e-242, 2.52e-242j)
| (-0.69330223855507760787 + 1.1743130113445140715e-999j)  +/-  (2.11e-241, 2.11e-241j)
| (-3.6830891459882073848e-1020 - 6.5747968184387748948e-1020j)  +/-  (3.84e-1018, 3.84e-1018j)
| (0.5975258816308875806 + 2.0834505059889316583e-1001j)  +/-  (2.66e-243, 2.66e-243j)
| (0.064203956686681625733 + 5.2587621088420281955e-1015j)  +/-  (2.6e-254, 2.6e-254j)
| (-0.31557918131088900878 - 4.0413560291475764855e-1007j)  +/-  (4.36e-249, 4.36e-249j)
| (-0.54541424387442191976 - 1.5530693304225201241e-1002j)  +/-  (2.09e-244, 2.09e-244j)
| (-0.12813502444490821627 - 7.1241392944407067207e-1011j)  +/-  (5.06e-253, 5.06e-253j)
| (0.37571742755949298204 - 2.2467479260113614789e-1006j)  +/-  (8.39e-248, 8.39e-248j)
| (0.434243749346802558 - 3.7165797715162203326e-1007j)  +/-  (1.33e-246, 1.33e-246j)
| (0.97575567907989692765 - 3.2268167901054845225e-1008j)  +/-  (4.27e-237, 4.27e-237j)
| (-0.434243749346802558 - 6.4857466133189944734e-1022j)  +/-  (1.2e-246, 1.2e-246j)
| (-0.25409192597105399968 + 1.2990400393612178586e-1025j)  +/-  (2.54e-250, 2.54e-250j)
| (0.12813502444490821627 + 1.8567991915063705881e-1027j)  +/-  (4.94e-253, 4.94e-253j)
| (0.49089683734372844131 + 8.3907410967095850845e-1021j)  +/-  (1.82e-245, 1.82e-245j)
| (0.31557918131088900878 + 1.0905048355427669241e-1024j)  +/-  (5.1e-249, 5.1e-249j)
| (-0.19152115560738434758 + 3.1745735887104001904e-1028j)  +/-  (1.11e-251, 1.11e-251j)
-------------------------------------------------
The weights are:
| (0.0024394398597399700267 + 1.7085688900624553733e-879j)  +/-  (5.13e-61, 2.13e-175j)
| (0.0058762760419998931994 - 5.5752209629785288669e-882j)  +/-  (2.09e-61, 8.67e-176j)
| (0.024150633192563131571 + 3.6284491243704725618e-881j)  +/-  (1.39e-61, 5.76e-176j)
| (0.055629315787025082165 - 3.1465797177214902162e-881j)  +/-  (1.23e-62, 5.09e-177j)
| (0.024150633192563131571 + 8.6927093270454965053e-880j)  +/-  (4.39e-62, 1.82e-176j)
| (0.020797609592264277592 - 9.0667694291427757254e-880j)  +/-  (4.38e-62, 1.81e-176j)
| (0.0024394398597399700267 + 1.7074219123966165183e-882j)  +/-  (3.97e-62, 1.64e-176j)
| (0.026892555756932373135 - 5.0191443652291307463e-881j)  +/-  (1.18e-62, 4.89e-177j)
| (0.035954788372977093332 - 7.9968230101175239533e-881j)  +/-  (1.19e-63, 4.92e-178j)
| (0.013366028153368181454 - 1.4731365258007821135e-881j)  +/-  (1.03e-62, 4.26e-177j)
| (0.026892555756932373135 - 8.9900822464870294272e-880j)  +/-  (4.82e-64, 2e-178j)
| (0.017149988721060519119 + 1.0219633398353988748e-879j)  +/-  (4.61e-64, 1.91e-178j)
| (0.064112951116559575978 + 3.1199442581937307441e-881j)  +/-  (7.13e-67, 2.95e-181j)
| (0.02838316796991635877 + 7.0139307967017833401e-881j)  +/-  (9.22e-64, 3.82e-178j)
| (0.0095635049906522821344 + 1.6788565015277144961e-879j)  +/-  (9.51e-65, 3.94e-179j)
| (0.030734357311530544346 + 8.884083822112125729e-880j)  +/-  (2.28e-66, 9.44e-181j)
| (0.028523171469449218301 - 1.0218627350030248907e-879j)  +/-  (4.8e-66, 1.99e-180j)
| (0.0058762760419998931994 - 2.6894278137765990136e-879j)  +/-  (5.16e-65, 2.14e-179j)
| (0.030734357311530544346 + 9.4006570062812941274e-881j)  +/-  (4.76e-67, 1.97e-181j)
| (0.0095635049906522821344 + 1.0005430383734095075e-881j)  +/-  (4.01e-66, 1.66e-180j)
| (0.02838316796991635877 + 9.8018995066908342227e-880j)  +/-  (2.9e-66, 1.2e-180j)
| (0.035954788372977093332 - 6.3190396392282239207e-880j)  +/-  (4.88e-68, 2.02e-182j)
| (0.020797609592264277592 - 2.6890534659967451407e-881j)  +/-  (2.37e-67, 9.81e-182j)
| (0.040812962435280026809 + 6.3050703983900899092e-881j)  +/-  (8.54e-70, 3.54e-184j)
| (0.017149988721060519119 + 2.0111865619933814303e-881j)  +/-  (2.42e-67, 1e-181j)
| (0.062073490711514640576 - 4.8001695286377943791e-881j)  +/-  (1.48e-73, 6.13e-188j)
| (0.040812962435280026809 + 4.1608917168024721662e-880j)  +/-  (1.35e-70, 5.59e-185j)
| (0.053360708661568265813 + 1.1534970892817805849e-880j)  +/-  (3.79e-73, 1.57e-187j)
| (0.028523171469449218301 - 9.0108333217008123113e-881j)  +/-  (1.28e-68, 5.29e-183j)
| (0.050814301913615499622 - 3.7463105731214731079e-881j)  +/-  (1.32e-72, 5.47e-187j)
| (0.059375916195586446405 - 2.8938187562387128404e-881j)  +/-  (4.08e-74, 1.69e-188j)
| (0.047954623233322139204 + 2.0000882072380188331e-880j)  +/-  (5.65e-73, 2.34e-187j)
| (0.044692305821131317985 - 2.8133367516301183945e-880j)  +/-  (3.01e-72, 1.25e-186j)
| (0.063023350667564370777 + 4.2736954863418880305e-881j)  +/-  (1.27e-75, 5.24e-190j)
| (0.047954623233322139204 + 4.2786438660030534496e-881j)  +/-  (3.38e-73, 1.4e-187j)
| (0.044692305821131317985 - 5.0827573953909794296e-881j)  +/-  (1.11e-72, 4.6e-187j)
| (0.064249466613503203872 - 3.3043175545481114465e-881j)  +/-  (7.04e-77, 2.92e-191j)
| (0.050814301913615499622 - 1.4896290485816039693e-880j)  +/-  (3.02e-75, 1.25e-189j)
| (0.064112951116559575978 + 3.5484893045646093334e-881j)  +/-  (3.85e-77, 1.6e-191j)
| (0.060856771403426132977 + 2.8510118814468922144e-881j)  +/-  (2.1e-77, 8.7e-192j)
| (0.053360708661568265813 + 3.3880429500422166717e-881j)  +/-  (1.07e-75, 4.44e-190j)
| (0.063703829912370769888 - 2.986591198316644488e-881j)  +/-  (7.61e-78, 3.16e-192j)
| (0.059375916195586446405 - 6.3823271065558673529e-881j)  +/-  (5.19e-79, 2.15e-193j)
| (0.057633217401830286884 + 7.5836709386995114208e-881j)  +/-  (5.71e-79, 2.36e-193j)
| (0.013366028153368181454 - 1.2486364839846660841e-879j)  +/-  (3.5e-77, 1.44e-191j)
| (0.057633217401830286884 + 2.9884488287958952257e-881j)  +/-  (3.44e-78, 1.42e-192j)
| (0.062073490711514640576 - 2.8535743340471084111e-881j)  +/-  (2.95e-79, 1.22e-193j)
| (0.063703829912370769888 - 3.8654025816660084223e-881j)  +/-  (1.13e-79, 4.8e-194j)
| (0.055629315787025082165 - 9.2259775529359063564e-881j)  +/-  (8.4e-80, 3.54e-194j)
| (0.060856771403426132977 + 5.4837919855160531627e-881j)  +/-  (4.57e-80, 1.96e-194j)
| (0.063023350667564370777 + 2.8987250602313591939e-881j)  +/-  (3.63e-80, 1.35e-194j)
