Starting with polynomial:
P : t
Extension levels are: 1 4 46
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 46 Kronrod extension for:
P2 : t^5 - 10/9*t^3 + 5/21*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^51 - 3074862911072572473401555995904660783/235787960091625877486601228484816929*t^49 + 105071650121552508094151343376986197143552/1312159997909898008212935836518006209885*t^47 - 37558284130813724741044953814587663897954664/122030879805620514763803032796174577519305*t^45 + 90540687737470876752451048199844855022525874/109039478648019571073186275816323433866087*t^43 - 23886693504179462855355744370370759309100890/14292361707914200037575226137927519313817*t^41 + 314071342491193110776084974988887913236237215944/120613240453087934117097333377970335489301663*t^39 - 90259835344736136192378837238386438943841056/28063949102584562826817751728319218085835*t^37 + 72034331798041258627221884299113102043869689021/22516641829973680908050109470021452644201615*t^35 - 944496568420984594940327602466095139529670850959/364769597645573630710411773414347532836066163*t^33 + 63154004266902897913764999684012165760251610400/36803062853129395691088799616517822597764019*t^31 - 6078107573265721245930239279231727385482404413168/6507018951548458638156700345101102763172406069*t^29 + 1004356736832717635638989746071757205062185431812/2404071041212484718530800620111244863241036725*t^27 - 995702071406304041523708994313902256955209686852/6499895778093014238990683158078550926540580775*t^25 + 846046227941468078836455106798619759936691571984/18459704009784160438733540168943084631375249401*t^23 - 615002029971336094682857828924423744784271177440/55379112029352481316200620506829253894125748203*t^21 + 2666887395804492098101828336059577667529729462397/1236800168655538749395147191319186670302141709867*t^19 - 8862356173238723991648021168111815039957254980833/26797336987536672903561522478582377856546403713785*t^17 + 66359356167426094848966268975796869887028395922976/1688232230214810392924375916150689804962423433968455*t^15 - 51656828438791050448905455588137289604195251048/14638545279758839227915697353971866112680572774993*t^13 + 3086497123839030870996345216341866930279587487090/13353731420973851877219404224673258479252224041433999*t^11 - 421543851344106833295219732281286187892433717778/40061194262921555631658212674019775437756672124301997*t^9 + 6903035942861546616697777596982076860888782904/22256219034956419795365673707788764132087040069056665*t^7 - 118632310585964593684332715964893745891777561152/22412012568201114733933233423743285481011649349540061655*t^5 + 576043164025592741500255715966813912353124917/13447207540920668840359940054245971288606989609724036993*t^3 - 22822382673439416583129201343282632832434433/219637723168370924392545687552684197713914163625492604219*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:
| (0.99982734713104895183 - 5.344313560506956353e-909j)  +/-  (6.62e-237, 6.62e-237j)
| (-0.99982734713104895183 - 4.9355540981208570529e-910j)  +/-  (6.61e-237, 6.61e-237j)
| (-0.9514875475709765947 + 4.7076525244426073693e-932j)  +/-  (3.6e-237, 3.6e-237j)
| (-0.68732654716692576485 - 2.3769069023877759924e-951j)  +/-  (9.07e-242, 9.07e-242j)
| (0.93068464560165464063 - 6.1196089699936099242e-948j)  +/-  (1.69e-237, 1.69e-237j)
| (0.9514875475709765947 + 1.4527871261175785917e-947j)  +/-  (3.76e-237, 3.76e-237j)
| (-0.99731906545803767905 - 1.2291794061468171474e-944j)  +/-  (1.45e-236, 1.45e-236j)
| (-0.9061798459386639928 - 1.9207690881117341212e-958j)  +/-  (5.99e-238, 5.99e-238j)
| (-0.73167232731688177623 + 7.4778483726822802735e-965j)  +/-  (5.81e-241, 5.81e-241j)
| (-0.96853548696056573493 - 3.6084120547115943215e-959j)  +/-  (7.25e-237, 7.25e-237j)
| (0.9061798459386639928 + 9.2046405851228658125e-977j)  +/-  (6e-238, 6e-238j)
| (0.96853548696056573493 + 5.8362426369503505411e-975j)  +/-  (7.45e-237, 7.45e-237j)
| (0.31077465902727517765 - 1.6110562169193641134e-989j)  +/-  (3.68e-249, 3.68e-249j)
| (-0.81137345381419151497 - 1.4241229565272688872e-976j)  +/-  (1.47e-239, 1.47e-239j)
| (0.99137109242207060123 + 1.8926351936354916958e-974j)  +/-  (1.44e-236, 1.44e-236j)
| (0.81137345381419151497 - 1.6266380874175959078e-981j)  +/-  (1.43e-239, 1.43e-239j)
| (-0.99137109242207060123 - 5.0097951758237978386e-976j)  +/-  (1.5e-236, 1.5e-236j)
| (0.99731906545803767905 - 3.6843375760073609576e-996j)  +/-  (1.47e-236, 1.47e-236j)
| (-0.77307632301695407733 - 1.3155771457393537539e-1001j)  +/-  (3.15e-240, 3.15e-240j)
| (-0.98181525533626155052 + 1.1376445439815575174e-998j)  +/-  (1.11e-236, 1.11e-236j)
| (0.87805454694089978246 + 2.8942187568798553525e-1014j)  +/-  (2.17e-238, 2.17e-238j)
| (0.77307632301695407733 + 2.2788215319460489424e-1015j)  +/-  (3.13e-240, 3.13e-240j)
| (-0.93068464560165464063 - 3.4440753914053972139e-1014j)  +/-  (1.59e-237, 1.59e-237j)
| (-0.84641196237287659935 - 7.7739754516328415296e-1021j)  +/-  (6.06e-239, 6.06e-239j)
| (-0.87805454694089978246 + 2.4713333912110396933e-1021j)  +/-  (2.21e-238, 2.21e-238j)
| (0.25013422746834279916 + 4.1822639956744452368e-1040j)  +/-  (1.89e-250, 1.89e-250j)
| (0.73167232731688177623 - 1.0746759367892733368e-1028j)  +/-  (5.74e-241, 5.74e-241j)
| (0.84641196237287659935 + 6.9311999605279994513e-1026j)  +/-  (5.88e-239, 5.88e-239j)
| (-0.12608108506441646303 - 4.5288586906818957727e-1044j)  +/-  (5.03e-253, 5.03e-253j)
| (-0.64021641975606411383 + 2.2873631607763986049e-1033j)  +/-  (1.49e-242, 1.49e-242j)
| (-0.25013422746834279916 + 1.0985142694561096251e-1041j)  +/-  (1.9e-250, 1.9e-250j)
| (0.64021641975606411383 - 2.012526201292716104e-1031j)  +/-  (1.23e-242, 1.23e-242j)
| (0.68732654716692576485 + 5.9952808972571640559e-1030j)  +/-  (8.79e-242, 8.79e-242j)
| (0.063167674093070538809 - 2.3172888381003962372e-1044j)  +/-  (1.95e-254, 1.95e-254j)
| (-0.59053084425470082063 + 2.7332063183701210442e-1033j)  +/-  (1.59e-243, 1.59e-243j)
| (-0.4842410233323090136 + 1.9630174992665526489e-1035j)  +/-  (1.31e-245, 1.31e-245j)
| (-1.2341995767510354254e-1052 - 2.4664980569081591417e-1052j)  +/-  (1.41e-1050, 1.41e-1050j)
| (0.53846931010568309104 + 1.5141498692991480735e-1033j)  +/-  (1.48e-244, 1.48e-244j)
| (0.98181525533626155052 + 5.8913882179253829002e-1039j)  +/-  (1.08e-236, 1.08e-236j)
| (-0.31077465902727517765 - 2.0201825187332905594e-1054j)  +/-  (3.66e-249, 3.66e-249j)
| (-0.53846931010568309104 - 2.7836287574566256732e-1049j)  +/-  (1.44e-244, 1.44e-244j)
| (-0.063167674093070538809 + 1.542927112055492894e-1059j)  +/-  (1.95e-254, 1.95e-254j)
| (0.37016424914080897256 - 4.3314811729161307648e-1051j)  +/-  (6.09e-248, 6.09e-248j)
| (0.59053084425470082063 + 8.2397402236019879775e-1050j)  +/-  (1.54e-243, 1.54e-243j)
| (0.18848699748008903131 + 6.7413038804409483583e-1059j)  +/-  (1.01e-251, 1.01e-251j)
| (-0.42806401829535023964 + 8.8218299505180297687e-1054j)  +/-  (9.23e-247, 9.23e-247j)
| (-0.37016424914080897256 - 8.3641805497858371277e-1055j)  +/-  (7.07e-248, 7.07e-248j)
| (0.12608108506441646303 - 1.9422786192485074321e-1061j)  +/-  (4.66e-253, 4.66e-253j)
| (0.4842410233323090136 + 6.13925059367676974e-1053j)  +/-  (1.4e-245, 1.4e-245j)
| (0.42806401829535023964 - 3.1873698216854986815e-1054j)  +/-  (9.34e-247, 9.34e-247j)
| (-0.18848699748008903131 + 1.9647030191912116321e-1059j)  +/-  (9.44e-252, 9.44e-252j)
-------------------------------------------------
The weights are:
| (0.00086842562640051006157 + 3.3282715936186170645e-909j)  +/-  (5.64e-62, 2.55e-174j)
| (0.00086842562640051006157 - 3.0506972145992200477e-910j)  +/-  (2.56e-62, 1.16e-174j)
| (0.018931433990759034903 + 1.9905823071763490204e-911j)  +/-  (1.11e-62, 5.03e-175j)
| (0.045758511012181668503 - 3.2459738681482519369e-912j)  +/-  (1.33e-63, 6.03e-176j)
| (0.022665339265377889246 + 1.9842870216825331789e-910j)  +/-  (2.32e-63, 1.05e-175j)
| (0.018931433990759034903 - 2.9388431921041034743e-910j)  +/-  (2.26e-63, 1.02e-175j)
| (0.0041983259059781597845 + 4.0287649136949079077e-910j)  +/-  (9.76e-63, 4.42e-175j)
| (0.026330590510800793307 + 6.1188873052360136133e-912j)  +/-  (7.59e-64, 3.43e-176j)
| (0.042903461617927927746 + 2.6135726763920718429e-912j)  +/-  (3.21e-64, 1.46e-176j)
| (0.015161937360056376886 - 3.5591316896387672102e-911j)  +/-  (2.73e-63, 1.24e-175j)
| (0.026330590510800793307 - 1.4093723915932442849e-910j)  +/-  (3.5e-65, 1.58e-177j)
| (0.015161937360056376886 + 4.6484181342180661338e-910j)  +/-  (3.28e-65, 1.48e-177j)
| (0.060055295456881497041 + 1.3422579973189573327e-911j)  +/-  (9.19e-68, 4.16e-180j)
| (0.03669194976426927948 + 7.3888517896362366736e-913j)  +/-  (9.05e-66, 4.1e-178j)
| (0.0077266366839985658346 + 1.6111347912375904875e-909j)  +/-  (7.25e-66, 3.28e-178j)
| (0.03669194976426927948 + 6.2558372437295022226e-911j)  +/-  (4.65e-68, 2.11e-180j)
| (0.0077266366839985658346 - 1.420042255050752355e-910j)  +/-  (6.14e-65, 2.78e-177j)
| (0.0041983259059781597845 - 4.4220563673984798915e-909j)  +/-  (9.29e-66, 4.2e-178j)
| (0.039877000475443348428 - 1.8085210125526953248e-912j)  +/-  (5.39e-67, 2.44e-179j)
| (0.011404646846492857864 + 6.7098790277927444974e-911j)  +/-  (2.93e-65, 1.33e-177j)
| (0.02990274724506759852 + 1.0422448039395039603e-910j)  +/-  (3.05e-68, 1.38e-180j)
| (0.039877000475443348428 - 5.0276523794008600919e-911j)  +/-  (8.75e-70, 3.96e-182j)
| (0.022665339265377889246 - 1.1255549537488572055e-911j)  +/-  (1.47e-66, 6.64e-179j)
| (0.033362159799537756655 + 7.4291222677164469397e-913j)  +/-  (4.1e-68, 1.86e-180j)
| (0.02990274724506759852 - 2.8840367846646986892e-912j)  +/-  (9.38e-68, 4.25e-180j)
| (0.061184877308989770339 - 1.2146887306589358824e-911j)  +/-  (1.22e-74, 5.52e-187j)
| (0.042903461617927927746 + 4.1207774966289298427e-911j)  +/-  (4.77e-73, 2.16e-185j)
| (0.033362159799537756655 - 7.9652396319847934821e-911j)  +/-  (1.55e-71, 6.99e-184j)
| (0.062701730665156057034 - 7.4610859467737274992e-912j)  +/-  (1.67e-76, 7.56e-189j)
| (0.048430246141557218155 + 3.7652696536105752739e-912j)  +/-  (1.7e-73, 7.71e-186j)
| (0.061184877308989770339 - 6.5250107989020533281e-912j)  +/-  (9.95e-77, 4.5e-189j)
| (0.048430246141557218155 + 2.9066289098359538063e-911j)  +/-  (3.96e-75, 1.79e-187j)
| (0.045758511012181668503 - 3.4353135461082756236e-911j)  +/-  (2.65e-74, 1.2e-186j)
| (0.063082868298340636379 + 9.3261917573510745144e-912j)  +/-  (1.03e-77, 4.66e-190j)
| (0.050907642087021434153 - 4.2115097870858257149e-912j)  +/-  (3.16e-75, 1.43e-187j)
| (0.055239675599004462767 - 4.9892743739551715285e-912j)  +/-  (7.69e-77, 3.48e-189j)
| (0.063210085563614165978 - 8.6247655349478504921e-912j)  +/-  (8.78e-78, 3.97e-190j)
| (0.053180543749035714058 + 2.1607565924548903841e-911j)  +/-  (3.16e-78, 1.43e-190j)
| (0.011404646846492857864 - 8.0519853673911099483e-910j)  +/-  (1.85e-74, 8.37e-187j)
| (0.060055295456881497041 + 6.1142345987005511075e-912j)  +/-  (3.38e-78, 1.53e-190j)
| (0.053180543749035714058 + 4.6126996485073416878e-912j)  +/-  (6.82e-77, 3.09e-189j)
| (0.063082868298340636379 + 8.0081703611280348522e-912j)  +/-  (2.84e-78, 1.28e-190j)
| (0.058684038630903740338 - 1.4935185675748399112e-911j)  +/-  (1.63e-79, 7.4e-192j)
| (0.050907642087021434153 - 2.4916183185451536379e-911j)  +/-  (9.68e-79, 4.38e-191j)
| (0.062068213240439526215 + 1.1061687654878487499e-911j)  +/-  (1.83e-79, 8.26e-192j)
| (0.057076659936571093314 + 5.3568884847233558915e-912j)  +/-  (3.32e-79, 1.5e-191j)
| (0.058684038630903740338 - 5.7282264597120490354e-912j)  +/-  (1.93e-79, 8.71e-192j)
| (0.062701730665156057034 - 1.0130925381072407604e-911j)  +/-  (3.81e-80, 1.73e-192j)
| (0.055239675599004462767 - 1.8933379251849300213e-911j)  +/-  (4.79e-81, 2.17e-193j)
| (0.057076659936571093314 + 1.6745330296289117428e-911j)  +/-  (4.2e-81, 1.91e-193j)
| (0.062068213240439526215 + 6.9704990469579311351e-912j)  +/-  (3.64e-81, 1.52e-193j)
