Starting with polynomial:
P : t
Extension levels are: 1 4 44
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 44 Kronrod extension for:
P2 : t^5 - 10/9*t^3 + 5/21*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^49 - 353916837235131723751618325714396/29381880970450890571028887803177*t^47 + 46419706019288419119013940352401812246/681806547919312915700725341472722285*t^45 - 10439103870567840274374649549967014912/43498769007038601790225487735535687*t^43 + 26859203794545804616461361300622764256/45418575304677936131722083013062233*t^41 - 578579494789127500870852688639622101708/534541693970440325242575284692193973*t^39 + 22569734858020160954054740330728308149034/14788986866515515665044582876484033253*t^37 - 1129167092807931746318619708705012759669848/665504408993198204927006229441781496385*t^35 + 2802312473010218149170546244309758707558033/1855582881545740877267064427972967231097*t^33 - 4704528488388425382449073329361517148360024/4329693390273395380289816998603590205893*t^31 + 1331209612664338250377359597716769364968956/2095012930777449377559588870292059777045*t^29 - 684065373117571774446656796558262166589344/2260137102661386274313054002925916705285*t^27 + 268202104697763096149830815165588401327848/2285893650839863610772462025751283277425*t^25 - 374689315404265518090103029232828061976/10159527337066060492322053447783481233*t^23 + 33300818644655899710127269637547871428092/3565994095310187232805040760172001912783*t^21 - 1952705043908763871147303096468592534064176/1035326952338391026591063500703271222011331*t^19 + 2172076721366148338272635482640857917566431/7247288666368737186137444504922898554079317*t^17 - 14347635786079151128212988220622036723953396/390074654689846736783280101294379539822504415*t^15 + 855609862284438131361309278448592102466/251647308804340467664026307761941860472667*t^13 - 196718932538843550555371014689332828524384/859878854184431378007977893622555337235103139*t^11 + 4912040298224257530719779011492921400/459910244705525786062387891044333394848513*t^9 - 59015915020800205921915988042615391700/183026422778212301343063567718857160134379383*t^7 + 2424393201368486899526121832900758250574/430417137566762595325104490085512421582682182355*t^5 - 1771348395450027843028330714933386986152/37962791533388460907674216025542195583592568483711*t^3 + 1467102465239690063736875506975806143/12654263844462820302558072008514065194530856161237*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:
| (-0.9061798459386639928 - 5.3768300356134230995e-826j)  +/-  (4.67e-239, 4.67e-239j)
| (-0.99351855907859570015 + 1.4323309390217703144e-826j)  +/-  (1.09e-238, 1.09e-238j)
| (-0.95300559978518769107 + 2.1596626856583789769e-829j)  +/-  (1.3e-238, 1.3e-238j)
| (0.99351855907859570015 - 1.5427191303281534302e-833j)  +/-  (1.22e-238, 1.22e-238j)
| (0.95300559978518769107 - 8.8726308584913733415e-844j)  +/-  (1.34e-238, 1.34e-238j)
| (0.93149861666037493548 - 1.0660084060630522334e-851j)  +/-  (8.55e-239, 8.55e-239j)
| (-0.84474996622318502844 - 1.0738338904431706125e-861j)  +/-  (7.52e-240, 7.52e-240j)
| (-0.8772030055670813663 - 4.527724980363845003e-861j)  +/-  (1.96e-239, 1.96e-239j)
| (0.97057422213314740516 - 4.4516977124169348278e-858j)  +/-  (1.58e-238, 1.58e-238j)
| (-0.99876847459605814305 - 3.8068508636007494649e-864j)  +/-  (3.83e-239, 3.83e-239j)
| (0.8772030055670813663 + 8.5541741059356700878e-873j)  +/-  (2.17e-239, 2.17e-239j)
| (0.99876847459605814305 + 3.7782088947976583346e-874j)  +/-  (3.69e-239, 3.69e-239j)
| (-0.93149861666037493548 - 9.7930932601263089745e-885j)  +/-  (8.38e-239, 8.38e-239j)
| (-0.80903035617952854083 + 2.6068016055732551071e-896j)  +/-  (2.57e-240, 2.57e-240j)
| (0.98410379726235776004 - 1.0866111172910432796e-898j)  +/-  (1.62e-238, 1.62e-238j)
| (0.84474996622318502844 - 1.644986926073942614e-910j)  +/-  (7.62e-240, 7.62e-240j)
| (0.31337594908935812141 + 1.6034363985228683166e-925j)  +/-  (3.28e-249, 3.28e-249j)
| (-0.97057422213314740516 - 1.1135471846976541952e-913j)  +/-  (1.72e-238, 1.72e-238j)
| (-0.77027734511031721803 + 9.0306671712318259263e-930j)  +/-  (7.25e-241, 7.25e-241j)
| (-0.98410379726235776004 + 1.9001992387635368357e-935j)  +/-  (1.6e-238, 1.6e-238j)
| (0.9061798459386639928 + 1.2420270620619619162e-943j)  +/-  (4.69e-239, 4.69e-239j)
| (0.72873556689501773703 + 2.0813683643268595671e-947j)  +/-  (1.65e-241, 1.65e-241j)
| (0.80903035617952854083 + 4.461551365059748321e-946j)  +/-  (2.53e-240, 2.53e-240j)
| (-0.72873556689501773703 - 9.6413088225793294706e-948j)  +/-  (1.66e-241, 1.66e-241j)
| (-0.68463698817172007163 + 1.6135948233476828266e-949j)  +/-  (3.11e-242, 3.11e-242j)
| (3.1689749426866406605e-970 + 1.498526289154246266e-969j)  +/-  (7.51e-968, 7.51e-968j)
| (0.77027734511031721803 - 1.3166768107696194086e-949j)  +/-  (7.04e-241, 7.04e-241j)
| (0.53846931010568309104 - 3.9152168234018687969e-955j)  +/-  (9.61e-245, 9.61e-245j)
| (-0.19057942382164989513 + 9.9744751762677349759e-962j)  +/-  (1.06e-251, 1.06e-251j)
| (-0.63816627294487000481 + 4.6267416135373228636e-952j)  +/-  (5.23e-243, 5.23e-243j)
| (-0.37257595030998498536 - 7.3337928739322104781e-958j)  +/-  (5.81e-248, 5.81e-248j)
| (0.68463698817172007163 - 3.2685324637382872641e-952j)  +/-  (3.36e-242, 3.36e-242j)
| (0.63816627294487000481 + 1.8323561592041684533e-957j)  +/-  (5.29e-243, 5.29e-243j)
| (0.063954378765259066835 + 5.6468952479564509722e-969j)  +/-  (2.04e-254, 2.04e-254j)
| (-0.58943170466761340571 - 1.202030976240717806e-956j)  +/-  (7.84e-244, 7.84e-244j)
| (-0.48529130083532908891 - 2.555306112869718808e-958j)  +/-  (9.68e-246, 9.68e-246j)
| (0.12758760803088743552 - 5.9810176021049342266e-970j)  +/-  (4.81e-253, 4.81e-253j)
| (0.58943170466761340571 - 9.0628961359303575664e-962j)  +/-  (7.67e-244, 7.67e-244j)
| (0.19057942382164989513 - 3.4106832931629168115e-967j)  +/-  (8.56e-252, 8.56e-252j)
| (-0.31337594908935812141 - 2.0398302997290067638e-963j)  +/-  (3.31e-249, 3.31e-249j)
| (-0.53846931010568309104 + 9.3070975679152311938e-962j)  +/-  (9.2e-245, 9.2e-245j)
| (-0.12758760803088743552 + 7.6650008979497270573e-971j)  +/-  (4.15e-253, 4.15e-253j)
| (0.37257595030998498536 + 2.3933843262168876649e-965j)  +/-  (6.06e-248, 6.06e-248j)
| (0.42995010611687945137 - 4.4969732153392840602e-964j)  +/-  (8.36e-247, 8.36e-247j)
| (-0.063954378765259066835 - 7.3063030050464761235e-973j)  +/-  (2.04e-254, 2.04e-254j)
| (-0.42995010611687945137 + 1.282056764575673545e-964j)  +/-  (7.93e-247, 7.93e-247j)
| (-0.25261233358241673891 - 2.7648753189201035132e-968j)  +/-  (1.75e-250, 1.75e-250j)
| (0.25261233358241673891 + 2.4418733139370671252e-968j)  +/-  (1.8e-250, 1.8e-250j)
| (0.48529130083532908891 - 4.5011482984934283456e-965j)  +/-  (1.01e-245, 1.01e-245j)
-------------------------------------------------
The weights are:
| (0.027175749349223262305 - 2.138181647279246531e-826j)  +/-  (7.91e-66, 2.37e-180j)
| (0.007338287014168009416 + 6.4155503437405568354e-827j)  +/-  (2.18e-66, 6.54e-181j)
| (0.019556700988496225622 + 4.6083310140404028194e-827j)  +/-  (2.11e-66, 6.34e-181j)
| (0.007338287014168009416 + 1.4055967784150149755e-828j)  +/-  (1.25e-66, 3.75e-181j)
| (0.019556700988496225622 - 6.8567577477885482792e-828j)  +/-  (6.46e-67, 1.94e-181j)
| (0.023436191719542080207 + 9.5852593314593208615e-828j)  +/-  (4.19e-67, 1.26e-181j)
| (0.034123461788418261608 - 4.9092613930318359003e-826j)  +/-  (3.58e-67, 1.07e-181j)
| (0.030747618542412843521 + 7.5428426712143109258e-826j)  +/-  (6.15e-67, 1.85e-181j)
| (0.015563779964420048409 + 4.6252865734973883897e-828j)  +/-  (1.49e-67, 4.47e-182j)
| (0.003159649053772654152 + 6.1749009779629857037e-827j)  +/-  (3e-68, 8.99e-183j)
| (0.030747618542412843521 + 1.695828549755715305e-827j)  +/-  (4.59e-69, 1.37e-183j)
| (0.003159649053772654152 - 3.9671216505329940993e-829j)  +/-  (2.65e-68, 7.95e-183j)
| (0.023436191719542080207 - 3.2276949204082775068e-826j)  +/-  (4.82e-68, 1.45e-182j)
| (0.037276707634396754519 + 4.085565189751311707e-826j)  +/-  (1.39e-69, 4.16e-184j)
| (0.011482745808077520331 - 2.8204400780864889406e-828j)  +/-  (5.51e-68, 1.65e-182j)
| (0.034123461788418261608 - 2.1872958991046967338e-827j)  +/-  (2.94e-70, 8.82e-185j)
| (0.060028857057219822337 + 9.5921707683000989132e-827j)  +/-  (2.97e-73, 8.91e-188j)
| (0.015563779964420048409 + 6.4985710767073726901e-827j)  +/-  (7.58e-69, 2.27e-183j)
| (0.040188140890988212385 - 3.7165645724019695224e-826j)  +/-  (2.01e-71, 6.04e-186j)
| (0.011482745808077520331 - 1.8028798435514282312e-826j)  +/-  (6.27e-69, 1.88e-183j)
| (0.027175749349223262305 - 1.2910459003830718367e-827j)  +/-  (1.29e-70, 3.87e-185j)
| (0.042856139742031405487 + 4.2911392885623333502e-827j)  +/-  (3.78e-74, 1.13e-188j)
| (0.037276707634396754519 + 2.7795787609653898165e-827j)  +/-  (9.61e-73, 2.88e-187j)
| (0.042856139742031405487 + 3.5183674765789497436e-826j)  +/-  (2.1e-73, 6.28e-188j)
| (0.045309676504109084496 - 3.3818215918772188365e-826j)  +/-  (2.02e-74, 6.05e-189j)
| (0.06400792678201999937 - 1.2258507589840714808e-826j)  +/-  (2.03e-78, 6.09e-193j)
| (0.040188140890988212385 - 3.4819696977738446965e-827j)  +/-  (2.91e-74, 8.73e-189j)
| (0.052073657485524790554 + 7.7349619348416364738e-827j)  +/-  (1.73e-77, 5.18e-192j)
| (0.062564889436090556464 + 1.5687656012018098905e-826j)  +/-  (5.85e-79, 1.75e-193j)
| (0.047613733910749096546 + 3.2478508820864016221e-826j)  +/-  (1.93e-76, 5.78e-191j)
| (0.058327039356189711258 - 2.145665819063288535e-826j)  +/-  (5.72e-79, 1.72e-193j)
| (0.045309676504109084496 - 5.1814649361439086005e-827j)  +/-  (5.77e-77, 1.73e-191j)
| (0.047613733910749096546 + 6.0995936907180365774e-827j)  +/-  (1.14e-77, 3.41e-192j)
| (0.063847293272886667549 + 1.1500694599066753179e-826j)  +/-  (2.08e-80, 6.24e-195j)
| (0.049850287974759285224 - 3.0830245203955999801e-826j)  +/-  (1.03e-78, 3.1e-193j)
| (0.054274274626802362228 - 2.6383223000325083679e-826j)  +/-  (6.13e-80, 1.84e-194j)
| (0.063365759789100215927 - 1.0884046314444489021e-826j)  +/-  (2.99e-81, 8.97e-196j)
| (0.049850287974759285224 - 6.9729297558374393197e-827j)  +/-  (2.74e-80, 8.2e-195j)
| (0.062564889436090556464 + 1.0380392753009176397e-826j)  +/-  (1.22e-81, 3.65e-196j)
| (0.060028857057219822337 + 1.9251177078160612705e-826j)  +/-  (5.85e-82, 1.75e-196j)
| (0.052073657485524790554 + 2.8767389881931235244e-826j)  +/-  (9.71e-81, 2.91e-195j)
| (0.063365759789100215927 - 1.4318880718248489713e-826j)  +/-  (1.39e-82, 4.16e-197j)
| (0.058327039356189711258 - 9.2344692795058707273e-827j)  +/-  (4.96e-83, 1.48e-197j)
| (0.056386338669254635734 + 8.8389923630603997088e-827j)  +/-  (3.53e-83, 1.06e-197j)
| (0.063847293272886667549 + 1.3187156626992044906e-826j)  +/-  (5.97e-83, 1.79e-197j)
| (0.056386338669254635734 + 2.3879319239549022184e-826j)  +/-  (6.37e-83, 1.91e-197j)
| (0.061449056030356494036 - 1.7325135424134749557e-826j)  +/-  (3.2e-83, 9.59e-198j)
| (0.061449056030356494036 - 9.9607531047896811233e-827j)  +/-  (6.81e-84, 2.09e-198j)
| (0.054274274626802362228 - 8.3532257243152602087e-827j)  +/-  (5.25e-84, 1.5e-198j)
