Starting with polynomial:
P : t
Extension levels are: 1 8 28
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P2 : t^9 - 36/17*t^7 + 126/85*t^5 - 84/221*t^3 + 63/2431*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^37 - 227410855942360222642876962072728438/25343614258090607133097670536183407*t^35 + 5592219494344183841527481972850121529317/151279015108220256401828595156424189725*t^33 - 8637931848618970945508438073379451004368/93212322440418541823348932369109854275*t^31 + 5590082576420822022211958385988974523672563164/35389456399341505681361772407918092823317875*t^29 - 390874658166061876180953045124283141754691176584/2017199014762465823837621027251331290929118875*t^27 + 55823185771272085406432259534229927358262230092/316085315703520285786521813386960743592881875*t^25 - 3546715747876137394661779357605391025785198736/29134820403976652429018532364363338105083025*t^23 + 8643945306457490102218663396247085408099768862/135079621872982661261813195507502749396294025*t^21 - 1156341987047304440434591042953156720075809012/45026540624327553753937731835834249798764675*t^19 + 6183029701686756568707526085729679027458298/789939309198729013226977751505864031557275*t^17 - 1248038271935292389337056816319093534909904/697005272822407952847333310152232969021125*t^15 + 1807987263353145141191081190407376198523628/5994245346272708394487066467309203533581675*t^13 - 187459632201140950356737119821286872847016/5155889353787014912740623604748475766647175*t^11 + 198954198461304378724286042307500575512078292/66155216298441188345374941472527692561849902425*t^9 - 12955481190851721478395873457820900420048464/80856375475872563533236039577533846464483214075*t^7 + 286796757964707358115104259978599282833913/57754553911337545380882885412524176046059438625*t^5 - 368131457075251637202598936294772200518266/4955340725592761393679751568394574304751899834025*t^3 + 9683742760613877026474740465158122784323/28080264111692314564185258887569254393594099059475*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:
| (-0.9975167353559043767 - 3.0341148855171276144e-955j)  +/-  (8.54e-244, 8.54e-244j)
| (-0.98695953627897874091 + 1.401234284369113449e-955j)  +/-  (2.53e-243, 2.53e-243j)
| (-0.90810136921068054389 + 3.73012657290670723e-957j)  +/-  (2.77e-243, 2.77e-243j)
| (0.9975167353559043767 + 2.4143359969775378707e-956j)  +/-  (8.2e-244, 8.2e-244j)
| (0.90810136921068054389 + 3.8773478007558122948e-976j)  +/-  (2.86e-243, 2.86e-243j)
| (0.94153764218116059068 + 3.4459197669587540877e-1004j)  +/-  (3.25e-243, 3.25e-243j)
| (0.088759139378282902859 - 4.180079512896582471e-1023j)  +/-  (2.32e-254, 2.32e-254j)
| (-0.87092658172791717146 + 1.6221443490812864472e-1015j)  +/-  (1.99e-243, 1.99e-243j)
| (-0.96816023950762608984 + 4.4967918255032688334e-1019j)  +/-  (3.29e-243, 3.29e-243j)
| (0.96816023950762608984 + 7.8498173037452153543e-1031j)  +/-  (3.68e-243, 3.68e-243j)
| (0.87092658172791717146 - 8.6292619424069534105e-1054j)  +/-  (2.09e-243, 2.09e-243j)
| (0.98695953627897874091 + 5.4790864879449539696e-1062j)  +/-  (2.33e-243, 2.33e-243j)
| (-0.94153764218116059068 + 2.855439904812287696e-1071j)  +/-  (3.43e-243, 3.43e-243j)
| (-0.8360311073266357943 - 1.3431948692362419796e-1073j)  +/-  (1.1e-243, 1.1e-243j)
| (0.32425342340380892904 + 1.8926244801166930361e-1081j)  +/-  (1.9e-250, 1.9e-250j)
| (0.8360311073266357943 + 1.4656286923233022917e-1073j)  +/-  (1.1e-243, 1.1e-243j)
| (0.7962251942155394918 - 6.796399792870103255e-1078j)  +/-  (3.35e-244, 3.35e-244j)
| (-0.39164668312726321991 + 6.8098480973898619871e-1086j)  +/-  (1.57e-249, 1.57e-249j)
| (-0.7962251942155394918 - 2.6263007624199580614e-1079j)  +/-  (3.28e-244, 3.28e-244j)
| (-0.74341125409750139663 + 2.0765772366326936723e-1082j)  +/-  (6.19e-245, 6.19e-245j)
| (0.74341125409750139663 - 1.579498188018714117e-1082j)  +/-  (5.74e-245, 5.74e-245j)
| (0.68156380270053036008 + 7.7008394743582302279e-1086j)  +/-  (8.45e-246, 8.45e-246j)
| (0.25486704925941614313 - 3.4008203107422526386e-1092j)  +/-  (1.4e-251, 1.4e-251j)
| (-0.68156380270053036008 + 3.854504308917813524e-1085j)  +/-  (9.15e-246, 9.15e-246j)
| (-0.54054246064540718965 - 1.3947453732692952112e-1085j)  +/-  (1.37e-247, 1.37e-247j)
| (7.2163578138531036014e-1094 - 2.0872109225155609417e-1093j)  +/-  (8.17e-1092, 8.17e-1092j)
| (0.61337143270059039731 - 6.1775960286825165604e-1087j)  +/-  (1.11e-246, 1.11e-246j)
| (0.39164668312726321991 + 1.0917162902315750076e-1094j)  +/-  (1.77e-249, 1.77e-249j)
| (-0.25486704925941614313 + 8.3435861038906454079e-1092j)  +/-  (1.58e-251, 1.58e-251j)
| (-0.61337143270059039731 + 3.4450375467482202217e-1089j)  +/-  (1.1e-246, 1.1e-246j)
| (-0.17504962631523811923 + 2.2014537058208994737e-1097j)  +/-  (7.24e-253, 7.24e-253j)
| (0.46524995272681206726 - 1.1676443500859580987e-1089j)  +/-  (1.56e-248, 1.56e-248j)
| (0.54054246064540718965 + 1.5590905849786352489e-1091j)  +/-  (1.33e-247, 1.33e-247j)
| (-0.088759139378282902859 + 1.6804636488193025519e-1097j)  +/-  (2.32e-254, 2.32e-254j)
| (-0.46524995272681206726 - 1.5456679398611508371e-1092j)  +/-  (1.53e-248, 1.53e-248j)
| (-0.32425342340380892904 + 1.1264069099101826216e-1095j)  +/-  (1.88e-250, 1.88e-250j)
| (0.17504962631523811923 + 3.6020550339164313063e-1098j)  +/-  (7.53e-253, 7.53e-253j)
-------------------------------------------------
The weights are:
| (0.0063679928220733613544 - 3.5436476571680172654e-955j)  +/-  (1.96e-79, 4.63e-199j)
| (0.014722505250332925038 + 7.9678471734833496753e-955j)  +/-  (1.34e-79, 3.16e-199j)
| (0.03614716602074795156 - 1.0753649839248398104e-954j)  +/-  (1.75e-80, 4.13e-200j)
| (0.0063679928220733613544 - 3.3499176553660161107e-956j)  +/-  (1.18e-80, 2.78e-200j)
| (0.03614716602074795156 - 1.1393134907038410238e-955j)  +/-  (5.61e-81, 1.32e-200j)
| (0.030285350350059859465 + 7.3286263391470405103e-956j)  +/-  (4.01e-81, 9.45e-201j)
| (0.088007690274844422367 + 4.4597626448073916079e-955j)  +/-  (2.66e-82, 6.27e-202j)
| (0.036841391897959501949 + 1.5513658163341568459e-954j)  +/-  (4.04e-81, 9.54e-201j)
| (0.022810276666658225392 - 8.3743422743784640281e-955j)  +/-  (1.58e-80, 3.72e-200j)
| (0.022810276666658225392 - 5.7437297842522377157e-956j)  +/-  (1.54e-81, 3.63e-201j)
| (0.036841391897959501949 + 1.9775939060671767315e-955j)  +/-  (1.99e-82, 4.68e-202j)
| (0.014722505250332925038 + 6.0368632366872524126e-956j)  +/-  (1.08e-81, 2.56e-201j)
| (0.030285350350059859465 + 8.4920728001683565894e-955j)  +/-  (5.04e-82, 1.19e-201j)
| (0.034425744556755762667 - 1.8104189079665186026e-954j)  +/-  (5.4e-83, 1.27e-202j)
| (0.06573707349175683077 - 6.2545351341125091308e-955j)  +/-  (1.97e-85, 4.64e-205j)
| (0.034425744556755762667 - 2.6730612912293711333e-955j)  +/-  (1.46e-83, 3.43e-203j)
| (0.046728682125289623192 + 2.4930845174483882095e-955j)  +/-  (2.64e-84, 6.22e-204j)
| (0.070708909766323276284 + 1.0400011290159928336e-954j)  +/-  (2.67e-87, 6.29e-207j)
| (0.046728682125289623192 + 1.453244435556003856e-954j)  +/-  (2.24e-85, 5.28e-205j)
| (0.057966963139239608461 - 9.8601146252017242213e-955j)  +/-  (3.02e-86, 7.12e-206j)
| (0.057966963139239608461 - 2.0191154509243421827e-955j)  +/-  (1.47e-86, 3.47e-206j)
| (0.065325295924885169386 + 1.8717511713240178293e-955j)  +/-  (1.74e-87, 4.09e-207j)
| (0.074719948784594220441 + 5.9493577289346164714e-955j)  +/-  (5.77e-89, 1.36e-208j)
| (0.065325295924885169386 + 7.6060719207141854308e-955j)  +/-  (1.48e-88, 3.49e-208j)
| (0.074526316497159291317 + 7.057426916370153261e-955j)  +/-  (1.28e-89, 3.02e-209j)
| (0.089124177426404147491 - 4.5305265412021573197e-955j)  +/-  (2.28e-90, 5.37e-210j)
| (0.070794129547324471741 - 2.0164124080761069398e-955j)  +/-  (1.7e-89, 4.01e-209j)
| (0.070708909766323276284 + 5.0356290188376026564e-955j)  +/-  (4.84e-90, 1.14e-209j)
| (0.074719948784594220441 + 9.4265405817785030833e-955j)  +/-  (1.34e-91, 3.15e-211j)
| (0.070794129547324471741 - 6.83547682203386611e-955j)  +/-  (8.99e-91, 2.12e-210j)
| (0.083928655334124672732 - 6.798634448820499818e-955j)  +/-  (9.52e-92, 2.24e-211j)
| (0.075393818836668752138 - 3.4444198501812455396e-955j)  +/-  (2.03e-91, 4.77e-211j)
| (0.074526316497159291317 + 2.4814480083696411209e-955j)  +/-  (2.05e-91, 4.83e-211j)
| (0.088007690274844422367 + 5.2222583637488765258e-955j)  +/-  (1.67e-92, 3.97e-212j)
| (0.075393818836668752138 - 8.288593569657304554e-955j)  +/-  (7.17e-93, 1.7e-212j)
| (0.06573707349175683077 - 1.1307470643382622097e-954j)  +/-  (8.91e-93, 2.14e-212j)
| (0.083928655334124672732 - 4.9706396487497429639e-955j)  +/-  (6.2e-93, 1.33e-212j)
