Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 37
-------------------------------------------------
Trying to find an order 37 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^39 - 411286697416806476491/555847452794224045*t^37 + 136759913960259947567121/555847452794224045*t^35 - 773847693524098917955521/15881355794120687*t^33 + 101999375448087673560051036/15881355794120687*t^31 - 9472129547642468965347516900/15881355794120687*t^29 + 640012795752798403596962784252/15881355794120687*t^27 - 2465015755301188999220868139044/1221642753393899*t^25 + 92302902261916548707004421991850/1221642753393899*t^23 - 2590936840678860335070694562077350/1221642753393899*t^21 + 54329867339894064819600894491393250/1221642753393899*t^19 - 843341857760543882278603794876066150/1221642753393899*t^17 + 9543813966386143366158667818010215900/1221642753393899*t^15 - 76971086323541760537060132759971278500/1221642753393899*t^13 + 428206190546374594507244284657791673500/1221642753393899*t^11 - 1567769395778203442081753470632011392500/1221642753393899*t^9 + 3522261208994325084683125269417269959875/1221642753393899*t^7 - 4344580401602443583431082931068400001125/1221642753393899*t^5 + 2410073472732099838506901601260226499375/1221642753393899*t^3 - 379972289494132967999452880128808368125/1221642753393899*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:
| (-5.1421723195847887743 + 1.6263945216528224182e-969j)  +/-  (2.47e-246, 2.47e-246j)
| (-8.0932690254894753167 - 7.524384614447940539e-970j)  +/-  (1.19e-245, 1.19e-245j)
| (-9.4944663744473536423 + 2.4588475604969110255e-971j)  +/-  (2.48e-246, 2.48e-246j)
| (11.281694434607018331 - 1.9461927376626278256e-972j)  +/-  (4.78e-248, 4.78e-248j)
| (8.0932690254894753167 - 1.3311642870327949744e-971j)  +/-  (1.15e-245, 1.15e-245j)
| (10.305958832270789348 - 5.0735731888611418741e-978j)  +/-  (5.33e-247, 5.33e-247j)
| (-7.4572418932708553825 - 2.9689079119194769615e-979j)  +/-  (1.58e-245, 1.58e-245j)
| (9.4944663744473536423 - 1.262302913818859174e-981j)  +/-  (2.5e-246, 2.5e-246j)
| (-2.5142475853569120911 + 7.8956999292067144123e-996j)  +/-  (1.89e-249, 1.89e-249j)
| (-8.7670919423420932116 - 4.7933233606196400385e-988j)  +/-  (6.79e-246, 6.79e-246j)
| (7.4572418932708553825 - 4.3082242763070041556e-989j)  +/-  (1.62e-245, 1.62e-245j)
| (4.6002438019344571096 + 6.9444287782457546754e-990j)  +/-  (9.56e-247, 9.56e-247j)
| (8.7670919423420932116 + 6.4707550499617719016e-997j)  +/-  (7.11e-246, 7.11e-246j)
| (-10.305958832270789348 - 1.3629707633093221298e-1003j)  +/-  (5.26e-247, 5.26e-247j)
| (-4.6002438019344571096 + 7.2050165888477113e-1002j)  +/-  (9.51e-247, 9.51e-247j)
| (5.1421723195847887743 + 1.5143690184768873197e-1004j)  +/-  (2.62e-246, 2.62e-246j)
| (4.0680433761576718809 + 2.8984960077868856854e-1021j)  +/-  (2.76e-247, 2.76e-247j)
| (6.2638940149236806715 - 5.422374779540712248e-1036j)  +/-  (9.94e-246, 9.94e-246j)
| (-6.2638940149236806715 + 2.2241225752472878586e-1043j)  +/-  (9.85e-246, 9.85e-246j)
| (3.0263669130143748308 - 2.816595632438437989e-1053j)  +/-  (1.29e-248, 1.29e-248j)
| (6.8495393864071386948 - 4.5794708765990672715e-1064j)  +/-  (1.32e-245, 1.32e-245j)
| (3.5438904941152791553 - 6.4732726333118948555e-1074j)  +/-  (6.72e-248, 6.72e-248j)
| (-2.884803322756261147e-1087 - 1.6961548739949638896e-1088j)  +/-  (1.13e-1085, 1.13e-1085j)
| (-2.0064508302782076497 + 3.9202453277355156707e-1082j)  +/-  (2.62e-250, 2.62e-250j)
| (-1.5020010844547653857 - 4.4244495525552255379e-1082j)  +/-  (2.27e-251, 2.27e-251j)
| (-6.8495393864071386948 - 4.0276785773409065618e-1077j)  +/-  (1.4e-245, 1.4e-245j)
| (5.6958712759930150723 + 1.5166619980442662338e-1088j)  +/-  (5.81e-246, 5.81e-246j)
| (1 + 4.898664806317183354e-1099j)  +/-  (1.86e-252, 1.86e-252j)
| (-11.281694434607018331 - 7.9819109893045495174e-1096j)  +/-  (5.13e-248, 5.13e-248j)
| (-4.0680433761576718809 - 7.8445516869746511265e-1094j)  +/-  (2.82e-247, 2.82e-247j)
| (-3.0263669130143748308 - 2.9246299609098939574e-1096j)  +/-  (1.39e-248, 1.39e-248j)
| (1.5020010844547653857 - 2.6181910528497186661e-1098j)  +/-  (2.63e-251, 2.63e-251j)
| (-3.5438904941152791553 - 4.1186055965414436393e-1095j)  +/-  (6.36e-248, 6.36e-248j)
| (-0.49960309298363248657 - 1.6432619973926354323e-1100j)  +/-  (1.43e-253, 1.43e-253j)
| (-5.6958712759930150723 + 1.1655568385980055537e-1097j)  +/-  (5.92e-246, 5.92e-246j)
| (2.5142475853569120911 - 2.3724401845296613053e-1103j)  +/-  (1.99e-249, 1.99e-249j)
| (-1 - 2.3521678731356793373e-1105j)  +/-  (1.97e-252, 1.97e-252j)
| (2.0064508302782076497 + 6.538291010241915727e-1104j)  +/-  (2.44e-250, 2.44e-250j)
| (0.49960309298363248657 + 6.4225798684816378378e-1107j)  +/-  (1.43e-253, 1.43e-253j)
-------------------------------------------------
The weights are:
| (3.9577703227465780613e-07 + 1.6574726605866740946e-975j)  +/-  (8.82e-76, 3.77e-198j)
| (1.557550984958795504e-15 + 1.3482184583977387178e-980j)  +/-  (1.64e-83, 7.04e-206j)
| (8.0966541787724367211e-21 + 2.0667197968750448654e-983j)  +/-  (2.79e-86, 1.19e-208j)
| (1.0331448744373048087e-28 - 6.1055266509446171506e-988j)  +/-  (5.61e-91, 2.4e-213j)
| (1.557550984958795504e-15 - 3.0071599152184568622e-981j)  +/-  (2.95e-86, 1.26e-208j)
| (3.0030298012223488263e-24 + 1.1149051559026556175e-985j)  +/-  (6.92e-90, 2.96e-212j)
| (2.0800596565149890723e-13 - 1.9937692612953612676e-979j)  +/-  (3.51e-85, 1.5e-207j)
| (8.0966541787724367211e-21 - 6.1451386573471576802e-984j)  +/-  (7.04e-89, 3.01e-211j)
| (0.0086221574505739670291 - 3.6429835511603456096e-974j)  +/-  (8.7e-73, 3.72e-195j)
| (5.6742469132676861736e-18 - 6.6009771571418907375e-982j)  +/-  (1.25e-87, 5.34e-210j)
| (2.0800596565149890723e-13 + 3.6638778186186728417e-980j)  +/-  (1.66e-86, 7.1e-209j)
| (5.4370842578984993117e-06 - 2.453799777121116411e-976j)  +/-  (2.81e-82, 1.2e-204j)
| (5.6742469132676861736e-18 + 1.7200807237858653709e-982j)  +/-  (3.56e-88, 1.52e-210j)
| (3.0030298012223488263e-24 - 3.3355171442757497904e-985j)  +/-  (2.33e-92, 9.98e-215j)
| (5.4370842578984993117e-06 - 4.4111983249523105026e-975j)  +/-  (1.69e-82, 7.21e-205j)
| (3.9577703227465780613e-07 + 6.259058575914504374e-977j)  +/-  (6.29e-84, 2.69e-206j)
| (5.3692600029448634017e-05 + 8.1708363493054314876e-976j)  +/-  (3.03e-82, 1.29e-204j)
| (6.9409496594894404313e-10 + 2.3521106575456740614e-978j)  +/-  (3.38e-86, 1.44e-208j)
| (6.9409496594894404313e-10 - 2.3916187617308119345e-977j)  +/-  (6.82e-88, 2.92e-210j)
| (0.0021065732241245665074 + 5.7868198397115095735e-975j)  +/-  (1.42e-81, 6.06e-204j)
| (1.5427610830805005091e-11 - 3.3259459486732650091e-979j)  +/-  (4.75e-87, 2.03e-209j)
| (0.00038926370059048864818 - 2.3363305753560320877e-975j)  +/-  (2.43e-82, 1.04e-204j)
| (0.19926023345471921999 + 8.9717403138903880611e-974j)  +/-  (2.41e-79, 1.03e-201j)
| (0.026966957459781937777 + 5.4040765570350823322e-974j)  +/-  (4.98e-81, 2.13e-203j)
| (0.064962410446809675059 - 7.2301342308513958993e-974j)  +/-  (1.82e-79, 7.79e-202j)
| (1.5427610830805005091e-11 + 2.3358441171477470028e-978j)  +/-  (1.15e-89, 4.9e-212j)
| (2.0160344167136749395e-08 - 1.337464412094372581e-977j)  +/-  (2.42e-86, 1.04e-208j)
| (0.12124226372664114662 + 5.8566899247850410275e-974j)  +/-  (5.38e-80, 2.3e-202j)
| (1.0331448744373048087e-28 + 1.6333402459800591229e-987j)  +/-  (5.8e-98, 2.48e-220j)
| (5.3692600029448634017e-05 + 7.006064319553440673e-975j)  +/-  (5.11e-87, 2.18e-209j)
| (0.0021065732241245665074 + 2.2341118201132908687e-974j)  +/-  (4.99e-86, 2.14e-208j)
| (0.064962410446809675059 - 3.9612191090784061003e-974j)  +/-  (2.78e-85, 1.19e-207j)
| (0.00038926370059048864818 - 1.2696945230222909732e-974j)  +/-  (8.13e-87, 3.48e-209j)
| (0.17602071093272267346 - 9.3388780774809555249e-974j)  +/-  (4.51e-85, 1.94e-207j)
| (2.0160344167136749395e-08 + 2.6178662353447886333e-976j)  +/-  (3.16e-89, 1.35e-211j)
| (0.0086221574505739670291 - 1.2503953245569717937e-974j)  +/-  (4.93e-87, 2.1e-209j)
| (0.12124226372664114662 + 8.6845033812000266795e-974j)  +/-  (7.33e-86, 3.23e-208j)
| (0.026966957459781937777 + 2.3704938867022692658e-974j)  +/-  (7.67e-87, 3.28e-209j)
| (0.17602071093272267346 - 7.6848931253342337726e-974j)  +/-  (4.2e-86, 1.72e-208j)
