Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 37
-------------------------------------------------
Trying to find an order 37 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^39 - 822573394833612952982/555847452794224045*t^37 + 136759913960259947567121/555847452794224045*t^35 - 773847693524098917955521/31762711588241374*t^33 + 25499843862021918390012759/15881355794120687*t^31 - 2368032386910617241336879225/31762711588241374*t^29 + 160003198938199600899240696063/63525423176482748*t^27 - 616253938825297249805217034761/9773142027151192*t^25 + 46151451130958274353502210995925/39092568108604768*t^23 - 1295468420339430167535347281038675/78185136217209536*t^21 + 27164933669947032409800447245696625/156370272434419072*t^19 - 421670928880271941139301897438033075/312740544868838144*t^17 + 2385953491596535841539666954502553975/312740544868838144*t^15 - 19242771580885440134265033189992819625/625481089737676288*t^13 + 107051547636593648626811071164447918375/1250962179475352576*t^11 - 391942348944550860520438367658002848125/2501924358950705152*t^9 + 3522261208994325084683125269417269959875/20015394871605641216*t^7 - 4344580401602443583431082931068400001125/40030789743211282432*t^5 + 2410073472732099838506901601260226499375/80061579486422564864*t^3 - 379972289494132967999452880128808368125/160123158972845129728*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:
| (-5.7228054098906491416 + 7.5635604166769429449e-865j)  +/-  (7.78e-246, 7.78e-246j)
| (-6.1992701637160344297 - 8.2947655474478266517e-877j)  +/-  (5.16e-246, 5.16e-246j)
| (-7.9773626379851559 - 2.7474017613862134073e-886j)  +/-  (3.74e-248, 3.74e-248j)
| (7.2874133769280678831 - 2.2488683563477001364e-885j)  +/-  (3.85e-247, 3.85e-247j)
| (0.7071067811865475244 - 7.3179494677597486702e-894j)  +/-  (1.23e-252, 1.23e-252j)
| (2.8765410574421069331 + 8.4473084434140650684e-888j)  +/-  (2.03e-247, 2.03e-247j)
| (5.7228054098906491416 + 2.1829027778909471436e-885j)  +/-  (8.33e-246, 8.33e-246j)
| (-4.8433557481328316137 - 1.5439200402257550603e-897j)  +/-  (1e-245, 1e-245j)
| (7.9773626379851559 - 1.9847395127981875498e-913j)  +/-  (3.99e-248, 3.99e-248j)
| (-4.0275892040203341521 + 2.9609298196871608829e-923j)  +/-  (3.94e-246, 3.94e-246j)
| (6.7136015571193780857 + 3.5488817191704825685e-933j)  +/-  (1.71e-246, 1.71e-246j)
| (5.9269428051664313314e-946 - 4.7167373096404073759e-946j)  +/-  (2.95e-944, 2.95e-944j)
| (-4.4292419345863637219 + 1.1008964799055550013e-940j)  +/-  (6.72e-246, 6.72e-246j)
| (4.4292419345863637219 - 6.6365059985692697812e-949j)  +/-  (8.01e-246, 8.01e-246j)
| (-1.062075152167512876 - 1.2187600099525245712e-955j)  +/-  (1.56e-251, 1.56e-251j)
| (-7.2874133769280678831 + 3.7526928694733019673e-949j)  +/-  (3.78e-247, 3.78e-247j)
| (-3.2528635874592396326 - 2.1184137765360304007e-955j)  +/-  (6.24e-247, 6.24e-247j)
| (5.2730663116802301247 + 2.487039577031846299e-960j)  +/-  (1.08e-245, 1.08e-245j)
| (-1.7778415171877755076 - 6.8794639775402998251e-967j)  +/-  (1.24e-249, 1.24e-249j)
| (2.1399645665510628489 + 9.1206842846207631029e-966j)  +/-  (7.99e-249, 7.99e-249j)
| (1.7778415171877755076 - 1.604553205178148427e-966j)  +/-  (1.3e-249, 1.3e-249j)
| (3.636064917208162763 - 2.44637717548159442e-962j)  +/-  (1.71e-246, 1.71e-246j)
| (1.4187749882070991809 - 7.6179602952684809009e-970j)  +/-  (1.74e-250, 1.74e-250j)
| (4.0275892040203341521 + 4.1079014792689699583e-964j)  +/-  (4.46e-246, 4.46e-246j)
| (-1.4187749882070991809 + 4.7999896044016107693e-971j)  +/-  (1.67e-250, 1.67e-250j)
| (2.5059090001714584848 - 9.0045983200270351773e-969j)  +/-  (4.06e-248, 4.06e-248j)
| (3.2528635874592396326 + 1.4828131749842587362e-966j)  +/-  (6.52e-247, 6.52e-247j)
| (-5.2730663116802301247 + 1.738845761401966743e-967j)  +/-  (1.08e-245, 1.08e-245j)
| (-2.8765410574421069331 + 9.4634388082522936107e-976j)  +/-  (1.96e-247, 1.96e-247j)
| (-0.7071067811865475244 + 5.7007700102760511501e-982j)  +/-  (1.23e-252, 1.23e-252j)
| (4.8433557481328316137 + 1.7932188732973896271e-973j)  +/-  (9.84e-246, 9.84e-246j)
| (-6.7136015571193780857 + 2.3883640874159370152e-974j)  +/-  (1.74e-246, 1.74e-246j)
| (1.062075152167512876 - 1.5166234674350164734e-984j)  +/-  (1.76e-251, 1.76e-251j)
| (-2.5059090001714584848 + 2.9131624897298374383e-980j)  +/-  (4.42e-248, 4.42e-248j)
| (-3.636064917208162763 - 3.3754995586127195143e-984j)  +/-  (1.76e-246, 1.76e-246j)
| (-0.35327273495049977344 + 4.2943835630760444611e-998j)  +/-  (9.45e-254, 9.45e-254j)
| (-2.1399645665510628489 + 6.476762964268484919e-995j)  +/-  (7.43e-249, 7.43e-249j)
| (0.35327273495049977344 + 9.334374702031363766e-998j)  +/-  (9.45e-254, 9.45e-254j)
| (6.1992701637160344297 - 1.7162147004975894015e-994j)  +/-  (4.71e-246, 4.71e-246j)
-------------------------------------------------
The weights are:
| (1.557550984958795504e-15 + 6.7516599336479181831e-879j)  +/-  (8.97e-92, 3.16e-213j)
| (5.6742469132676861736e-18 + 1.486205659868190408e-880j)  +/-  (3.44e-93, 1.21e-214j)
| (1.0331448744373048087e-28 - 1.3164282632445917942e-886j)  +/-  (5.75e-98, 2.02e-219j)
| (3.0030298012223488263e-24 - 3.9182205509565721884e-885j)  +/-  (1.78e-98, 6.25e-220j)
| (0.12124226372664114662 - 1.6558945103677086519e-873j)  +/-  (8.18e-78, 2.88e-199j)
| (5.3692600029448634017e-05 - 2.5902019249773987986e-875j)  +/-  (7.83e-85, 2.76e-206j)
| (1.557550984958795504e-15 + 1.0292706227990010491e-880j)  +/-  (4.26e-95, 1.5e-216j)
| (1.5427610830805005091e-11 + 1.3422988599762681968e-877j)  +/-  (5.74e-92, 2.02e-213j)
| (1.0331448744373048087e-28 + 2.1663696721049433964e-887j)  +/-  (1.66e-100, 5.83e-222j)
| (2.0160344167136749395e-08 + 2.5308763484958542975e-876j)  +/-  (2.01e-90, 7.08e-212j)
| (8.0966541787724367211e-21 + 2.1406074419005922563e-883j)  +/-  (9.62e-98, 3.38e-219j)
| (0.19926023345471921999 - 2.3860430921051380502e-873j)  +/-  (5.85e-78, 2.06e-199j)
| (6.9409496594894404313e-10 - 6.1385962820771154433e-877j)  +/-  (2.3e-91, 8.08e-213j)
| (6.9409496594894404313e-10 - 7.8217365135257099993e-878j)  +/-  (1.96e-93, 6.92e-215j)
| (0.064962410446809675059 + 1.6713952008643882848e-873j)  +/-  (2.34e-78, 8.23e-200j)
| (3.0030298012223488263e-24 + 3.2581264889939572515e-884j)  +/-  (3.1e-99, 1.09e-220j)
| (5.4370842578984993117e-06 + 2.8647175772079704724e-875j)  +/-  (1.79e-89, 6.3e-211j)
| (2.0800596565149890723e-13 - 1.2425896010666785407e-879j)  +/-  (2.29e-95, 8.05e-217j)
| (0.0086221574505739670291 + 7.1827881077108839115e-874j)  +/-  (3.35e-85, 1.18e-206j)
| (0.0021065732241245665074 - 1.779392204025142443e-874j)  +/-  (2.56e-87, 9.01e-209j)
| (0.0086221574505739670291 + 3.7777861042303738671e-874j)  +/-  (6.16e-86, 2.17e-207j)
| (3.9577703227465780613e-07 - 2.0357525256926044892e-876j)  +/-  (1.58e-92, 5.57e-214j)
| (0.026966957459781937777 - 7.0231193679130046377e-874j)  +/-  (1.1e-85, 3.89e-207j)
| (2.0160344167136749395e-08 + 4.4002143204573255079e-877j)  +/-  (1.51e-93, 5.31e-215j)
| (0.026966957459781937777 - 1.1653303229155411005e-873j)  +/-  (1.37e-87, 4.84e-209j)
| (0.00038926370059048864818 + 7.2994153746776911204e-875j)  +/-  (5.55e-90, 1.95e-211j)
| (5.4370842578984993117e-06 + 7.883184813844550548e-876j)  +/-  (7.56e-92, 2.66e-213j)
| (2.0800596565149890723e-13 - 3.0380627146395085289e-878j)  +/-  (2.88e-98, 1.01e-219j)
| (5.3692600029448634017e-05 - 7.8257115345140651334e-875j)  +/-  (2.7e-94, 9.5e-216j)
| (0.12124226372664114662 - 2.1227862931035069002e-873j)  +/-  (8.96e-90, 3.15e-211j)
| (1.5427610830805005091e-11 + 1.1172309987792010616e-878j)  +/-  (6.64e-97, 2.35e-218j)
| (8.0966541787724367211e-21 - 2.6868761428421338832e-882j)  +/-  (3.77e-102, 1.33e-223j)
| (0.064962410446809675059 + 1.1481295969812725601e-873j)  +/-  (1.34e-90, 4.68e-212j)
| (0.00038926370059048864818 + 1.8671662630218824346e-874j)  +/-  (3.06e-94, 1.07e-215j)
| (3.9577703227465780613e-07 - 9.1301932237530817006e-876j)  +/-  (6.32e-96, 2.24e-217j)
| (0.17602071093272267346 + 2.3899060615774168319e-873j)  +/-  (1.91e-92, 5.91e-214j)
| (0.0021065732241245665074 - 3.904988306732105213e-874j)  +/-  (8.24e-94, 2.85e-215j)
| (0.17602071093272267346 + 2.1120002708610597343e-873j)  +/-  (1.36e-92, 3.65e-214j)
| (5.6742469132676861736e-18 - 5.9396084976246567616e-882j)  +/-  (5e-102, 2.3e-223j)
