Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 39
-------------------------------------------------
Trying to find an order 39 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^41 - 1266194631996487348358/298132551856770427*t^39 + 378549460575093139139769/298132551856770427*t^37 - 3135218193437021981977311/16115273073338942*t^35 + 297436009492121706478003095/16115273073338942*t^33 - 19097240756740866880852226535/16115273073338942*t^31 + 1742964166453072343624106448185/32230546146677884*t^29 - 116341746107006195230965589714635/64461092293355768*t^27 + 11547160316616675570159571226880885/257844369173423072*t^25 - 429511080411451916960063731876751625/515688738346846144*t^23 + 11995155468472737267344653098294085875/1031377476693692288*t^21 - 250542993321136874315994153983848607625/2062754953387384576*t^19 + 969311946972085086943983929029351966125/1031377476693692288*t^17 - 21886887586510204314256070937047551444875/4125509906774769152*t^15 + 176195900580495097224169739808030347758125/8251019813549538304*t^13 - 978848750163251042875378527458661110334375/16502039627099076608*t^11 + 14320333737984004227544773108839010669489375/132016317016792612864*t^9 - 32149052812002296362347723102610089328689375/264032634033585225728*t^7 + 39634808502789975185269365441115397759968125/528065268067170451456*t^5 - 21980204592058212954982309085536328756034375/1056130536134340902912*t^3 + 1732498774224917133302502990154841507090625/1056130536134340902912*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
Positive weights:   41 out of 41
Indefinite weights: 0 out of 41
Negative weights:   0 out of 41
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (5.7226009850865931172 + 3.7077927701688979584e-947j)  +/-  (9.24e-246, 9.24e-246j)
| (-0.35327288180783071643 + 2.1441774686745906945e-966j)  +/-  (8.89e-254, 8.89e-254j)
| (-26.302817306407869515 + 5.6256711664972041157e-965j)  +/-  (4.06e-252, 4.06e-252j)
| (26.302817306407869515 + 9.5098192038924264409e-965j)  +/-  (4.06e-252, 4.06e-252j)
| (-7.2869883339019935177 + 3.1651438869539146616e-959j)  +/-  (4.91e-247, 4.91e-247j)
| (-6.7132699494777871537 - 1.2169635540897248404e-958j)  +/-  (2.16e-246, 2.16e-246j)
| (-4.027519079806531314 + 1.2173852939359132616e-958j)  +/-  (4.4e-246, 4.4e-246j)
| (2.1399548959447354123 - 7.1190062700304155554e-961j)  +/-  (1.07e-248, 1.07e-248j)
| (-2.5058929572972803647 + 1.3139212903260759357e-960j)  +/-  (4.55e-248, 4.55e-248j)
| (7.2869883339019935177 - 4.0785014798219560986e-957j)  +/-  (4.91e-247, 4.91e-247j)
| (1.062074413204782617 - 1.0379021471747957496e-972j)  +/-  (1.55e-251, 1.55e-251j)
| (6.7132699494777871537 - 2.7779795756871600883e-965j)  +/-  (2.11e-246, 2.11e-246j)
| (4.8432326064311984243 + 1.8924184232473324581e-967j)  +/-  (1.03e-245, 1.03e-245j)
| (-2.1399548959447354123 - 8.0926725336262637455e-978j)  +/-  (1.04e-248, 1.04e-248j)
| (-5.2729068515316216759 + 3.4268206142087927799e-974j)  +/-  (1.16e-245, 1.16e-245j)
| (3.2528272675909375821 + 1.4280143501482667977e-974j)  +/-  (6.55e-247, 6.55e-247j)
| (4.027519079806531314 + 1.5928088109163134285e-975j)  +/-  (4.3e-246, 4.3e-246j)
| (-4.8432326064311984243 + 7.3314287084910609207e-981j)  +/-  (1.06e-245, 1.06e-245j)
| (-3.6360136902194106569 + 9.1702664395846350404e-983j)  +/-  (2.13e-246, 2.13e-246j)
| (-3.2528272675909375821 - 6.3974961794408530152e-983j)  +/-  (7.04e-247, 7.04e-247j)
| (4.4291481576088077559 + 7.0977169545224819907e-981j)  +/-  (7.21e-246, 7.21e-246j)
| (1.4187726101679762234 + 1.7893572241924185506e-998j)  +/-  (1.74e-250, 1.74e-250j)
| (7.9768037123341956099 - 4.6409014191687714679e-993j)  +/-  (4.86e-248, 4.86e-248j)
| (-1.7778362768289265747 - 1.7324331165262857641e-1012j)  +/-  (1.42e-249, 1.42e-249j)
| (6.1990096664823704649 + 1.1908511980078315392e-1014j)  +/-  (5.16e-246, 5.16e-246j)
| (5.2729068515316216759 + 1.8360305569332920255e-1036j)  +/-  (1.2e-245, 1.2e-245j)
| (2.1711399822980037694e-1064 - 9.7721247299728066967e-1066j)  +/-  (8.91e-1063, 8.91e-1063j)
| (-4.4291481576088077559 - 9.9440685823303866365e-1041j)  +/-  (8.14e-246, 8.14e-246j)
| (-5.7226009850865931172 + 3.8375360537961422907e-1040j)  +/-  (8.66e-246, 8.66e-246j)
| (-6.1990096664823704649 + 3.869536328316010644e-1044j)  +/-  (5.52e-246, 5.52e-246j)
| (2.5058929572972803647 - 1.0067370127927954152e-1043j)  +/-  (4.73e-248, 4.73e-248j)
| (3.6360136902194106569 + 6.2151992392086749708e-1053j)  +/-  (2.07e-246, 2.07e-246j)
| (0.35327288180783071643 + 2.1143486382824951191e-1070j)  +/-  (9.41e-254, 9.41e-254j)
| (-7.9768037123341956099 - 1.2722200741112269297e-1063j)  +/-  (4.56e-248, 4.56e-248j)
| (-1.4187726101679762234 - 1.192906110596841127e-1065j)  +/-  (1.69e-250, 1.69e-250j)
| (-1.062074413204782617 + 1.6294262255142808161e-1066j)  +/-  (1.73e-251, 1.73e-251j)
| (1.7778362768289265747 + 4.5752188667241645403e-1063j)  +/-  (1.42e-249, 1.42e-249j)
| (0.7071067811865475244 - 4.2333922468853825523e-1073j)  +/-  (1.29e-252, 1.29e-252j)
| (2.8765162868078924763 + 4.2133879542189436703e-1071j)  +/-  (2.06e-247, 2.06e-247j)
| (-2.8765162868078924763 + 4.1033075872112592645e-1079j)  +/-  (2.03e-247, 2.03e-247j)
| (-0.7071067811865475244 + 2.6959541336335281889e-1085j)  +/-  (1.24e-252, 1.24e-252j)
-------------------------------------------------
The weights are:
| (1.5610303635176785868e-15 - 3.3072109683816175694e-961j)  +/-  (4.86e-85, 1.81e-207j)
| (0.17602071716180923663 - 9.8746117138302282601e-956j)  +/-  (4.21e-66, 1.56e-188j)
| (9.6870289498921975859e-77 + 1.1222792290129438025e-992j)  +/-  (7.08e-112, 2.63e-234j)
| (9.6870289498921975859e-77 - 1.7464083092101534657e-992j)  +/-  (6.41e-112, 2.38e-234j)
| (3.0211571379007141922e-24 + 1.9881269675177635118e-967j)  +/-  (2.24e-90, 8.31e-213j)
| (8.1315684523905257817e-21 - 1.0723161798988573259e-965j)  +/-  (4.4e-89, 1.64e-211j)
| (2.017065926590452881e-08 - 2.1076651695492469478e-959j)  +/-  (7.02e-82, 2.61e-204j)
| (0.0021066295249063319758 + 1.8379678689752285809e-956j)  +/-  (2.24e-73, 8.3e-196j)
| (0.00038928709305674169048 - 3.4442855380938033536e-957j)  +/-  (2.07e-75, 7.67e-198j)
| (3.0211571379007141922e-24 - 1.6533445096336660849e-966j)  +/-  (3.57e-92, 1.33e-214j)
| (0.064962304850576388818 - 7.8263149075032189609e-956j)  +/-  (4.21e-66, 1.56e-188j)
| (8.1315684523905257817e-21 + 1.3460786926949652525e-964j)  +/-  (9e-91, 3.34e-213j)
| (1.5444828865465103358e-11 - 6.5014004415119219971e-960j)  +/-  (1.63e-86, 6.06e-209j)
| (0.0021066295249063319758 + 8.3748654776087315928e-957j)  +/-  (2.37e-76, 8.82e-199j)
| (2.0833691720150457216e-13 + 6.0585493309917968144e-962j)  +/-  (1.51e-88, 5.6e-211j)
| (5.4381809549003120605e-06 - 1.3605638255687555693e-957j)  +/-  (1.43e-82, 5.32e-205j)
| (2.017065926590452881e-08 - 1.2123304684829183395e-958j)  +/-  (5.05e-85, 1.88e-207j)
| (1.5444828865465103358e-11 - 5.4109574275544685346e-961j)  +/-  (1.54e-87, 5.73e-210j)
| (3.95907327184893747e-07 + 9.7068017049856398815e-959j)  +/-  (2.69e-84, 9.99e-207j)
| (5.4381809549003120605e-06 - 3.7438719169258020599e-958j)  +/-  (2.45e-83, 9.1e-206j)
| (6.9462690816700301173e-10 + 2.9557625300113287636e-959j)  +/-  (3.12e-87, 1.16e-209j)
| (0.026966973958882474863 + 5.4638746626355661295e-956j)  +/-  (2.94e-78, 1.09e-200j)
| (1.0421776813831594489e-28 + 6.7951998720456943032e-969j)  +/-  (5.81e-97, 2.16e-219j)
| (0.0086222323179294902828 - 1.7742865821641789702e-956j)  +/-  (9.06e-81, 3.36e-203j)
| (5.6918781109886697686e-18 - 7.3679309604254295086e-963j)  +/-  (4.38e-92, 1.63e-214j)
| (2.0833691720150457216e-13 + 1.481380504986771343e-960j)  +/-  (6.93e-90, 2.57e-212j)
| (0.19926034384165694982 + 1.1153848700474946553e-955j)  +/-  (3.41e-80, 1.27e-202j)
| (6.9462690816700301173e-10 + 3.7659925108390445561e-960j)  +/-  (2.88e-89, 1.07e-211j)
| (1.5610303635176785868e-15 - 5.0571218764817381254e-963j)  +/-  (2.31e-93, 8.59e-216j)
| (5.6918781109886697686e-18 + 2.9443561866947816048e-964j)  +/-  (8.86e-95, 3.29e-217j)
| (0.00038928709305674169048 - 8.8106497362059460048e-957j)  +/-  (3.58e-88, 1.33e-210j)
| (3.95907327184893747e-07 + 4.3536267277355605025e-958j)  +/-  (6.46e-90, 2.4e-212j)
| (0.17602071716180923663 - 1.117400468171829755e-955j)  +/-  (3.6e-85, 1.34e-207j)
| (1.0421776813831594489e-28 - 1.1181332322907598905e-969j)  +/-  (6.53e-101, 2.43e-223j)
| (0.026966973958882474863 + 3.2928642515933882268e-956j)  +/-  (5.54e-87, 2.06e-209j)
| (0.064962304850576388818 - 5.3760484890068112476e-956j)  +/-  (9.1e-87, 3.38e-209j)
| (0.0086222323179294902828 - 3.3735676460014583823e-956j)  +/-  (8.18e-88, 3.04e-210j)
| (0.12124212939719662322 + 9.9306479976262824211e-956j)  +/-  (4.01e-87, 1.48e-209j)
| (5.3698805591245819219e-05 + 3.7038289131383839313e-957j)  +/-  (3.45e-89, 1.28e-211j)
| (5.3698805591245819219e-05 + 1.2258718454734623763e-957j)  +/-  (1.12e-89, 4.27e-212j)
| (0.12124212939719662322 + 7.7464024094901915704e-956j)  +/-  (7.64e-88, 2.67e-210j)
