Starting with polynomial:
P : 2*t
Extension levels are: 1 2 38
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 38 Kronrod extension for:
P2 : 2*t^3 - 3*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^41 - 797765011935897511/1022870211820812*t^39 + 93461891597073053977/681913474547208*t^37 - 6541585512284644635567/454608983031472*t^35 + 917339918149900137429355/909217966062944*t^33 - 22746741371572927772398335/454608983031472*t^31 + 1648867440059108123541281595/909217966062944*t^29 - 89022020581636231993858149195/1818435932125888*t^27 + 3615726887948163960079376252985/3636871864251776*t^25 - 221707508191802549428548414002625/14547487457007104*t^23 + 5119873896832639121750668468498125/29094974914014208*t^21 - 88401367786060135092854821197569625/58189949828028416*t^19 + 1126600560423470889070101004859767125/116379899656056832*t^17 - 5196673140992290000658262686191027875/116379899656056832*t^15 + 33752690513655876669431516256059169375/232759799312113664*t^13 - 148357728843321807336415524301565274375/465519598624227328*t^11 + 208315021433119314985884188248101804375/465519598624227328*t^9 - 2738375092237201811784918111860695794375/7448313577987637248*t^7 + 2272256752385151884247725363869336876875/14896627155975274496*t^5 - 710390823066790344603357682755015084375/29793254311950548992*t^3 + 33728555942261954624607933994714771875/59586508623901097984*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:
| (-6.3281130511078127175 - 3.6650579665586004696e-859j)  +/-  (7e-246, 7e-246j)
| (-8.0986499489419668893 - 1.9225476477267459715e-863j)  +/-  (4.97e-248, 4.97e-248j)
| (6.8401056565126561815 + 3.6998406116403651873e-859j)  +/-  (2.48e-246, 2.48e-246j)
| (-7.411461031645263333 + 1.4593860206031700748e-862j)  +/-  (5.54e-247, 5.54e-247j)
| (5.4064876904808625165 - 2.9702855178604258505e-859j)  +/-  (1.55e-245, 1.55e-245j)
| (8.0986499489419668893 + 7.9546647666024532097e-865j)  +/-  (5.07e-248, 5.07e-248j)
| (6.3281130511078127175 + 5.2403404295252548589e-862j)  +/-  (7.04e-246, 7.04e-246j)
| (-4.9790801236740072629 + 2.4905254463838163972e-862j)  +/-  (1.56e-245, 1.56e-245j)
| (-6.8401056565126561815 + 2.1091435593229621098e-863j)  +/-  (2.64e-246, 2.64e-246j)
| (5.8539412295604501249 - 1.8663205562029914704e-863j)  +/-  (1.23e-245, 1.23e-245j)
| (2.6566570427997393227 - 3.1862985747236763643e-864j)  +/-  (1.08e-247, 1.08e-247j)
| (-4.567304912645531764 - 6.6450760138528008652e-869j)  +/-  (1.27e-245, 1.27e-245j)
| (-1.2247448713915890491 + 2.481887738639054471e-875j)  +/-  (5.57e-251, 5.57e-251j)
| (-5.8539412295604501249 - 2.1530679427186316347e-868j)  +/-  (1.28e-245, 1.28e-245j)
| (7.411461031645263333 - 2.6133721378260530243e-869j)  +/-  (5.52e-247, 5.52e-247j)
| (3.7789684634579174415 - 7.2630659699833923259e-870j)  +/-  (3.59e-246, 3.59e-246j)
| (-4.1680410203610983209 - 1.3941829399605838775e-876j)  +/-  (7.82e-246, 7.82e-246j)
| (2.293524519980622214 + 4.6681197068349696714e-877j)  +/-  (2.35e-248, 2.35e-248j)
| (-1.9343259424555572828 - 5.4385172212671137781e-887j)  +/-  (4.11e-249, 4.11e-249j)
| (4.1680410203610983209 + 1.052484597000387355e-881j)  +/-  (6.7e-246, 6.7e-246j)
| (3.3982932828496797726 - 1.9577141973109836239e-898j)  +/-  (1.29e-246, 1.29e-246j)
| (1.2839117876745110461e-914 + 7.4831366675549489229e-915j)  +/-  (6.09e-913, 6.09e-913j)
| (3.0245821602862108663 + 4.391316250419043632e-915j)  +/-  (4.3e-247, 4.3e-247j)
| (-3.3982932828496797726 - 6.0777512163347048432e-923j)  +/-  (1.39e-246, 1.39e-246j)
| (-2.293524519980622214 + 4.7907709094281326888e-925j)  +/-  (2.55e-248, 2.55e-248j)
| (1.9343259424555572828 - 5.0920639881924850965e-933j)  +/-  (4.35e-249, 4.35e-249j)
| (0.87297512154017234553 + 3.9021765000011891681e-948j)  +/-  (4.44e-252, 4.44e-252j)
| (4.567304912645531764 + 4.1667977816985303697e-958j)  +/-  (1.38e-245, 1.38e-245j)
| (-2.6566570427997393227 - 1.0309506260591703866e-972j)  +/-  (1.18e-247, 1.18e-247j)
| (-1.5782993543854850584 - 1.1647211385951906087e-975j)  +/-  (5.69e-250, 5.69e-250j)
| (-5.4064876904808625165 - 2.5831760981654547305e-972j)  +/-  (1.71e-245, 1.71e-245j)
| (4.9790801236740072629 - 4.1853250101510634463e-977j)  +/-  (1.68e-245, 1.68e-245j)
| (-3.7789684634579174415 - 2.9977524326989783453e-983j)  +/-  (3.38e-246, 3.38e-246j)
| (-0.87297512154017234553 + 5.3336486601944032037e-991j)  +/-  (5.07e-252, 5.07e-252j)
| (-0.16921984691375583782 + 6.2488208659218274013e-993j)  +/-  (2.4e-254, 2.4e-254j)
| (-3.0245821602862108663 + 2.1310647681586423222e-989j)  +/-  (4.64e-247, 4.64e-247j)
| (1.5782993543854850584 + 2.5996709988138191745e-992j)  +/-  (6.4e-250, 6.4e-250j)
| (0.52215026889337444878 + 5.5455803781637622892e-996j)  +/-  (3.38e-253, 3.38e-253j)
| (1.2247448713915890491 - 1.2667251626014073993e-993j)  +/-  (5.44e-251, 5.44e-251j)
| (0.16921984691375583782 - 4.2175114796060284731e-997j)  +/-  (2.4e-254, 2.4e-254j)
| (-0.52215026889337444878 + 2.6471772574833492225e-996j)  +/-  (3.38e-253, 3.38e-253j)
-------------------------------------------------
The weights are:
| (1.1243235312536758281e-18 + 6.5128603300049131754e-877j)  +/-  (1.03e-90, 1.67e-212j)
| (1.4644951193576220945e-29 - 8.618890626468388035e-882j)  +/-  (3.01e-95, 4.89e-217j)
| (1.4512486592811960648e-21 + 1.2401230343966112075e-876j)  +/-  (8.16e-94, 1.33e-215j)
| (4.8292365811171187105e-25 + 1.8803179851620034674e-879j)  +/-  (7.35e-94, 1.19e-215j)
| (4.9771974994945986476e-14 + 8.4338144742566868339e-872j)  +/-  (1.85e-90, 3.01e-212j)
| (1.4644951193576220945e-29 + 5.3298741849858248551e-881j)  +/-  (1.72e-97, 2.79e-219j)
| (1.1243235312536758281e-18 - 6.0031576758672512951e-875j)  +/-  (7.84e-93, 1.27e-214j)
| (4.0450639079895293564e-12 - 2.018441296678603609e-873j)  +/-  (1.33e-90, 2.16e-212j)
| (1.4512486592811960648e-21 - 1.310607117235254008e-877j)  +/-  (2.48e-94, 4.03e-216j)
| (3.3960533296803533045e-16 + 2.4106594001852521454e-873j)  +/-  (1.91e-92, 3.1e-214j)
| (0.00017741477666304566114 + 1.0642622240786331153e-867j)  +/-  (3.99e-84, 6.48e-206j)
| (1.9927902210147469691e-10 + 3.9773096032706409561e-872j)  +/-  (3.1e-90, 5.03e-212j)
| (0.044381029596550142278 - 4.1025872751394903871e-867j)  +/-  (4.9e-76, 7.96e-198j)
| (3.3960533296803533045e-16 - 5.1124808499962355535e-875j)  +/-  (9.89e-93, 1.61e-214j)
| (4.8292365811171187105e-25 - 1.4582190126435052164e-878j)  +/-  (5.42e-97, 8.81e-219j)
| (1.3628805955155298852e-07 + 3.1270381377811591673e-869j)  +/-  (8.65e-90, 1.41e-211j)
| (6.3376290751725506788e-09 - 3.1884054227340892909e-871j)  +/-  (1.33e-90, 2.17e-212j)
| (0.0010579636142684522996 - 2.7798022883027936374e-867j)  +/-  (2.52e-85, 4.09e-207j)
| (0.0047833018619577235136 - 8.1808638216420763475e-868j)  +/-  (8.37e-85, 1.36e-206j)
| (6.3376290751725506788e-09 - 6.9411720041761255187e-870j)  +/-  (4.71e-91, 7.65e-213j)
| (2.0527509915754884069e-06 - 1.390908575258535726e-868j)  +/-  (2.89e-89, 4.7e-211j)
| (-0.015495501861619533058 - 9.887893171544651618e-866j)  +/-  (2.85e-83, 4.64e-205j)
| (2.2254002938153069698e-05 + 7.1170208272992655526e-868j)  +/-  (2.28e-88, 3.71e-210j)
| (2.0527509915754884069e-06 - 8.2895515433359485316e-870j)  +/-  (5.8e-92, 9.42e-214j)
| (0.0010579636142684522996 + 3.1519365639836123754e-868j)  +/-  (4.75e-89, 7.72e-211j)
| (0.0047833018619577235136 + 1.9145887827237433764e-867j)  +/-  (1.55e-87, 2.51e-209j)
| (0.092452064034978015029 + 5.2497866094183394986e-867j)  +/-  (1.11e-85, 1.81e-207j)
| (1.9927902210147469691e-10 + 1.5005403122119669981e-870j)  +/-  (2.34e-93, 3.8e-215j)
| (0.00017741477666304566114 - 1.0769449263362389441e-868j)  +/-  (8.76e-91, 1.42e-212j)
| (0.016573651608199172071 + 1.9113896353094090371e-867j)  +/-  (2.44e-88, 3.97e-210j)
| (4.9771974994945986476e-14 + 9.2121047163248922758e-874j)  +/-  (2.04e-96, 3.32e-218j)
| (4.0450639079895293564e-12 - 3.5803288965420461533e-871j)  +/-  (4.58e-95, 7.44e-217j)
| (1.3628805955155298852e-07 + 1.8024659739265148755e-870j)  +/-  (2.3e-93, 3.73e-215j)
| (0.092452064034978015029 + 8.3862725126883466837e-867j)  +/-  (1.91e-89, 3.09e-211j)
| (0.19760850613198259898 + 6.2525884633263396062e-866j)  +/-  (5.52e-89, 9.01e-211j)
| (2.2254002938153069698e-05 + 3.2188532717196100295e-869j)  +/-  (3.05e-92, 4.96e-214j)
| (0.016573651608199172071 - 9.4963247917067174506e-868j)  +/-  (5.46e-91, 8.89e-213j)
| (0.1506893697232180627 - 1.4691673438327347897e-866j)  +/-  (3.79e-90, 6.21e-212j)
| (0.044381029596550142278 - 1.0710333168880335335e-867j)  +/-  (7.82e-91, 1.27e-212j)
| (0.19760850613198259898 + 5.9271573058881396426e-866j)  +/-  (7.47e-90, 1.27e-211j)
| (0.1506893697232180627 - 1.7863100588555376313e-866j)  +/-  (1.49e-90, 2.15e-212j)
