Starting with polynomial:
P : t
Extension levels are: 1 4 8 26
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P2 : t^5 - 10*t^3 + 15*t
Solvable: 1
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P3 : t^13 - 170/3*t^11 + 3251/3*t^9 - 8652*t^7 + 29631*t^5 - 41790*t^3 + 19215*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^39 - 5202701469556038537182507144760312538011811/9207890989550589640350126401413210598967*t^37 + 19654481193003794350865218132958327758101386293/138118364843258844605251896021198158984505*t^35 - 55550904541184988271681382475546863360251560857719/2624248932021918047499786024402765020705595*t^33 + 1817802766725555229379582724133667519208151760409838/874749644007306015833262008134255006901865*t^31 - 373947461850434524809379263644639981933658818225726122/2624248932021918047499786024402765020705595*t^29 + 3698673677557692396122200407566970063998881828345156646/524849786404383609499957204880553004141119*t^27 - 24873622893940691137210408968271370713999018960793431922/97194404889700668425918000903806111877985*t^25 + 133826471553618499891427935449698573721669355066133183200/19438880977940133685183600180761222375597*t^23 - 2671577171734386415108428046274127749825861806698169332760/19438880977940133685183600180761222375597*t^21 + 691411254190403685217980046122371180880909008435410989620/341032999612984801494449125978267059221*t^19 - 7462598584126416825105478164772804250943279917370045434700/341032999612984801494449125978267059221*t^17 + 58008859481133274990470704474801901668979323070873519658890/341032999612984801494449125978267059221*t^15 - 317602106152966413532895946211294843675953342870229920100650/341032999612984801494449125978267059221*t^13 + 1188772725853902644261864502929956510018919502063416387220750/341032999612984801494449125978267059221*t^11 - 2923439501101634933910570427817666712592858731888463300123350/341032999612984801494449125978267059221*t^9 + 4469581812378790930408519025237549274822750886334910652864875/341032999612984801494449125978267059221*t^7 - 3895080142787386768870158242531170359092874858701290916806575/341032999612984801494449125978267059221*t^5 + 1638433588839839559652210405068126022097703781388273519218875/341032999612984801494449125978267059221*t^3 - 218056402088079953964415313268933592554539604993378811144875/341032999612984801494449125978267059221*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:
| (4.4565588526990514937 - 7.9888254310445249793e-937j)  +/-  (1.71e-246, 1.71e-246j)
| (9.2932759945290976503 + 6.4344424897959933077e-942j)  +/-  (1.3e-247, 1.3e-247j)
| (8.4588161841725745993 + 8.5009744680889171413e-948j)  +/-  (5.34e-247, 5.34e-247j)
| (10.295829188607342701 + 1.8468042943938375809e-959j)  +/-  (1.47e-248, 1.47e-248j)
| (5.1842688974446196437 - 6.1516391401368402337e-968j)  +/-  (4.3e-246, 4.3e-246j)
| (-8.4588161841725745993 + 2.4615737727421731819e-971j)  +/-  (5.17e-247, 5.17e-247j)
| (-4.8100372286572189248 + 1.5433749934294330509e-970j)  +/-  (3.81e-246, 3.81e-246j)
| (-2.8569700138728056542 + 3.8841295699821654971e-975j)  +/-  (1.21e-248, 1.21e-248j)
| (-6.3663977096093038617 - 1.6966141953982113643e-974j)  +/-  (3.06e-246, 3.06e-246j)
| (7.0181664562359391159 - 1.8474144861694154303e-988j)  +/-  (2.45e-246, 2.45e-246j)
| (-9.2932759945290976503 + 4.8787737779048203845e-1002j)  +/-  (1.39e-247, 1.39e-247j)
| (2.8569700138728056542 + 6.1363054283302068695e-998j)  +/-  (1.19e-248, 1.19e-248j)
| (-10.295829188607342701 + 5.5917304574044900221e-1002j)  +/-  (1.35e-248, 1.35e-248j)
| (-1.3556261799742658658 - 1.7832864908787620475e-1003j)  +/-  (5.88e-250, 5.88e-250j)
| (-3.9309600114055574643 - 9.7687357457988730685e-999j)  +/-  (3.01e-247, 3.01e-247j)
| (1.3556261799742658658 - 7.9905191909411560256e-1005j)  +/-  (5.94e-250, 5.94e-250j)
| (1.3914415524206883869 + 2.2912969418919680669e-1004j)  +/-  (6.88e-250, 6.88e-250j)
| (-1.8550647122034955328 - 1.5665857157680788587e-1005j)  +/-  (5.34e-250, 5.34e-250j)
| (5.7497581585936295663 + 2.0821340207236760052e-1005j)  +/-  (3.59e-246, 3.59e-246j)
| (3.3890184837354506755 + 7.9236621990672749834e-1018j)  +/-  (5.93e-248, 5.93e-248j)
| (7.7106927187588603205 - 2.0403130713265968919e-1029j)  +/-  (1.34e-246, 1.34e-246j)
| (-5.1842688974446196437 - 6.5483892331358911767e-1032j)  +/-  (3.98e-246, 3.98e-246j)
| (-7.7106927187588603205 - 1.5796639995528343567e-1036j)  +/-  (1.3e-246, 1.3e-246j)
| (6.3663977096093038617 + 2.9644095668744642819e-1040j)  +/-  (3.17e-246, 3.17e-246j)
| (-3.3890184837354506755 - 6.4891377687481579584e-1049j)  +/-  (5.72e-248, 5.72e-248j)
| (-7.0181664562359391159 + 2.2003463687015244912e-1047j)  +/-  (2.14e-246, 2.14e-246j)
| (-5.7497581585936295663 + 1.9326000142249522972e-1048j)  +/-  (3.36e-246, 3.36e-246j)
| (4.8100372286572189248 - 9.8957980546439309852e-1050j)  +/-  (3.46e-246, 3.46e-246j)
| (-2.3428958730659075168 - 7.8963885743263362501e-1059j)  +/-  (2.09e-249, 2.09e-249j)
| (-0.48042532300273527149 + 6.0006895317195656413e-1062j)  +/-  (2.01e-253, 2.01e-253j)
| (-1.3914415524206883869 - 1.5707104145778093158e-1059j)  +/-  (6.67e-250, 6.67e-250j)
| (0.9467370109606977334 + 1.1022030057486043684e-1060j)  +/-  (5.55e-252, 5.55e-252j)
| (0.48042532300273527149 - 4.0103190500694738627e-1062j)  +/-  (1.61e-253, 1.61e-253j)
| (3.9309600114055574643 + 1.9887327863819266049e-1058j)  +/-  (2.91e-247, 2.91e-247j)
| (-4.4565588526990514937 - 3.6742742706996592653e-1064j)  +/-  (1.69e-246, 1.69e-246j)
| (-0.9467370109606977334 - 4.677561490648554199e-1070j)  +/-  (5.7e-252, 5.7e-252j)
| (2.3428958730659075168 + 5.1017058178830823372e-1067j)  +/-  (2.03e-249, 2.03e-249j)
| (1.8550647122034955328 + 5.330412538747830799e-1068j)  +/-  (4.78e-250, 4.78e-250j)
| (3.4456149640518040825e-1199 - 1.2053672173513387161e-1198j)  +/-  (4.89e-1197, 4.89e-1197j)
-------------------------------------------------
The weights are:
| (9.3857732794847224399e-06 + 9.2001414145893159268e-942j)  +/-  (1.88e-77, 3.32e-200j)
| (6.301532466544232253e-20 - 3.6350078992674831887e-952j)  +/-  (6.82e-90, 1.21e-212j)
| (9.0784610612569895528e-17 + 3.1890684291752070917e-950j)  +/-  (1.45e-88, 2.57e-211j)
| (4.415449909455768068e-24 + 1.2703007958761703097e-954j)  +/-  (5.7e-92, 1.01e-214j)
| (2.9793604210330615951e-07 - 8.3283978574479680802e-943j)  +/-  (1.18e-81, 2.1e-204j)
| (9.0784610612569895528e-17 - 9.882386263303585771e-951j)  +/-  (2.53e-92, 4.49e-215j)
| (9.7051807783394716021e-07 - 3.3735612737443664962e-943j)  +/-  (3.47e-84, 6.16e-207j)
| (0.0035326639345381737741 - 3.5262849132839911621e-941j)  +/-  (3.05e-77, 5.41e-200j)
| (3.99813371666542753e-10 + 2.1824641568402578821e-946j)  +/-  (2.13e-88, 3.78e-211j)
| (5.392340903189372648e-12 + 4.8065378580261933012e-947j)  +/-  (1.09e-88, 1.93e-211j)
| (6.301532466544232253e-20 + 1.2786702606960473292e-952j)  +/-  (2.08e-94, 3.69e-217j)
| (0.0035326639345381737741 - 1.6122634692853415417e-940j)  +/-  (1.29e-79, 2.28e-202j)
| (4.415449909455768068e-24 - 5.0280874818005226864e-955j)  +/-  (1.84e-96, 3.26e-219j)
| (-0.010624589031155796859 - 2.6196547334116154376e-938j)  +/-  (1.64e-72, 2.91e-195j)
| (9.5468374134305835354e-05 - 2.3557058014364344929e-942j)  +/-  (1.52e-83, 2.69e-206j)
| (-0.010624589031155796859 - 4.9101091961060074402e-938j)  +/-  (3.28e-73, 5.82e-196j)
| (0.077961477910997863706 + 4.6776601280754516343e-938j)  +/-  (1.76e-73, 3.12e-196j)
| (0.033735525739097379752 - 7.9661818948770080515e-940j)  +/-  (1.44e-77, 2.55e-200j)
| (1.5799791123029346269e-08 + 3.0078835882559012263e-944j)  +/-  (1.2e-88, 2.12e-211j)
| (0.00068885302369623366666 + 6.3567308187040941343e-941j)  +/-  (1.11e-83, 1.96e-206j)
| (3.5152970549159768276e-14 - 1.498716732077281488e-948j)  +/-  (2.83e-92, 5.01e-215j)
| (2.9793604210330615951e-07 + 6.2864506382595279134e-944j)  +/-  (3.48e-89, 6.18e-212j)
| (3.5152970549159768276e-14 + 4.0083208945941032175e-949j)  +/-  (1.55e-94, 2.74e-217j)
| (3.99813371666542753e-10 - 1.2367909831832630168e-945j)  +/-  (4.17e-91, 7.4e-214j)
| (0.00068885302369623366666 + 8.649544159615005598e-942j)  +/-  (1.24e-86, 2.19e-209j)
| (5.392340903189372648e-12 - 1.0730072909916228346e-947j)  +/-  (1.74e-93, 3.09e-216j)
| (1.5799791123029346269e-08 - 3.8111622079780619135e-945j)  +/-  (3.79e-91, 6.71e-214j)
| (9.7051807783394716021e-07 + 8.8439440178088318312e-942j)  +/-  (9.28e-90, 1.65e-212j)
| (0.012881457083391772776 + 1.5516250400875083318e-940j)  +/-  (4.03e-86, 7.15e-209j)
| (0.16895051642516106523 - 2.7673069919871722353e-939j)  +/-  (5.85e-84, 1.04e-206j)
| (0.077961477910997863706 + 2.451705880578794301e-938j)  +/-  (1.7e-83, 3.01e-206j)
| (0.11641895568228426778 + 5.8561519151287986844e-939j)  +/-  (2e-84, 3.55e-207j)
| (0.16895051642516106523 - 3.4360392393469357098e-939j)  +/-  (1.82e-84, 3.23e-207j)
| (9.5468374134305835354e-05 - 3.7592409453656012728e-941j)  +/-  (2.72e-89, 4.82e-212j)
| (9.3857732794847224399e-06 + 8.4124665164631648174e-943j)  +/-  (2.49e-89, 4.41e-212j)
| (0.11641895568228426778 + 3.8039837940370355738e-939j)  +/-  (2.72e-85, 4.83e-208j)
| (0.012881457083391772776 + 4.9914316112738097909e-940j)  +/-  (5.24e-88, 9.29e-211j)
| (0.033735525739097379752 - 1.9327178404844413165e-939j)  +/-  (2.45e-87, 4.35e-210j)
| (0.1926980008508464659 + 2.768637268542254621e-939j)  +/-  (1.7e-86, 2.98e-209j)
