Starting with polynomial:
P : 2*t
Extension levels are: 1 12 22
-------------------------------------------------
Trying to find an order 12 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P2 : 2*t^13 - 78*t^11 + 2145/2*t^9 - 6435*t^7 + 135135/8*t^5 - 135135/8*t^3 + 135135/32*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^35 - 104183722427/223695465*t^33 + 24873990856187/521956085*t^31 - 591674800572735/208782434*t^29 + 45596621094915231/417564868*t^27 - 2403865619382591639/835129736*t^25 + 89260171836985059867/1670259472*t^23 - 2368721040450715174851/3340518944*t^21 + 100743876918977484060/14913031*t^19 - 43954691390526095723115/954433984*t^17 + 848281767170782919763195/3817735936*t^15 - 5681688841339608923704395/7635471872*t^13 + 25634833400255804580276135/15270943744*t^11 - 74494649048573508097832775/30541887488*t^9 + 130202704547271829486760175/61083774976*t^7 - 17482543304387570834364225/17452507136*t^5 + 14344888314278558359612575/69810028544*t^3 - 1557077815890323403759225/139620057088*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: 1
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   35 out of 35
Indefinite weights: 0 out of 35
Negative weights:   0 out of 35
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (6.2002100251253861253 + 5.3864049674046234606e-435j)  +/-  (9.36e-121, 9.36e-121j)
| (-6.9204179943811755764 - 2.7141171554712938043e-438j)  +/-  (1.15e-121, 1.15e-121j)
| (-3.2466089783724099881 + 4.0543059769279307281e-435j)  +/-  (5.28e-120, 5.28e-120j)
| (6.9204179943811755764 + 3.0490268088203973356e-437j)  +/-  (1.25e-121, 1.25e-121j)
| (3.2466089783724099881 + 2.1294830058089612617e-434j)  +/-  (5.34e-120, 5.34e-120j)
| (-6.2002100251253861253 + 1.7594198541870527405e-441j)  +/-  (9.28e-121, 9.28e-121j)
| (5.0638600284246997997 - 3.0829612254777006994e-440j)  +/-  (6.78e-120, 6.78e-120j)
| (5.6008496108457594383 + 2.1885638059265705783e-444j)  +/-  (3.11e-120, 3.11e-120j)
| (-2.5197356856782378834 + 6.1927895218521347971e-447j)  +/-  (1.26e-120, 1.26e-120j)
| (-5.0638600284246997997 - 5.4148889418239281902e-446j)  +/-  (7.2e-120, 7.2e-120j)
| (1.853107651601512142 + 1.4850408768677314021e-454j)  +/-  (1.06e-121, 1.06e-121j)
| (-5.6008496108457594383 + 4.4946974371447053165e-452j)  +/-  (3.33e-120, 3.33e-120j)
| (1.520953507202042134 + 4.1815114550573999656e-459j)  +/-  (2.08e-122, 2.08e-122j)
| (-1.853107651601512142 + 3.7782142497790207838e-458j)  +/-  (9.7e-122, 9.7e-122j)
| (-4.5674683015120210249 - 3.3550027414205153919e-455j)  +/-  (9.21e-120, 9.21e-120j)
| (1.2200550365907484262 + 5.8323251006555320833e-464j)  +/-  (3.85e-123, 3.85e-123j)
| (2.8645751322696344862 + 9.7862621273880175649e-460j)  +/-  (3.01e-120, 3.01e-120j)
| (-1.520953507202042134 + 3.6207330578171780174e-467j)  +/-  (2.03e-122, 2.03e-122j)
| (-2.1908379211042131419 - 2.6852492191201688464e-465j)  +/-  (4.33e-121, 4.33e-121j)
| (-2.8645751322696344862 + 4.533381817779616725e-464j)  +/-  (3.29e-120, 3.29e-120j)
| (2.5197356856782378834 - 1.034178098116154109e-465j)  +/-  (1.32e-120, 1.32e-120j)
| (2.1908379211042131419 + 1.6433804948895479014e-468j)  +/-  (4.67e-121, 4.67e-121j)
| (-1.2200550365907484262 - 1.0416061201680071373e-471j)  +/-  (3.67e-123, 3.67e-123j)
| (-3.6609245074365333367 - 2.3169816339403837379e-467j)  +/-  (7.54e-120, 7.54e-120j)
| (-0.92627173019387270833 - 1.305265127214061673e-478j)  +/-  (4.94e-124, 4.94e-124j)
| (4.5674683015120210249 + 1.9169638439222008609e-473j)  +/-  (9.04e-120, 9.04e-120j)
| (0.92627173019387270833 + 8.2079141762855605692e-487j)  +/-  (4.99e-124, 4.99e-124j)
| (4.1013375961786396412 - 3.669288799482869212e-481j)  +/-  (1.08e-119, 1.08e-119j)
| (0.28563199730146026621 + 1.3191506821553655948e-497j)  +/-  (2.34e-126, 2.34e-126j)
| (-0.60576387917106011308 + 3.3143668509368693865e-497j)  +/-  (3.43e-125, 3.43e-125j)
| (4.8223162213665322878e-501 + 9.6755895667120849367e-502j)  +/-  (1.72e-499, 1.72e-499j)
| (3.6609245074365333367 - 1.3450203981070939992e-494j)  +/-  (8.49e-120, 8.49e-120j)
| (0.60576387917106011308 - 7.5908207487499325024e-501j)  +/-  (3.43e-125, 3.43e-125j)
| (-4.1013375961786396412 - 4.1018263688365389395e-500j)  +/-  (1.15e-119, 1.15e-119j)
| (-0.28563199730146026621 - 2.1871869470280603831e-507j)  +/-  (2.34e-126, 2.34e-126j)
-------------------------------------------------
The weights are:
| (7.3251084398742711199e-18 + 1.2221042184135350929e-447j)  +/-  (6.72e-42, 2.18e-100j)
| (7.4302321364435934285e-22 + 2.9136548331004238466e-450j)  +/-  (2.94e-44, 9.55e-103j)
| (5.9630491665646529883e-06 + 1.0599908173044115184e-439j)  +/-  (1.45e-33, 4.71e-92j)
| (7.4302321364435934285e-22 - 5.6444835774255416005e-450j)  +/-  (7.86e-44, 2.55e-102j)
| (5.9630491665646529883e-06 - 6.5574395038158048857e-439j)  +/-  (1.57e-34, 5.11e-93j)
| (7.3251084398742711199e-18 - 5.8036925710441537232e-448j)  +/-  (2.71e-43, 8.81e-102j)
| (2.1193036784281340412e-12 + 3.1192342371724574426e-444j)  +/-  (3.45e-40, 1.12e-98j)
| (7.556561751894246188e-15 - 8.3804356538458871035e-446j)  +/-  (3.48e-41, 1.13e-99j)
| (0.00032614454228954568878 + 3.5494200565189573905e-439j)  +/-  (9.85e-34, 3.2e-92j)
| (2.1193036784281340412e-12 - 1.2249812005434250421e-444j)  +/-  (4.9e-42, 1.59e-100j)
| (0.0061862805508493730543 - 2.8210756425929747223e-437j)  +/-  (3.43e-32, 1.11e-90j)
| (7.556561751894246188e-15 + 3.6412303591940668342e-446j)  +/-  (3.25e-43, 1.05e-101j)
| (0.017797509078732090715 + 6.1421923271920588476e-437j)  +/-  (9.3e-31, 3.02e-89j)
| (0.0061862805508493730543 - 2.4659205535907391776e-438j)  +/-  (3.68e-33, 1.19e-91j)
| (2.3583458242596584119e-10 + 2.7820661787161115154e-443j)  +/-  (2.43e-41, 7.88e-100j)
| (0.036615419900507810815 - 1.1034984042643422175e-436j)  +/-  (1.82e-30, 5.91e-89j)
| (5.5915299141719668707e-05 + 2.1930354303774241355e-438j)  +/-  (9.41e-38, 3.06e-96j)
| (0.017797509078732090715 + 1.1318135266823255451e-437j)  +/-  (1.36e-32, 4.43e-91j)
| (0.0015439211295513218988 + 4.9647961095823744369e-440j)  +/-  (7.84e-35, 2.55e-93j)
| (5.5915299141719668707e-05 - 2.8381160687765509043e-439j)  +/-  (4.58e-37, 1.49e-95j)
| (0.00032614454228954568878 - 5.3847947576639049422e-438j)  +/-  (1.83e-37, 5.96e-96j)
| (0.0015439211295513218988 + 1.2652466500020757071e-437j)  +/-  (1.86e-36, 6.04e-95j)
| (0.036615419900507810815 - 3.1804504057656908835e-437j)  +/-  (3.15e-34, 1.02e-92j)
| (3.6490233095263322633e-07 + 8.9666762932057173449e-441j)  +/-  (1.21e-40, 3.94e-99j)
| (0.073585580466726101565 + 6.1627370544163263506e-437j)  +/-  (5.84e-35, 1.88e-93j)
| (2.3583458242596584119e-10 - 7.9893228520929732538e-443j)  +/-  (2.65e-44, 8.6e-103j)
| (0.073585580466726101565 + 1.5069324009208903752e-436j)  +/-  (2.43e-36, 7.44e-95j)
| (1.2652578374560998468e-08 + 1.6689070529813224857e-441j)  +/-  (1.65e-43, 5.32e-102j)
| (0.15881716866165530111 + 2.1779321055541498206e-436j)  +/-  (1.09e-36, 3.26e-95j)
| (0.1280335801226723004 - 1.0301389093360013555e-436j)  +/-  (6.53e-37, 1.93e-95j)
| (0.15406427881167418648 - 2.2301314738906239001e-436j)  +/-  (4e-37, 1.22e-95j)
| (3.6490233095263322633e-07 - 3.6222619488090657175e-440j)  +/-  (1.4e-42, 4.65e-101j)
| (0.1280335801226723004 - 1.8090263987256758358e-436j)  +/-  (1.97e-37, 6.11e-96j)
| (1.2652578374560998468e-08 - 5.0078599895867629539e-442j)  +/-  (7.05e-44, 2.49e-102j)
| (0.15881716866165530111 + 1.6790121731168500604e-436j)  +/-  (1.82e-37, 5.06e-96j)
