Starting with polynomial:
P : t
Extension levels are: 1 12 22
-------------------------------------------------
Trying to find an order 12 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P2 : t^13 - 78*t^11 + 2145*t^9 - 25740*t^7 + 135135*t^5 - 270270*t^3 + 135135*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^35 - 104183722427/223695465*t^33 + 49747981712374/521956085*t^31 - 1183349601145470/104391217*t^29 + 91193242189830462/104391217*t^27 - 4807731238765183278/104391217*t^25 + 178520343673970119734/104391217*t^23 - 4737442080901430349702/104391217*t^21 + 12895216245629117959680/14913031*t^19 - 175818765562104382892460/14913031*t^17 + 1696563534341565839526390/14913031*t^15 - 11363377682679217847408790/14913031*t^13 + 51269666800511609160552270/14913031*t^11 - 148989298097147016195665550/14913031*t^9 + 260405409094543658973520350/14913031*t^7 - 34965086608775141668728450/2130433*t^5 + 14344888314278558359612575/2130433*t^3 - 1557077815890323403759225/2130433*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:
| (-3.0983127009868550217 + 4.1535926706381307536e-911j)  +/-  (1.47e-248, 1.47e-248j)
| (6.4593756177075050484 - 2.6091893852322268112e-911j)  +/-  (2.91e-247, 2.91e-247j)
| (-8.7684211070939494708 + 1.4098470716478279365e-918j)  +/-  (3.02e-248, 3.02e-248j)
| (-9.7869489849446719869 - 1.4441645107579657293e-917j)  +/-  (3.52e-249, 3.52e-249j)
| (-7.161379530157217057 - 2.8422189121189273003e-915j)  +/-  (2.12e-247, 2.12e-247j)
| (-5.1773290892407881068 + 2.1202137304692742482e-917j)  +/-  (2.93e-247, 2.93e-247j)
| (5.8001672523865003059 + 1.21955882303319855e-923j)  +/-  (3.22e-247, 3.22e-247j)
| (-6.4593756177075050484 - 3.7287490929368179093e-929j)  +/-  (3.2e-247, 3.2e-247j)
| (-7.9207974804701445468 - 1.9327807008966820745e-931j)  +/-  (1.04e-247, 1.04e-247j)
| (9.7869489849446719869 + 7.5448218606724520632e-931j)  +/-  (3.85e-249, 3.85e-249j)
| (7.9207974804701445468 - 4.1596712957194258294e-929j)  +/-  (1.09e-247, 1.09e-247j)
| (-2.6206899734322147806 + 1.6118122351305067087e-934j)  +/-  (3.24e-249, 3.24e-249j)
| (7.161379530157217057 - 1.3634813765579598838e-932j)  +/-  (2.27e-247, 2.27e-247j)
| (3.5634443802816340916 + 1.8163267440070876335e-946j)  +/-  (4.19e-248, 4.19e-248j)
| (-5.8001672523865003059 - 7.8579185623299840062e-961j)  +/-  (3.26e-247, 3.26e-247j)
| (8.7684211070939494708 - 4.8863535642651654862e-973j)  +/-  (3.04e-248, 3.04e-248j)
| (4.5913984489365206271 + 2.1941381301404610971e-984j)  +/-  (1.69e-247, 1.69e-247j)
| (-1.7254183795882391615 - 4.9381334624331334412e-1000j)  +/-  (1.09e-250, 1.09e-250j)
| (-1.3099460432829670698 - 1.0089912431641317813e-1000j)  +/-  (1.51e-251, 1.51e-251j)
| (-3.5634443802816340916 + 1.0484371538352671211e-995j)  +/-  (4.5e-248, 4.5e-248j)
| (5.1773290892407881068 + 6.206838189656948714e-1006j)  +/-  (2.51e-247, 2.51e-247j)
| (0.40394464443144039485 + 1.1423420346657870065e-1015j)  +/-  (6.54e-254, 6.54e-254j)
| (-4.5913984489365206271 + 1.7072196524291736379e-1009j)  +/-  (1.67e-247, 1.67e-247j)
| (2.6206899734322147806 - 1.6350164395508710401e-1009j)  +/-  (3.64e-249, 3.64e-249j)
| (-2.150953077624052883 + 6.4971730681543692965e-1020j)  +/-  (6.37e-250, 6.37e-250j)
| (3.0983127009868550217 + 2.95438099925564535e-1014j)  +/-  (1.51e-248, 1.51e-248j)
| (0.8566794935194500339 + 1.9755231957039298187e-1029j)  +/-  (1.21e-252, 1.21e-252j)
| (4.05112100249241973 + 8.1592323656546220649e-1027j)  +/-  (9.85e-248, 9.85e-248j)
| (2.150953077624052883 + 3.1445541881830137216e-1038j)  +/-  (6.78e-250, 6.78e-250j)
| (-0.40394464443144039485 - 1.5970525645601493056e-1042j)  +/-  (6.54e-254, 6.54e-254j)
| (-4.05112100249241973 - 6.0252391305045714528e-1039j)  +/-  (1.07e-247, 1.07e-247j)
| (1.7254183795882391615 - 1.0091851354368834897e-1044j)  +/-  (1.22e-250, 1.22e-250j)
| (1.3099460432829670698 + 1.6167923117361720463e-1044j)  +/-  (1.55e-251, 1.55e-251j)
| (4.9007179405806804315e-1056 - 4.9376615956850868366e-1056j)  +/-  (2.43e-1054, 2.43e-1054j)
| (-0.8566794935194500339 + 2.6775864641496764605e-1048j)  +/-  (1.01e-252, 1.01e-252j)
-------------------------------------------------
The weights are:
| (0.0015439211295513218988 + 1.5315247010307018108e-913j)  +/-  (1.3e-76, 2.07e-200j)
| (2.3583458242596584119e-10 + 7.474007502932934157e-920j)  +/-  (5.58e-88, 8.92e-212j)
| (7.3251084398742711199e-18 + 2.7649828129273274088e-924j)  +/-  (1.96e-92, 3.13e-216j)
| (7.4302321364435934285e-22 - 1.3338198942652835313e-926j)  +/-  (3e-94, 4.79e-218j)
| (2.1193036784281340412e-12 + 6.1681806249115987849e-921j)  +/-  (3.18e-90, 5.09e-214j)
| (3.6490233095263322633e-07 - 3.2919810593667597615e-917j)  +/-  (7.68e-87, 1.23e-210j)
| (1.2652578374560998468e-08 - 8.52486690256286251e-919j)  +/-  (1.84e-90, 2.94e-214j)
| (2.3583458242596584119e-10 - 1.4015544837707846838e-919j)  +/-  (2.24e-89, 3.57e-213j)
| (7.556561751894246188e-15 - 1.7924614402998945957e-922j)  +/-  (9.63e-92, 1.54e-215j)
| (7.4302321364435934285e-22 + 6.610149571710645481e-927j)  +/-  (3.69e-99, 5.9e-223j)
| (7.556561751894246188e-15 + 7.1056596786452204493e-923j)  +/-  (3.58e-96, 5.72e-220j)
| (0.0061862805508493730543 - 4.0168156664786811175e-913j)  +/-  (7e-84, 1.12e-207j)
| (2.1193036784281340412e-12 - 1.9857016569398735906e-921j)  +/-  (8.37e-95, 1.34e-218j)
| (0.00032614454228954568878 - 2.8664835101253311124e-915j)  +/-  (1.55e-89, 2.48e-213j)
| (1.2652578374560998468e-08 + 2.3811458004801544544e-918j)  +/-  (1.07e-91, 1.72e-215j)
| (7.3251084398742711199e-18 - 1.2387651139428527449e-924j)  +/-  (5.4e-98, 8.62e-222j)
| (5.9630491665646529883e-06 - 8.0436128184107536674e-917j)  +/-  (7.21e-92, 1.15e-215j)
| (0.036615419900507810815 - 8.260744138362870927e-913j)  +/-  (1.23e-84, 1.96e-208j)
| (0.073585580466726101565 + 1.013979934125922804e-912j)  +/-  (2.67e-83, 4.26e-207j)
| (0.00032614454228954568878 + 3.9836838561071237138e-914j)  +/-  (2.72e-89, 4.35e-213j)
| (3.6490233095263322633e-07 + 8.9860325189379750536e-918j)  +/-  (6.38e-93, 1.02e-216j)
| (0.15881716866165530111 + 1.0205762088531936193e-912j)  +/-  (1.61e-85, 2.57e-209j)
| (5.9630491665646529883e-06 + 3.9249992059824899515e-916j)  +/-  (1.54e-91, 2.46e-215j)
| (0.0061862805508493730543 - 3.4173690365733401838e-914j)  +/-  (3.27e-90, 5.22e-214j)
| (0.017797509078732090715 + 5.5633764461852233087e-913j)  +/-  (4.9e-88, 7.83e-212j)
| (0.0015439211295513218988 + 1.0597277218680062991e-914j)  +/-  (7.35e-91, 1.17e-214j)
| (0.1280335801226723004 - 6.4818093193245969076e-913j)  +/-  (1.46e-88, 2.33e-212j)
| (5.5915299141719668707e-05 + 5.6949514797629605998e-916j)  +/-  (4.1e-92, 6.56e-216j)
| (0.017797509078732090715 + 1.0185152206914599197e-913j)  +/-  (2.84e-90, 4.53e-214j)
| (0.15881716866165530111 + 1.3234049120291878318e-912j)  +/-  (4.22e-89, 6.72e-213j)
| (5.5915299141719668707e-05 - 4.1093670482261534729e-915j)  +/-  (2.88e-92, 4.61e-216j)
| (0.036615419900507810815 - 2.3771085840165333367e-913j)  +/-  (3.46e-90, 5.52e-214j)
| (0.073585580466726101565 + 4.1469867795510749926e-913j)  +/-  (6.22e-90, 9.96e-214j)
| (0.15406427881167418648 - 1.3427825880635823559e-912j)  +/-  (7.53e-90, 1.22e-213j)
| (0.1280335801226723004 - 1.1377146782098275817e-912j)  +/-  (2.74e-90, 4.06e-214j)
