Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 6 26
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P2 : 4*t^5 - 14*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P3 : 4*t^11 - 6923/82*t^9 + 97479/164*t^7 - 566685/328*t^5 + 1313235/656*t^3 - 418635/656*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^37 - 9677760980250929714296375932722228873871700280671937713461681871189/8737455613503311821968931966238301890759133372843957012681019146*t^35 + 4758253990583310088300420805205125221782817719718150704171100527529559/34949822454013247287875727864953207563036533491375828050724076584*t^33 - 229234777374127007505224926849209154675634318525622975162685852375694989/23299881636008831525250485243302138375357688994250552033816051056*t^31 + 65253625553933673889995397200910576573130424381690190172965729366452050219/139799289816052989151502911459812830252146133965503312202896306336*t^29 - 4300458815499615342371391563519482204513922298263249873764201100892457663997/279598579632105978303005822919625660504292267931006624405792612672*t^27 + 7524989455853686842775325311007710540104296818468555925738891961706172306515/20711005898674516911333764660713011889206834661556046252280934272*t^25 - 259439269578128536074970937134006332882697872180627314726436491228408094815425/41422011797349033822667529321426023778413669323112092504561868544*t^23 + 598620211391254930114632391356492975019981880398222582863649847467550520968975/7531274872245278876848641694804731596075212604202198637193067008*t^21 - 11206638068362490007645514260531605245985400453795530195227815676451109170223525/15062549744490557753697283389609463192150425208404397274386134016*t^19 + 154112464093225887246182943756196193477098369620365432269436211663617593533807075/30125099488981115507394566779218926384300850416808794548772268032*t^17 - 1540837870802419301094147570820648029903471172823255379651210957439283258635240125/60250198977962231014789133558437852768601700833617589097544536064*t^15 + 11003084701740830138636680475523673759821042164652829730396288042659580505658985625/120500397955924462029578267116875705537203401667235178195089072128*t^13 - 54582289403737741643258876392907662856437220924301990066139471451485209740426253375/241000795911848924059156534233751411074406803334470356390178144256*t^11 + 180287208498045758760871504344841942462323148574314337395600107700943168942848183875/482001591823697848118313068467502822148813606668940712780356288512*t^9 - 371336395763594672528826390866627300258911489568298582852048598150625703917687276625/964003183647395696236626136935005644297627213337881425560712577024*t^7 + 428604813259731233285957779194655792624361589682719369257061341577092040887203168125/1928006367294791392473252273870011288595254426675762851121425154048*t^5 - 228241990123102841642641235412367136689065688287006547625134632025350034090034458125/3856012734589582784946504547740022577190508853351525702242850308096*t^3 + 17831462585522020446778732358198722830316435255985870577135054102541799038308230625/3856012734589582784946504547740022577190508853351525702242850308096*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:
| (-7.2923776680602610432 + 1.3816907735035494294e-936j)  +/-  (8.05e-249, 8.05e-249j)
| (-5.9894197635317259875 + 1.3307857550030052239e-933j)  +/-  (2.5e-247, 2.5e-247j)
| (-5.4583275522849112871 + 2.4220118629198161263e-933j)  +/-  (5.3e-247, 5.3e-247j)
| (6.5813943717550437161 - 6.4531564224135052545e-938j)  +/-  (5.98e-248, 5.98e-248j)
| (-6.5813943717550437161 + 2.371576898278158599e-938j)  +/-  (6.37e-248, 6.37e-248j)
| (4.9659988986978325521 + 2.6282955003090949861e-937j)  +/-  (8.31e-247, 8.31e-247j)
| (5.4583275522849112871 - 5.4722144337887177776e-937j)  +/-  (5.39e-247, 5.39e-247j)
| (7.2923776680602610432 + 9.6829541019874753543e-939j)  +/-  (7.7e-249, 7.7e-249j)
| (-1.3866480207208212553 - 1.2718393029101161539e-938j)  +/-  (2.66e-250, 2.66e-250j)
| (-3.2137281525534003284 + 4.8545438693014480859e-935j)  +/-  (3.6e-247, 3.6e-247j)
| (-4.9659988986978325521 - 4.5110954934802842214e-943j)  +/-  (9.26e-247, 9.26e-247j)
| (1.0498242882510985417 + 3.403315832857534095e-955j)  +/-  (2.3e-251, 2.3e-251j)
| (-1.7320508075688772935 + 3.1631828495287931505e-952j)  +/-  (2.9e-249, 2.9e-249j)
| (1.7320508075688772935 + 3.0958539383966373904e-953j)  +/-  (3.08e-249, 3.08e-249j)
| (4.5010922415777308103 + 4.8179864550911851417e-951j)  +/-  (1.01e-246, 1.01e-246j)
| (2.1324303319308354501 + 4.0432839234852336807e-951j)  +/-  (9.86e-248, 9.86e-248j)
| (5.9894197635317259875 + 7.35475341306129511e-952j)  +/-  (2.44e-247, 2.44e-247j)
| (-4.5010922415777308103 + 3.4346355262078567586e-951j)  +/-  (1.01e-246, 1.01e-246j)
| (-2.8071488894410374115 - 4.5166112123550542837e-959j)  +/-  (2.12e-247, 2.12e-247j)
| (4.0568530737971230998 + 4.4990375696860081017e-966j)  +/-  (8.49e-247, 8.49e-247j)
| (2.3311021660228306933 - 9.0403807229278706012e-964j)  +/-  (2.35e-246, 2.35e-246j)
| (0.7071067811865475244 - 1.7471061537773789167e-973j)  +/-  (1.5e-252, 1.5e-252j)
| (2.8071488894410374115 - 1.0724356118757687328e-969j)  +/-  (2.16e-247, 2.16e-247j)
| (3.6288440749938735129 - 1.6904935373789935275e-968j)  +/-  (5.91e-247, 5.91e-247j)
| (-1.0498242882510985417 - 6.8746982471687169651e-972j)  +/-  (2.37e-251, 2.37e-251j)
| (-2.3311021660228306933 + 2.3395575303864603809e-965j)  +/-  (2.18e-246, 2.18e-246j)
| (0.35589890379552448563 - 2.2460103908656158807e-995j)  +/-  (8.25e-254, 8.25e-254j)
| (1.3866480207208212553 - 6.3190697621514282159e-992j)  +/-  (2.68e-250, 2.68e-250j)
| (-2.7021415400927256929e-1004 - 7.1037191643450416943e-1004j)  +/-  (2.81e-1002, 2.81e-1002j)
| (-0.7071067811865475244 - 1.0565398266678378851e-994j)  +/-  (1.55e-252, 1.55e-252j)
| (-0.35589890379552448563 + 1.8612196502078052872e-995j)  +/-  (8.25e-254, 8.25e-254j)
| (2.3142743884833336815 - 7.6670052102463815667e-988j)  +/-  (2.28e-246, 2.28e-246j)
| (-2.3142743884833336815 - 5.3585776927632722765e-996j)  +/-  (2.45e-246, 2.45e-246j)
| (-4.0568530737971230998 + 1.374603970401927584e-1028j)  +/-  (7.98e-247, 7.98e-247j)
| (-3.6288440749938735129 - 9.3644151758332204176e-1053j)  +/-  (5.84e-247, 5.84e-247j)
| (3.2137281525534003284 + 2.4239828869908731194e-1060j)  +/-  (3.58e-247, 3.58e-247j)
| (-2.1324303319308354501 + 2.6450583667268871918e-1062j)  +/-  (9.8e-248, 9.8e-248j)
-------------------------------------------------
The weights are:
| (3.7106846244253552141e-24 - 1.2132708889867702792e-951j)  +/-  (2.62e-95, 2.83e-219j)
| (8.2652908951098864073e-17 - 1.52718653012172733e-947j)  +/-  (1.56e-92, 1.68e-216j)
| (3.3057474028530326191e-14 + 1.2723006855537774881e-945j)  +/-  (2.01e-91, 2.16e-215j)
| (5.5376932388127187489e-20 - 1.0010074446540538309e-949j)  +/-  (6.69e-97, 7.21e-221j)
| (5.5376932388127187489e-20 + 2.6397571651838756975e-949j)  +/-  (2.9e-94, 3.13e-218j)
| (5.2473816997018550888e-12 + 3.9303362573880718152e-945j)  +/-  (3.13e-93, 3.38e-217j)
| (3.3057474028530326191e-14 - 1.9381317294036575925e-946j)  +/-  (1.56e-94, 1.68e-218j)
| (3.7106846244253552141e-24 + 5.0162679125525115687e-952j)  +/-  (4.03e-99, 4.34e-223j)
| (0.027865529948010521468 + 7.3505128296096508525e-938j)  +/-  (5.33e-79, 5.74e-203j)
| (7.560838962485525144e-06 + 1.8648955558597744971e-939j)  +/-  (4.56e-89, 4.91e-213j)
| (5.2473816997018550888e-12 - 2.2143521814674214457e-944j)  +/-  (2.96e-93, 3.19e-217j)
| (0.063411528615731932213 - 4.0014727158755065613e-938j)  +/-  (5.97e-78, 6.44e-202j)
| (0.010026817070800917849 - 6.8174182137096721305e-938j)  +/-  (1.81e-82, 1.95e-206j)
| (0.010026817070800917849 - 1.9849420360378029921e-938j)  +/-  (7.11e-84, 7.66e-208j)
| (4.0686415160893134574e-10 - 5.7760811904255322968e-944j)  +/-  (1.05e-93, 1.13e-217j)
| (0.0035386429897468548637 + 3.0737938799625759535e-938j)  +/-  (9.11e-87, 9.82e-211j)
| (8.2652908951098864073e-17 + 6.1195023157066458308e-948j)  +/-  (6.07e-97, 6.54e-221j)
| (4.0686415160893134574e-10 + 3.8112770067117806201e-943j)  +/-  (5.04e-94, 5.43e-218j)
| (8.6578502252067508543e-05 - 7.6266446111739101579e-939j)  +/-  (5.15e-90, 5.55e-214j)
| (1.7489694719055540009e-08 + 6.6303670057072273193e-943j)  +/-  (1.87e-93, 2.01e-217j)
| (0.0099480665184692518146 + 1.5819387731715389292e-937j)  +/-  (3.16e-89, 3.41e-213j)
| (0.11886138157858671132 + 5.0385809045258540487e-938j)  +/-  (5.77e-86, 6.21e-210j)
| (8.6578502252067508543e-05 - 4.995338309045565766e-940j)  +/-  (2.36e-91, 2.54e-215j)
| (4.5366674942868791935e-07 - 6.3597656129967675585e-942j)  +/-  (2.62e-93, 2.82e-217j)
| (0.063411528615731932213 - 7.8450597179959165762e-938j)  +/-  (2.03e-87, 2.19e-211j)
| (0.0099480665184692518146 + 1.0197997242023277844e-936j)  +/-  (1.35e-91, 1.45e-215j)
| (0.1761318768863002594 - 5.9472781793102709055e-938j)  +/-  (1.37e-87, 1.48e-211j)
| (0.027865529948010521468 + 2.8899573017913601805e-938j)  +/-  (3.24e-89, 3.5e-213j)
| (0.20123094402707388939 + 6.7517902696777592278e-938j)  +/-  (7.95e-88, 8.57e-212j)
| (0.11886138157858671132 + 7.8821543399901832886e-938j)  +/-  (6.73e-89, 7.26e-213j)
| (0.1761318768863002594 - 7.4324883356384412696e-938j)  +/-  (1.42e-88, 1.54e-212j)
| (-0.010493926530986767901 - 1.8030020690507909478e-937j)  +/-  (6.58e-90, 7.1e-214j)
| (-0.010493926530986767901 - 1.1369840335109955345e-936j)  +/-  (1.39e-91, 1.49e-215j)
| (1.7489694719055540009e-08 - 6.0943137590537135251e-942j)  +/-  (1.4e-97, 1.52e-221j)
| (4.5366674942868791935e-07 + 1.098954237292856713e-940j)  +/-  (1.14e-96, 1.24e-220j)
| (7.560838962485525144e-06 + 5.5025377975573978879e-941j)  +/-  (1.16e-95, 1.34e-219j)
| (0.0035386429897468548637 + 1.5581718253067901058e-937j)  +/-  (6.47e-93, 6.82e-217j)
