Starting with polynomial:
P : 2*t
Extension levels are: 1 2 52
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 52 Kronrod extension for:
P2 : 2*t^3 - 1*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^55 - 27*t^53 + 689/4*t^51 - 5525/8*t^49 + 62475/32*t^47 - 264845/64*t^45 + 1747977/256*t^43 - 4601817/512*t^41 + 314457495/32768*t^39 - 550858165/65536*t^37 + 1595093643/262144*t^35 - 1917334783/524288*t^33 + 1917334783/1048576*t^31 - 1594920705/2097152*t^29 + 2202509545/8388608*t^27 - 1257042033/16777216*t^25 + 18855630495/1073741824*t^23 - 7195285845/2147483648*t^21 + 4418157975/8589934592*t^19 - 1074687075/17179869184*t^17 + 405992895/68719476736*t^15 - 57998985/137438953472*t^13 + 12096045/549755813888*t^11 - 876525/1099511627776*t^9 + 2629575/140737488355328*t^7 - 71253/281474976710656*t^5 + 1827/1125899906842624*t^3 - 7/2251799813685248*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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:
| (-0.99371220989324258353 - 2.8133975980434734524e-819j)  +/-  (9.43e-237, 9.43e-237j)
| (-0.99842681501781656213 + 2.8135087087107510543e-828j)  +/-  (3.09e-237, 3.09e-237j)
| (-0.9438833303083675629 - 3.4977645205128099687e-842j)  +/-  (1.14e-236, 1.14e-236j)
| (0.99842681501781656213 - 2.1828866633147090526e-844j)  +/-  (2.92e-237, 2.92e-237j)
| (0.9438833303083675629 - 5.944778424600340648e-846j)  +/-  (1.2e-236, 1.2e-236j)
| (0.92387953251128675613 - 1.5501122407873901953e-848j)  +/-  (6.91e-237, 6.91e-237j)
| (0.96091732194509954321 - 3.2543139142579351517e-850j)  +/-  (1.66e-236, 1.66e-236j)
| (-0.8752234219087536975 + 5.686151320547625965e-855j)  +/-  (1.65e-237, 1.65e-237j)
| (0.8752234219087536975 - 4.7474466538632682422e-857j)  +/-  (1.41e-237, 1.41e-237j)
| (0.98587101851823587392 - 4.4358213532761331105e-855j)  +/-  (1.39e-236, 1.39e-236j)
| (0.84672419922828416835 + 3.0782192364636966702e-868j)  +/-  (5.06e-238, 5.06e-238j)
| (-0.7071067811865475244 + 9.9969158884534681441e-868j)  +/-  (1.83e-240, 1.83e-240j)
| (-0.38268343236508977173 + 2.0204487808299447283e-874j)  +/-  (4.79e-247, 4.79e-247j)
| (-0.84672419922828416835 - 2.4476245109468377541e-863j)  +/-  (5.48e-238, 5.48e-238j)
| (0.97492791218182360702 + 2.4084934957086372059e-866j)  +/-  (1.76e-236, 1.76e-236j)
| (0.81556086895926017135 + 6.5417818275228131299e-880j)  +/-  (1.53e-238, 1.53e-238j)
| (0.90096886790241912624 - 2.0296143769102565026e-880j)  +/-  (3.45e-237, 3.45e-237j)
| (-0.96091732194509954321 - 3.5550798859603245741e-889j)  +/-  (1.65e-236, 1.65e-236j)
| (-0.78183148246802980871 + 2.4207151592609475936e-908j)  +/-  (4.48e-239, 4.48e-239j)
| (-0.97492791218182360702 + 6.1578854314353816929e-906j)  +/-  (1.54e-236, 1.54e-236j)
| (0.99371220989324258353 - 5.0492299329020904066e-918j)  +/-  (9.97e-237, 9.97e-237j)
| (0.78183148246802980871 - 4.8693781993937134053e-922j)  +/-  (3.52e-239, 3.52e-239j)
| (-0.92387953251128675613 - 6.5283080268366141608e-917j)  +/-  (6.24e-237, 6.24e-237j)
| (-0.81556086895926017135 + 8.0777196891575239159e-921j)  +/-  (1.57e-238, 1.57e-238j)
| (-0.74564216488316560949 - 3.4313859927860162446e-923j)  +/-  (7.86e-240, 7.86e-240j)
| (0.22252093395631440429 - 2.4594301597199098899e-935j)  +/-  (9.28e-251, 9.28e-251j)
| (0.74564216488316560949 - 3.8778674598254551627e-925j)  +/-  (8.77e-240, 8.77e-240j)
| (0.7071067811865475244 - 4.5086771718980259502e-926j)  +/-  (1.73e-240, 1.73e-240j)
| (-0.27683551142484938763 + 9.5990151059004862869e-935j)  +/-  (1.74e-249, 1.74e-249j)
| (-0.66634657795200394558 + 4.7432049656364976413e-924j)  +/-  (3.19e-241, 3.19e-241j)
| (-0.90096886790241912624 - 9.6538253131803968654e-924j)  +/-  (2.83e-237, 2.83e-237j)
| (0.66634657795200394558 + 2.6222716777910678878e-935j)  +/-  (3.44e-241, 3.44e-241j)
| (0.62348980185873353053 - 5.012029732498672773e-937j)  +/-  (5.34e-242, 5.34e-242j)
| (-0.98587101851823587392 - 3.7879222298804273245e-938j)  +/-  (1.27e-236, 1.27e-236j)
| (-0.57867129617980574163 - 4.6240961902806632567e-948j)  +/-  (6.18e-243, 6.18e-243j)
| (-0.62348980185873353053 - 6.194260160383155238e-952j)  +/-  (4.91e-242, 4.91e-242j)
| (-5.9885046128579750421e-980 - 3.7407254711359525717e-980j)  +/-  (3.88e-978, 3.88e-978j)
| (0.57867129617980574163 + 5.0864983250839346655e-954j)  +/-  (6.09e-243, 6.09e-243j)
| (0.27683551142484938763 - 2.9639664996722076946e-960j)  +/-  (1.49e-249, 1.49e-249j)
| (-0.056070447237191788191 + 1.2642067686932983198e-965j)  +/-  (1.44e-254, 1.44e-254j)
| (-0.53203207651533656356 + 1.105063979747080425e-955j)  +/-  (8.28e-244, 8.28e-244j)
| (-0.22252093395631440429 + 1.9128897802889707652e-963j)  +/-  (8.5e-251, 8.5e-251j)
| (0.43388373911755812048 + 8.8127857483698163982e-958j)  +/-  (6.11e-246, 6.11e-246j)
| (0.53203207651533656356 - 1.5897826615272950386e-956j)  +/-  (7.21e-244, 7.21e-244j)
| (0.056070447237191788191 + 5.8102683997587383406e-969j)  +/-  (1.07e-254, 1.07e-254j)
| (-0.48371888710523979107 - 1.7660681464903624072e-960j)  +/-  (7.97e-245, 7.97e-245j)
| (-0.33027906195516708177 + 2.0958048026506088668e-962j)  +/-  (3.23e-248, 3.23e-248j)
| (0.11196447610330785847 - 6.9928327617989177804e-968j)  +/-  (2.65e-253, 2.65e-253j)
| (0.48371888710523979107 - 1.9468599534839804372e-959j)  +/-  (7.44e-245, 7.44e-245j)
| (0.16750622330473640809 + 3.7759092413148260267e-966j)  +/-  (4.64e-252, 4.64e-252j)
| (-0.16750622330473640809 + 1.8990248725726532401e-966j)  +/-  (4.93e-252, 4.93e-252j)
| (-0.43388373911755812048 + 4.9638349301882735694e-960j)  +/-  (6.07e-246, 6.07e-246j)
| (-0.11196447610330785847 - 3.9841014315624977163e-968j)  +/-  (2.24e-253, 2.24e-253j)
| (0.33027906195516708177 + 2.2253552088869429029e-962j)  +/-  (3.49e-248, 3.49e-248j)
| (0.38268343236508977173 + 7.839585946169349385e-963j)  +/-  (4.62e-247, 4.62e-247j)
-------------------------------------------------
The weights are:
| (0.00022385792694800350877 - 7.4885023645915110948e-821j)  +/-  (5.57e-53, 4.57e-167j)
| (5.6140983096048361311e-05 - 3.350161942857340527e-821j)  +/-  (3.98e-53, 3.26e-167j)
| (0.0019479331922497338508 - 1.0998261680551302828e-820j)  +/-  (5.48e-54, 4.5e-168j)
| (5.6140983096048361311e-05 + 7.9285082605544361121e-824j)  +/-  (5.09e-54, 4.17e-168j)
| (0.0019479331922497338508 - 2.8284079189826918649e-822j)  +/-  (2.64e-54, 2.17e-168j)
| (0.0026151180251201113893 + 3.8367743326778665172e-822j)  +/-  (1.45e-54, 1.19e-168j)
| (0.0013685339354617484969 + 1.969800429183639378e-822j)  +/-  (1.01e-54, 8.26e-169j)
| (0.0041782850311130663968 + 9.9209193390678752395e-821j)  +/-  (1.72e-56, 1.41e-170j)
| (0.0041782850311130663968 + 6.2897709702641914052e-822j)  +/-  (6.98e-56, 5.72e-170j)
| (0.00050104169367528961701 + 7.1208397741538261514e-823j)  +/-  (8.33e-56, 6.83e-170j)
| (0.0050546094721646596386 - 7.7267685488837143947e-822j)  +/-  (1.48e-56, 1.22e-170j)
| (0.0089285714285714285714 - 8.7645309264268387092e-821j)  +/-  (2.65e-59, 2.18e-173j)
| (0.015242024832022745754 + 7.017979786117558298e-821j)  +/-  (6.13e-60, 5.02e-174j)
| (0.0050546094721646596386 - 9.6746844164244668395e-821j)  +/-  (1.11e-58, 9.11e-173j)
| (0.00088420653658554351575 - 1.2636258505509776831e-822j)  +/-  (9.31e-56, 7.64e-170j)
| (0.0059796512325431510556 + 9.2982848350479122875e-822j)  +/-  (5.85e-58, 4.8e-172j)
| (0.0033616981976898791917 - 4.9917602255077137096e-822j)  +/-  (2.71e-56, 2.22e-170j)
| (0.0013685339354617484969 + 1.1740336165574556468e-820j)  +/-  (8.1e-60, 6.64e-174j)
| (0.0069417773753900499617 - 9.2174404206130495584e-821j)  +/-  (8.54e-61, 7e-175j)
| (0.00088420653658554351575 - 1.324310648398895618e-820j)  +/-  (3.83e-60, 3.14e-174j)
| (0.00022385792694800350877 - 3.1689323545420736202e-823j)  +/-  (6.81e-58, 5.59e-172j)
| (0.0069417773753900499617 - 1.0999436340302759283e-821j)  +/-  (9.92e-61, 8.13e-175j)
| (0.0026151180251201113893 + 1.0535707713344140566e-820j)  +/-  (2.69e-60, 2.21e-174j)
| (0.0059796512325431510556 + 9.4431713749484514667e-821j)  +/-  (6.7e-61, 5.49e-175j)
| (0.0079288886062204655494 + 8.9922651406302245978e-821j)  +/-  (1.11e-61, 9.11e-176j)
| (0.016972936320557313627 - 3.9261895274806424294e-821j)  +/-  (3.5e-66, 2.87e-180j)
| (0.0079288886062204655494 + 1.2824940394915307052e-821j)  +/-  (3.79e-62, 3.11e-176j)
| (0.0089285714285714285714 - 1.4769132734228261815e-821j)  +/-  (3.28e-63, 2.69e-177j)
| (0.016488608921681108646 + 6.4709890669530299025e-821j)  +/-  (8.67e-67, 7.11e-181j)
| (0.0099282542509223915935 + 8.532394351909356489e-821j)  +/-  (2.53e-64, 2.07e-178j)
| (0.0033616981976898791917 - 1.0197814140301529694e-820j)  +/-  (3.8e-62, 3.11e-176j)
| (0.0099282542509223915935 + 1.682598646185291875e-821j)  +/-  (1.02e-64, 8.39e-179j)
| (0.010915365481752807181 - 1.8989132362927677254e-821j)  +/-  (8.73e-66, 7.16e-180j)
| (0.00050104169367528961701 + 1.7977236251102806787e-820j)  +/-  (1.16e-62, 9.5e-177j)
| (0.011877491624599706087 + 8.0512800874239539522e-821j)  +/-  (1.54e-66, 1.26e-180j)
| (0.010915365481752807181 - 8.2948147902467960313e-821j)  +/-  (1.03e-65, 8.42e-180j)
| (0.017857142857142857143 - 5.0557135528812933096e-821j)  +/-  (1.58e-70, 1.29e-184j)
| (0.011877491624599706087 + 2.1251880544208277633e-821j)  +/-  (3.75e-68, 3.08e-182j)
| (0.016488608921681108646 + 3.6511035361529163705e-821j)  +/-  (1.91e-70, 1.56e-184j)
| (0.017801001874046808782 + 5.3411972418099698258e-821j)  +/-  (8.85e-71, 7.25e-185j)
| (0.012802533384978197504 - 7.8016388633171061722e-821j)  +/-  (1.23e-68, 1.01e-182j)
| (0.016972936320557313627 - 6.1919292675413356643e-821j)  +/-  (1.38e-70, 1.13e-184j)
| (0.014495444659452977951 - 2.8566520699630664603e-821j)  +/-  (2.28e-71, 1.87e-185j)
| (0.012802533384978197504 - 2.3607243383399236219e-821j)  +/-  (2.68e-70, 2.2e-184j)
| (0.017801001874046808782 + 4.770634723759536056e-821j)  +/-  (6.42e-72, 5.27e-186j)
| (0.013678857826029790746 + 7.5459940493889065271e-821j)  +/-  (8.8e-71, 7.22e-185j)
| (0.015909209664893123292 - 6.746562549901856782e-821j)  +/-  (2.52e-71, 2.07e-185j)
| (0.017633284930194853634 - 4.4867945707758107819e-821j)  +/-  (9.82e-73, 8.05e-187j)
| (0.013678857826029790746 + 2.6047959778481012274e-821j)  +/-  (1.23e-72, 1.01e-186j)
| (0.017356101163467567526 + 4.2050325741779017492e-821j)  +/-  (5.47e-73, 4.49e-187j)
| (0.017356101163467567526 + 5.9101016170164071325e-821j)  +/-  (1.91e-73, 1.56e-187j)
| (0.014495444659452977951 - 7.2846329468406296002e-821j)  +/-  (4.39e-73, 3.6e-187j)
| (0.017633284930194853634 - 5.6262624349871873104e-821j)  +/-  (1.34e-73, 1.1e-187j)
| (0.015909209664893123292 - 3.380606296603054618e-821j)  +/-  (6.93e-75, 5.69e-189j)
| (0.015242024832022745754 + 3.1155196062747018951e-821j)  +/-  (6.32e-75, 5.17e-189j)
