Starting with polynomial:
P : 2*t
Extension levels are: 1 56
-------------------------------------------------
Trying to find an order 56 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^57 - 1596*t^55 + 592515*t^53 - 136080945*t^51 + 173503204875/8*t^49 - 5100994223325/2*t^47 + 1838058251804775/8*t^45 - 129976976377623375/8*t^43 + 117369209668993907625/128*t^41 - 2673409775793750118125/64*t^39 + 396199328772633767506125/256*t^37 - 11994034225571549507230875/256*t^35 + 2378816788071690652267456875/2048*t^33 - 6038534923566599348063544375/256*t^31 + 401131248494066956692792590625/1024*t^29 - 5428642896286372813909126393125/1024*t^27 + 1905453656596516857682103363986875/32768*t^25 - 8406413190866986136832808958765625/16384*t^23 + 236313615254371943624300074063078125/65536*t^21 - 1305943663247844951607974093506484375/65536*t^19 + 44663273283076297344992713997921765625/524288*t^17 - 36155983133918907374517911331650953125/131072*t^15 + 345125293551044115847670971802122734375/524288*t^13 - 585212454282205239915615995664468984375/524288*t^11 + 10728894995173762731786293253848598046875/8388608*t^9 - 3862402198262554583443065571385495296875/4194304*t^7 + 6239265089501049711715721307622723171875/16777216*t^5 - 1155419461018712909576985427337541328125/16777216*t^3 + 495179769008019818390136611716089140625/134217728*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: 0
  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:
| (-9.2313849407386559136 + 5.8964283863522999912e-846j)  +/-  (1.74e-244, 1.74e-244j)
| (7.7811416453357013504 + 8.849915773335561748e-845j)  +/-  (1.84e-242, 1.84e-242j)
| (9.2313849407386559136 + 3.0883001229199787281e-846j)  +/-  (1.99e-244, 1.99e-244j)
| (8.2211122660677174688 + 3.5904058478283178149e-845j)  +/-  (5.21e-243, 5.21e-243j)
| (-6.97334515429562482 - 8.7164766705786989299e-843j)  +/-  (7.21e-242, 7.21e-242j)
| (6.97334515429562482 - 1.0607865242358736733e-846j)  +/-  (6.98e-242, 6.98e-242j)
| (8.6977298758606241635 - 8.9339081330169271895e-849j)  +/-  (1.24e-243, 1.24e-243j)
| (-5.1905639023838362284 - 4.6988346740806018769e-845j)  +/-  (6.25e-242, 6.25e-242j)
| (-4.8589492677211485311 + 9.4531091973831856492e-854j)  +/-  (3.2e-242, 3.2e-242j)
| (-8.2211122660677174688 - 3.2998691954049089478e-862j)  +/-  (5.87e-243, 5.87e-243j)
| (-6.2295737517233464887 - 1.4806495736333899739e-870j)  +/-  (1.19e-241, 1.19e-241j)
| (5.1905639023838362284 + 1.4103571083527705089e-878j)  +/-  (5.67e-242, 5.67e-242j)
| (7.367318376778573388 - 3.505087898331832452e-880j)  +/-  (4.42e-242, 4.42e-242j)
| (-9.8755270017367683053 - 5.6952639529646591661e-882j)  +/-  (1.07e-245, 1.07e-245j)
| (5.5287966039093661247 + 2.002075192220448499e-878j)  +/-  (9.94e-242, 9.94e-242j)
| (-7.367318376778573388 + 1.3746244894853970187e-877j)  +/-  (4.33e-242, 4.33e-242j)
| (-7.7811416453357013504 + 1.8944762976864337696e-883j)  +/-  (2e-242, 2e-242j)
| (3.8958003472863841389 + 1.3450651508443472987e-887j)  +/-  (2.54e-243, 2.54e-243j)
| (-1.1741477394031905613 + 1.2711695625668848341e-895j)  +/-  (1.63e-250, 1.63e-250j)
| (6.5950705250038870948 - 7.7278587201828781186e-886j)  +/-  (1.13e-241, 1.13e-241j)
| (4.5330849920738157789 + 1.0978713010538398916e-887j)  +/-  (1.6e-242, 1.6e-242j)
| (2.0634488697846302516 - 1.1272920708923950227e-895j)  +/-  (1.71e-247, 1.71e-247j)
| (6.2295737517233464887 - 1.2800006606856051871e-888j)  +/-  (1.27e-241, 1.27e-241j)
| (-8.6977298758606241635 + 1.679086889142893059e-888j)  +/-  (1.32e-243, 1.32e-243j)
| (9.8755270017367683053 + 3.3566369523693111377e-899j)  +/-  (1.01e-245, 1.01e-245j)
| (-6.5950705250038870948 - 2.1513548885720832188e-893j)  +/-  (1.29e-241, 1.29e-241j)
| (4.2122424936406228582 - 3.937757815527604798e-905j)  +/-  (5.59e-243, 5.59e-243j)
| (-4.5330849920738157789 + 3.2956811262588249844e-903j)  +/-  (1.67e-242, 1.67e-242j)
| (-2.6642064637087908672 - 5.4944216201992704018e-914j)  +/-  (6.35e-246, 6.35e-246j)
| (-3.2740334921948342322 + 9.9813310192928713596e-911j)  +/-  (1.57e-244, 1.57e-244j)
| (5.874699302021254124 + 6.3352850793105867422e-916j)  +/-  (1.12e-241, 1.12e-241j)
| (2.6642064637087908672 - 5.1732189889365988982e-920j)  +/-  (6.42e-246, 6.42e-246j)
| (4.8589492677211485311 - 1.3751797392253422373e-916j)  +/-  (2.9e-242, 2.9e-242j)
| (-2.9678201464818932339 - 4.4602652102227268035e-916j)  +/-  (3.63e-245, 3.63e-245j)
| (-3.5832210121368792795 + 4.6449605507015443198e-925j)  +/-  (6.01e-244, 6.01e-244j)
| (-5.5287966039093661247 + 4.9562516680148704651e-940j)  +/-  (8.47e-242, 8.47e-242j)
| (1.1741477394031905613 - 5.097332504049870627e-966j)  +/-  (2.2e-250, 2.2e-250j)
| (2.9678201464818932339 - 3.3837305043479489641e-960j)  +/-  (3.86e-245, 3.86e-245j)
| (3.2740334921948342322 + 3.1641287630419909311e-959j)  +/-  (1.49e-244, 1.49e-244j)
| (2.3628529934485321917 - 1.4971312649502694751e-962j)  +/-  (1.12e-246, 1.12e-246j)
| (-0.87983638589173075575 - 4.6234927696033590684e-967j)  +/-  (1.77e-251, 1.77e-251j)
| (3.5832210121368792795 + 2.145525678917110943e-959j)  +/-  (6.19e-244, 6.19e-244j)
| (1.4693573011471874601 + 7.6789880392512365044e-965j)  +/-  (1.92e-249, 1.92e-249j)
| (1.765706525113276386 + 3.6830180904998783612e-964j)  +/-  (2.26e-248, 2.26e-248j)
| (-5.874699302021254124 - 5.2704576472831132003e-958j)  +/-  (1.08e-241, 1.08e-241j)
| (-1.4693573011471874601 - 5.7566422911222164613e-971j)  +/-  (1.94e-249, 1.94e-249j)
| (0.29298593604778870078 - 6.3507585331717650338e-977j)  +/-  (5.41e-254, 5.41e-254j)
| (-4.2122424936406228582 - 1.9965005013279273667e-963j)  +/-  (6.52e-243, 6.52e-243j)
| (0.87983638589173075575 + 5.3420490854341049647e-974j)  +/-  (1.68e-251, 1.68e-251j)
| (-3.8958003472863841389 + 1.3118361834763525214e-972j)  +/-  (2.18e-243, 2.18e-243j)
| (-2.3628529934485321917 - 3.6295810344883016989e-977j)  +/-  (1.23e-246, 1.23e-246j)
| (-0.58619098157190685789 + 1.509820123023623949e-982j)  +/-  (1.12e-252, 1.12e-252j)
| (-1.765706525113276386 + 1.4697836657829766288e-977j)  +/-  (2.09e-248, 2.09e-248j)
| (0.58619098157190685789 - 5.1112826682646814213e-983j)  +/-  (1.39e-252, 1.39e-252j)
| (-1.119833797221029882e-1007 - 2.8058399056564153986e-1007j)  +/-  (1.72e-1005, 1.72e-1005j)
| (-2.0634488697846302516 - 4.6508227048121326615e-978j)  +/-  (1.62e-247, 1.62e-247j)
| (-0.29298593604778870078 - 2.9481826165744963953e-985j)  +/-  (5.41e-254, 5.41e-254j)
-------------------------------------------------
The weights are:
| (3.1676532592040594158e-38 + 1.2605693183641804577e-870j)  +/-  (4.6e-63, 2.22e-184j)
| (1.2177489113774996318e-27 + 7.7265875318291421974e-866j)  +/-  (3.21e-59, 1.55e-180j)
| (3.1676532592040594158e-38 - 3.5443745943707899799e-871j)  +/-  (8e-64, 3.87e-185j)
| (1.1425667416637609401e-30 - 2.289101305504082803e-867j)  +/-  (5.74e-61, 2.77e-182j)
| (1.6551524268275670716e-22 - 2.1804122262108311488e-862j)  +/-  (2.33e-60, 1.13e-181j)
| (1.6551524268275670716e-22 + 3.0380047670228047718e-863j)  +/-  (2.02e-58, 9.76e-180j)
| (3.9455659495142158574e-34 + 4.1077759674235058717e-869j)  +/-  (1.86e-62, 9e-184j)
| (3.7620445709792723342e-13 - 9.1716187393772477879e-857j)  +/-  (7.71e-55, 3.73e-176j)
| (1.0343698282290557128e-11 + 2.7934523726609108909e-856j)  +/-  (1.35e-53, 6.52e-175j)
| (1.1425667416637609401e-30 + 1.0069269069225503309e-866j)  +/-  (1.52e-65, 7.35e-187j)
| (2.8422012770154218632e-18 - 4.7017992442720599969e-860j)  +/-  (3.05e-59, 1.47e-180j)
| (3.7620445709792723342e-13 - 1.6971726509456044034e-858j)  +/-  (4.22e-57, 2.04e-178j)
| (6.0874894952247994839e-25 - 1.7844918822769311464e-864j)  +/-  (5.49e-62, 2.66e-183j)
| (1.8532693509133021613e-43 - 2.6316535563100455097e-873j)  +/-  (4.35e-71, 2.1e-192j)
| (1.0231867053048799962e-14 + 2.7105706628982295441e-859j)  +/-  (1.92e-58, 9.27e-180j)
| (6.0874894952247994839e-25 + 1.0108191032289049644e-863j)  +/-  (1.02e-63, 4.93e-185j)
| (1.2177489113774996318e-27 - 3.833813992022452038e-865j)  +/-  (6.54e-65, 3.16e-186j)
| (4.5451136372147906339e-08 - 6.7401553963674280875e-856j)  +/-  (2.04e-55, 9.86e-177j)
| (0.041889765046735709508 + 1.4646894488247493506e-852j)  +/-  (3.31e-37, 1.6e-158j)
| (2.7023037009826131709e-20 - 4.0063781292153661795e-862j)  +/-  (2.75e-62, 1.33e-183j)
| (2.1711820867790604071e-10 - 4.3530265419557824625e-857j)  +/-  (5.66e-58, 2.74e-179j)
| (0.0023837485085920406822 - 1.9337294238462055312e-853j)  +/-  (1.33e-48, 6.43e-170j)
| (2.8422012770154218632e-18 + 4.2403033453580508169e-861j)  +/-  (8.94e-62, 4.32e-183j)
| (3.9455659495142158574e-34 - 1.6193841509942414542e-868j)  +/-  (1.8e-70, 8.71e-192j)
| (1.8532693509133021613e-43 + 8.2064707300883991453e-874j)  +/-  (1.02e-73, 4.95e-195j)
| (2.7023037009826131709e-20 + 3.4219583766962593207e-861j)  +/-  (5.28e-65, 2.55e-186j)
| (3.5392928504599964007e-09 + 1.8175260633913859636e-856j)  +/-  (4.64e-58, 2.24e-179j)
| (2.1711820867790604071e-10 - 6.4522757588937588189e-856j)  +/-  (1.92e-61, 9.26e-183j)
| (0.00014106809290716541952 - 1.3518544692688309668e-853j)  +/-  (7.79e-57, 3.77e-178j)
| (3.838217761111717708e-06 - 2.940186743035601417e-854j)  +/-  (4.29e-59, 2.07e-180j)
| (2.0289151212621726319e-16 - 3.6975695063585787851e-860j)  +/-  (1.42e-62, 6.87e-184j)
| (0.00014106809290716541952 - 4.3441410870741730091e-854j)  +/-  (2.4e-57, 1.16e-178j)
| (1.0343698282290557128e-11 + 9.1930212129298451275e-858j)  +/-  (1.32e-60, 6.36e-182j)
| (2.5719969899786572259e-05 + 6.5615927596745837732e-854j)  +/-  (3.53e-59, 1.71e-180j)
| (4.6537978174531677833e-07 + 1.2209431901801704275e-854j)  +/-  (3.05e-61, 1.48e-182j)
| (1.0231867053048799962e-14 - 8.6269933638188431383e-858j)  +/-  (1.77e-65, 8.56e-187j)
| (0.041889765046735709508 + 9.2396489228435615854e-853j)  +/-  (8.08e-54, 3.91e-175j)
| (2.5719969899786572259e-05 + 1.7858482765852775963e-854j)  +/-  (5.75e-60, 2.78e-181j)
| (3.838217761111717708e-06 - 6.6491010661842144924e-855j)  +/-  (7.95e-61, 3.84e-182j)
| (0.00063727093666638962511 + 9.6017790505868328962e-854j)  +/-  (1.64e-59, 7.93e-181j)
| (0.076470090775027325532 - 1.8437429730498133272e-852j)  +/-  (2.33e-57, 1.12e-178j)
| (4.6537978174531677833e-07 + 2.2336371343501613208e-855j)  +/-  (2.11e-61, 1.02e-182j)
| (0.019261320181035364282 - 5.9874406928058354279e-853j)  +/-  (9.48e-59, 4.58e-180j)
| (0.0074161177470805387707 + 3.556862076385183358e-853j)  +/-  (2.74e-59, 1.32e-180j)
| (2.0289151212621726319e-16 + 6.0151020478954250601e-859j)  +/-  (9.44e-70, 4.56e-191j)
| (0.019261320181035364282 - 1.0720559909555057164e-852j)  +/-  (1.51e-62, 7.29e-184j)
| (0.15173988855603494033 - 2.0413301607374930706e-852j)  +/-  (2.26e-61, 1.09e-182j)
| (3.5392928504599964007e-09 + 1.7501677999843954623e-855j)  +/-  (2.97e-67, 1.44e-188j)
| (0.076470090775027325532 - 1.3089486067321016124e-852j)  +/-  (2.7e-62, 1.3e-183j)
| (4.5451136372147906339e-08 - 4.7377544752921169027e-855j)  +/-  (8.28e-67, 4e-188j)
| (0.00063727093666638962511 + 2.5667974101765813221e-853j)  +/-  (1.33e-65, 6.4e-187j)
| (0.11739113235599759667 + 2.1385997859486165545e-852j)  +/-  (5.95e-64, 2.74e-185j)
| (0.0074161177470805387707 + 7.2282849337450286481e-853j)  +/-  (2.62e-65, 1.24e-186j)
| (0.11739113235599759667 + 1.7042871065553077721e-852j)  +/-  (5.32e-64, 2.46e-185j)
| (0.16527905002840502783 + 2.2508004137646920656e-852j)  +/-  (1.96e-64, 9.05e-186j)
| (0.0023837485085920406822 - 4.4886006478508001066e-853j)  +/-  (5.35e-66, 2.68e-187j)
| (0.15173988855603494033 - 2.2857574112043849296e-852j)  +/-  (1.39e-64, 6.28e-186j)
