Starting with polynomial:
P : t
Extension levels are: 1 56
-------------------------------------------------
Trying to find an order 56 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^57 - 1596*t^55 + 1185030*t^53 - 544323780*t^51 + 173503204875*t^49 - 40807953786600*t^47 + 7352233007219100*t^45 - 1039815811020987000*t^43 + 117369209668993907625*t^41 - 10693639103175000472500*t^39 + 792398657545267535012250*t^37 - 47976136902286198028923500*t^35 + 2378816788071690652267456875*t^33 - 96616558777065589569016710000*t^31 + 3209049987952535653542340725000*t^29 - 86858286340581965022546022290000*t^27 + 1905453656596516857682103363986875*t^25 - 33625652763467944547331235835062500*t^23 + 472627230508743887248600148126156250*t^21 - 5223774652991379806431896374025937500*t^19 + 44663273283076297344992713997921765625*t^17 - 289247865071351258996143290653207625000*t^15 + 1380501174204176463390683887208490937500*t^13 - 4681699634257641919324927965315751875000*t^11 + 10728894995173762731786293253848598046875*t^9 - 15449608793050218333772262285541981187500*t^7 + 12478530179002099423431442615245446343750*t^5 - 4621677844074851638307941709350165312500*t^3 + 495179769008019818390136611716089140625*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:
| (9.3268381812675453916 - 1.7198052262768252363e-722j)  +/-  (1.57e-241, 1.57e-241j)
| (-13.96610422143784552 + 2.8488513891612895255e-729j)  +/-  (1.47e-245, 1.47e-245j)
| (13.055149782679357506 - 1.9607998155964092753e-733j)  +/-  (3.2e-244, 3.2e-244j)
| (7.3405658671154390163 + 8.1987063460714053003e-730j)  +/-  (8.15e-242, 8.15e-242j)
| (9.8617992923135757283 + 3.8784428517396634041e-730j)  +/-  (1.48e-241, 1.48e-241j)
| (-10.418961566760794366 + 4.3559284494038873148e-742j)  +/-  (6.03e-242, 6.03e-242j)
| (-8.3080794277822128171 - 6.6858306091303443487e-757j)  +/-  (1.84e-241, 1.84e-241j)
| (-6.871591953294067001 - 1.0950981736484789722e-763j)  +/-  (4.32e-242, 4.32e-242j)
| (-5.9570104625108344189 + 9.1691220313463027588e-770j)  +/-  (9.15e-243, 9.15e-243j)
| (-11.626408464464774737 - 3.5827055405824694831e-778j)  +/-  (8.94e-243, 8.94e-243j)
| (12.300447552299751066 - 1.7408775772339252011e-788j)  +/-  (2.06e-243, 2.06e-243j)
| (-7.3405658671154390163 + 2.4591394106393981719e-787j)  +/-  (7.99e-242, 7.99e-242j)
| (11.004196045579848314 - 8.058555593228453376e-797j)  +/-  (2.7e-242, 2.7e-242j)
| (-5.5094936874302181678 + 3.3016348392475739959e-801j)  +/-  (3.08e-243, 3.08e-243j)
| (11.626408464464774737 + 7.4593704909844997642e-807j)  +/-  (8.84e-243, 8.84e-243j)
| (1.6604956572937025859 + 1.448489534724280076e-824j)  +/-  (3.12e-250, 3.12e-250j)
| (2.4970861149858654135 - 1.2059758483169489602e-823j)  +/-  (2.75e-248, 2.75e-248j)
| (-13.055149782679357506 + 3.9702179432883565824e-824j)  +/-  (3.02e-244, 3.02e-244j)
| (-8.8099476874906005993 + 7.7360482206135629071e-858j)  +/-  (1.95e-241, 1.95e-241j)
| (-1.6604956572937025859 + 2.606227506527092037e-889j)  +/-  (2.72e-250, 2.72e-250j)
| (5.0674397523442232958 - 1.084455853258062969e-879j)  +/-  (1.01e-243, 1.01e-243j)
| (2.9181573769128586778 - 6.7949527944971796857e-889j)  +/-  (2.36e-247, 2.36e-247j)
| (13.96610422143784552 + 4.1953174733969426785e-884j)  +/-  (1.57e-245, 1.57e-245j)
| (-7.8188991408509344311 - 3.1507367358227479592e-895j)  +/-  (1.54e-241, 1.54e-241j)
| (-9.8617992923135757283 - 6.7783414782468045696e-915j)  +/-  (1.42e-241, 1.42e-241j)
| (-4.1971315018387990012 - 1.1711031085846063984e-930j)  +/-  (4.57e-245, 4.57e-245j)
| (4.1971315018387990012 - 3.5550193019424600187e-929j)  +/-  (4.55e-245, 4.55e-245j)
| (-12.300447552299751066 + 8.9757625005940202133e-925j)  +/-  (2.03e-243, 2.03e-243j)
| (10.418961566760794366 - 4.1628716696638126794e-929j)  +/-  (6.58e-242, 6.58e-242j)
| (5.5094936874302181678 + 1.8136439257465924043e-933j)  +/-  (2.67e-243, 2.67e-243j)
| (-9.3268381812675453916 + 8.15387482186180883e-933j)  +/-  (1.84e-241, 1.84e-241j)
| (-11.004196045579848314 + 8.7950701376478370572e-949j)  +/-  (3.08e-242, 3.08e-242j)
| (3.7677569139390351035 - 4.5062184218932829289e-958j)  +/-  (8.69e-246, 8.69e-246j)
| (-5.0674397523442232958 + 3.2030825114303998227e-954j)  +/-  (8.96e-244, 8.96e-244j)
| (5.9570104625108344189 - 3.5501665256059898451e-955j)  +/-  (7.8e-243, 7.8e-243j)
| (-3.7677569139390351035 - 3.8084521310714277796e-957j)  +/-  (8.96e-246, 8.96e-246j)
| (6.4107502751807243459 - 1.0977783929943795389e-955j)  +/-  (2.16e-242, 2.16e-242j)
| (3.3415787492287801274 - 1.6850258153287245264e-960j)  +/-  (1.53e-246, 1.53e-246j)
| (-6.4107502751807243459 - 1.7285070780933680477e-953j)  +/-  (2.56e-242, 2.56e-242j)
| (8.8099476874906005993 - 1.1843490817367847364e-953j)  +/-  (1.88e-241, 1.88e-241j)
| (-2.0779850232542805982 - 5.2549926682677742328e-963j)  +/-  (3.32e-249, 3.32e-249j)
| (-4.6301825683256814031 + 1.941886860369416128e-958j)  +/-  (2.24e-244, 2.24e-244j)
| (0.41434468434335906286 + 1.2050530723592973476e-969j)  +/-  (9.05e-254, 9.05e-254j)
| (6.871591953294067001 + 5.1623335871160716557e-955j)  +/-  (4.34e-242, 4.34e-242j)
| (7.8188991408509344311 - 8.4748731609559294141e-955j)  +/-  (1.45e-241, 1.45e-241j)
| (-1.2442765495974136978 + 1.1280486166984200875e-967j)  +/-  (1.99e-251, 1.99e-251j)
| (8.3080794277822128171 + 8.1934295155256698313e-961j)  +/-  (1.76e-241, 1.76e-241j)
| (1.2442765495974136978 - 2.3756094075223397343e-976j)  +/-  (1.63e-251, 1.63e-251j)
| (2.0779850232542805982 + 4.3643654309170770226e-972j)  +/-  (3.32e-249, 3.32e-249j)
| (0.8289992362797877095 - 1.1878374533950102616e-976j)  +/-  (1.55e-252, 1.55e-252j)
| (-2.4970861149858654135 - 4.58669564943093e-971j)  +/-  (2.59e-248, 2.59e-248j)
| (-0.8289992362797877095 - 6.4917392210167133931e-976j)  +/-  (1.26e-252, 1.26e-252j)
| (4.6301825683256814031 + 2.1014644154328520739e-965j)  +/-  (2.11e-244, 2.11e-244j)
| (-2.9181573769128586778 + 6.5111005955748856997e-970j)  +/-  (2.48e-247, 2.48e-247j)
| (-3.3415787492287801274 - 9.9898771633030196886e-969j)  +/-  (1.78e-246, 1.78e-246j)
| (2.1312658495293382985e-994 - 3.1050808783440916608e-994j)  +/-  (2.15e-992, 2.15e-992j)
| (-0.41434468434335906286 + 3.3448172411573352578e-976j)  +/-  (9.05e-254, 9.05e-254j)
-------------------------------------------------
The weights are:
| (2.7023037009826131709e-20 + 2.1673358094713861116e-741j)  +/-  (2.04e-54, 8.81e-175j)
| (1.8532693509133021613e-43 - 5.2240437218145578179e-755j)  +/-  (2.16e-65, 9.33e-186j)
| (3.1676532592040594158e-38 - 1.3494368239234110906e-751j)  +/-  (2.95e-63, 1.27e-183j)
| (3.7620445709792723342e-13 + 8.7187855210807988186e-739j)  +/-  (7.11e-50, 3.07e-170j)
| (1.6551524268275670716e-22 + 6.7987134101202163519e-743j)  +/-  (5.91e-56, 2.55e-176j)
| (6.0874894952247994839e-25 + 1.1168756678293387514e-745j)  +/-  (6.33e-60, 2.73e-180j)
| (2.0289151212621726319e-16 + 2.2830624135975712017e-741j)  +/-  (3.95e-55, 1.7e-175j)
| (1.0343698282290557128e-11 - 5.6120726367385357642e-739j)  +/-  (2.01e-51, 8.69e-172j)
| (3.5392928504599964007e-09 - 1.1002289468836814255e-737j)  +/-  (7.91e-49, 3.41e-169j)
| (1.1425667416637609401e-30 + 1.4419508570390977616e-748j)  +/-  (3.11e-63, 1.34e-183j)
| (3.9455659495142158574e-34 + 1.8882990040659902641e-749j)  +/-  (4.86e-65, 2.1e-185j)
| (3.7620445709792723342e-13 + 1.0401659622789947787e-739j)  +/-  (1.91e-53, 8.24e-174j)
| (1.2177489113774996318e-27 + 5.8811752371127414615e-746j)  +/-  (7.29e-63, 3.14e-183j)
| (4.5451136372147906339e-08 + 4.0616544965185784373e-737j)  +/-  (1.27e-49, 5.46e-170j)
| (1.1425667416637609401e-30 - 1.3140109811453500791e-747j)  +/-  (5.45e-64, 2.35e-184j)
| (0.041889765046735709508 - 7.545843796035363345e-734j)  +/-  (3.83e-31, 1.65e-151j)
| (0.0074161177470805387707 - 3.5638611120963305649e-734j)  +/-  (1.71e-38, 7.36e-159j)
| (3.1676532592040594158e-38 + 2.2476657233422006918e-752j)  +/-  (2.84e-68, 1.22e-188j)
| (2.8422012770154218632e-18 - 2.6274028949408419612e-742j)  +/-  (5.62e-59, 2.43e-179j)
| (0.041889765046735709508 - 5.2651855254404963067e-734j)  +/-  (2.74e-34, 1.18e-154j)
| (4.6537978174531677833e-07 - 4.526443021764030148e-736j)  +/-  (9.35e-53, 4.03e-173j)
| (0.0023837485085920406822 + 2.1532574546368110231e-734j)  +/-  (2.22e-43, 9.57e-164j)
| (1.8532693509133021613e-43 + 2.6230842686308973856e-754j)  +/-  (7.32e-71, 3.16e-191j)
| (1.0231867053048799962e-14 - 1.6675552869827001692e-740j)  +/-  (8.3e-57, 3.58e-177j)
| (1.6551524268275670716e-22 - 1.8951126266523849669e-744j)  +/-  (4.19e-62, 1.8e-182j)
| (2.5719969899786572259e-05 - 1.0599535283343154184e-735j)  +/-  (2.03e-51, 8.73e-172j)
| (2.5719969899786572259e-05 - 2.7942351946747245503e-735j)  +/-  (1.42e-52, 6.11e-173j)
| (3.9455659495142158574e-34 - 2.5960551164056660736e-750j)  +/-  (8.44e-68, 3.64e-188j)
| (6.0874894952247994839e-25 - 2.0196045615274382914e-744j)  +/-  (2.18e-65, 9.39e-186j)
| (4.5451136372147906339e-08 + 1.5783244540180815848e-736j)  +/-  (4.6e-57, 1.98e-177j)
| (2.7023037009826131709e-20 + 2.4909357153386174735e-743j)  +/-  (2.05e-61, 8.83e-182j)
| (1.2177489113774996318e-27 - 4.8515456775281536412e-747j)  +/-  (4.9e-65, 2.11e-185j)
| (0.00014106809290716541952 + 6.0386172808548213307e-735j)  +/-  (1.87e-53, 8.05e-174j)
| (4.6537978174531677833e-07 - 1.3395859692654206042e-736j)  +/-  (5.97e-56, 2.57e-176j)
| (3.5392928504599964007e-09 - 4.9889448427748587985e-737j)  +/-  (2.11e-59, 9.1e-180j)
| (0.00014106809290716541952 + 2.5637613432696926056e-735j)  +/-  (3.67e-55, 1.58e-175j)
| (2.1711820867790604071e-10 + 1.4277478591557204973e-737j)  +/-  (8.26e-61, 3.56e-181j)
| (0.00063727093666638962511 - 1.1920920330222930592e-734j)  +/-  (3.84e-54, 1.65e-174j)
| (2.1711820867790604071e-10 + 2.646475428318668106e-738j)  +/-  (6.98e-59, 3.01e-179j)
| (2.8422012770154218632e-18 - 9.2215173210065499888e-741j)  +/-  (8.4e-66, 3.62e-186j)
| (0.019261320181035364282 + 3.4395946163703688331e-734j)  +/-  (2.32e-54, 1e-174j)
| (3.838217761111717708e-06 + 3.9676042593883990369e-736j)  +/-  (1.39e-57, 6e-178j)
| (0.15173988855603494033 + 1.2353715156753611138e-733j)  +/-  (3.11e-53, 1.34e-173j)
| (1.0343698282290557128e-11 - 3.6998540768098335066e-738j)  +/-  (1.42e-62, 6.11e-183j)
| (1.0231867053048799962e-14 - 1.8975073269121042805e-739j)  +/-  (8.32e-65, 3.59e-185j)
| (0.076470090775027325532 + 7.3939451850753177112e-734j)  +/-  (4.49e-56, 1.94e-176j)
| (2.0289151212621726319e-16 + 3.9535593469967424351e-740j)  +/-  (1.15e-65, 4.94e-186j)
| (0.076470090775027325532 + 9.6703165461111020219e-734j)  +/-  (9.78e-57, 4.22e-177j)
| (0.019261320181035364282 + 5.4114499646102535832e-734j)  +/-  (7.78e-58, 3.35e-178j)
| (0.11739113235599759667 - 1.1396058450064265894e-733j)  +/-  (1.11e-56, 4.8e-177j)
| (0.0074161177470805387707 - 2.0586388033838308142e-734j)  +/-  (2.59e-60, 1.11e-180j)
| (0.11739113235599759667 - 9.5356918356798562646e-734j)  +/-  (3.34e-59, 1.44e-179j)
| (3.838217761111717708e-06 + 1.1789314430012390087e-735j)  +/-  (2.6e-61, 1.12e-181j)
| (0.0023837485085920406822 + 1.1270046612838401124e-734j)  +/-  (3.15e-61, 1.36e-181j)
| (0.00063727093666638962511 - 5.6324121711360944495e-735j)  +/-  (1.44e-61, 6.23e-182j)
| (0.16527905002840502783 - 1.232033854827733354e-733j)  +/-  (2.58e-60, 1.17e-180j)
| (0.15173988855603494033 + 1.1302837428687521389e-733j)  +/-  (1.63e-60, 6.52e-181j)
