Starting with polynomial:
P : t
Extension levels are: 1 58
-------------------------------------------------
Trying to find an order 58 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^59 - 59/4*t^57 + 413/4*t^55 - 29205/64*t^53 + 365859/256*t^51 - 3455335/1024*t^49 + 3194555/512*t^47 - 37948505/4096*t^45 + 368323725/32768*t^43 - 1478205883/131072*t^41 + 1236866147/131072*t^39 - 27773267119/4194304*t^37 + 65592184047/16777216*t^35 - 130526252535/67108864*t^33 + 13674178837/16777216*t^31 - 38536322177/134217728*t^29 + 181927288417/2147483648*t^27 - 178869686931/8589934592*t^25 + 36355627425/8589934592*t^23 - 96820776195/137438953472*t^21 + 52134264105/549755813888*t^19 - 22343256045/2199023255552*t^17 + 933256395/1099511627776*t^15 - 473390925/8796093022208*t^13 + 175830915/70368744177664*t^11 - 22754589/281474976710656*t^9 + 477369/281474976710656*t^7 - 371287/18014398509481984*t^5 + 8555/72057594037927936*t^3 - 59/288230376151711744*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
Positive weights:   59 out of 59
Indefinite weights: 0 out of 59
Negative weights:   0 out of 59
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.99681200703075014926 + 1.8737969519480770628e-866j)  +/-  (1.3e-234, 1.3e-234j)
| (-0.99964561112345257676 + 1.2202452525759453265e-870j)  +/-  (4.45e-235, 4.45e-235j)
| (-0.92131197787041298969 + 7.8037630674135845604e-886j)  +/-  (2.59e-235, 2.59e-235j)
| (0.99115283100400715864 - 1.0041401758891804313e-885j)  +/-  (1.61e-234, 1.61e-234j)
| (0.89931213017121922813 + 3.0240317101143312135e-889j)  +/-  (1.07e-235, 1.07e-235j)
| (0.95742203836200547842 + 8.813130192718368706e-888j)  +/-  (8.22e-235, 8.22e-235j)
| (-0.98268412459252094086 - 8.9974731136190700929e-887j)  +/-  (1.5e-234, 1.5e-234j)
| (-0.89931213017121922813 + 1.194946220505846339e-899j)  +/-  (1e-235, 1e-235j)
| (-0.99115283100400715864 + 3.2658821069020761957e-897j)  +/-  (1.54e-234, 1.54e-234j)
| (0.99964561112345257676 - 4.4584239772876919994e-909j)  +/-  (4.03e-235, 4.03e-235j)
| (0.92131197787041298969 - 4.2349587613365978433e-914j)  +/-  (2.45e-235, 2.45e-235j)
| (0.98268412459252094086 - 6.399671096900670758e-913j)  +/-  (1.4e-234, 1.4e-234j)
| (-0.94070026667103327781 - 1.0428486193640564672e-911j)  +/-  (5.27e-235, 5.27e-235j)
| (-0.87476308453196128518 - 5.8707726089733304138e-921j)  +/-  (4.14e-236, 4.14e-236j)
| (0.94070026667103327781 - 3.3703117263310805006e-923j)  +/-  (5.52e-235, 5.52e-235j)
| (0.81830277590816905628 - 9.308019612167155412e-928j)  +/-  (3.87e-237, 3.87e-237j)
| (0.87476308453196128518 - 1.0118971034261127562e-925j)  +/-  (4.23e-236, 4.23e-236j)
| (-0.63824418364482009399 + 2.624772767721265324e-936j)  +/-  (8.59e-241, 8.59e-241j)
| (-0.78655155580264248111 - 1.6102959501881346871e-929j)  +/-  (8.69e-238, 8.69e-238j)
| (-0.97142989326470996237 - 1.2502522509454571897e-929j)  +/-  (1.25e-234, 1.25e-234j)
| (-0.59636735853850141391 + 6.1164110363771921856e-960j)  +/-  (1.28e-241, 1.28e-241j)
| (0.71645674029831513859 + 9.7759667608959930486e-952j)  +/-  (3.06e-239, 3.06e-239j)
| (-0.99681200703075014926 + 3.5502712364990838683e-956j)  +/-  (1.2e-234, 1.2e-234j)
| (-0.8477344278896709379 + 1.7527417087961574473e-974j)  +/-  (1.28e-236, 1.28e-236j)
| (-0.81830277590816905628 - 2.1286176743917056087e-976j)  +/-  (4.08e-237, 4.08e-237j)
| (0.8477344278896709379 - 9.2049661576812362782e-977j)  +/-  (1.37e-236, 1.37e-236j)
| (0.78655155580264248111 - 1.3133199181796228809e-978j)  +/-  (8.58e-238, 8.58e-238j)
| (0.75257076985613850393 - 6.9198007746295651999e-980j)  +/-  (2.08e-238, 2.08e-238j)
| (-0.95742203836200547842 + 1.3028696904568810078e-979j)  +/-  (8.71e-235, 8.71e-235j)
| (-0.67831183626961608477 + 6.7805013577234305242e-985j)  +/-  (5.39e-240, 5.39e-240j)
| (-0.1590634960190720532 - 3.0097640719937382504e-996j)  +/-  (5.27e-252, 5.27e-252j)
| (0.67831183626961608477 - 6.0943676362223272717e-983j)  +/-  (5.64e-240, 5.64e-240j)
| (0.63824418364482009399 + 4.065793703574026103e-984j)  +/-  (8.97e-241, 8.97e-241j)
| (0.10629348564736540674 + 4.1183982775087586103e-998j)  +/-  (2.67e-253, 2.67e-253j)
| (-0.71645674029831513859 - 1.0976151622045116868e-984j)  +/-  (3.4e-239, 3.4e-239j)
| (-0.75257076985613850393 + 9.78383294398287106e-983j)  +/-  (1.8e-238, 1.8e-238j)
| (0.97142989326470996237 - 9.0978878411866639391e-991j)  +/-  (1.2e-234, 1.2e-234j)
| (0.59636735853850141391 + 1.9033499605493263023e-1000j)  +/-  (1.11e-241, 1.11e-241j)
| (0.31407671202194881542 + 1.9693550230322097984e-1008j)  +/-  (3.75e-248, 3.75e-248j)
| (-0.31407671202194881542 - 6.403567580693620009e-1010j)  +/-  (3.34e-248, 3.34e-248j)
| (-0.55280006536119338305 - 1.2788961028757165725e-1004j)  +/-  (1.32e-242, 1.32e-242j)
| (-0.26310256422752125115 + 2.83213121880928278e-1011j)  +/-  (2.06e-249, 2.06e-249j)
| (0.41321218576837817962 + 2.5193201831239095597e-1006j)  +/-  (8.74e-246, 8.74e-246j)
| (0.55280006536119338305 - 6.1966488222569316225e-1003j)  +/-  (1.26e-242, 1.26e-242j)
| (-0.10629348564736540674 + 1.5954786128648851394e-1015j)  +/-  (2.67e-253, 2.67e-253j)
| (-0.50766580033883995811 - 3.2514087652145650291e-1006j)  +/-  (1.26e-243, 1.26e-243j)
| (-0.36416057525282217832 + 3.5437251954017621343e-1011j)  +/-  (5.69e-247, 5.69e-247j)
| (0.1590634960190720532 + 4.6606408162540734863e-1014j)  +/-  (4.89e-252, 4.89e-252j)
| (0.50766580033883995811 + 3.1710051822977389341e-1007j)  +/-  (1.46e-243, 1.46e-243j)
| (0.26310256422752125115 - 3.6201525796200016011e-1015j)  +/-  (1.77e-249, 1.77e-249j)
| (-0.21138262362962432071 + 4.1726516686818676959e-1016j)  +/-  (1.09e-250, 1.09e-250j)
| (-0.46109250144932584609 - 2.166806363658858842e-1009j)  +/-  (9.4e-245, 9.4e-245j)
| (0.053222174842178654659 - 1.0762930779460076382e-1019j)  +/-  (1.33e-254, 1.33e-254j)
| (0.36416057525282217832 - 6.8950138688704744253e-1013j)  +/-  (5.47e-247, 5.47e-247j)
| (0.46109250144932584609 + 1.3739455622875948038e-1009j)  +/-  (1.11e-244, 1.11e-244j)
| (-1.7616753259422856728e-1038 + 8.4180236364477690439e-1037j)  +/-  (4.97e-1035, 4.97e-1035j)
| (-0.41321218576837817962 + 7.8142995086161857918e-1012j)  +/-  (8.27e-246, 8.27e-246j)
| (-0.053222174842178654659 + 1.2135065290305634849e-1019j)  +/-  (1.06e-254, 1.06e-254j)
| (0.21138262362962432071 + 5.5278990530357573257e-1016j)  +/-  (1e-250, 1e-250j)
-------------------------------------------------
The weights are:
| (0.016949152542372881356 - 2.4865648452156500156e-866j)  +/-  (5.19e-47, 4.75e-158j)
| (0.016949152542372881356 + 6.7663592468178145773e-869j)  +/-  (1.3e-47, 1.19e-158j)
| (0.016949152542372881356 - 8.1075663162258540077e-868j)  +/-  (1.03e-47, 9.39e-159j)
| (0.016949152542372881356 + 9.3356539888646972291e-866j)  +/-  (1.75e-47, 1.6e-158j)
| (0.016949152542372881356 + 1.785378422488478835e-866j)  +/-  (2.16e-48, 1.97e-159j)
| (0.016949152542372881356 - 2.9173866415945561429e-866j)  +/-  (1.68e-48, 1.53e-159j)
| (0.016949152542372881356 - 3.8108266483552136855e-868j)  +/-  (1.16e-48, 1.07e-159j)
| (0.016949152542372881356 + 9.2142968974030220718e-868j)  +/-  (4.03e-49, 3.69e-160j)
| (0.016949152542372881356 + 2.7790143147904566942e-868j)  +/-  (1.42e-48, 1.3e-159j)
| (0.016949152542372881356 - 3.7395600898384705961e-866j)  +/-  (3.24e-48, 2.97e-159j)
| (0.016949152542372881356 - 2.0499946196787753055e-866j)  +/-  (1.53e-49, 1.4e-160j)
| (0.016949152542372881356 - 5.2205441364026746176e-866j)  +/-  (7.31e-49, 6.69e-160j)
| (0.016949152542372881356 + 7.0142574988952227609e-868j)  +/-  (7.87e-51, 7.2e-162j)
| (0.016949152542372881356 - 1.0335794635061720747e-867j)  +/-  (1.92e-51, 1.75e-162j)
| (0.016949152542372881356 + 2.4065648245323793713e-866j)  +/-  (1.67e-49, 1.53e-160j)
| (0.016949152542372881356 - 1.2817346948637962922e-866j)  +/-  (6.66e-53, 6.09e-164j)
| (0.016949152542372881356 - 1.5803533340101368834e-866j)  +/-  (1.7e-51, 1.56e-162j)
| (0.016949152542372881356 + 1.8758191871697614109e-867j)  +/-  (3e-55, 2.75e-166j)
| (0.016949152542372881356 + 1.3805954894805291865e-867j)  +/-  (1.91e-54, 1.75e-165j)
| (0.016949152542372881356 + 4.8650182419350333259e-868j)  +/-  (1.89e-52, 1.73e-163j)
| (0.016949152542372881356 - 2.0071178783175266353e-867j)  +/-  (3.08e-56, 2.82e-167j)
| (0.016949152542372881356 + 9.9054559964175738786e-867j)  +/-  (2.32e-56, 2.12e-167j)
| (0.016949152542372881356 - 1.8118014901758917098e-868j)  +/-  (3.52e-52, 3.22e-163j)
| (0.016949152542372881356 + 1.1473669089969919664e-867j)  +/-  (4.72e-54, 4.32e-165j)
| (0.016949152542372881356 - 1.2629728628260275798e-867j)  +/-  (1.39e-54, 1.27e-165j)
| (0.016949152542372881356 + 1.4163102318927848968e-866j)  +/-  (6.42e-56, 5.87e-167j)
| (0.016949152542372881356 + 1.1690952843563097589e-866j)  +/-  (1.93e-57, 1.77e-168j)
| (0.016949152542372881356 - 1.0732461949511891997e-866j)  +/-  (3.44e-58, 3.15e-169j)
| (0.016949152542372881356 - 5.93344521900336307e-868j)  +/-  (1.47e-55, 1.35e-166j)
| (0.016949152542372881356 - 1.7478005022918816976e-867j)  +/-  (1.38e-59, 1.26e-170j)
| (0.016949152542372881356 + 3.4008223876332408451e-867j)  +/-  (4.14e-64, 3.79e-175j)
| (0.016949152542372881356 - 9.1834007937804979302e-867j)  +/-  (1.24e-60, 1.13e-171j)
| (0.016949152542372881356 + 8.54648568513717669e-867j)  +/-  (1.07e-61, 9.76e-173j)
| (0.016949152542372881356 - 4.4453010821927897663e-867j)  +/-  (7.05e-66, 6.45e-177j)
| (0.016949152542372881356 + 1.62276777113486113e-867j)  +/-  (2.36e-60, 2.16e-171j)
| (0.016949152542372881356 - 1.5004497129467900599e-867j)  +/-  (6.02e-60, 5.51e-171j)
| (0.016949152542372881356 + 3.7218867543936128885e-866j)  +/-  (9.31e-59, 8.52e-170j)
| (0.016949152542372881356 - 7.9796084604959739877e-867j)  +/-  (3.03e-63, 2.77e-174j)
| (0.016949152542372881356 - 5.5358342439295461713e-867j)  +/-  (1.78e-66, 1.63e-177j)
| (0.016949152542372881356 - 2.8839492135875008234e-867j)  +/-  (1.3e-66, 1.19e-177j)
| (0.016949152542372881356 + 2.1420162080750756104e-867j)  +/-  (1.65e-64, 1.51e-175j)
| (0.016949152542372881356 + 3.0490879781898089103e-867j)  +/-  (7.58e-67, 6.94e-178j)
| (0.016949152542372881356 - 6.2116552077269416421e-867j)  +/-  (1.63e-67, 1.49e-178j)
| (0.016949152542372881356 + 7.4710471578859748581e-867j)  +/-  (7.54e-66, 6.9e-177j)
| (0.016949152542372881356 - 3.5889176805295844216e-867j)  +/-  (2.63e-68, 2.41e-179j)
| (0.016949152542372881356 - 2.2808627055422332957e-867j)  +/-  (1.64e-66, 1.5e-177j)
| (0.016949152542372881356 + 2.7250962427114495689e-867j)  +/-  (1.33e-67, 1.22e-178j)
| (0.016949152542372881356 + 4.6916551493817153568e-867j)  +/-  (1.37e-69, 1.25e-180j)
| (0.016949152542372881356 - 7.011559283660236451e-867j)  +/-  (2.88e-68, 2.64e-179j)
| (0.016949152542372881356 + 5.23469305840773958e-867j)  +/-  (1.05e-69, 9.62e-181j)
| (0.016949152542372881356 - 3.2211436441999810917e-867j)  +/-  (4.4e-69, 4.03e-180j)
| (0.016949152542372881356 + 2.4240386822135636969e-867j)  +/-  (1.06e-68, 9.69e-180j)
| (0.016949152542372881356 + 4.2132768189835163444e-867j)  +/-  (1.23e-70, 1.13e-181j)
| (0.016949152542372881356 + 5.860363398057951227e-867j)  +/-  (3.33e-70, 3.05e-181j)
| (0.016949152542372881356 + 6.5937555952262215946e-867j)  +/-  (6.26e-70, 5.73e-181j)
| (0.016949152542372881356 - 3.9940592744671443239e-867j)  +/-  (2.16e-71, 1.98e-182j)
| (0.016949152542372881356 - 2.5719627724877876529e-867j)  +/-  (5.08e-71, 4.66e-182j)
| (0.016949152542372881356 + 3.7863249525971091092e-867j)  +/-  (1.73e-71, 1.58e-182j)
| (0.016949152542372881356 - 4.9541017053363040064e-867j)  +/-  (1.48e-71, 1.34e-182j)
