Starting with polynomial:
P : t
Extension levels are: 1 50
-------------------------------------------------
Trying to find an order 50 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^51 - 1275*t^49 + 749700*t^47 - 270141900*t^45 + 66860120250*t^43 - 12074937717150*t^41 + 1650241488010500*t^39 - 174689848945111500*t^37 + 14542929924680532375*t^35 - 961449256131657418125*t^33 + 50764520723751511677000*t^31 - 2145954739685859357255000*t^29 + 72604802026038241587127500*t^27 - 1960329654703032522852442500*t^25 + 42007064029350696918266625000*t^23 - 708519146628381754688097075000*t^21 + 9299313799497510530281274109375*t^19 - 93540156453769076510476345453125*t^17 + 706747848761810800301376832312500*t^15 - 3905711795788954422718135125937500*t^13 + 15232276003576922248600726991156250*t^11 - 39894056199844320174906665929218750*t^9 + 65281182872472523922574544247812500*t^7 - 59604558274866217494524583878437500*t^5 + 24835232614527590622718576616015625*t^3 - 2980227913743310874726229193921875*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:
| (-7.337561286333264224 - 1.9248171447190159751e-516j)  +/-  (4.5e-243, 4.5e-243j)
| (10.74058140389968344 - 3.2811306773388936696e-515j)  +/-  (8.18e-244, 8.18e-244j)
| (12.200547299075756214 - 2.0202693209946806502e-519j)  +/-  (3.16e-245, 3.16e-245j)
| (-13.130057881095919351 + 1.5236415785336869413e-523j)  +/-  (2e-246, 2e-246j)
| (-11.429691934140612543 - 1.3997942397429069264e-523j)  +/-  (1.84e-244, 1.84e-244j)
| (13.130057881095919351 - 2.7485027674105049799e-522j)  +/-  (1.92e-246, 1.92e-246j)
| (10.103877888840050591 - 2.7428143174899151798e-519j)  +/-  (2.15e-243, 2.15e-243j)
| (-8.9333009185735982701 + 4.131933619284515729e-525j)  +/-  (4.97e-243, 4.97e-243j)
| (2.1974128530461654593 - 3.3063165195114861217e-531j)  +/-  (2.23e-249, 2.23e-249j)
| (4.9130448951801842624 + 4.8350908575322077747e-526j)  +/-  (8.1e-245, 8.1e-245j)
| (11.429691934140612543 - 4.7178158571054213223e-524j)  +/-  (2.22e-244, 2.22e-244j)
| (-3.5382435448567513522 - 2.6762999581479556374e-533j)  +/-  (8.29e-247, 8.29e-247j)
| (9.5044726973078160633 - 6.9495707810255962173e-528j)  +/-  (3.62e-243, 3.62e-243j)
| (-9.5044726973078160633 - 5.7327039736632741012e-532j)  +/-  (4.11e-243, 4.11e-243j)
| (1.755425247853960429 + 9.7581864261592913901e-539j)  +/-  (2.09e-250, 2.09e-250j)
| (-5.3820214400516843153 - 2.944316705324830136e-533j)  +/-  (2.45e-244, 2.45e-244j)
| (-3.0883138312883406103 - 6.0194143283419860996e-537j)  +/-  (1.42e-247, 1.42e-247j)
| (-1.755425247853960429 - 4.9937900760563842365e-539j)  +/-  (2.19e-250, 2.19e-250j)
| (5.3820214400516843153 + 7.0267818950193587902e-531j)  +/-  (2.42e-244, 2.42e-244j)
| (-6.3414100930173041173 + 7.1020212596310100325e-538j)  +/-  (1.38e-243, 1.38e-243j)
| (-4.9130448951801842624 + 9.3370131385890473731e-540j)  +/-  (8.29e-245, 8.29e-245j)
| (-2.6415458108961150818 + 5.7019705553161074984e-544j)  +/-  (2.09e-248, 2.09e-248j)
| (-10.74058140389968344 + 1.6092466703862153654e-537j)  +/-  (7.7e-244, 7.7e-244j)
| (-10.103877888840050591 - 2.884052957148474407e-536j)  +/-  (1.94e-243, 1.94e-243j)
| (1.3151220442826487801 + 2.3184928743063671607e-545j)  +/-  (1.86e-251, 1.86e-251j)
| (5.8577868465799740028 - 3.7579608497202213987e-536j)  +/-  (7.69e-244, 7.69e-244j)
| (-5.8577868465799740028 - 7.4642099189397185769e-540j)  +/-  (6.82e-244, 6.82e-244j)
| (-12.200547299075756214 - 2.3873822786870203148e-541j)  +/-  (2.77e-245, 2.77e-245j)
| (3.0883138312883406103 + 4.4495202143501371048e-544j)  +/-  (1.32e-247, 1.32e-247j)
| (2.6415458108961150818 - 5.5113497436760080502e-546j)  +/-  (2.01e-248, 2.01e-248j)
| (-7.85350692853823115 + 1.200459695878731821e-538j)  +/-  (5.43e-243, 5.43e-243j)
| (-0.87606407720720904649 + 5.154610179540257285e-554j)  +/-  (1.53e-252, 1.53e-252j)
| (-4.4499401327924338974 - 1.6650186507595651398e-547j)  +/-  (1.96e-245, 1.96e-245j)
| (-8.3843827320177424041 + 6.0795807976896182034e-544j)  +/-  (5.69e-243, 5.69e-243j)
| (1.2074371498444285552e-587 - 1.2706861138866046817e-587j)  +/-  (8.94e-586, 8.94e-586j)
| (4.4499401327924338974 + 2.8064946671140044787e-548j)  +/-  (2.08e-245, 2.08e-245j)
| (-2.1974128530461654593 - 2.8472544735751419467e-561j)  +/-  (2.21e-249, 2.21e-249j)
| (3.5382435448567513522 + 6.1432885278115121483e-553j)  +/-  (8.3e-247, 8.3e-247j)
| (3.9919082922226269841 - 7.7108334234135496053e-553j)  +/-  (4.54e-246, 4.54e-246j)
| (0.43782784888264942324 - 9.1512690579454542784e-569j)  +/-  (9.78e-254, 9.78e-254j)
| (-6.8341582108278208913 - 1.9202363723822168298e-557j)  +/-  (2.59e-243, 2.59e-243j)
| (-3.9919082922226269841 + 1.552456370609544043e-568j)  +/-  (4.55e-246, 4.55e-246j)
| (-1.3151220442826487801 + 1.5613822345200218513e-582j)  +/-  (2.15e-251, 2.15e-251j)
| (0.87606407720720904649 - 2.0305743124817996682e-578j)  +/-  (1.22e-252, 1.22e-252j)
| (6.3414100930173041173 + 1.7304964221664381397e-595j)  +/-  (1.68e-243, 1.68e-243j)
| (-0.43782784888264942324 - 3.0221613999386220526e-630j)  +/-  (9.78e-254, 9.78e-254j)
| (8.3843827320177424041 + 6.5098762907154554103e-655j)  +/-  (6.48e-243, 6.48e-243j)
| (7.85350692853823115 - 2.0086686706402301358e-707j)  +/-  (6.08e-243, 6.08e-243j)
| (7.337561286333264224 + 8.3101157232023617216e-732j)  +/-  (4.38e-243, 4.38e-243j)
| (8.9333009185735982701 + 2.4388587010845113839e-747j)  +/-  (5.28e-243, 5.28e-243j)
| (6.8341582108278208913 + 3.0347902165688747298e-756j)  +/-  (2.9e-243, 2.9e-243j)
-------------------------------------------------
The weights are:
| (4.1375081728177041891e-13 - 2.9217971331449616647e-528j)  +/-  (5.68e-62, 8.95e-182j)
| (2.3446957482393700162e-26 - 1.048280842052651719e-536j)  +/-  (1.42e-70, 2.24e-190j)
| (1.5723350586954239161e-33 - 2.5128869876729824493e-540j)  +/-  (1.72e-73, 2.71e-193j)
| (1.5690801964937500191e-38 - 2.6774179887080248977e-542j)  +/-  (3.19e-76, 5.02e-196j)
| (1.2372659688248712834e-29 - 1.0642442737482426642e-537j)  +/-  (3.28e-73, 5.16e-193j)
| (1.5690801964937500191e-38 + 7.5775647915149235246e-543j)  +/-  (8.79e-76, 1.38e-195j)
| (1.6688471099346569794e-23 + 2.8995962104578904024e-535j)  +/-  (1.42e-70, 2.24e-190j)
| (1.0454604068634189581e-18 - 7.9332444588338120529e-532j)  +/-  (7.68e-70, 1.21e-189j)
| (0.015804226771688884535 + 1.6323881823283835765e-524j)  +/-  (6.65e-45, 1.05e-164j)
| (1.0658575923596073117e-06 + 1.0433786787414656155e-526j)  +/-  (1.5e-59, 2.36e-179j)
| (1.2372659688248712834e-29 + 2.3208024391801527265e-538j)  +/-  (7.45e-73, 1.17e-192j)
| (0.00034455204485488941683 - 6.0489523644969371914e-525j)  +/-  (9.08e-56, 1.43e-175j)
| (5.6415347397817096973e-21 - 5.5212796490374304649e-534j)  +/-  (3.69e-70, 5.82e-190j)
| (5.6415347397817096973e-21 + 4.2915739653137042949e-533j)  +/-  (5.41e-72, 8.53e-192j)
| (0.037694249294395804702 - 2.6435506238062918219e-524j)  +/-  (5.52e-45, 8.69e-165j)
| (9.6632158405631948642e-08 - 1.9681257101336380058e-526j)  +/-  (2.32e-63, 3.66e-183j)
| (0.001518295443624229401 + 1.13533597376437678e-524j)  +/-  (4.67e-55, 7.36e-175j)
| (0.037694249294395804702 - 4.3062090759814391135e-524j)  +/-  (1.13e-47, 1.77e-167j)
| (9.6632158405631948642e-08 - 3.0258504685978267219e-527j)  +/-  (3.44e-64, 5.42e-184j)
| (3.606146068112204082e-10 - 2.3602346949330336162e-527j)  +/-  (3.22e-66, 5.08e-186j)
| (1.0658575923596073117e-06 + 5.2720929949832956596e-526j)  +/-  (2.26e-62, 3.56e-182j)
| (0.0054253149262015721441 - 1.9419638538883182428e-524j)  +/-  (1.84e-54, 2.89e-174j)
| (2.3446957482393700162e-26 + 5.5710615763729946695e-536j)  +/-  (6.93e-76, 1.09e-195j)
| (1.6688471099346569794e-23 - 1.8283762381499616458e-534j)  +/-  (1.38e-74, 2.17e-194j)
| (0.073860185025412183305 + 3.8887610921493255428e-524j)  +/-  (1.7e-51, 2.68e-171j)
| (6.7698950399994594654e-09 + 7.7201674521443423827e-528j)  +/-  (1.18e-69, 1.86e-189j)
| (6.7698950399994594654e-09 + 6.8842110517196482251e-527j)  +/-  (1.92e-66, 3.02e-186j)
| (1.5723350586954239161e-33 + 1.0095523910820597727e-539j)  +/-  (1.84e-79, 2.9e-199j)
| (0.001518295443624229401 + 4.6272305543898734839e-525j)  +/-  (3.85e-63, 6.06e-183j)
| (0.0054253149262015721441 - 9.1385389012063861421e-525j)  +/-  (4e-61, 6.31e-181j)
| (8.4385064767501512511e-15 - 2.2043868514330022933e-529j)  +/-  (1.59e-71, 2.5e-191j)
| (0.11920610275663929835 - 6.615669810589736755e-524j)  +/-  (4.57e-57, 7.19e-177j)
| (9.2075482145801228223e-06 - 1.3010389806704582794e-525j)  +/-  (7.36e-66, 1.16e-185j)
| (1.1688351866055957414e-16 + 1.2786834614439490267e-530j)  +/-  (2.07e-72, 3.26e-192j)
| (0.17464095287361134895 - 7.0514552319541385346e-524j)  +/-  (2.66e-58, 4.19e-178j)
| (9.2075482145801228223e-06 - 3.187141914016725328e-526j)  +/-  (1.84e-69, 2.89e-189j)
| (0.015804226771688884535 + 3.0280919012955580628e-524j)  +/-  (2.21e-62, 3.48e-182j)
| (0.00034455204485488941683 - 2.1131040383720517673e-525j)  +/-  (1.51e-67, 2.38e-187j)
| (6.299576672310492593e-05 + 8.6736103924426149415e-526j)  +/-  (1.01e-68, 1.59e-188j)
| (0.15875322435043708235 + 6.3444857200984807053e-524j)  +/-  (8.88e-62, 1.4e-181j)
| (1.4319976965602284536e-11 + 9.3070950237918649711e-528j)  +/-  (3.42e-71, 5.39e-191j)
| (6.299576672310492593e-05 + 2.9371980697309356255e-525j)  +/-  (4.99e-67, 7.87e-187j)
| (0.073860185025412183305 + 5.587153865972225853e-524j)  +/-  (1.33e-63, 2.1e-183j)
| (0.11920610275663929835 - 5.2044093227105245773e-524j)  +/-  (6.96e-65, 1.1e-184j)
| (3.606146068112204082e-10 - 1.7187920549314254737e-528j)  +/-  (6.94e-76, 1.09e-195j)
| (0.15875322435043708235 + 7.1496793481385548641e-524j)  +/-  (4.42e-65, 6.97e-185j)
| (1.1688351866055957414e-16 - 8.5137005878790707631e-532j)  +/-  (9.88e-81, 1.56e-200j)
| (8.4385064767501512511e-15 + 7.4867796012959719137e-531j)  +/-  (4.57e-80, 7.2e-200j)
| (4.1375081728177041891e-13 - 5.4267533865934554918e-530j)  +/-  (1.9e-79, 2.99e-199j)
| (1.0454604068634189581e-18 + 7.7801332449249235431e-533j)  +/-  (2.5e-82, 3.96e-202j)
| (1.4319976965602284536e-11 + 3.305996865310179339e-529j)  +/-  (1.2e-78, 1.88e-198j)
