Starting with polynomial:
P : t
Extension levels are: 1 82
-------------------------------------------------
Trying to find an order 82 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^83 - 83/4*t^81 + 415/2*t^79 - 85241/64*t^77 + 1578577/256*t^75 - 22464365/1024*t^73 + 63892155/1024*t^71 - 1193774475/8192*t^69 + 18670632789/65536*t^67 - 123966273563/262144*t^65 + 22076185703/32768*t^63 - 435502936141/524288*t^61 + 1870822472155/2097152*t^59 - 7035114834851/8388608*t^57 + 5811616602703/8388608*t^55 - 33844120215741/67108864*t^53 + 348038788487247/1073741824*t^51 - 790997246561925/4294967296*t^49 + 198763410674535/2147483648*t^47 - 11308591944166965/274877906944*t^45 + 17770644483690945/1099511627776*t^43 - 24649603638668085/4398046511104*t^41 + 7530802900040175/4398046511104*t^39 - 16174854924434115/35184372088832*t^37 + 30430659264613335/281474976710656*t^35 - 24974127258544737/1125899906842624*t^33 + 1112208096534381/281474976710656*t^31 - 2736384999409985/4503599627370496*t^29 + 1442821181507083/18014398509481984*t^27 - 646781908951451/72057594037927936*t^25 + 61017161221835/72057594037927936*t^23 - 38306059030085/576460752303423488*t^21 + 78865415650175/18446744073709551616*t^19 - 16346649789309/73786976294838206464*t^17 + 333605097741/36893488147419103232*t^15 - 333605097741/1180591620717411303424*t^13 + 30757916813/4722366482869645213696*t^11 - 1987879465/18889465931478580854784*t^9 + 20925047/18889465931478580854784*t^7 - 1024303/151115727451828646838272*t^5 + 23821/1208925819614629174706176*t^3 - 83/4835703278458516698824704*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: 0
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
  current precision for roots: 848
  current precision for roots: 1696
 current precision for weights: 848
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (0.99552627280855894995 + 2.5783663935814284719e-1708j)  +/-  (4.13e-480, 4.13e-480j)
| (-0.9698873816105272035 + 2.9349705163733277483e-1724j)  +/-  (2.45e-480, 2.45e-480j)
| (-0.93604473781427276299 - 3.3075705910803335878e-1727j)  +/-  (5.11e-481, 5.11e-481j)
| (-0.9983886888289512525 - 1.7010968016969431516e-1723j)  +/-  (2.76e-480, 2.76e-480j)
| (0.92205860303761354567 + 5.3254889743610229571e-1726j)  +/-  (2.4e-481, 2.4e-481j)
| (0.93604473781427276299 + 7.9430504970065072365e-1739j)  +/-  (5.01e-481, 5.01e-481j)
| (-0.99123777499193736998 - 8.3110223735925122038e-1748j)  +/-  (4.43e-480, 4.43e-480j)
| (-0.92205860303761354567 + 5.68476283850376349e-1751j)  +/-  (2.46e-481, 2.46e-481j)
| (0.26186448496080674737 + 2.6938133157962024467e-1772j)  +/-  (2.97e-501, 2.97e-501j)
| (-0.99982092266973775422 + 7.4093901798186981773e-1749j)  +/-  (1.01e-480, 1.01e-480j)
| (0.87226472736219378641 + 5.080734291015989088e-1751j)  +/-  (1.53e-482, 1.53e-482j)
| (0.9983886888289512525 - 2.6950847936194842371e-1761j)  +/-  (2.74e-480, 2.74e-480j)
| (-0.94868999752061644313 - 8.7121072060614504042e-1797j)  +/-  (9.41e-481, 9.41e-481j)
| (-0.87226472736219378641 - 4.1172861405482197778e-1799j)  +/-  (1.54e-482, 1.54e-482j)
| (0.98552933861089916923 + 5.3751759980530207741e-1794j)  +/-  (3.91e-480, 3.91e-480j)
| (0.8531342035272766981 - 3.8248397857144321175e-1814j)  +/-  (5.22e-483, 5.22e-483j)
| (0.90675162819398263405 + 6.1982256375737649159e-1811j)  +/-  (1.05e-481, 1.05e-481j)
| (-0.43874910597176514886 + 2.5538367009648812026e-1834j)  +/-  (2.49e-495, 2.49e-495j)
| (-0.76469109261717461538 - 1.8163634920830518448e-1823j)  +/-  (2.17e-485, 2.17e-485j)
| (-0.95997626794392277265 + 2.2241095628179995107e-1817j)  +/-  (1.57e-480, 1.57e-480j)
| (0.89014574037739660091 + 6.2873075828331682248e-1817j)  +/-  (4.19e-482, 4.19e-482j)
| (0.78852832153036583447 - 2.1645681899806192676e-1830j)  +/-  (9.12e-485, 9.12e-485j)
| (-0.81123599121859230435 + 5.5540501784585776092e-1831j)  +/-  (3.93e-484, 3.93e-484j)
| (-0.89014574037739660091 + 1.0458200852440649505e-1828j)  +/-  (4.2e-482, 4.2e-482j)
| (-0.78852832153036583447 - 1.9112514734254291995e-1830j)  +/-  (9.25e-485, 9.25e-485j)
| (0.99982092266973775422 + 1.3478543710114396924e-1822j)  +/-  (1.01e-480, 1.01e-480j)
| (0.76469109261717461538 - 1.2133556619523077732e-1843j)  +/-  (2.21e-485, 2.21e-485j)
| (0.95997626794392277265 + 4.9404722586381009223e-1837j)  +/-  (1.64e-480, 1.64e-480j)
| (-0.98552933861089916923 - 3.1467913998262905002e-1844j)  +/-  (4.11e-480, 4.11e-480j)
| (-0.62981052202827121203 + 1.9886291635742880692e-1856j)  +/-  (2.21e-489, 2.21e-489j)
| (-0.90675162819398263405 - 9.0629175751220384001e-1848j)  +/-  (1.12e-481, 1.12e-481j)
| (0.81123599121859230435 + 5.8962803741700172414e-1850j)  +/-  (3.88e-484, 3.88e-484j)
| (0.68675131121350106825 + 1.4598673294442306432e-1853j)  +/-  (1.09e-487, 1.09e-487j)
| (-0.99552627280855894995 + 1.8054534485203805283e-1846j)  +/-  (4.1e-480, 4.1e-480j)
| (-0.71376611268713892637 + 1.4667417023737689409e-1854j)  +/-  (9.14e-487, 9.14e-487j)
| (-0.7397584510798208032 + 1.4661430745198253302e-1853j)  +/-  (4.41e-486, 4.41e-486j)
| (0.94868999752061644313 + 7.0976679036992813873e-1845j)  +/-  (9.36e-481, 9.36e-481j)
| (0.59996610144869562883 + 3.4445961809043635353e-1868j)  +/-  (3.1e-490, 3.1e-490j)
| (0.83278157316376096772 - 1.6615238075536986027e-1860j)  +/-  (1.36e-483, 1.36e-483j)
| (-0.8531342035272766981 + 2.8313642796649977478e-1863j)  +/-  (4.92e-483, 4.92e-483j)
| (-0.59996610144869562883 - 1.9047232963367199285e-1869j)  +/-  (3.11e-490, 3.11e-490j)
| (-0.97840914094557274163 + 7.9658702705399074337e-1859j)  +/-  (3.23e-480, 3.23e-480j)
| (0.65875274510179373947 + 1.3759543252009041735e-1866j)  +/-  (1.67e-488, 1.67e-488j)
| (0.62981052202827121203 - 1.53227444180801008e-1867j)  +/-  (2.16e-489, 2.16e-489j)
| (0.99123777499193736998 + 4.7055545051110247553e-1856j)  +/-  (4.27e-480, 4.27e-480j)
| (-0.56926223520806598932 - 3.7704567114939716428e-1892j)  +/-  (3.48e-491, 3.48e-491j)
| (-0.83278157316376096772 - 6.5957790411045492153e-1885j)  +/-  (1.4e-483, 1.4e-483j)
| (0.97840914094557274163 - 9.5484508672694610378e-1885j)  +/-  (3.28e-480, 3.28e-480j)
| (0.50545326585658081855 - 1.9211878697503529763e-1930j)  +/-  (4.5e-493, 4.5e-493j)
| (0.7397584510798208032 + 6.3624856443752462782e-1924j)  +/-  (4.31e-486, 4.31e-486j)
| (-0.65875274510179373947 + 1.2487566865909001148e-1928j)  +/-  (1.62e-488, 1.62e-488j)
| (-0.53774290629901200257 - 6.0660579323051681806e-1933j)  +/-  (3.86e-492, 3.86e-492j)
| (-0.68675131121350106825 - 4.0595594416474150552e-1928j)  +/-  (1.12e-487, 1.12e-487j)
| (0.56926223520806598932 + 1.9761094918311374505e-1930j)  +/-  (3.5e-491, 3.5e-491j)
| (0.53774290629901200257 + 1.0956304069384388763e-1930j)  +/-  (4e-492, 4e-492j)
| (0.9698873816105272035 + 6.493446866576144264e-1937j)  +/-  (2.46e-480, 2.46e-480j)
| (-0.50545326585658081855 - 4.9561054869958762368e-1970j)  +/-  (4.54e-493, 4.54e-493j)
| (-0.47243956847967099872 - 9.5093268835792437354e-1972j)  +/-  (2.64e-494, 2.64e-494j)
| (0.71376611268713892637 + 6.0178618276470779647e-1975j)  +/-  (9.01e-487, 9.01e-487j)
| (0.40443013959587697617 - 5.3234771762730284435e-1984j)  +/-  (1.86e-496, 1.86e-496j)
| (0.1508242971613738284 + 3.8260173153446921083e-1994j)  +/-  (3.39e-505, 3.39e-505j)
| (-0.40443013959587697617 + 3.9079235281566474987e-1986j)  +/-  (1.82e-496, 1.82e-496j)
| (-0.36953183094075690666 + 8.0064992599660220591e-1988j)  +/-  (1.36e-497, 1.36e-497j)
| (-0.037841476717670287463 - 1.4410307802865456121e-1998j)  +/-  (1.27e-509, 1.27e-509j)
| (0.43874910597176514886 - 1.7527996216335746967e-1982j)  +/-  (2.37e-495, 2.37e-495j)
| (0.47243956847967099872 + 1.3387009468477420439e-1982j)  +/-  (2.62e-494, 2.62e-494j)
| (-0.1508242971613738284 - 1.4711200908116572213e-1994j)  +/-  (3.21e-505, 3.21e-505j)
| (-0.33410417149738975715 - 5.982077091048906653e-1989j)  +/-  (7.29e-499, 7.29e-499j)
| (-0.18812486236863375531 - 3.9744127952222765016e-1993j)  +/-  (6.77e-504, 6.77e-504j)
| (0.11330767760126984353 + 2.3653372983593765044e-1995j)  +/-  (1.66e-506, 1.66e-506j)
| (0.36953183094075690666 + 3.5211295757253504163e-1986j)  +/-  (1.34e-497, 1.34e-497j)
| (0.075628745884456700689 - 4.4473221608185906206e-1997j)  +/-  (6.52e-508, 6.52e-508j)
| (-0.22515594052269399464 + 8.543471822870196033e-1992j)  +/-  (1.31e-502, 1.31e-502j)
| (-0.26186448496080674737 + 1.28048983551695658e-1990j)  +/-  (3.05e-501, 3.05e-501j)
| (0.037841476717670287463 + 1.1710237435826701758e-1998j)  +/-  (1.27e-509, 1.27e-509j)
| (0.33410417149738975715 + 2.0284063607516772645e-1987j)  +/-  (7.18e-499, 7.18e-499j)
| (0.22515594052269399464 - 1.3371505411703071105e-1991j)  +/-  (1.34e-502, 1.34e-502j)
| (-0.075628745884456700689 + 1.9540642188632396023e-1997j)  +/-  (6.34e-508, 6.34e-508j)
| (-0.29819791104666545071 - 3.8788866729556162683e-1989j)  +/-  (4.73e-500, 4.73e-500j)
| (-0.11330767760126984353 - 1.9023423864426462043e-1996j)  +/-  (1.78e-506, 1.78e-506j)
| (0.18812486236863375531 + 3.2589636963359771406e-1993j)  +/-  (6.62e-504, 6.62e-504j)
| (0.29819791104666545071 + 2.2965797661596769141e-1989j)  +/-  (4.83e-500, 4.83e-500j)
| (4.2461582035735049937e-2240 - 2.8895045933539893717e-2239j)  +/-  (2.42e-2237, 2.42e-2237j)
-------------------------------------------------
The weights are:
| (0.012048192771084337349 - 1.7320575685028286651e-1708j)  +/-  (1.8e-140, 4.81e-372j)
| (0.012048192771084337349 - 4.0742160602309733299e-1710j)  +/-  (8.93e-141, 2.38e-372j)
| (0.012048192771084337349 + 5.9894676467481437256e-1710j)  +/-  (5.44e-141, 1.45e-372j)
| (0.012048192771084337349 + 9.3567736640795623468e-1711j)  +/-  (1.45e-141, 3.88e-373j)
| (0.012048192771084337349 - 1.7321049626892673841e-1708j)  +/-  (6.05e-143, 1.61e-374j)
| (0.012048192771084337349 + 1.9449871420826341086e-1708j)  +/-  (4.96e-143, 1.32e-374j)
| (0.012048192771084337349 + 2.1858760689654460423e-1710j)  +/-  (6.49e-142, 1.73e-373j)
| (0.012048192771084337349 - 6.6361451328882555793e-1710j)  +/-  (2.98e-142, 7.94e-374j)
| (0.012048192771084337349 - 4.3249548264182358096e-1709j)  +/-  (1.97e-144, 5.26e-376j)
| (0.012048192771084337349 - 3.1181747503133128273e-1711j)  +/-  (8.51e-142, 2.27e-373j)
| (0.012048192771084337349 + 1.3044111568343329938e-1708j)  +/-  (4.41e-144, 1.17e-375j)
| (0.012048192771084337349 - 6.5177845807729236056e-1708j)  +/-  (1.5e-144, 3.99e-376j)
| (0.012048192771084337349 - 5.3472549172243599298e-1710j)  +/-  (2.72e-142, 7.25e-374j)
| (0.012048192771084337349 + 8.6082294579093360082e-1710j)  +/-  (1.78e-144, 4.75e-376j)
| (0.012048192771084337349 - 5.5746624726305382804e-1708j)  +/-  (9.95e-145, 2.65e-376j)
| (0.012048192771084337349 - 1.2045671992220391971e-1708j)  +/-  (8.29e-145, 2.21e-376j)
| (0.012048192771084337349 + 1.561643202741976034e-1708j)  +/-  (4.06e-144, 1.08e-375j)
| (0.012048192771084337349 + 2.0598783782214158829e-1709j)  +/-  (1.1e-147, 2.93e-379j)
| (0.012048192771084337349 - 1.2036224930823452096e-1709j)  +/-  (1.35e-146, 3.61e-378j)
| (0.012048192771084337349 + 4.709002044682388689e-1710j)  +/-  (1.99e-143, 5.29e-375j)
| (0.012048192771084337349 - 1.4216699183817672769e-1708j)  +/-  (3.61e-145, 9.62e-377j)
| (0.012048192771084337349 + 9.7681211153275162463e-1709j)  +/-  (1.35e-147, 3.59e-379j)
| (0.012048192771084337349 - 1.0640184785600998467e-1709j)  +/-  (1.3e-146, 3.47e-378j)
| (0.012048192771084337349 - 7.9449836394034981018e-1710j)  +/-  (1.72e-145, 4.59e-377j)
| (0.012048192771084337349 + 1.1333627710307111681e-1709j)  +/-  (8.29e-147, 2.21e-378j)
| (0.012048192771084337349 + 1.4487423757827797689e-1708j)  +/-  (2.73e-147, 7.27e-379j)
| (0.012048192771084337349 - 9.1781383235606679591e-1709j)  +/-  (1.73e-149, 4.61e-381j)
| (0.012048192771084337349 + 2.5902852890875062871e-1708j)  +/-  (1.07e-147, 2.84e-379j)
| (0.012048192771084337349 - 2.8131231446405805463e-1710j)  +/-  (1e-145, 2.67e-377j)
| (0.012048192771084337349 + 1.5712319176073233692e-1709j)  +/-  (1.22e-151, 3.25e-383j)
| (0.012048192771084337349 + 7.287805859760082849e-1710j)  +/-  (3.22e-146, 8.58e-378j)
| (0.012048192771084337349 - 1.0431523673978992942e-1708j)  +/-  (4.64e-150, 1.24e-381j)
| (0.012048192771084337349 + 7.7398251324328844703e-1709j)  +/-  (3.18e-153, 8.49e-385j)
| (0.012048192771084337349 - 1.5602127333461496842e-1710j)  +/-  (1.14e-145, 3.05e-377j)
| (0.012048192771084337349 - 1.3471718762880709554e-1709j)  +/-  (5.3e-151, 1.41e-382j)
| (0.012048192771084337349 + 1.2748676980301811871e-1709j)  +/-  (3.48e-150, 9.29e-382j)
| (0.012048192771084337349 - 2.2196940187389691161e-1708j)  +/-  (2.8e-150, 7.47e-382j)
| (0.012048192771084337349 - 6.6495812597477210496e-1709j)  +/-  (5.26e-156, 1.4e-387j)
| (0.012048192771084337349 + 1.1183909249438099747e-1708j)  +/-  (1.05e-150, 2.81e-382j)
| (0.012048192771084337349 - 9.2781134384150164757e-1710j)  +/-  (1.28e-149, 3.42e-381j)
| (0.012048192771084337349 - 1.6485879500374385521e-1709j)  +/-  (7.6e-155, 2.03e-386j)
| (0.012048192771084337349 + 3.4424143497513071629e-1710j)  +/-  (1.62e-147, 4.31e-379j)
| (0.012048192771084337349 - 7.3449785240907046742e-1709j)  +/-  (1.14e-155, 3.03e-387j)
| (0.012048192771084337349 + 6.9829670815667688445e-1709j)  +/-  (3.25e-156, 8.68e-388j)
| (0.012048192771084337349 + 1.0126669459728321242e-1707j)  +/-  (9.63e-153, 2.57e-384j)
| (0.012048192771084337349 + 1.7274347615484769933e-1709j)  +/-  (3.41e-157, 9.1e-389j)
| (0.012048192771084337349 + 9.9552269365583347553e-1710j)  +/-  (9.74e-152, 2.6e-383j)
| (0.012048192771084337349 + 3.9697676270659512864e-1708j)  +/-  (2.65e-153, 7.06e-385j)
| (0.012048192771084337349 + 5.7886806593161171887e-1709j)  +/-  (1.4e-160, 3.74e-392j)
| (0.012048192771084337349 + 8.6494791503397470893e-1709j)  +/-  (1.53e-155, 4.07e-387j)
| (0.012048192771084337349 - 1.4952703272589594646e-1709j)  +/-  (7.92e-156, 2.11e-387j)
| (0.012048192771084337349 - 1.8078746640217855893e-1709j)  +/-  (5.33e-159, 1.42e-390j)
| (0.012048192771084337349 + 1.4206122881965920869e-1709j)  +/-  (2.34e-155, 6.25e-387j)
| (0.012048192771084337349 + 6.3413045079653231878e-1709j)  +/-  (3.8e-160, 1.01e-391j)
| (0.012048192771084337349 - 6.0551752309599479844e-1709j)  +/-  (5.79e-161, 1.54e-392j)
| (0.012048192771084337349 - 3.123192736371853934e-1708j)  +/-  (1.87e-155, 4.98e-387j)
| (0.012048192771084337349 + 1.890016528485596756e-1709j)  +/-  (4.96e-161, 1.32e-392j)
| (0.012048192771084337349 - 1.9739764323637330603e-1709j)  +/-  (4.78e-162, 1.27e-393j)
| (0.012048192771084337349 - 8.1725912886365879387e-1709j)  +/-  (1.47e-158, 3.93e-390j)
| (0.012048192771084337349 - 5.0869957399028644295e-1709j)  +/-  (1.12e-165, 2.98e-397j)
| (0.012048192771084337349 + 3.8477145618674016364e-1709j)  +/-  (1.58e-168, 4.22e-400j)
| (0.012048192771084337349 - 2.1478550938322305599e-1709j)  +/-  (1.03e-164, 2.76e-396j)
| (0.012048192771084337349 + 2.2380489249359267296e-1709j)  +/-  (5.66e-166, 1.51e-397j)
| (0.012048192771084337349 - 3.1793401145557977336e-1709j)  +/-  (3.72e-170, 9.91e-402j)
| (0.012048192771084337349 + 5.3063110650709410164e-1709j)  +/-  (4.53e-166, 1.21e-397j)
| (0.012048192771084337349 - 5.5396743030119956898e-1709j)  +/-  (2.39e-165, 6.37e-397j)
| (0.012048192771084337349 + 2.8352339827606861815e-1709j)  +/-  (7.93e-171, 2.11e-402j)
| (0.012048192771084337349 - 2.330612833884525259e-1709j)  +/-  (9.01e-169, 2.4e-400j)
| (0.012048192771084337349 - 2.7280668605411138185e-1709j)  +/-  (9.86e-171, 2.63e-402j)
| (0.012048192771084337349 - 3.7027205337597721755e-1709j)  +/-  (5.66e-172, 1.51e-403j)
| (0.012048192771084337349 + 4.8803417686197416567e-1709j)  +/-  (2.52e-170, 6.72e-402j)
| (0.012048192771084337349 + 3.5638386250579803254e-1709j)  +/-  (2.23e-172, 5.96e-404j)
| (0.012048192771084337349 + 2.6242384138389377676e-1709j)  +/-  (1.09e-171, 2.9e-403j)
| (0.012048192771084337349 - 2.523522676387267099e-1709j)  +/-  (1.29e-171, 3.43e-403j)
| (0.012048192771084337349 - 3.4305938160108235127e-1709j)  +/-  (2.47e-173, 6.58e-405j)
| (0.012048192771084337349 - 4.6851379348830714381e-1709j)  +/-  (7.4e-173, 1.98e-404j)
| (0.012048192771084337349 + 4.1582093975617018163e-1709j)  +/-  (1.12e-173, 2.98e-405j)
| (0.012048192771084337349 + 3.0605899989597874299e-1709j)  +/-  (3.65e-174, 9.72e-406j)
| (0.012048192771084337349 + 2.4257115195424762261e-1709j)  +/-  (3.05e-173, 8.12e-405j)
| (0.012048192771084337349 - 2.9459856514416594519e-1709j)  +/-  (4.1e-174, 1.09e-405j)
| (0.012048192771084337349 - 3.9993482728242429624e-1709j)  +/-  (6.93e-175, 1.88e-406j)
| (0.012048192771084337349 + 4.5003212660951064621e-1709j)  +/-  (6.66e-175, 1.84e-406j)
| (0.012048192771084337349 + 3.3025571371297880343e-1709j)  +/-  (6.7e-175, 1.73e-406j)
