Starting with polynomial:
P : t
Extension levels are: 1 80
-------------------------------------------------
Trying to find an order 80 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^81 - 81/4*t^79 + 3159/16*t^77 - 39501/32*t^75 + 1423575/256*t^73 - 9845145/512*t^71 + 108734157/2048*t^69 - 492452379/4096*t^67 + 14915235753/65536*t^65 - 11969016345/32768*t^63 + 65846447667/131072*t^61 - 156492206793/262144*t^59 + 1293517709289/2097152*t^57 - 2335355502291/4194304*t^55 + 7394462517915/16777216*t^53 - 10292494292613/33554432*t^51 + 201891234201255/1073741824*t^49 - 1745765378093205/17179869184*t^47 + 3328346338128315/68719476736*t^45 - 2797167126270825/137438953472*t^43 + 8281448901713295/1099511627776*t^41 - 5389514364607065/2199023255552*t^39 + 6153513319220085/8796093022208*t^37 - 3072143831034915/17592186044416*t^35 + 10689623271729675/281474976710656*t^33 - 2015757531240453/281474976710656*t^31 + 1310947205631903/1125899906842624*t^29 - 365051142309021/2251799813685248*t^27 + 345371835446001/18014398509481984*t^25 - 68707924823475/36028797018963968*t^23 + 22723013046195/144115188075855872*t^21 - 3078601767549/288230376151711744*t^19 + 10743691882671/18446744073709551616*t^17 - 1844876383893/73786976294838206464*t^15 + 242443079235/295147905179352825856*t^13 - 11745689553/590295810358705651712*t^11 + 1595093643/4722366482869645213696*t^9 - 35272341/9444732965739290427392*t^7 + 906633/37778931862957161709568*t^5 - 5535/75557863725914323419136*t^3 + 81/1208925819614629174706176*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:
| (0.99981197044850139894 - 1.9366496118008890126e-1853j)  +/-  (1.77e-481, 1.77e-481j)
| (-0.96838996052780587728 + 7.4766570759412865575e-1852j)  +/-  (4.16e-481, 4.16e-481j)
| (-0.93288370473200049901 + 1.7938236892255087846e-1872j)  +/-  (8.22e-482, 8.22e-482j)
| (-0.99830815827126820805 + 4.7875623829299720507e-1893j)  +/-  (4.93e-481, 4.93e-481j)
| (0.93288370473200049901 + 6.499416914006283885e-1915j)  +/-  (8.09e-482, 8.09e-482j)
| (0.91821610688027401476 + 1.1144525564814553446e-1915j)  +/-  (3.77e-482, 3.77e-482j)
| (0.94614815687575043038 - 1.4454618741507479925e-1914j)  +/-  (1.58e-481, 1.58e-481j)
| (-0.91821610688027401476 + 1.1833089703631760852e-1915j)  +/-  (3.85e-482, 3.85e-482j)
| (-0.95798951231548887444 - 4.3230318408384464522e-1929j)  +/-  (2.68e-481, 2.68e-481j)
| (-0.99530279579316581936 - 6.9329203110132398862e-1963j)  +/-  (6.8e-481, 6.8e-481j)
| (0.88476179717665777235 - 1.7463995362306263755e-1994j)  +/-  (6.36e-483, 6.36e-483j)
| (-0.99981197044850139894 + 1.7144874153863805678e-1989j)  +/-  (1.74e-481, 1.74e-481j)
| (-0.88476179717665777235 + 1.6483355976702606573e-2009j)  +/-  (6.48e-483, 6.48e-483j)
| (-0.86602540378443864676 - 1.3667195478157427083e-2008j)  +/-  (2.19e-483, 2.19e-483j)
| (0.99530279579316581936 + 3.5501354790741136575e-2005j)  +/-  (7.08e-481, 7.08e-481j)
| (0.80212319275504378508 - 1.9856697258935506599e-2011j)  +/-  (5.13e-485, 5.13e-485j)
| (0.82467500410910673401 - 1.6279275014425639678e-2010j)  +/-  (1.88e-484, 1.88e-484j)
| (0.99830815827126820805 - 6.3075783831632365737e-2007j)  +/-  (5.04e-481, 5.04e-481j)
| (-0.80212319275504378508 + 1.4988690577548063445e-2010j)  +/-  (5.12e-485, 5.12e-485j)
| (-0.9773338582506355232 - 4.6672031318192383023e-2005j)  +/-  (5.59e-481, 5.59e-481j)
| (0.96838996052780587728 + 6.7024787803054433961e-2032j)  +/-  (4.03e-481, 4.03e-481j)
| (0.75343589632766074436 + 1.1247030618384635312e-2039j)  +/-  (2.55e-486, 2.55e-486j)
| (0.95798951231548887444 + 2.0848825287798649226e-2033j)  +/-  (2.62e-481, 2.62e-481j)
| (-0.84598642591984106086 + 1.0859736930503631152e-2036j)  +/-  (6.92e-484, 6.92e-484j)
| (-0.77836491192416001194 - 4.2388270126094131374e-2040j)  +/-  (1.21e-485, 1.21e-485j)
| (0.90216742478103768027 - 3.6393124122930644245e-2036j)  +/-  (1.64e-482, 1.64e-482j)
| (0.72737364157304869599 + 1.0866661206112879735e-2041j)  +/-  (5.14e-487, 5.14e-487j)
| (0.9773338582506355232 + 1.4237595175247083168e-2033j)  +/-  (5.78e-481, 5.78e-481j)
| (-0.98480775301220805937 - 2.9673109378741883516e-2034j)  +/-  (7.01e-481, 7.01e-481j)
| (-0.61260054519320283957 + 2.1692410432956673715e-2068j)  +/-  (2.37e-490, 2.37e-490j)
| (-0.90216742478103768027 - 9.9941686050835432544e-2058j)  +/-  (1.63e-482, 1.63e-482j)
| (0.86602540378443864676 - 1.3256743560009316893e-2069j)  +/-  (2.17e-483, 2.17e-483j)
| (0.64278760968653932632 - 4.233182164358546939e-2076j)  +/-  (1.73e-489, 1.73e-489j)
| (-0.99080040336484530851 - 4.7363322057185442867e-2065j)  +/-  (7.63e-481, 7.63e-481j)
| (-0.70021734776716851474 - 8.1048935029977151117e-2088j)  +/-  (6.48e-488, 6.48e-488j)
| (-0.72737364157304869599 - 1.1302560216551404087e-2086j)  +/-  (5.09e-487, 5.09e-487j)
| (0.98480775301220805937 - 1.2079229224113079225e-2079j)  +/-  (6.86e-481, 6.86e-481j)
| (0.61260054519320283957 + 2.3037020254264597018e-2091j)  +/-  (2.37e-490, 2.37e-490j)
| (0.84598642591984106086 - 2.1555836562828864462e-2083j)  +/-  (7.07e-484, 7.07e-484j)
| (-0.94614815687575043038 + 1.8622227123214937876e-2087j)  +/-  (1.58e-481, 1.58e-481j)
| (-0.5814920712880266679 + 1.0473793834782333944e-2097j)  +/-  (2.82e-491, 2.82e-491j)
| (0.99080040336484530851 - 5.177543774669411875e-2092j)  +/-  (7.93e-481, 7.93e-481j)
| (0.67200786055552240996 - 2.3891057995400478687e-2102j)  +/-  (1.15e-488, 1.15e-488j)
| (0.5814920712880266679 + 2.9127445396017354304e-2104j)  +/-  (2.77e-491, 2.77e-491j)
| (-0.41381072450513915146 - 5.2571879366015193116e-2109j)  +/-  (1.64e-496, 1.64e-496j)
| (-0.64278760968653932632 + 1.5013649620884414486e-2101j)  +/-  (1.7e-489, 1.7e-489j)
| (-0.67200786055552240996 - 1.8721624782604019667e-2100j)  +/-  (1.13e-488, 1.13e-488j)
| (0.77836491192416001194 + 5.6061598309676034682e-2100j)  +/-  (1.16e-485, 1.16e-485j)
| (0.48311259929663848322 + 4.3704705331520272053e-2108j)  +/-  (2.11e-494, 2.11e-494j)
| (0.70021734776716851474 - 6.3656867024607656136e-2101j)  +/-  (6.79e-488, 6.79e-488j)
| (-0.26817261276063736254 + 1.0361108059449644539e-2113j)  +/-  (2.89e-501, 2.89e-501j)
| (-0.51669937115186291572 - 1.7157193992517505961e-2106j)  +/-  (3.53e-493, 3.53e-493j)
| (0.03877537125681671149 + 9.8080590254365865588e-2122j)  +/-  (1.29e-509, 1.29e-509j)
| (0.54950897807080603526 + 2.4973517489713981409e-2105j)  +/-  (3.12e-492, 3.12e-492j)
| (0.51669937115186291572 + 5.7030188155274968983e-2106j)  +/-  (3.52e-493, 3.52e-493j)
| (-0.75343589632766074436 + 1.0404633891105070681e-2098j)  +/-  (2.53e-486, 2.53e-486j)
| (-0.48311259929663848322 - 1.1235758969193089141e-2107j)  +/-  (2.12e-494, 2.12e-494j)
| (-0.82467500410910673401 + 1.6656698628699305021e-2114j)  +/-  (1.91e-484, 1.91e-484j)
| (0.15451879280784048707 + 1.4439876445935177902e-2135j)  +/-  (3.16e-505, 3.16e-505j)
| (0.37819985817164246894 + 3.6368098522277045231e-2128j)  +/-  (1.21e-497, 1.21e-497j)
| (0.26817261276063736254 + 1.4106334125608151188e-2131j)  +/-  (2.86e-501, 2.86e-501j)
| (-0.54950897807080603526 + 1.7600457067747539116e-2125j)  +/-  (3.15e-492, 3.15e-492j)
| (-0.44879918020046217279 + 2.3659498973928894109e-2128j)  +/-  (2.07e-495, 2.07e-495j)
| (-0.077492420671930946262 + 1.2258803725268694829e-2140j)  +/-  (5.96e-508, 5.96e-508j)
| (0.41381072450513915146 - 1.349215731732638645e-2128j)  +/-  (1.67e-496, 1.67e-496j)
| (0.44879918020046217279 + 4.1191275782107054474e-2128j)  +/-  (2.08e-495, 2.08e-495j)
| (-0.03877537125681671149 - 2.6181697648208412559e-2141j)  +/-  (1.25e-509, 1.25e-509j)
| (-0.34202014332566873304 + 2.0359254949371417513e-2132j)  +/-  (6.69e-499, 6.69e-499j)
| (-0.23061587074244017845 + 3.974414116823174583e-2136j)  +/-  (1.24e-502, 1.24e-502j)
| (0.23061587074244017845 + 1.426994504191991894e-2134j)  +/-  (1.4e-502, 1.4e-502j)
| (0.30532599769511311325 - 4.9941228181747463298e-2132j)  +/-  (4.38e-500, 4.38e-500j)
| (0.077492420671930946262 - 1.3091787069422207247e-2139j)  +/-  (6.28e-508, 6.28e-508j)
| (-0.19271226054808968602 - 2.656517282208085763e-2136j)  +/-  (6.54e-504, 6.54e-504j)
| (-0.37819985817164246894 - 9.1136937629270726444e-2131j)  +/-  (1.22e-497, 1.22e-497j)
| (-9.8179719289538120217e-2190 - 2.8456417013754465421e-2190j)  +/-  (8.28e-2188, 8.28e-2188j)
| (0.34202014332566873304 + 6.8778861384991705547e-2131j)  +/-  (6.7e-499, 6.7e-499j)
| (0.11609291412523022968 - 6.8273984306427080543e-2139j)  +/-  (1.6e-506, 1.6e-506j)
| (-0.11609291412523022968 + 6.6408177992957785133e-2139j)  +/-  (1.63e-506, 1.63e-506j)
| (-0.30532599769511311325 - 2.5543140119449827916e-2133j)  +/-  (4.26e-500, 4.26e-500j)
| (-0.15451879280784048707 + 4.9133579546426862918e-2138j)  +/-  (3.02e-505, 3.02e-505j)
| (0.19271226054808968602 - 1.2681248220127069112e-2136j)  +/-  (6.43e-504, 6.43e-504j)
-------------------------------------------------
The weights are:
| (0.012345679012345679012 + 3.1822693474376622977e-1852j)  +/-  (7.99e-134, 1.16e-366j)
| (0.012345679012345679012 + 7.3392744851777852943e-1853j)  +/-  (3.73e-134, 5.42e-367j)
| (0.012345679012345679012 - 3.776736453497846667e-1852j)  +/-  (2.82e-134, 4.1e-367j)
| (0.012345679012345679012 + 7.1557948596685479315e-1853j)  +/-  (8.23e-135, 1.19e-367j)
| (0.012345679012345679012 - 7.3363919235881150099e-1853j)  +/-  (2.52e-135, 3.66e-368j)
| (0.012345679012345679012 + 6.7620039662630253448e-1853j)  +/-  (1.37e-135, 1.98e-368j)
| (0.012345679012345679012 + 8.0638707759473235923e-1853j)  +/-  (1.16e-135, 1.68e-368j)
| (0.012345679012345679012 + 2.946649915097253976e-1852j)  +/-  (3.88e-136, 5.63e-369j)
| (0.012345679012345679012 - 1.0222435672134518858e-1851j)  +/-  (5.41e-136, 7.85e-369j)
| (0.012345679012345679012 - 1.325142630710182765e-1852j)  +/-  (8.76e-137, 1.27e-369j)
| (0.012345679012345679012 + 5.9251786849662472628e-1853j)  +/-  (2.81e-139, 4.08e-372j)
| (0.012345679012345679012 - 2.2716851604624513929e-1853j)  +/-  (9.33e-137, 1.35e-369j)
| (0.012345679012345679012 + 2.0926790634712339302e-1852j)  +/-  (1.13e-138, 1.65e-371j)
| (0.012345679012345679012 - 1.8405262979745141576e-1852j)  +/-  (3.22e-139, 4.68e-372j)
| (0.012345679012345679012 + 2.6654355140353559507e-1852j)  +/-  (1.95e-141, 2.83e-374j)
| (0.012345679012345679012 + 4.9725706612238714999e-1853j)  +/-  (2.17e-142, 3.16e-375j)
| (0.012345679012345679012 - 5.1492195056025199174e-1853j)  +/-  (3.61e-142, 5.24e-375j)
| (0.012345679012345679012 - 4.7782777463609442158e-1852j)  +/-  (2.73e-141, 3.97e-374j)
| (0.012345679012345679012 + 1.3699026217966255353e-1852j)  +/-  (2.82e-143, 4.09e-376j)
| (0.012345679012345679012 + 8.7458341224490218277e-1852j)  +/-  (5.42e-140, 7.88e-373j)
| (0.012345679012345679012 + 1.0264554633452038048e-1852j)  +/-  (1.51e-142, 2.19e-375j)
| (0.012345679012345679012 + 4.7036662656651497667e-1853j)  +/-  (1.52e-145, 2.2e-378j)
| (0.012345679012345679012 - 9.0063053799068979109e-1853j)  +/-  (2.74e-142, 3.98e-375j)
| (0.012345679012345679012 + 1.6475774369402773635e-1852j)  +/-  (4.11e-144, 5.96e-377j)
| (0.012345679012345679012 - 1.2661009465960030192e-1852j)  +/-  (8.5e-146, 1.23e-378j)
| (0.012345679012345679012 - 6.3006338300437669627e-1853j)  +/-  (2.2e-143, 3.19e-376j)
| (0.012345679012345679012 - 4.6032529548822213878e-1853j)  +/-  (4.68e-147, 6.79e-380j)
| (0.012345679012345679012 - 1.20151699146452869e-1852j)  +/-  (2.69e-143, 3.91e-376j)
| (0.012345679012345679012 - 3.9031126061649481075e-1852j)  +/-  (8.19e-144, 1.19e-376j)
| (0.012345679012345679012 - 8.8250145141436653945e-1853j)  +/-  (2.67e-151, 3.88e-384j)
| (0.012345679012345679012 - 2.4385070091504613923e-1852j)  +/-  (7.47e-145, 1.08e-377j)
| (0.012345679012345679012 - 5.6166542311525158047e-1853j)  +/-  (4.03e-146, 5.85e-379j)
| (0.012345679012345679012 + 4.4049424202789987442e-1853j)  +/-  (3.32e-151, 4.83e-384j)
| (0.012345679012345679012 + 2.2262297807514504021e-1852j)  +/-  (7.41e-144, 1.08e-376j)
| (0.012345679012345679012 + 1.0369136615810869361e-1852j)  +/-  (7.16e-151, 1.04e-383j)
| (0.012345679012345679012 - 1.1026110980730236319e-1852j)  +/-  (2.24e-150, 3.26e-383j)
| (0.012345679012345679012 + 1.4598701032386482151e-1852j)  +/-  (4.37e-146, 6.34e-379j)
| (0.012345679012345679012 - 4.3668097836699133506e-1853j)  +/-  (5.48e-153, 7.96e-386j)
| (0.012345679012345679012 + 5.3613720172730758161e-1853j)  +/-  (9.08e-148, 1.32e-380j)
| (0.012345679012345679012 + 5.406589573711902678e-1852j)  +/-  (2.18e-146, 3.17e-379j)
| (0.012345679012345679012 + 8.4154912774343584584e-1853j)  +/-  (2.57e-154, 3.73e-387j)
| (0.012345679012345679012 - 1.8771999356847780053e-1852j)  +/-  (3.37e-146, 4.9e-379j)
| (0.012345679012345679012 - 4.4559836557631562856e-1853j)  +/-  (3.1e-152, 4.5e-385j)
| (0.012345679012345679012 + 4.3403336810477902043e-1853j)  +/-  (1.97e-154, 2.86e-387j)
| (0.012345679012345679012 - 6.8684616702747079607e-1853j)  +/-  (1.69e-158, 2.46e-391j)
| (0.012345679012345679012 + 9.2810595626199679206e-1853j)  +/-  (3.15e-154, 4.57e-387j)
| (0.012345679012345679012 - 9.7921464421589339774e-1853j)  +/-  (9.68e-154, 1.41e-386j)
| (0.012345679012345679012 - 4.825572793542317973e-1853j)  +/-  (1.36e-151, 1.97e-384j)
| (0.012345679012345679012 - 4.3214633711410682102e-1853j)  +/-  (4.67e-159, 6.78e-392j)
| (0.012345679012345679012 + 4.5214623956678836059e-1853j)  +/-  (2.71e-153, 3.93e-386j)
| (0.012345679012345679012 - 6.0279202541967242079e-1853j)  +/-  (1.72e-162, 2.49e-395j)
| (0.012345679012345679012 + 7.710195875514494044e-1853j)  +/-  (3.84e-159, 5.58e-392j)
| (0.012345679012345679012 - 4.9533699434318633004e-1853j)  +/-  (5.65e-164, 8.2e-397j)
| (0.012345679012345679012 - 4.3244867510936441971e-1853j)  +/-  (5.87e-158, 8.53e-391j)
| (0.012345679012345679012 + 4.3184263085406718312e-1853j)  +/-  (7.56e-159, 1.1e-391j)
| (0.012345679012345679012 + 1.1781681347539382423e-1852j)  +/-  (9.24e-157, 1.34e-389j)
| (0.012345679012345679012 - 7.4044959964789843145e-1853j)  +/-  (1.49e-161, 2.17e-394j)
| (0.012345679012345679012 - 1.49457804167193424e-1852j)  +/-  (3.92e-156, 5.69e-389j)
| (0.012345679012345679012 + 4.6969660438615977831e-1853j)  +/-  (2.7e-166, 3.92e-399j)
| (0.012345679012345679012 + 4.3801048529367583075e-1853j)  +/-  (1.33e-164, 1.93e-397j)
| (0.012345679012345679012 - 4.5064241114945415829e-1853j)  +/-  (5.57e-166, 8.08e-399j)
| (0.012345679012345679012 - 8.0457078533871319024e-1853j)  +/-  (1.68e-161, 2.44e-394j)
| (0.012345679012345679012 + 7.1249352494050645887e-1853j)  +/-  (1.74e-163, 2.53e-396j)
| (0.012345679012345679012 + 5.2821975921751897605e-1853j)  +/-  (2.17e-168, 3.15e-401j)
| (0.012345679012345679012 - 4.3527032333639771951e-1853j)  +/-  (5e-165, 7.25e-398j)
| (0.012345679012345679012 + 4.333038552368539988e-1853j)  +/-  (2.2e-164, 3.2e-397j)
| (0.012345679012345679012 - 5.1639167184405594961e-1853j)  +/-  (4.34e-169, 6.3e-402j)
| (0.012345679012345679012 - 6.4149548303568865023e-1853j)  +/-  (5.4e-168, 7.84e-401j)
| (0.012345679012345679012 + 5.855562908711225825e-1853j)  +/-  (4.33e-169, 6.29e-402j)
| (0.012345679012345679012 + 4.5628203668501789291e-1853j)  +/-  (4e-169, 5.8e-402j)
| (0.012345679012345679012 + 4.4571228905427328683e-1853j)  +/-  (1.62e-168, 2.35e-401j)
| (0.012345679012345679012 + 4.8602846467099675781e-1853j)  +/-  (2.88e-170, 4.18e-403j)
| (0.012345679012345679012 - 5.6957264673239406296e-1853j)  +/-  (9.17e-171, 1.33e-403j)
| (0.012345679012345679012 + 6.6325196613541139298e-1853j)  +/-  (2.3e-169, 3.34e-402j)
| (0.012345679012345679012 + 5.0544564813160272714e-1853j)  +/-  (9.95e-171, 1.44e-403j)
| (0.012345679012345679012 - 4.4149754594413083918e-1853j)  +/-  (7.67e-170, 1.11e-402j)
| (0.012345679012345679012 - 4.7748966451086254821e-1853j)  +/-  (6.14e-171, 8.91e-404j)
| (0.012345679012345679012 - 5.4098282057227676406e-1853j)  +/-  (8.29e-172, 1.2e-404j)
| (0.012345679012345679012 + 6.2139404837406757356e-1853j)  +/-  (9.25e-172, 1.34e-404j)
| (0.012345679012345679012 + 5.5474295242221798486e-1853j)  +/-  (5.61e-172, 8.15e-405j)
| (0.012345679012345679012 - 4.6263138965700114521e-1853j)  +/-  (4.78e-172, 6.83e-405j)
