Starting with polynomial:
P : t
Extension levels are: 1 40 42
-------------------------------------------------
Trying to find an order 40 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 42 Kronrod extension for:
P2 : t^41 - 41/4*t^39 + 779/16*t^37 - 4551/32*t^35 + 73185/256*t^33 - 53669/128*t^31 + 237677/512*t^29 - 405449/1024*t^27 + 4312503/16384*t^25 - 35937525/262144*t^23 + 58659315/1048576*t^21 - 37328655/2097152*t^19 + 73370115/16777216*t^17 - 13706505/16777216*t^15 + 7614725/67108864*t^13 - 1522945/134217728*t^11 + 3350479/4294967296*t^9 - 591261/17179869184*t^7 + 59983/68719476736*t^5 - 1435/137438953472*t^3 + 41/1099511627776*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^83 - 21*t^81 + 3401/16*t^79 - 5525/4*t^77 + 1657579/256*t^75 - 5971985/256*t^73 + 137629455/2048*t^71 - 162813579/1024*t^69 + 20640442305/65536*t^67 - 34720377329/65536*t^65 + 100273759157/131072*t^63 - 3916792061/4096*t^61 + 2183806885741/2097152*t^59 - 2082158136035/2097152*t^57 + 13958588707697/16777216*t^55 - 5154822841707/8388608*t^53 + 430378742828151/1073741824*t^51 - 248222120190795/1073741824*t^49 + 8106194519678325/68719476736*t^47 - 914808642643455/17179869184*t^45 + 23364978736232595/1099511627776*t^43 - 8232763135095345/1099511627776*t^41 + 20451120164687415/8796093022208*t^39 - 2791046030456775/4398046511104*t^37 + 42719234588752995/281474976710656*t^35 - 8915937632568603/281474976710656*t^33 + 6464589917377977/1125899906842624*t^31 - 126479131407559/140737488355328*t^29 + 2172923466125125/18014398509481984*t^27 - 248038436099363/18014398509481984*t^25 + 190742247267145/144115188075855872*t^23 - 7628634009535/72057594037927936*t^21 + 128123043930959/18446744073709551616*t^19 - 6772585417995/18446744073709551616*t^17 + 4513717165821/295147905179352825856*t^15 - 36003011061/73786976294838206464*t^13 + 54249295919/4722366482869645213696*t^11 - 895743277/4722366482869645213696*t^9 + 77122435/37778931862957161709568*t^7 - 241367/18889465931478580854784*t^5 + 45961/1208925819614629174706176*t^3 - 41/1208925819614629174706176*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:
| (1 - 9.5124556017717433245e-1853j)  +/-  (2.84e-479, 2.84e-479j)
| (-0.97369542387777904436 - 6.8140069369571507302e-1875j)  +/-  (7.27e-480, 7.27e-480j)
| (-0.91250361647655001597 + 3.2483113021775868976e-1877j)  +/-  (2.12e-481, 2.12e-481j)
| (-0.99706580118374046214 + 1.7058973972642645377e-1873j)  +/-  (2.72e-479, 2.72e-479j)
| (0.94114004797956157414 - 1.6373654522508467663e-1876j)  +/-  (1.19e-480, 1.19e-480j)
| (0.92750245110209466461 + 5.9843814833245387956e-1881j)  +/-  (5.32e-481, 5.32e-481j)
| (-0.96425349545314098385 - 4.6767508541617064503e-1885j)  +/-  (4.21e-480, 4.21e-480j)
| (-0.92750245110209466461 - 2.8162394362508713797e-1886j)  +/-  (5.41e-481, 5.41e-481j)
| (-0.076549252836495646867 + 2.6018655649691449421e-1914j)  +/-  (6.66e-508, 6.66e-508j)
| (-0.99926618105081002039 - 1.8733059933242705432e-1884j)  +/-  (3.07e-479, 3.07e-479j)
| (0.85956960698720116004 - 1.5235409940015217375e-1890j)  +/-  (8.61e-483, 8.61e-483j)
| (0.98828042378034852632 - 1.6911640362122018638e-1886j)  +/-  (1.7e-479, 1.7e-479j)
| (-0.89616555696105561114 + 2.8709007033766125326e-1909j)  +/-  (7.92e-482, 7.92e-482j)
| (-0.83936542613194995964 + 2.2376505181973655179e-1911j)  +/-  (2.26e-483, 2.26e-483j)
| (-0.99340208975967506879 - 9.8253847507146565921e-1905j)  +/-  (2.22e-479, 2.22e-479j)
| (0.83936542613194995964 + 8.2726893151274106406e-1910j)  +/-  (2.21e-483, 2.21e-483j)
| (0.89616555696105561114 + 1.7935464620932311214e-1905j)  +/-  (7.97e-482, 7.97e-482j)
| (-1 - 5.5653609229933747432e-1908j)  +/-  (1.58e-479, 1.58e-479j)
| (-0.77148917982194292363 - 1.0370825175379465138e-1917j)  +/-  (3.29e-485, 3.29e-485j)
| (-0.98170831999685493768 + 9.7640437394074418677e-1912j)  +/-  (1.16e-479, 1.16e-479j)
| (0.91250361647655001597 + 7.2833841488753272907e-1910j)  +/-  (2.08e-481, 2.08e-481j)
| (0.77148917982194292363 - 6.6496990161687908484e-1927j)  +/-  (3.4e-485, 3.4e-485j)
| (0.99340208975967506879 - 4.1911717362543205407e-1928j)  +/-  (2.25e-479, 2.25e-479j)
| (-0.85956960698720116004 + 9.5460560250215513988e-1971j)  +/-  (8.6e-483, 8.6e-483j)
| (-0.79529287127342644197 + 9.3467996964938385946e-1972j)  +/-  (1.56e-484, 1.56e-484j)
| (0.99926618105081002039 - 6.481163796745458881e-1963j)  +/-  (3.11e-479, 3.11e-479j)
| (0.74655322161196265054 - 4.1250466494005936959e-1988j)  +/-  (6.7e-486, 6.7e-486j)
| (0.95339639205493054595 - 5.1599149744918830119e-1981j)  +/-  (2.43e-480, 2.43e-480j)
| (-0.95339639205493054595 + 2.3484554856856540462e-1990j)  +/-  (2.3e-480, 2.3e-480j)
| (-0.63624244232655983326 + 1.4360421641484733791e-1999j)  +/-  (3.22e-489, 3.22e-489j)
| (0.96425349545314098385 + 1.1685333398412777462e-1987j)  +/-  (4.32e-480, 4.32e-480j)
| (0.87851225091094237703 - 2.242150036792594594e-2004j)  +/-  (2.74e-482, 2.74e-482j)
| (0.66532570016556536356 + 3.5865270056165688003e-2019j)  +/-  (2.37e-488, 2.37e-488j)
| (-0.98828042378034852632 + 4.6367781116505540663e-2009j)  +/-  (1.72e-479, 1.72e-479j)
| (-0.72052159360078700864 + 3.1207950179095776976e-2029j)  +/-  (1.22e-486, 1.22e-486j)
| (-0.74655322161196265054 - 9.8670739933804837596e-2029j)  +/-  (6.57e-486, 6.57e-486j)
| (0.98170831999685493768 - 2.174250360469733199e-2019j)  +/-  (1.13e-479, 1.13e-479j)
| (0.63624244232655983326 - 8.1950331691987360077e-2057j)  +/-  (3.25e-489, 3.25e-489j)
| (0.8179293607667176653 - 4.6890352686922840861e-2048j)  +/-  (6.09e-484, 6.09e-484j)
| (-0.8179293607667176653 - 4.9123915364435930473e-2055j)  +/-  (6.25e-484, 6.25e-484j)
| (-0.54356755000122115073 - 1.1734086190111023466e-2063j)  +/-  (4.88e-492, 4.88e-492j)
| (-0.26498150219666168233 + 7.3641097020003698547e-2072j)  +/-  (3.18e-501, 3.18e-501j)
| (0.79529287127342644197 + 5.4203885648324761125e-2051j)  +/-  (1.58e-484, 1.58e-484j)
| (0.60622541096663801827 + 7.176195013390840668e-2064j)  +/-  (3.91e-490, 3.91e-490j)
| (0.99706580118374046214 - 1.7968846901797240145e-2052j)  +/-  (2.72e-479, 2.72e-479j)
| (-0.57531866021862059959 - 7.2837984733773662024e-2090j)  +/-  (4.81e-491, 4.81e-491j)
| (-0.69343250079224172863 + 5.432759592581474721e-2087j)  +/-  (1.47e-487, 1.47e-487j)
| (0.69343250079224172863 - 7.4939399922636496881e-2086j)  +/-  (1.53e-487, 1.53e-487j)
| (0.51101867944711036626 - 1.7109510537303504639e-2091j)  +/-  (5.16e-493, 5.16e-493j)
| (0.72052159360078700864 - 3.3279207325752968699e-2084j)  +/-  (1.21e-486, 1.21e-486j)
| (-0.66532570016556536356 - 1.0996985824556483306e-2086j)  +/-  (2.36e-488, 2.36e-488j)
| (-0.47771981851226292267 - 7.3202648954132416733e-2093j)  +/-  (3.18e-494, 3.18e-494j)
| (-0.87851225091094237703 + 4.3467544537843596895e-2080j)  +/-  (2.79e-482, 2.79e-482j)
| (0.57531866021862059959 + 5.2229706104269253424e-2089j)  +/-  (4.77e-491, 4.77e-491j)
| (0.54356755000122115073 - 5.0322592381529773734e-2091j)  +/-  (4.88e-492, 4.88e-492j)
| (0.97369542387777904436 - 2.8756544550648239358e-2088j)  +/-  (7.37e-480, 7.37e-480j)
| (-0.51101867944711036626 - 7.6947933108598544624e-2105j)  +/-  (5.23e-493, 5.23e-493j)
| (-0.60622541096663801827 + 1.0279251283937881181e-2100j)  +/-  (3.95e-490, 3.95e-490j)
| (0.038302733690035348803 - 2.8697453922484220733e-2121j)  +/-  (1.29e-509, 1.29e-509j)
| (0.40906863717133988836 - 4.5846700355433934848e-2108j)  +/-  (2.1e-496, 2.1e-496j)
| (-0.94114004797956157414 - 1.2701755404761800019e-2115j)  +/-  (1.21e-480, 1.21e-480j)
| (-0.443719837866959686 - 9.3485894194474210627e-2132j)  +/-  (2.72e-495, 2.72e-495j)
| (-0.40906863717133988836 + 9.6275996844143006225e-2133j)  +/-  (2.04e-496, 2.04e-496j)
| (0.11468342539840043433 - 2.1311807875951967347e-2143j)  +/-  (1.66e-506, 1.66e-506j)
| (0.443719837866959686 + 2.9336279330890202657e-2131j)  +/-  (2.74e-495, 2.74e-495j)
| (0.47771981851226292267 - 4.8569621714746690518e-2130j)  +/-  (3.07e-494, 3.07e-494j)
| (-0.038302733690035348803 - 5.856302911280498272e-2146j)  +/-  (1.36e-509, 1.36e-509j)
| (-0.33801687840850275828 - 8.1591321402448397224e-2136j)  +/-  (7.89e-499, 7.89e-499j)
| (-0.19039110916466836871 + 5.063342210999285197e-2141j)  +/-  (7e-504, 7e-504j)
| (0.33801687840850275828 - 5.5291284047007013419e-2135j)  +/-  (7.87e-499, 7.87e-499j)
| (0.37381707184076879139 - 3.0451254652802999365e-2134j)  +/-  (1.55e-497, 1.55e-497j)
| (0.15264928421887449854 - 3.8040419578848614989e-2141j)  +/-  (3.35e-505, 3.35e-505j)
| (-0.2278535089031375756 + 1.5766159057364411407e-2139j)  +/-  (1.42e-502, 1.42e-502j)
| (-0.37381707184076879139 + 1.492500919114742772e-2134j)  +/-  (1.49e-497, 1.49e-497j)
| (-1.4251562243775421653e-2199 + 1.2209258717783772143e-2199j)  +/-  (1.56e-2197, 1.56e-2197j)
| (0.26498150219666168233 + 1.9388124795123882458e-2137j)  +/-  (3e-501, 3e-501j)
| (0.2278535089031375756 - 1.253207507495480218e-2139j)  +/-  (1.34e-502, 1.34e-502j)
| (-0.11468342539840043433 + 1.4603440953319445802e-2143j)  +/-  (1.78e-506, 1.78e-506j)
| (-0.30172059859519231597 - 8.7948241981964759667e-2138j)  +/-  (5.01e-500, 5.01e-500j)
| (-0.15264928421887449854 + 5.2434911400256214149e-2142j)  +/-  (3.11e-505, 3.11e-505j)
| (0.19039110916466836871 - 2.2515315665501458003e-2140j)  +/-  (6.96e-504, 6.96e-504j)
| (0.30172059859519231597 + 1.9110030426143166448e-2136j)  +/-  (4.81e-500, 4.81e-500j)
| (0.076549252836495646867 + 3.8797656929448494982e-2144j)  +/-  (6.24e-508, 6.24e-508j)
-------------------------------------------------
The weights are:
| (0.0060975609756097560976 + 1.300132270205570894e-1851j)  +/-  (1.98e-138, 4.52e-369j)
| (0.012195121951219512195 + 5.8775814502953034031e-1855j)  +/-  (9.73e-139, 2.22e-369j)
| (0.012195121951219512195 - 6.0656385232299503361e-1855j)  +/-  (3.99e-139, 9.11e-370j)
| (0.012195121951219512195 + 5.8087998928431144726e-1855j)  +/-  (1.73e-139, 3.95e-370j)
| (0.012195121951219512195 - 1.9708741196201797268e-1853j)  +/-  (1.08e-140, 2.46e-371j)
| (0.012195121951219512195 + 1.6001307338339453671e-1853j)  +/-  (9.75e-141, 2.23e-371j)
| (0.012195121951219512195 - 5.9058342717830239119e-1855j)  +/-  (2.16e-139, 4.94e-370j)
| (0.012195121951219512195 + 6.0184388379292959238e-1855j)  +/-  (9.24e-140, 2.11e-370j)
| (0.012195121951219512195 - 1.0775684978045896757e-1854j)  +/-  (3.56e-143, 8.13e-374j)
| (0.012195121951219512195 - 5.8024067639755367457e-1855j)  +/-  (5.61e-140, 1.28e-370j)
| (0.012195121951219512195 + 8.2607157631891583199e-1854j)  +/-  (6.96e-144, 1.59e-374j)
| (0.012195121951219512195 + 9.8984429082553865116e-1853j)  +/-  (1.39e-144, 3.17e-375j)
| (0.012195121951219512195 + 6.1179022946227991832e-1855j)  +/-  (2.59e-141, 5.91e-372j)
| (0.012195121951219512195 - 6.3068248685699580314e-1855j)  +/-  (6.09e-143, 1.39e-373j)
| (0.012195121951219512195 - 5.8194759960923515093e-1855j)  +/-  (1.25e-140, 2.86e-371j)
| (0.012195121951219512195 - 7.2217053480938651749e-1854j)  +/-  (1.08e-144, 2.48e-375j)
| (0.012195121951219512195 + 1.1172165297372307043e-1853j)  +/-  (1.5e-144, 3.42e-375j)
| (0.0060975609756097560976 + 2.9001389029791900344e-1855j)  +/-  (2.95e-140, 6.74e-371j)
| (0.012195121951219512195 + 6.548476696359366286e-1855j)  +/-  (1.01e-145, 2.3e-376j)
| (0.012195121951219512195 - 5.8538158692976425363e-1855j)  +/-  (3.21e-141, 7.33e-372j)
| (0.012195121951219512195 - 1.3258325824184133123e-1853j)  +/-  (6.76e-145, 1.54e-375j)
| (0.012195121951219512195 + 5.0765891973419612463e-1854j)  +/-  (1.95e-147, 4.44e-378j)
| (0.012195121951219512195 - 1.7582166457822955618e-1852j)  +/-  (1.09e-146, 2.49e-377j)
| (0.012195121951219512195 + 6.2383013619541283312e-1855j)  +/-  (8.91e-145, 2.03e-375j)
| (0.012195121951219512195 - 6.4616507966682467629e-1855j)  +/-  (4.53e-146, 1.03e-376j)
| (0.012195121951219512195 - 1.5808471046873270424e-1851j)  +/-  (1.63e-146, 3.72e-377j)
| (0.012195121951219512195 - 4.5771170127701669239e-1854j)  +/-  (1.33e-149, 3.04e-380j)
| (0.012195121951219512195 + 2.4891968934229415426e-1853j)  +/-  (3.47e-147, 7.92e-378j)
| (0.012195121951219512195 + 5.9386592803692177375e-1855j)  +/-  (2.61e-145, 5.96e-376j)
| (0.012195121951219512195 - 7.0897535180801351107e-1855j)  +/-  (3.42e-152, 7.8e-383j)
| (0.012195121951219512195 - 3.2452279625578330888e-1853j)  +/-  (1.17e-147, 2.67e-378j)
| (0.012195121951219512195 - 9.548745201800450391e-1854j)  +/-  (9.76e-148, 2.23e-378j)
| (0.012195121951219512195 + 3.4662224191267820391e-1854j)  +/-  (4.54e-153, 1.04e-383j)
| (0.012195121951219512195 + 5.8344665436379658944e-1855j)  +/-  (8.68e-145, 1.98e-375j)
| (0.012195121951219512195 + 6.7424644102481631151e-1855j)  +/-  (1.21e-151, 2.77e-382j)
| (0.012195121951219512195 - 6.6419708648844672433e-1855j)  +/-  (7.74e-151, 1.77e-381j)
| (0.012195121951219512195 - 6.341984776642805043e-1853j)  +/-  (4.32e-149, 9.85e-380j)
| (0.012195121951219512195 - 3.1890899219009620917e-1854j)  +/-  (6.13e-155, 1.4e-385j)
| (0.012195121951219512195 + 6.3714587155665843e-1854j)  +/-  (4.57e-151, 1.04e-381j)
| (0.012195121951219512195 + 6.3811916250828292951e-1855j)  +/-  (2.6e-150, 5.94e-381j)
| (0.012195121951219512195 + 7.5154181700098467952e-1855j)  +/-  (8.65e-157, 1.98e-387j)
| (0.012195121951219512195 + 9.1705337918160858201e-1855j)  +/-  (2.44e-159, 5.58e-390j)
| (0.012195121951219512195 - 5.6669035827333463254e-1854j)  +/-  (4.22e-152, 9.63e-383j)
| (0.012195121951219512195 + 2.9459888817086467404e-1854j)  +/-  (9.95e-157, 2.27e-387j)
| (0.012195121951219512195 + 3.9535683634093114902e-1852j)  +/-  (4.99e-150, 1.14e-380j)
| (0.012195121951219512195 - 7.3639422326825295688e-1855j)  +/-  (3.35e-157, 7.65e-388j)
| (0.012195121951219512195 - 6.8503206395824163566e-1855j)  +/-  (6.73e-155, 1.54e-385j)
| (0.012195121951219512195 - 3.784013518032829396e-1854j)  +/-  (2.3e-155, 5.25e-386j)
| (0.012195121951219512195 - 2.3723923848052208998e-1854j)  +/-  (2.61e-160, 5.96e-391j)
| (0.012195121951219512195 + 4.1507878055330958158e-1854j)  +/-  (4.7e-155, 1.07e-385j)
| (0.012195121951219512195 + 6.9659380208708975614e-1855j)  +/-  (2.7e-156, 6.18e-387j)
| (0.012195121951219512195 + 7.8503079315779592982e-1855j)  +/-  (9.75e-161, 2.23e-391j)
| (0.012195121951219512195 - 6.1753952396591137127e-1855j)  +/-  (9e-154, 2.06e-384j)
| (0.012195121951219512195 - 2.731590612831865871e-1854j)  +/-  (4.42e-159, 1.01e-389j)
| (0.012195121951219512195 + 2.5415711814415904406e-1854j)  +/-  (5.21e-160, 1.19e-390j)
| (0.012195121951219512195 + 4.4100903044459697833e-1853j)  +/-  (1.1e-153, 2.51e-384j)
| (0.012195121951219512195 - 7.6773078782596281952e-1855j)  +/-  (3.84e-161, 8.78e-392j)
| (0.012195121951219512195 + 7.2222463501778758764e-1855j)  +/-  (2.49e-159, 5.69e-390j)
| (0.012195121951219512195 + 1.2062585616394780318e-1854j)  +/-  (8.7e-168, 1.99e-398j)
| (0.012195121951219512195 + 1.9630969587377152445e-1854j)  +/-  (2e-165, 4.56e-396j)
| (0.012195121951219512195 - 5.9761559316604771695e-1855j)  +/-  (1.16e-156, 2.65e-387j)
| (0.012195121951219512195 - 8.0351847412834148872e-1855j)  +/-  (1.69e-163, 3.86e-394j)
| (0.012195121951219512195 + 8.2327824961064378002e-1855j)  +/-  (1.5e-164, 3.42e-395j)
| (0.012195121951219512195 + 1.3103285248146534121e-1854j)  +/-  (2.95e-169, 6.73e-400j)
| (0.012195121951219512195 - 2.0853800659428088618e-1854j)  +/-  (4.61e-166, 1.05e-396j)
| (0.012195121951219512195 + 2.2211364748461427882e-1854j)  +/-  (2.62e-165, 5.98e-396j)
| (0.012195121951219512195 + 1.1172613954977677579e-1854j)  +/-  (1.47e-169, 3.36e-400j)
| (0.012195121951219512195 + 8.6699620902502970698e-1855j)  +/-  (5e-168, 1.14e-398j)
| (0.012195121951219512195 + 9.7451631842724390069e-1855j)  +/-  (9.8e-170, 2.24e-400j)
| (0.012195121951219512195 + 1.7523944695187168074e-1854j)  +/-  (6.04e-170, 1.38e-400j)
| (0.012195121951219512195 - 1.8525825426155454974e-1854j)  +/-  (4.51e-169, 1.03e-399j)
| (0.012195121951219512195 - 1.3690382737474710304e-1854j)  +/-  (9.53e-172, 2.18e-402j)
| (0.012195121951219512195 - 9.4478335793328748126e-1855j)  +/-  (8.28e-171, 1.89e-401j)
| (0.012195121951219512195 - 8.4440322148371974861e-1855j)  +/-  (8.91e-170, 2.04e-400j)
| (0.012195121951219512195 - 1.1600555611916760152e-1854j)  +/-  (1.65e-171, 3.76e-402j)
| (0.012195121951219512195 + 1.5782671656000427504e-1854j)  +/-  (2.03e-172, 4.64e-403j)
| (0.012195121951219512195 - 1.502377559915832192e-1854j)  +/-  (1.22e-172, 2.78e-403j)
| (0.012195121951219512195 + 1.0407040553034679488e-1854j)  +/-  (1.39e-172, 3.18e-403j)
| (0.012195121951219512195 - 8.9117093364244200373e-1855j)  +/-  (4.44e-172, 1.01e-402j)
| (0.012195121951219512195 - 1.0064254384002160644e-1854j)  +/-  (1.23e-172, 2.81e-403j)
| (0.012195121951219512195 + 1.4328592167444744687e-1854j)  +/-  (6.43e-174, 1.48e-404j)
| (0.012195121951219512195 - 1.6613057163906897143e-1854j)  +/-  (6.51e-174, 1.55e-404j)
| (0.012195121951219512195 - 1.2562181196505966811e-1854j)  +/-  (6.18e-174, 1.36e-404j)
