Starting with polynomial:
P : 2*t^2 - 1
Extension levels are: 2 80
-------------------------------------------------
Trying to find an order 80 Kronrod extension for:
P1 : 2*t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^82 - 41*t^80 + 3239/8*t^78 - 41041/16*t^76 + 1499575/128*t^74 - 10520395/256*t^72 + 117939165/1024*t^70 - 542520159/2048*t^68 + 16700823273/32768*t^66 - 54525518905/65536*t^64 + 76335726467/65536*t^62 - 184828244237/131072*t^60 + 1557838058569/1048576*t^58 - 2870798562781/2097152*t^56 + 9287877703115/8388608*t^54 - 13224828848913/16777216*t^52 + 265698834146343/536870912*t^50 - 294553006180335/1073741824*t^48 + 4614663763491915/34359738368*t^46 - 3990122803019325/68719476736*t^44 + 12176310231149295/549755813888*t^42 - 8184077368477395/1099511627776*t^40 + 9672091435473285/4398046511104*t^38 - 5010670802607015/8796093022208*t^36 + 18142083940473675/140737488355328*t^34 - 7142251993407531/281474976710656*t^32 + 2433074854897071/562949953421312*t^30 - 712718896889041/1125899906842624*t^28 + 712718896889041/9007199254740992*t^26 - 150705036752725/18014398509481984*t^24 + 53326397620195/72057594037927936*t^22 - 7791522991945/144115188075855872*t^20 + 29607787369391/9223372036854775808*t^18 - 2801478953319/18446744073709551616*t^16 + 823964398035/147573952589676412928*t^14 - 45581009253/295147905179352825856*t^12 + 7266537707/2361183241434822606848*t^10 - 196392911/4722366482869645213696*t^8 + 6577753/18889465931478580854784*t^6 - 58835/37778931862957161709568*t^4 + 1681/604462909807314587353088*t^2 - 1/1208925819614629174706176
-------------------------------------------------
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
Positive weights:   82 out of 82
Indefinite weights: 0 out of 82
Negative weights:   0 out of 82
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.99541657611194493753 + 1.0236776916425863589e-1829j)  +/-  (1.45e-480, 1.45e-480j)
| (-0.95900089315181296124 - 2.0877007097641686354e-1846j)  +/-  (5.29e-481, 5.29e-481j)
| (-0.92017185916334176075 - 5.6976006733755329125e-1848j)  +/-  (7.96e-482, 7.96e-482j)
| (-0.9983491598032411498 - 1.0658093115690028823e-1845j)  +/-  (1.03e-480, 1.03e-480j)
| (0.92017185916334176075 + 2.391885629314292155e-1846j)  +/-  (8.32e-482, 8.32e-482j)
| (0.93449270238241096993 - 2.4174430072492037423e-1847j)  +/-  (1.65e-481, 1.65e-481j)
| (0.98517512351346995787 + 5.4630697381405030564e-1850j)  +/-  (1.43e-480, 1.43e-480j)
| (-0.93449270238241096993 + 2.5945958513491728032e-1868j)  +/-  (1.67e-481, 1.67e-481j)
| (-0.88750173527115444159 + 9.8143042807961455154e-1871j)  +/-  (1.31e-482, 1.31e-482j)
| (0.94744204869570424876 + 4.6011875525534564207e-1866j)  +/-  (3.08e-481, 3.08e-481j)
| (0.88750173527115444159 - 1.0756398294842966491e-1873j)  +/-  (1.31e-482, 1.31e-482j)
| (-0.99541657611194493753 - 4.0987229582545621821e-1879j)  +/-  (1.39e-480, 1.39e-480j)
| (-0.8287994545849945211 + 1.9749933850709924378e-1881j)  +/-  (4.16e-484, 4.16e-484j)
| (-0.84962339829684530823 + 1.9651204061813277181e-1880j)  +/-  (1.56e-483, 1.56e-483j)
| (0.99981652843179433518 - 1.6140927110253086835e-1874j)  +/-  (3.81e-481, 3.81e-481j)
| (0.84962339829684530823 + 5.079622607453321351e-1899j)  +/-  (1.55e-483, 1.55e-483j)
| (0.78353478190286408484 - 1.4183165283480290463e-1900j)  +/-  (2.67e-485, 2.67e-485j)
| (0.90450053685074168486 - 2.0027068735395867025e-1896j)  +/-  (3.36e-482, 3.36e-482j)
| (-0.78353478190286408484 + 6.6229264773003714643e-1901j)  +/-  (2.8e-485, 2.8e-485j)
| (-0.90450053685074168486 + 3.259537200222458412e-1898j)  +/-  (3.35e-482, 3.35e-482j)
| (0.019154881221114105446 - 1.7737968196968057928e-1924j)  +/-  (1.04e-510, 1.04e-510j)
| (0.75916048508167049439 + 1.9711221757726862553e-1900j)  +/-  (6.55e-486, 6.55e-486j)
| (-0.31992743609025903456 - 2.2540493960581707284e-1915j)  +/-  (1.54e-499, 1.54e-499j)
| (-0.86920040251000527429 - 1.3275500106256850519e-1898j)  +/-  (4.59e-483, 4.59e-483j)
| (-0.80675913338343815615 - 1.2836064986276535385e-1900j)  +/-  (1.13e-484, 1.13e-484j)
| (0.9983491598032411498 - 2.5936165127005223053e-1893j)  +/-  (9.93e-481, 9.93e-481j)
| (0.73367201556161853067 - 1.7103538651648049553e-1918j)  +/-  (1.32e-486, 1.32e-486j)
| (0.95900089315181296124 + 4.8857295770585619335e-1911j)  +/-  (5.45e-481, 5.45e-481j)
| (-0.97788128535025917428 - 2.1938979731698277505e-1925j)  +/-  (1.16e-480, 1.16e-480j)
| (-0.65090349353077123481 + 3.4962405593282879087e-1938j)  +/-  (4.41e-489, 4.41e-489j)
| (-0.96915227155255184312 - 9.2516951507462562123e-1927j)  +/-  (8.8e-481, 8.8e-481j)
| (0.86920040251000527429 - 3.7517475426654150766e-1927j)  +/-  (4.66e-483, 4.66e-483j)
| (0.67950377010120567584 - 3.1084385995212353955e-1946j)  +/-  (2.98e-488, 2.98e-488j)
| (-0.52738987577172938844 + 3.1859303579451297572e-1953j)  +/-  (9.84e-493, 9.84e-493j)
| (-0.73367201556161853067 + 8.8733024863049332926e-1948j)  +/-  (1.31e-486, 1.31e-486j)
| (-0.75916048508167049439 + 4.8921769039958706796e-1947j)  +/-  (6.2e-486, 6.2e-486j)
| (0.96915227155255184312 - 9.9681562874190758282e-1939j)  +/-  (8.69e-481, 8.69e-481j)
| (0.62134792632504311932 + 2.7766181932179417389e-1973j)  +/-  (5.84e-490, 5.84e-490j)
| (0.8287994545849945211 - 7.4860203946284426761e-1963j)  +/-  (4.21e-484, 4.21e-484j)
| (-0.98517512351346995787 + 5.7838818639486123135e-1975j)  +/-  (1.4e-480, 1.4e-480j)
| (-0.62134792632504311932 + 5.7273360431440439665e-1987j)  +/-  (5.93e-490, 5.93e-490j)
| (-0.2464627244524591623 + 4.0867337232171954255e-1999j)  +/-  (4.16e-502, 4.16e-502j)
| (0.7071067811865475244 - 1.376480347146719949e-1976j)  +/-  (2.57e-487, 2.57e-487j)
| (0.5908804453545605718 - 1.8922936976609320139e-1988j)  +/-  (7.22e-491, 7.22e-491j)
| (-0.5908804453545605718 - 6.5236904925764591919e-1998j)  +/-  (7.03e-491, 7.03e-491j)
| (-0.1336908832846485014 + 9.6191906522292084193e-2013j)  +/-  (6.54e-506, 6.54e-506j)
| (-0.7071067811865475244 + 3.2461297555096406712e-1995j)  +/-  (2.62e-487, 2.62e-487j)
| (0.3915146863195289328 - 2.7578911212097839308e-2004j)  +/-  (3.98e-497, 3.98e-497j)
| (0.52738987577172938844 - 1.4570348281247247873e-1994j)  +/-  (9.88e-493, 9.88e-493j)
| (0.057436531233723242687 + 4.8832878662553864255e-2015j)  +/-  (1.02e-508, 1.02e-508j)
| (-0.20916068407261674477 - 7.3085023636847482573e-2010j)  +/-  (2.57e-503, 2.57e-503j)
| (-0.55954576584906404267 - 7.1578073526761173567e-1999j)  +/-  (8.77e-492, 8.77e-492j)
| (0.99102308132887121567 + 6.8898057291627011363e-1985j)  +/-  (1.53e-480, 1.53e-480j)
| (0.55954576584906404267 - 3.2413828623375689484e-2039j)  +/-  (8.65e-492, 8.65e-492j)
| (0.49445996832549024552 + 1.7723257555201869608e-2045j)  +/-  (6.18e-494, 6.18e-494j)
| (0.97788128535025917428 + 2.6030748960246611866e-2032j)  +/-  (1.17e-480, 1.17e-480j)
| (-0.46080437269050485889 + 2.0633554734402177775e-2071j)  +/-  (6.04e-495, 6.04e-495j)
| (-0.49445996832549024552 - 2.2123881878485137124e-2070j)  +/-  (6.25e-494, 6.25e-494j)
| (-0.99981652843179433518 + 4.3073322462886488068e-2054j)  +/-  (3.87e-481, 3.87e-481j)
| (0.42647248309441968424 + 4.1320846816298224282e-2075j)  +/-  (5.21e-496, 5.21e-496j)
| (-0.99102308132887121567 + 1.4549423574878216039e-2057j)  +/-  (1.61e-480, 1.61e-480j)
| (-0.67950377010120567584 + 1.594608777134265051e-2069j)  +/-  (2.88e-488, 2.88e-488j)
| (-0.42647248309441968424 + 1.0916886836847284102e-2078j)  +/-  (5.34e-496, 5.34e-496j)
| (-0.057436531233723242687 + 6.4882718684676624736e-2091j)  +/-  (9.31e-509, 9.31e-509j)
| (0.46080437269050485889 - 6.8228080924026272899e-2077j)  +/-  (6.23e-495, 6.23e-495j)
| (0.2464627244524591623 - 7.6468712810239212003e-2084j)  +/-  (4.03e-502, 4.03e-502j)
| (-0.94744204869570424876 - 8.7338004312438381755e-2073j)  +/-  (3.03e-481, 3.03e-481j)
| (-0.3915146863195289328 - 1.0387348053319777865e-2088j)  +/-  (4.04e-497, 4.04e-497j)
| (-0.095633885216342283461 - 3.3911167127010220104e-2098j)  +/-  (3.37e-507, 3.37e-507j)
| (0.80675913338343815615 + 1.9621494367584460414e-2083j)  +/-  (1.14e-484, 1.14e-484j)
| (0.35598228775322329895 + 5.2380263612090271022e-2098j)  +/-  (3.19e-498, 3.19e-498j)
| (0.65090349353077123481 + 1.6901880861908761389e-2098j)  +/-  (4.56e-489, 4.56e-489j)
| (-0.019154881221114105446 - 1.9746216327772914307e-2120j)  +/-  (1.04e-510, 1.04e-510j)
| (-0.17155167154597827739 + 1.5982087797119287491e-2115j)  +/-  (9.19e-505, 9.19e-505j)
| (0.095633885216342283461 - 9.6507901597185423364e-2119j)  +/-  (3.73e-507, 3.73e-507j)
| (0.28340304679735717369 - 3.8326512928400023161e-2111j)  +/-  (9.07e-501, 9.07e-501j)
| (0.17155167154597827739 + 1.9423179551857200135e-2115j)  +/-  (9.42e-505, 9.42e-505j)
| (-0.35598228775322329895 - 2.3424717789558519779e-2111j)  +/-  (3.24e-498, 3.24e-498j)
| (-0.28340304679735717369 + 3.5490345231487413319e-2112j)  +/-  (8.82e-501, 8.82e-501j)
| (0.1336908832846485014 + 1.5156437953665322295e-2116j)  +/-  (6.77e-506, 6.77e-506j)
| (0.20916068407261674477 - 2.4627938961917034574e-2113j)  +/-  (2.64e-503, 2.64e-503j)
| (0.31992743609025903456 - 6.7754603502548156452e-2110j)  +/-  (1.51e-499, 1.51e-499j)
-------------------------------------------------
The weights are:
| (0.012195121951219512195 - 6.7936107555779509195e-1830j)  +/-  (2.14e-143, 1.05e-376j)
| (0.012195121951219512195 - 1.8928873375014496357e-1831j)  +/-  (9.77e-144, 4.79e-377j)
| (0.012195121951219512195 + 2.6679853359095193373e-1831j)  +/-  (7.82e-144, 3.83e-377j)
| (0.012195121951219512195 - 3.7605525552891303903e-1832j)  +/-  (1.57e-144, 7.71e-378j)
| (0.012195121951219512195 - 6.7921869630306021818e-1830j)  +/-  (8.8e-145, 4.31e-378j)
| (0.012195121951219512195 + 7.6274341577621550944e-1830j)  +/-  (6.63e-145, 3.25e-378j)
| (0.012195121951219512195 - 2.1866082469092081819e-1829j)  +/-  (1.1e-145, 5.38e-379j)
| (0.012195121951219512195 - 2.4078480822185317208e-1831j)  +/-  (3.48e-145, 1.71e-378j)
| (0.012195121951219512195 + 3.1946456963800501482e-1831j)  +/-  (8.48e-146, 4.16e-379j)
| (0.012195121951219512195 - 8.7051922592272597642e-1830j)  +/-  (1.22e-145, 5.98e-379j)
| (0.012195121951219512195 - 5.5740775163349887896e-1830j)  +/-  (1.74e-146, 8.51e-380j)
| (0.012195121951219512195 + 6.2706783209735032124e-1832j)  +/-  (7.04e-147, 3.45e-380j)
| (0.012195121951219512195 - 4.0040264049136459817e-1831j)  +/-  (2.48e-147, 1.21e-380j)
| (0.012195121951219512195 + 3.7313294462413737643e-1831j)  +/-  (5.47e-147, 2.68e-380j)
| (0.012195121951219512195 + 5.682887777885365202e-1830j)  +/-  (4.02e-148, 1.97e-381j)
| (0.012195121951219512195 - 4.7220673073846118135e-1830j)  +/-  (8.26e-149, 4.05e-382j)
| (0.012195121951219512195 + 3.8280605479727251071e-1830j)  +/-  (4.21e-150, 2.06e-383j)
| (0.012195121951219512195 + 6.1233360496974271093e-1830j)  +/-  (2e-147, 9.81e-381j)
| (0.012195121951219512195 - 4.5594070551236926277e-1831j)  +/-  (2.28e-150, 1.12e-383j)
| (0.012195121951219512195 - 2.9301776214632583004e-1831j)  +/-  (1.03e-148, 5.04e-382j)
| (0.012195121951219512195 - 1.3368776091091215888e-1830j)  +/-  (3e-154, 1.47e-387j)
| (0.012195121951219512195 - 3.5964263864865856298e-1830j)  +/-  (3.21e-151, 1.57e-384j)
| (0.012195121951219512195 + 9.4026634183577234635e-1831j)  +/-  (4.52e-154, 2.22e-387j)
| (0.012195121951219512195 - 3.4616175912742340941e-1831j)  +/-  (3.6e-149, 1.77e-382j)
| (0.012195121951219512195 + 4.2799635737719358469e-1831j)  +/-  (3.29e-150, 1.61e-383j)
| (0.012195121951219512195 - 2.5566741215591308898e-1829j)  +/-  (3.48e-150, 1.71e-383j)
| (0.012195121951219512195 + 3.3888456794784184956e-1830j)  +/-  (5.15e-153, 2.52e-386j)
| (0.012195121951219512195 + 1.0159062741762062511e-1829j)  +/-  (1.53e-150, 7.52e-384j)
| (0.012195121951219512195 - 1.3836460106727364008e-1831j)  +/-  (1.32e-152, 6.47e-386j)
| (0.012195121951219512195 + 6.0194513536558509362e-1831j)  +/-  (4.43e-156, 2.17e-389j)
| (0.012195121951219512195 + 1.6376518448443506101e-1831j)  +/-  (3.83e-152, 1.88e-385j)
| (0.012195121951219512195 + 5.1139174560487116946e-1830j)  +/-  (3.33e-152, 1.63e-385j)
| (0.012195121951219512195 + 3.0316028731930191682e-1830j)  +/-  (4.8e-156, 2.35e-389j)
| (0.012195121951219512195 + 7.2831514827548969039e-1831j)  +/-  (7.85e-158, 3.85e-391j)
| (0.012195121951219512195 - 5.1299391333640348421e-1831j)  +/-  (3.32e-155, 1.63e-388j)
| (0.012195121951219512195 + 4.8426350631270219872e-1831j)  +/-  (2.26e-154, 1.11e-387j)
| (0.012195121951219512195 - 1.2249628732510454667e-1829j)  +/-  (6.6e-154, 3.23e-387j)
| (0.012195121951219512195 + 2.7342898788195713418e-1830j)  +/-  (2.31e-159, 1.13e-392j)
| (0.012195121951219512195 + 4.383828677532298818e-1830j)  +/-  (5.47e-155, 2.68e-388j)
| (0.012195121951219512195 + 1.1306744704822826636e-1831j)  +/-  (1.41e-155, 6.93e-389j)
| (0.012195121951219512195 - 6.326290078451870119e-1831j)  +/-  (9.16e-159, 4.49e-392j)
| (0.012195121951219512195 + 1.0187091724758484859e-1830j)  +/-  (1.24e-162, 6.06e-396j)
| (0.012195121951219512195 - 3.2015714015910032579e-1830j)  +/-  (4.83e-158, 2.37e-391j)
| (0.012195121951219512195 - 2.6032996588201325153e-1830j)  +/-  (5.88e-161, 2.88e-394j)
| (0.012195121951219512195 + 6.638912870223482463e-1831j)  +/-  (3.86e-160, 1.89e-393j)
| (0.012195121951219512195 - 1.1457400117844473558e-1830j)  +/-  (2.48e-164, 1.22e-397j)
| (0.012195121951219512195 + 5.4216254377641929145e-1831j)  +/-  (7.82e-159, 3.83e-392j)
| (0.012195121951219512195 - 1.9890245602139034273e-1830j)  +/-  (4.92e-165, 2.41e-398j)
| (0.012195121951219512195 - 2.3697002884500417453e-1830j)  +/-  (2.48e-163, 1.22e-396j)
| (0.012195121951219512195 + 1.3893972811008681721e-1830j)  +/-  (1.07e-165, 5.26e-399j)
| (0.012195121951219512195 - 1.0597149501413709309e-1830j)  +/-  (1.6e-164, 7.83e-398j)
| (0.012195121951219512195 - 6.9577235304960961961e-1831j)  +/-  (1.12e-161, 5.49e-395j)
| (0.012195121951219512195 + 3.9721831476880755208e-1829j)  +/-  (4.12e-159, 2.02e-392j)
| (0.012195121951219512195 + 2.4821570568518470808e-1830j)  +/-  (3.72e-163, 1.82e-396j)
| (0.012195121951219512195 + 2.2649436221385448487e-1830j)  +/-  (1.4e-164, 6.88e-398j)
| (0.012195121951219512195 + 1.5570575652198047979e-1829j)  +/-  (2.9e-159, 1.42e-392j)
| (0.012195121951219512195 + 7.9557206155928410832e-1831j)  +/-  (1.51e-165, 7.41e-399j)
| (0.012195121951219512195 - 7.6156543172006342603e-1831j)  +/-  (7.93e-165, 3.89e-398j)
| (0.012195121951219512195 + 1.2532087205651340724e-1832j)  +/-  (1.97e-164, 9.64e-398j)
| (0.012195121951219512195 + 2.0752805850975045563e-1830j)  +/-  (1.47e-168, 7.22e-402j)
| (0.012195121951219512195 - 8.7854498229587851351e-1832j)  +/-  (1.01e-163, 4.95e-397j)
| (0.012195121951219512195 - 5.7180162181798886087e-1831j)  +/-  (2.28e-164, 1.12e-397j)
| (0.012195121951219512195 - 8.3038730947420332155e-1831j)  +/-  (1.21e-167, 5.92e-401j)
| (0.012195121951219512195 - 1.2378050793488343255e-1830j)  +/-  (3.13e-171, 1.53e-404j)
| (0.012195121951219512195 - 2.1670449999273615468e-1830j)  +/-  (1.76e-169, 8.64e-403j)
| (0.012195121951219512195 - 1.6891746157519427024e-1830j)  +/-  (5.11e-173, 2.51e-406j)
| (0.012195121951219512195 + 2.1495515904832985494e-1831j)  +/-  (2.1e-165, 1.03e-398j)
| (0.012195121951219512195 + 8.6606721132731987437e-1831j)  +/-  (2.05e-169, 1e-402j)
| (0.012195121951219512195 + 1.1909612144107083658e-1830j)  +/-  (2.16e-171, 1.06e-404j)
| (0.012195121951219512195 - 4.0884930266317678132e-1830j)  +/-  (3.13e-168, 1.54e-401j)
| (0.012195121951219512195 + 1.9077329484988762732e-1830j)  +/-  (2.02e-172, 9.91e-406j)
| (0.012195121951219512195 - 2.8765071844337485064e-1830j)  +/-  (2.92e-169, 1.43e-402j)
| (0.012195121951219512195 + 1.2863977111688312492e-1830j)  +/-  (1.71e-172, 8.38e-406j)
| (0.012195121951219512195 + 1.1020263645784570138e-1830j)  +/-  (4.86e-172, 2.38e-405j)
| (0.012195121951219512195 - 1.4441251154915396034e-1830j)  +/-  (4.46e-174, 2.19e-407j)
| (0.012195121951219512195 + 1.7582003113950176246e-1830j)  +/-  (1.23e-174, 6.02e-408j)
| (0.012195121951219512195 - 1.5609716695268955379e-1830j)  +/-  (3.15e-175, 1.54e-408j)
| (0.012195121951219512195 - 9.0267195934506418151e-1831j)  +/-  (1.13e-173, 5.52e-407j)
| (0.012195121951219512195 - 9.7892023748462608118e-1831j)  +/-  (7.33e-174, 3.59e-407j)
| (0.012195121951219512195 + 1.5012475601029004689e-1830j)  +/-  (1.92e-175, 9.43e-409j)
| (0.012195121951219512195 + 1.6235280958047960234e-1830j)  +/-  (7.88e-176, 3.87e-409j)
| (0.012195121951219512195 - 1.8309305499260108489e-1830j)  +/-  (7.01e-176, 3.4e-409j)
