Starting with polynomial:
P : 2*t^2 - 1
Extension levels are: 2 84
-------------------------------------------------
Trying to find an order 84 Kronrod extension for:
P1 : 2*t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^86 - 43*t^84 + 3569/8*t^82 - 47601/16*t^80 + 458595/32*t^78 - 3400397/64*t^76 + 323037715/2048*t^74 - 1577802655/4096*t^72 + 25851689655/32768*t^70 - 90089221525/65536*t^68 + 1080122350705/524288*t^66 - 2808318111833/1048576*t^64 + 1593910279689/524288*t^62 - 3176063581551/1048576*t^60 + 44616131264645/16777216*t^58 - 69249262892449/33554432*t^56 + 761741891816939/536870912*t^54 - 929286144237033/1073741824*t^52 + 4026906625027143/8589934592*t^50 - 3875067255033975/17179869184*t^48 + 3311421108847215/34359738368*t^46 - 2510857763851185/68719476736*t^44 + 107966883845600955/8796093022208*t^42 - 64154235328545495/17592186044416*t^40 + 134516945043724425/140737488355328*t^38 - 62010106469336571/281474976710656*t^36 + 100170171988928307/2251799813685248*t^34 - 35276501246571739/4503599627370496*t^32 + 5387051914501103/4503599627370496*t^30 - 1417645240658185/9007199254740992*t^28 + 2551761433184733/144115188075855872*t^26 - 486406138290345/288230376151711744*t^24 + 1243037908964215/9223372036854775808*t^22 - 164174818165085/18446744073709551616*t^20 + 70572885636575/147573952589676412928*t^18 - 6049104483135/295147905179352825856*t^16 + 403273632209/590295810358705651712*t^14 - 20241533663/1180591620717411303424*t^12 + 11718782647/37778931862957161709568*t^10 - 287695155/75557863725914323419136*t^8 + 17511879/604462909807314587353088*t^6 - 142373/1208925819614629174706176*t^4 + 1849/9671406556917033397649408*t^2 - 1/19342813113834066795298816
-------------------------------------------------
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:   86 out of 86
Indefinite weights: 0 out of 86
Negative weights:   0 out of 86
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.95217901172404691689 + 4.7963694341819420637e-1777j)  +/-  (1.15e-479, 1.15e-479j)
| (-0.95217901172404691689 + 2.2598091486740625872e-1774j)  +/-  (1.19e-479, 1.19e-479j)
| (-0.91304950884994166778 - 4.6994889945069347061e-1793j)  +/-  (1.51e-480, 1.51e-480j)
| (-0.97988422366347940052 + 6.6083694605657663911e-1809j)  +/-  (3.92e-479, 3.92e-479j)
| (0.92733582745357030895 + 7.939363228883386918e-1827j)  +/-  (3.24e-480, 3.24e-480j)
| (0.96270272904914589952 - 1.9915658768331991806e-1825j)  +/-  (1.83e-479, 1.83e-479j)
| (0.97194190898492459836 + 6.4786598867371986872e-1825j)  +/-  (2.97e-479, 2.97e-479j)
| (-0.92733582745357030895 + 6.7513749198646596463e-1826j)  +/-  (3.15e-480, 3.15e-480j)
| (-0.94038479883995681036 + 5.3289884755791642546e-1840j)  +/-  (6.38e-480, 6.38e-480j)
| (-0.99183761197522280051 - 2.9623610903170635727e-1856j)  +/-  (4.81e-479, 4.81e-479j)
| (0.88084270467843630343 + 9.2823074942375451127e-1878j)  +/-  (2.34e-481, 2.34e-481j)
| (0.99849911748582580277 - 9.2157077879802055694e-1875j)  +/-  (3.09e-479, 3.09e-479j)
| (-0.89754490531055026769 + 7.5528513114420694517e-1880j)  +/-  (6.1e-481, 6.1e-481j)
| (-0.86296519275434438265 - 8.6321480644988514434e-1881j)  +/-  (7.56e-482, 7.56e-482j)
| (0.99583273616342471584 + 6.8877183952413623831e-1877j)  +/-  (4.62e-479, 4.62e-479j)
| (0.89754490531055026769 + 2.3459309998136094995e-1881j)  +/-  (6.36e-481, 6.36e-481j)
| (0.91304950884994166778 - 9.5333380631251108741e-1882j)  +/-  (1.39e-480, 1.39e-480j)
| (0.99983319818113645492 - 1.071789785218628015e-1877j)  +/-  (1.13e-479, 1.13e-479j)
| (-0.7568359028663363009 - 2.1135395583838401773e-1884j)  +/-  (8.47e-485, 8.47e-485j)
| (-0.96270272904914589952 + 2.2565713122593129496e-1878j)  +/-  (1.91e-479, 1.91e-479j)
| (0.65360493888318925692 + 4.4682242883379886044e-1913j)  +/-  (6.19e-488, 6.19e-488j)
| (0.7802019532087692 - 6.579931391301561683e-1909j)  +/-  (3.88e-484, 3.88e-484j)
| (-0.99583273616342471584 + 7.0826472409561714139e-1902j)  +/-  (4.5e-479, 4.5e-479j)
| (-0.8439362235607069513 - 1.4176848466153394505e-1930j)  +/-  (2.49e-482, 2.49e-482j)
| (-0.7802019532087692 - 6.192897215940096207e-1937j)  +/-  (4e-484, 4e-484j)
| (0.9865190756284465668 + 1.2371539141662565137e-1929j)  +/-  (4.81e-479, 4.81e-479j)
| (0.7071067811865475244 + 3.7402972578243444615e-1941j)  +/-  (3.6e-486, 3.6e-486j)
| (0.99183761197522280051 - 4.486769733130946099e-1932j)  +/-  (5.08e-479, 5.08e-479j)
| (-0.80252697754195078801 - 1.0132205182324558594e-1935j)  +/-  (1.69e-483, 1.69e-483j)
| (-0.62552770698764536486 + 5.4055961440577903893e-1943j)  +/-  (8.37e-489, 8.37e-489j)
| (-0.82378118751314440939 + 2.5850437359331172301e-1934j)  +/-  (6.26e-483, 6.26e-483j)
| (0.80252697754195078801 + 2.2327464697356131613e-1938j)  +/-  (1.68e-483, 1.68e-483j)
| (0.73246000391178613668 - 6.7256526757236901528e-1942j)  +/-  (1.83e-485, 1.83e-485j)
| (-0.99849911748582580277 - 4.8963192763209652488e-1931j)  +/-  (3.04e-479, 3.04e-479j)
| (-0.7071067811865475244 + 5.8342055869270192591e-1961j)  +/-  (2.22e-486, 2.22e-486j)
| (-0.73246000391178613668 + 9.261553958019935359e-1961j)  +/-  (1.83e-485, 1.83e-485j)
| (0.7568359028663363009 - 1.0387055814010625694e-1960j)  +/-  (8.39e-485, 8.39e-485j)
| (0.59661583143374700055 + 7.2703783575881523107e-1966j)  +/-  (1.14e-489, 1.14e-489j)
| (0.94038479883995681036 + 3.6625048023011701758e-1954j)  +/-  (6.4e-480, 6.4e-480j)
| (-0.16364630585868818525 + 6.6096403458928061642e-1980j)  +/-  (1.01e-504, 1.01e-504j)
| (-0.53644352038410572762 - 1.0233397934595060695e-1966j)  +/-  (1.41e-491, 1.41e-491j)
| (0.62552770698764536486 - 1.5530880161198898101e-1964j)  +/-  (8.61e-489, 8.61e-489j)
| (0.53644352038410572762 + 3.3151415192509127289e-1967j)  +/-  (1.43e-491, 1.43e-491j)
| (0.56690788943128460346 + 7.9792063503805582552e-1969j)  +/-  (1.24e-490, 1.24e-490j)
| (-0.9865190756284465668 + 7.1647993380805849316e-1953j)  +/-  (4.59e-479, 4.59e-479j)
| (-0.65360493888318925692 - 1.8740153159824397873e-1982j)  +/-  (6.16e-488, 6.16e-488j)
| (-0.68081006357834211832 - 1.7289795752598088948e-1981j)  +/-  (3.83e-487, 3.83e-487j)
| (-0.99983319818113645492 + 4.0137512323770717461e-1972j)  +/-  (1.08e-479, 1.08e-479j)
| (0.47340905104864339457 + 2.4252119092788684923e-2005j)  +/-  (9.47e-494, 9.47e-494j)
| (0.68081006357834211832 + 2.1102320054070784506e-1998j)  +/-  (3.94e-487, 3.94e-487j)
| (-0.56690788943128460346 + 1.2084589660711050431e-2003j)  +/-  (1.24e-490, 1.24e-490j)
| (-0.47340905104864339457 + 5.4911555585647505094e-2007j)  +/-  (9.37e-494, 9.37e-494j)
| (0.86296519275434438265 + 9.1741584899931182832e-1992j)  +/-  (7.62e-482, 7.62e-482j)
| (0.4409230578582564374 - 1.2975066406723688052e-2006j)  +/-  (8.61e-495, 8.61e-495j)
| (0.8439362235607069513 - 1.6250562645790472685e-1992j)  +/-  (2.47e-482, 2.47e-482j)
| (0.82378118751314440939 - 1.1065819583112803206e-1993j)  +/-  (6.31e-483, 6.31e-483j)
| (-0.50526337299912928224 + 3.0354437724482316809e-2005j)  +/-  (1.63e-492, 1.63e-492j)
| (-0.59661583143374700055 + 1.1027974975976240618e-2002j)  +/-  (1.16e-489, 1.16e-489j)
| (0.19956680138595266078 - 2.055836551907130289e-2017j)  +/-  (2.97e-503, 2.97e-503j)
| (0.40784873959457112939 - 1.0641620614824611175e-2008j)  +/-  (6.44e-496, 6.44e-496j)
| (0.97988422366347940052 - 1.2877354646878541227e-1992j)  +/-  (4.08e-479, 4.08e-479j)
| (-0.97194190898492459836 - 6.4006016148444352447e-2009j)  +/-  (2.9e-479, 2.9e-479j)
| (-0.4409230578582564374 + 3.0110307584316412518e-2028j)  +/-  (8.6e-495, 8.6e-495j)
| (-0.054767804228643680451 + 2.702318321952242144e-2041j)  +/-  (9.71e-509, 9.71e-509j)
| (0.34011237864966627 + 1.2195973605660759402e-2030j)  +/-  (2.55e-498, 2.55e-498j)
| (0.50526337299912928224 + 1.514365174561212954e-2026j)  +/-  (1.59e-492, 1.59e-492j)
| (-0.091198473590663457783 + 3.9463464550961533867e-2040j)  +/-  (3.64e-507, 3.64e-507j)
| (-0.40784873959457112939 + 3.7442826581212696186e-2028j)  +/-  (6.48e-496, 6.48e-496j)
| (-0.88084270467843630343 - 1.3653061342774685569e-2038j)  +/-  (2.24e-481, 2.24e-481j)
| (0.054767804228643680451 + 1.2113546123619203187e-2065j)  +/-  (9.82e-509, 9.82e-509j)
| (0.37423022742825314923 + 5.2524266095868581725e-2053j)  +/-  (4.89e-497, 4.89e-497j)
| (0.30554071681564361349 - 9.5463311506452614178e-2058j)  +/-  (1.61e-499, 1.61e-499j)
| (-0.34011237864966627 - 1.9035444662915112332e-2055j)  +/-  (2.59e-498, 2.59e-498j)
| (-0.37423022742825314923 - 2.6428916431627695219e-2054j)  +/-  (5.02e-497, 5.02e-497j)
| (-0.12750745653210784969 - 9.748551592225302554e-2063j)  +/-  (7.31e-506, 7.31e-506j)
| (0.2705613710072573827 - 5.4100515709476878519e-2057j)  +/-  (1.04e-500, 1.04e-500j)
| (0.16364630585868818525 - 7.9662476746445132161e-2061j)  +/-  (1.08e-504, 1.08e-504j)
| (-0.018264058006924801835 + 1.1411436773835528887e-2067j)  +/-  (1.11e-510, 1.11e-510j)
| (-0.30554071681564361349 + 6.5759628682335587575e-2057j)  +/-  (1.62e-499, 1.62e-499j)
| (-0.19956680138595266078 + 2.6731505550371870528e-2060j)  +/-  (2.84e-503, 2.84e-503j)
| (0.12750745653210784969 + 7.9363316195550260144e-2063j)  +/-  (7.54e-506, 7.54e-506j)
| (0.23522101427963562859 + 2.5021556468900607732e-2058j)  +/-  (4.55e-502, 4.55e-502j)
| (0.091198473590663457783 - 6.4218038567206994296e-2064j)  +/-  (3.85e-507, 3.85e-507j)
| (-0.23522101427963562859 - 2.3160378401189328639e-2060j)  +/-  (4.83e-502, 4.83e-502j)
| (-0.2705613710072573827 + 2.9120514181390226441e-2057j)  +/-  (1.06e-500, 1.06e-500j)
| (0.018264058006924801835 - 1.1929424014243015349e-2067j)  +/-  (1.11e-510, 1.11e-510j)
-------------------------------------------------
The weights are:
| (0.011627906976744186047 - 1.4082695225539385019e-1776j)  +/-  (7.52e-128, 1.93e-359j)
| (0.011627906976744186047 + 1.3403512890959711993e-1775j)  +/-  (3.04e-128, 7.79e-360j)
| (0.011627906976744186047 - 8.9643405997023004999e-1775j)  +/-  (1.89e-128, 4.84e-360j)
| (0.011627906976744186047 + 6.1946649217678233072e-1775j)  +/-  (7.95e-129, 2.04e-360j)
| (0.011627906976744186047 - 1.9873334020284718575e-1776j)  +/-  (5.71e-129, 1.46e-360j)
| (0.011627906976744186047 + 7.4585442001008329521e-1777j)  +/-  (6.37e-129, 1.63e-360j)
| (0.011627906976744186047 - 8.3409618356214066855e-1777j)  +/-  (2.11e-129, 5.39e-361j)
| (0.011627906976744186047 + 1.2955315825055070498e-1774j)  +/-  (2.15e-129, 5.51e-361j)
| (0.011627906976744186047 - 2.4800671430772965566e-1774j)  +/-  (1.59e-129, 4.07e-361j)
| (0.011627906976744186047 + 2.7649266475821654377e-1775j)  +/-  (1.69e-131, 4.32e-363j)
| (0.011627906976744186047 + 2.3422612237020370227e-1776j)  +/-  (3.45e-132, 8.83e-364j)
| (0.011627906976744186047 + 2.1987684123729143457e-1777j)  +/-  (4.98e-133, 1.28e-364j)
| (0.011627906976744186047 + 6.941133695307099213e-1775j)  +/-  (5.04e-132, 1.29e-363j)
| (0.011627906976744186047 + 4.8711915439641033048e-1775j)  +/-  (2.22e-133, 5.7e-365j)
| (0.011627906976744186047 - 3.6449060514419193978e-1777j)  +/-  (3.54e-133, 9.06e-365j)
| (0.011627906976744186047 - 2.197343537760156203e-1776j)  +/-  (1.33e-133, 3.39e-365j)
| (0.011627906976744186047 + 2.0707478189742771881e-1776j)  +/-  (2.69e-133, 6.9e-365j)
| (0.011627906976744186047 - 7.3471351108174115763e-1778j)  +/-  (2.08e-133, 5.33e-365j)
| (0.011627906976744186047 - 2.8782386171073704262e-1775j)  +/-  (1.26e-137, 3.22e-369j)
| (0.011627906976744186047 + 2.211035772290668076e-1774j)  +/-  (1.2e-134, 3.06e-366j)
| (0.011627906976744186047 + 4.0996635916911556213e-1776j)  +/-  (4.05e-139, 1.04e-370j)
| (0.011627906976744186047 - 3.1717200101626670676e-1776j)  +/-  (7.39e-138, 1.89e-369j)
| (0.011627906976744186047 - 1.7965935163358334762e-1775j)  +/-  (1.69e-136, 4.33e-368j)
| (0.011627906976744186047 - 4.2627002919104797416e-1775j)  +/-  (1.89e-136, 4.83e-368j)
| (0.011627906976744186047 + 3.1287563893647873936e-1775j)  +/-  (7.12e-138, 1.82e-369j)
| (0.011627906976744186047 - 6.3895302359223274686e-1777j)  +/-  (1.29e-135, 3.31e-367j)
| (0.011627906976744186047 + 3.7176164444080964963e-1776j)  +/-  (1.26e-140, 3.22e-372j)
| (0.011627906976744186047 + 5.0539167760402853656e-1777j)  +/-  (2.52e-135, 6.45e-367j)
| (0.011627906976744186047 - 3.4292170511897131882e-1775j)  +/-  (2.77e-138, 7.1e-370j)
| (0.011627906976744186047 + 2.0550275964573394994e-1775j)  +/-  (9.23e-143, 2.36e-374j)
| (0.011627906976744186047 + 3.7977440482813606835e-1775j)  +/-  (5.35e-138, 1.37e-369j)
| (0.011627906976744186047 + 2.9968870552627361091e-1776j)  +/-  (1.36e-140, 3.48e-372j)
| (0.011627906976744186047 - 3.5321075369105225102e-1776j)  +/-  (1.42e-141, 3.63e-373j)
| (0.011627906976744186047 + 1.0168060379139178199e-1775j)  +/-  (4.17e-140, 1.07e-371j)
| (0.011627906976744186047 - 2.4821683820476494293e-1775j)  +/-  (3.73e-142, 9.55e-374j)
| (0.011627906976744186047 + 2.6655250088875561548e-1775j)  +/-  (2.62e-141, 6.72e-373j)
| (0.011627906976744186047 + 3.3501491835312690325e-1776j)  +/-  (1.67e-141, 4.28e-373j)
| (0.011627906976744186047 + 4.4974534031660904675e-1776j)  +/-  (1.89e-145, 4.84e-377j)
| (0.011627906976744186047 + 2.071904328548796439e-1776j)  +/-  (1.17e-139, 3e-371j)
| (0.011627906976744186047 + 1.0775586253030679607e-1775j)  +/-  (1.77e-150, 4.52e-382j)
| (0.011627906976744186047 - 1.7468438985594280579e-1775j)  +/-  (9.61e-148, 2.46e-379j)
| (0.011627906976744186047 - 4.296496208175396598e-1776j)  +/-  (6.67e-145, 1.71e-376j)
| (0.011627906976744186047 + 4.9126675692222287649e-1776j)  +/-  (1.07e-147, 2.74e-379j)
| (0.011627906976744186047 - 4.7027600216425763722e-1776j)  +/-  (1.09e-146, 2.78e-378j)
| (0.011627906976744186047 - 4.0981985699232247323e-1775j)  +/-  (3.44e-144, 8.82e-376j)
| (0.011627906976744186047 - 2.180847058153805938e-1775j)  +/-  (7.76e-148, 1.99e-379j)
| (0.011627906976744186047 + 2.3221011565374246108e-1775j)  +/-  (3.62e-147, 9.27e-379j)
| (0.011627906976744186047 - 3.2959296430536270033e-1776j)  +/-  (4.55e-145, 1.17e-376j)
| (0.011627906976744186047 + 5.347423459298031106e-1776j)  +/-  (3.84e-152, 9.84e-384j)
| (0.011627906976744186047 - 3.9067588423698172835e-1776j)  +/-  (8.67e-148, 2.22e-379j)
| (0.011627906976744186047 + 1.8398539433239612046e-1775j)  +/-  (4.56e-151, 1.17e-382j)
| (0.011627906976744186047 - 1.5833799644246171813e-1775j)  +/-  (1.04e-153, 2.66e-385j)
| (0.011627906976744186047 - 2.4973056222640122646e-1776j)  +/-  (8.19e-148, 2.1e-379j)
| (0.011627906976744186047 - 5.5729088894920522186e-1776j)  +/-  (3.4e-154, 8.7e-386j)
| (0.011627906976744186047 + 2.6590483109819068941e-1776j)  +/-  (2.15e-148, 5.5e-380j)
| (0.011627906976744186047 - 2.8258535336571482209e-1776j)  +/-  (1.64e-148, 4.2e-380j)
| (0.011627906976744186047 + 1.6617072317466925277e-1775j)  +/-  (6.97e-155, 1.79e-386j)
| (0.011627906976744186047 - 1.9420421016449468422e-1775j)  +/-  (6.78e-153, 1.74e-384j)
| (0.011627906976744186047 + 7.3405850887995336586e-1776j)  +/-  (1.14e-160, 2.92e-392j)
| (0.011627906976744186047 + 5.8042722848818432551e-1776j)  +/-  (3.07e-157, 7.88e-389j)
| (0.011627906976744186047 + 7.5683985955279404292e-1777j)  +/-  (6.16e-150, 1.58e-381j)
| (0.011627906976744186047 - 1.0235763803576440918e-1774j)  +/-  (2.21e-151, 5.67e-383j)
| (0.011627906976744186047 + 1.5109850842941431246e-1775j)  +/-  (8.33e-158, 2.13e-389j)
| (0.011627906976744186047 - 9.5869650322590758105e-1776j)  +/-  (2.14e-162, 5.49e-394j)
| (0.011627906976744186047 + 6.2862437550031737453e-1776j)  +/-  (1.35e-159, 3.46e-391j)
| (0.011627906976744186047 - 5.1274538536499051297e-1776j)  +/-  (9.23e-156, 2.36e-387j)
| (0.011627906976744186047 + 9.9645399630073606291e-1776j)  +/-  (1.89e-162, 4.84e-394j)
| (0.011627906976744186047 - 1.4437926532859492378e-1775j)  +/-  (3.96e-160, 1.01e-391j)
| (0.011627906976744186047 - 5.7077642059957204144e-1775j)  +/-  (7.14e-155, 1.83e-386j)
| (0.011627906976744186047 + 8.5482738341830759211e-1776j)  +/-  (3.02e-163, 7.73e-395j)
| (0.011627906976744186047 - 6.0419076749986867534e-1776j)  +/-  (1.83e-159, 4.69e-391j)
| (0.011627906976744186047 - 6.5377472066198224026e-1776j)  +/-  (4.79e-161, 1.23e-392j)
| (0.011627906976744186047 - 1.3226577290799096215e-1775j)  +/-  (4.65e-163, 1.19e-394j)
| (0.011627906976744186047 + 1.3811897826209336027e-1775j)  +/-  (3.36e-162, 8.62e-394j)
| (0.011627906976744186047 - 1.0360179130165435638e-1775j)  +/-  (2.68e-164, 6.87e-396j)
| (0.011627906976744186047 + 6.7969266052254110246e-1776j)  +/-  (2.04e-163, 5.23e-395j)
| (0.011627906976744186047 - 7.6263355888650243052e-1776j)  +/-  (5.41e-165, 1.38e-396j)
| (0.011627906976744186047 + 9.2259397940368238719e-1776j)  +/-  (1.45e-165, 3.73e-397j)
| (0.011627906976744186047 + 1.2677542085270387004e-1775j)  +/-  (2.04e-165, 5.23e-397j)
| (0.011627906976744186047 - 1.1212685568348404685e-1775j)  +/-  (5.9e-166, 1.51e-397j)
| (0.011627906976744186047 + 7.9223181213295229259e-1776j)  +/-  (2.81e-166, 7.2e-398j)
| (0.011627906976744186047 - 7.0643369765931192631e-1776j)  +/-  (9.9e-166, 2.53e-397j)
| (0.011627906976744186047 - 8.2293355987765190714e-1776j)  +/-  (1.38e-166, 3.55e-398j)
| (0.011627906976744186047 + 1.1673659717517787954e-1775j)  +/-  (1.67e-167, 4.31e-399j)
| (0.011627906976744186047 - 1.2160995845486912395e-1775j)  +/-  (1.65e-167, 4.26e-399j)
| (0.011627906976744186047 - 8.8801127942031417348e-1776j)  +/-  (1.67e-167, 4.19e-399j)
