Starting with polynomial:
P : 4*t^2 - 1
Extension levels are: 2 81
-------------------------------------------------
Trying to find an order 81 Kronrod extension for:
P1 : 4*t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^83 - 82*t^81 + 810*t^79 - 5135*t^77 + 1502501/64*t^75 - 10555545/128*t^73 + 59273445/256*t^71 - 273273675/512*t^69 + 16871053725/16384*t^67 - 55262073757/32768*t^65 + 19416404293/8192*t^63 - 47223209943/16384*t^61 + 1600342114735/524288*t^59 - 2966614689395/1048576*t^57 + 4831343922729/2097152*t^55 - 6931928236959/4194304*t^53 + 280946973839103/268435456*t^51 - 314492881163175/536870912*t^49 + 155658092696925/536870912*t^47 - 136248095712855/1073741824*t^45 + 13488561475572645/274877906944*t^43 - 9206478467454345/549755813888*t^41 + 5534686468704225/1099511627776*t^39 - 2923166552608575/2199023255552*t^37 + 21631432489303455/70368744177664*t^35 - 8725899885515631/140737488355328*t^33 + 763805560270599/70368744177664*t^31 - 230779457781565/140737488355328*t^29 + 956086325095055/4503599627370496*t^27 - 210398934237219/9007199254740992*t^25 + 38962765599485/18014398509481984*t^23 - 5999744185435/36028797018963968*t^21 + 48459472266975/4611686018427387904*t^19 - 4923689695575/9223372036854775808*t^17 + 196947587823/9223372036854775808*t^15 - 12058015581/18446744073709551616*t^13 + 17417133617/1180591620717411303424*t^11 - 550858165/2361183241434822606848*t^9 + 11344905/4722366482869645213696*t^7 - 135751/9444732965739290427392*t^5 + 12341/302231454903657293676544*t^3 - 21/604462909807314587353088*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
Positive weights:   83 out of 83
Indefinite weights: 0 out of 83
Negative weights:   0 out of 83
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.99371220989324258353 + 7.9146593896895278726e-1685j)  +/-  (8e-481, 8e-481j)
| (-0.96592582628906828675 + 1.4333715055856656937e-1706j)  +/-  (9.21e-481, 9.21e-481j)
| (-0.93087374864420425564 + 3.6951892718936967797e-1709j)  +/-  (2.33e-481, 2.33e-481j)
| (-0.9993007047883985527 + 3.2475390441643546104e-1709j)  +/-  (1.24e-481, 1.24e-481j)
| (0.91656225586997618582 - 1.9821674519249237345e-1707j)  +/-  (1.16e-481, 1.16e-481j)
| (0.93087374864420425564 - 4.6295200747841346539e-1707j)  +/-  (2.39e-481, 2.39e-481j)
| (-0.82623877431599487195 + 7.4632138186761980394e-1714j)  +/-  (8.66e-484, 8.66e-484j)
| (-0.91656225586997618582 + 1.4968465941360442863e-1711j)  +/-  (1.16e-481, 1.16e-481j)
| (-0.98883082622512854507 - 2.8182602930398648519e-1711j)  +/-  (1.11e-480, 1.11e-480j)
| (0.99720379718118014823 + 3.1500115060405935984e-1708j)  +/-  (4.51e-481, 4.51e-481j)
| (0.88411539350460978945 + 8.7528898643470752235e-1725j)  +/-  (2.23e-482, 2.23e-482j)
| (-0.99720379718118014823 - 4.2568093736402948572e-1723j)  +/-  (4.5e-481, 4.5e-481j)
| (-0.9438833303083675629 + 2.852003973014461783e-1724j)  +/-  (4.27e-481, 4.27e-481j)
| (-0.86602540378443864676 + 1.0040303117737196328e-1727j)  +/-  (8.4e-483, 8.4e-483j)
| (-0.99371220989324258353 - 3.448049644167462991e-1724j)  +/-  (8.18e-481, 8.18e-481j)
| (0.82623877431599487195 - 2.5070065461266731965e-1726j)  +/-  (8.58e-484, 8.58e-484j)
| (0.84672419922828416835 + 8.7434898741373189418e-1727j)  +/-  (2.94e-483, 2.94e-483j)
| (0.18591160716291458111 - 4.2113820218607488789e-1748j)  +/-  (6.81e-504, 6.81e-504j)
| (-0.80459777976666832735 + 4.3714393099683727682e-1728j)  +/-  (2.46e-484, 2.46e-484j)
| (-0.95557280578614073281 + 9.3159701646792125235e-1724j)  +/-  (6.42e-481, 6.42e-481j)
| (0.96592582628906828675 + 2.122193294690968187e-1722j)  +/-  (9.06e-481, 9.06e-481j)
| (0.75797172314545298179 - 1.2446085443284458118e-1752j)  +/-  (1.5e-485, 1.5e-485j)
| (0.97492791218182360702 - 7.2043366133738570367e-1746j)  +/-  (1.12e-480, 1.12e-480j)
| (-0.88411539350460978945 + 4.4644178520370099567e-1781j)  +/-  (2.23e-482, 2.23e-482j)
| (-0.78183148246802980871 - 1.230560312624583262e-1784j)  +/-  (6.06e-485, 6.06e-485j)
| (0.9993007047883985527 - 2.0717862416079575688e-1778j)  +/-  (1.25e-481, 1.25e-481j)
| (0.73305187182982632852 + 1.9047228104004773279e-1813j)  +/-  (3.03e-486, 3.03e-486j)
| (0.95557280578614073281 - 6.1054266594150732325e-1807j)  +/-  (6.42e-481, 6.42e-481j)
| (-0.84672419922828416835 + 8.5933158675759557117e-1836j)  +/-  (2.95e-483, 2.95e-483j)
| (-0.62348980185873353053 - 7.459439061123455733e-1842j)  +/-  (1.89e-489, 1.89e-489j)
| (-0.90096886790241912624 + 5.8676336726711635708e-1834j)  +/-  (5.47e-482, 5.47e-482j)
| (0.86602540378443864676 - 9.0940252572010034484e-1832j)  +/-  (8.47e-483, 8.47e-483j)
| (0.7071067811865475244 - 5.1021991614376987054e-1850j)  +/-  (4.57e-487, 4.57e-487j)
| (0.98883082622512854507 + 4.4639748559942839136e-1842j)  +/-  (1.12e-480, 1.12e-480j)
| (-0.7071067811865475244 + 2.1071248857804606348e-1868j)  +/-  (6.47e-487, 6.47e-487j)
| (-0.73305187182982632852 + 2.2588264441279982409e-1868j)  +/-  (3.02e-486, 3.02e-486j)
| (0.9438833303083675629 + 1.2477647295882397142e-1861j)  +/-  (4.12e-481, 4.12e-481j)
| (0.59382018557350161165 - 2.6944576349757714057e-1891j)  +/-  (2.24e-490, 2.24e-490j)
| (0.80459777976666832735 - 4.4509172091015423933e-1883j)  +/-  (2.47e-484, 2.47e-484j)
| (-0.75797172314545298179 - 1.4607481768016046547e-1886j)  +/-  (1.45e-485, 1.45e-485j)
| (-0.53203207651533656356 - 3.8494834100154300204e-1893j)  +/-  (3.38e-492, 3.38e-492j)
| (0.98256647323328823615 - 1.3384505689607140107e-1881j)  +/-  (1.26e-480, 1.26e-480j)
| (0.68017273777091939019 - 2.7196725863585769756e-1908j)  +/-  (8.14e-488, 8.14e-488j)
| (0.56332005806362202775 + 1.3892499799628866496e-1911j)  +/-  (2.92e-491, 2.92e-491j)
| (-0.59382018557350161165 + 9.3486672763556875636e-1912j)  +/-  (2.22e-490, 2.22e-490j)
| (-0.65228741127812115437 - 1.2583349722669449668e-1909j)  +/-  (1.29e-488, 1.29e-488j)
| (-0.68017273777091939019 - 1.5596291471527150398e-1908j)  +/-  (7.91e-488, 7.91e-488j)
| (0.78183148246802980871 - 3.5198364483906161683e-1905j)  +/-  (6.32e-485, 6.32e-485j)
| (0.46726862827306198914 - 4.7607484015529420715e-1915j)  +/-  (2.36e-494, 2.36e-494j)
| (0.90096886790241912624 + 6.4153525000963343478e-1901j)  +/-  (5.41e-482, 5.41e-482j)
| (-0.56332005806362202775 + 1.0313838987254338422e-1920j)  +/-  (2.88e-491, 2.88e-491j)
| (-0.5 - 1.3045116174875339474e-1922j)  +/-  (2.24e-493, 2.24e-493j)
| (-0.97492791218182360702 + 4.744455716725624129e-1914j)  +/-  (1.14e-480, 1.14e-480j)
| (0.65228741127812115437 - 8.4254766900799645298e-1928j)  +/-  (1.26e-488, 1.26e-488j)
| (0.62348980185873353053 - 2.7893378994422393754e-1929j)  +/-  (1.85e-489, 1.85e-489j)
| (-0.98256647323328823615 - 2.4474226965816285821e-1940j)  +/-  (1.22e-480, 1.22e-480j)
| (-0.46726862827306198914 + 4.7772064136933527749e-1955j)  +/-  (2.37e-494, 2.37e-494j)
| (-0.43388373911755812048 + 5.487379713366338147e-1957j)  +/-  (2.08e-495, 2.08e-495j)
| (0.53203207651533656356 + 1.8341749960592772828e-1952j)  +/-  (3.37e-492, 3.37e-492j)
| (0.36534102436639501454 + 8.0671087354757036669e-1960j)  +/-  (1.2e-497, 1.2e-497j)
| (0.074730093586424254291 - 1.0586843929046252583e-1970j)  +/-  (6.35e-508, 6.35e-508j)
| (-0.33027906195516708177 + 1.0145818407725628561e-1962j)  +/-  (6.77e-499, 6.77e-499j)
| (-0.36534102436639501454 - 8.4991579780470354365e-1961j)  +/-  (1.2e-497, 1.2e-497j)
| (-0.037391194276325621096 - 1.2110627966147724402e-1971j)  +/-  (1.29e-509, 1.29e-509j)
| (0.43388373911755812048 - 1.9869174007740547046e-1956j)  +/-  (2.12e-495, 2.12e-495j)
| (0.5 + 2.1714458402696300583e-1957j)  +/-  (3.81e-493, 3.81e-493j)
| (-0.074730093586424254291 - 7.7376169709129462948e-1973j)  +/-  (6.3e-508, 6.3e-508j)
| (-0.39989202431974097188 - 4.5174226761807754778e-1961j)  +/-  (1.69e-496, 1.69e-496j)
| (-0.18591160716291458111 - 7.9675827001976229851e-1969j)  +/-  (6.74e-504, 6.74e-504j)
| (0.22252093395631440429 - 3.4718793892932507955e-1967j)  +/-  (1.26e-502, 1.26e-502j)
| (0.33027906195516708177 - 6.9936304926705400694e-1964j)  +/-  (6.8e-499, 6.8e-499j)
| (0.14904226617617444693 + 9.9677342481489529092e-1970j)  +/-  (3.44e-505, 3.44e-505j)
| (-0.22252093395631440429 - 2.4327200720181328378e-1967j)  +/-  (1.28e-502, 1.28e-502j)
| (-0.25881904510252076235 - 2.5085588315334880162e-1966j)  +/-  (2.93e-501, 2.93e-501j)
| (0.037391194276325621096 - 1.5623310027737070053e-1973j)  +/-  (1.29e-509, 1.29e-509j)
| (0.29475517441090421683 - 2.4207754302096528206e-1965j)  +/-  (4.21e-500, 4.21e-500j)
| (0.39989202431974097188 + 2.3680373159818169799e-1961j)  +/-  (1.71e-496, 1.71e-496j)
| (-0.14904226617617444693 + 8.9505499901720305207e-1970j)  +/-  (3.17e-505, 3.17e-505j)
| (-0.29475517441090421683 + 1.0272561403693545363e-1964j)  +/-  (4.05e-500, 4.05e-500j)
| (-0.11196447610330785847 - 1.3610203302775785028e-1971j)  +/-  (1.69e-506, 1.69e-506j)
| (0.11196447610330785847 + 5.4218844804834147469e-1971j)  +/-  (1.66e-506, 1.66e-506j)
| (0.25881904510252076235 + 1.6980650776254731997e-1966j)  +/-  (3.02e-501, 3.02e-501j)
| (-3.2971439113471491423e-2214 + 2.1816497780867115793e-2215j)  +/-  (2.74e-2212, 2.74e-2212j)
-------------------------------------------------
The weights are:
| (0.00014923861796533567251 - 1.4044452986929791728e-1686j)  +/-  (6.36e-137, 6.92e-369j)
| (0.00079746783461643662641 - 3.2208429152143487908e-1688j)  +/-  (3.14e-137, 3.41e-369j)
| (0.0015889769533938909017 + 6.5345022956190924956e-1688j)  +/-  (1.88e-137, 2.05e-369j)
| (1.6644064397737212946e-05 - 6.6096962843409654024e-1690j)  +/-  (1.87e-138, 2.04e-370j)
| (0.0019037337037445274394 - 1.9530023088887536032e-1686j)  +/-  (1.83e-139, 1.99e-371j)
| (0.0015889769533938909017 + 2.0013557165790215359e-1686j)  +/-  (1.3e-139, 1.42e-371j)
| (0.0037777319978190772944 + 1.6428718293894356842e-1687j)  +/-  (8.71e-139, 9.48e-371j)
| (0.0019037337037445274394 - 7.887559669489751789e-1688j)  +/-  (7.5e-138, 8.16e-370j)
| (0.00026444758460630516184 + 1.0557211220407737456e-1688j)  +/-  (9.58e-139, 1.04e-370j)
| (6.6483177231377707918e-05 - 1.5070272043564782732e-1686j)  +/-  (7.14e-142, 7.77e-374j)
| (0.0025992853686689165015 - 1.8771036447507419109e-1686j)  +/-  (3.17e-141, 3.44e-373j)
| (6.6483177231377707918e-05 + 2.6429628425356617954e-1689j)  +/-  (9.21e-139, 1e-370j)
| (0.0012986221281664892339 - 5.3045909773729362319e-1688j)  +/-  (2.88e-139, 3.13e-371j)
| (0.0029761904761904761905 + 1.2666052310091097624e-1687j)  +/-  (2.75e-141, 2.99e-373j)
| (0.00014923861796533567251 - 5.9432339525672584027e-1689j)  +/-  (4.69e-139, 5.1e-371j)
| (0.0037777319978190772944 + 1.7853256503165307698e-1686j)  +/-  (7.94e-144, 8.64e-376j)
| (0.0033697396481097730924 - 1.8144569360499036798e-1686j)  +/-  (1.4e-143, 1.52e-375j)
| (0.011493296122882168188 - 1.1260888364033452054e-1686j)  +/-  (3.09e-146, 3.36e-378j)
| (0.0041978858666017606141 - 1.8475589293271919049e-1687j)  +/-  (1.15e-142, 1.25e-374j)
| (0.0010342930100238400479 + 4.199527938515621016e-1688j)  +/-  (1.85e-139, 2.01e-371j)
| (0.00079746783461643662641 - 2.2715033288010040841e-1686j)  +/-  (3.16e-145, 3.43e-377j)
| (0.0050652246060941997207 - 1.700578803521359643e-1686j)  +/-  (2.17e-146, 2.36e-378j)
| (0.00058947102439036234383 + 2.4837033834408144876e-1686j)  +/-  (1.55e-145, 1.69e-377j)
| (0.0025992853686689165015 - 1.095545635413656864e-1687j)  +/-  (2.61e-143, 2.84e-375j)
| (0.0046278515835933666411 + 2.0629100341352831024e-1687j)  +/-  (1.05e-145, 1.14e-377j)
| (1.6644064397737212946e-05 + 2.3572017696988788456e-1687j)  +/-  (5.5e-146, 5.98e-378j)
| (0.0055075589667474746768 + 1.6723086302386172616e-1686j)  +/-  (3.06e-148, 3.33e-380j)
| (0.0010342930100238400479 + 2.1463567864058788634e-1686j)  +/-  (1.24e-145, 1.35e-377j)
| (0.0033697396481097730924 - 1.4491313807169970425e-1687j)  +/-  (2.4e-144, 2.61e-376j)
| (0.0072769103211685381208 + 3.561352643815422943e-1687j)  +/-  (2.07e-150, 2.25e-382j)
| (0.0022411321317932527945 + 9.3618908629568155111e-1688j)  +/-  (8.77e-144, 9.54e-376j)
| (0.0029761904761904761905 + 1.8447899681830445752e-1686j)  +/-  (4.63e-147, 5.04e-379j)
| (0.005952380952380952381 - 1.6437604831269021904e-1686j)  +/-  (5.03e-150, 5.47e-382j)
| (0.00026444758460630516184 + 4.2877444202079307232e-1686j)  +/-  (1.31e-146, 1.42e-378j)
| (0.005952380952380952381 - 2.7699048542409466293e-1687j)  +/-  (1.33e-149, 1.45e-381j)
| (0.0055075589667474746768 + 2.5244012052265693573e-1687j)  +/-  (6.11e-149, 6.64e-381j)
| (0.0012986221281664892339 - 2.0626897305295452567e-1686j)  +/-  (5.13e-147, 5.57e-379j)
| (0.0077068760381601441478 - 1.5253442202144524058e-1686j)  +/-  (4.34e-154, 4.72e-386j)
| (0.0041978858666017606141 - 1.7568641784081314059e-1686j)  +/-  (1.84e-149, 2e-381j)
| (0.0050652246060941997207 - 2.2886279158800904794e-1687j)  +/-  (5.77e-149, 6.28e-381j)
| (0.0085350222566521316695 - 4.4274649852256565285e-1687j)  +/-  (5.02e-155, 5.46e-387j)
| (0.00041146578187973657358 - 2.9218450188143412067e-1686j)  +/-  (9.65e-148, 1.05e-379j)
| (0.0063972029380144300851 + 1.6148423660467246155e-1686j)  +/-  (7.9e-153, 8.6e-385j)
| (0.0081270299069428274675 + 1.4945131617719667791e-1686j)  +/-  (6.76e-156, 7.35e-388j)
| (0.0077068760381601441478 - 3.8422711230824260171e-1687j)  +/-  (5.82e-154, 6.33e-386j)
| (0.0068395372986677050412 - 3.2887375796301229435e-1687j)  +/-  (6.45e-153, 7.01e-385j)
| (0.0063972029380144300851 + 3.0248006215576397267e-1687j)  +/-  (2.36e-152, 2.57e-384j)
| (0.0046278515835933666411 + 1.7287022484433028357e-1686j)  +/-  (3.07e-152, 3.33e-384j)
| (0.0093054765360929882604 - 1.3990041822764750895e-1686j)  +/-  (1.58e-159, 1.71e-391j)
| (0.0022411321317932527945 + 1.912568286808928361e-1686j)  +/-  (8.81e-151, 9.58e-383j)
| (0.0081270299069428274675 + 4.1311072921871281689e-1687j)  +/-  (5.59e-156, 6.08e-388j)
| (0.0089285714285714285714 + 4.7309382105611312015e-1687j)  +/-  (4.28e-158, 4.66e-390j)
| (0.00058947102439036234383 + 2.3698909342675620541e-1688j)  +/-  (2.33e-153, 2.53e-385j)
| (0.0068395372986677050412 - 1.5854913972741115037e-1686j)  +/-  (9.21e-157, 1e-388j)
| (0.0072769103211685381208 + 1.5556666844432806394e-1686j)  +/-  (1.95e-157, 2.12e-389j)
| (0.00041146578187973657358 - 1.6478503471678120667e-1688j)  +/-  (8.64e-154, 9.4e-386j)
| (0.0093054765360929882604 - 5.041111787226627057e-1687j)  +/-  (9.19e-161, 9.99e-393j)
| (0.0096636297729686519674 + 5.3575620030378054373e-1687j)  +/-  (4.94e-162, 5.38e-394j)
| (0.0085350222566521316695 - 1.4631730750590194019e-1686j)  +/-  (2.04e-161, 2.22e-393j)
| (0.01031578495136801386 + 1.2993263553119178656e-1686j)  +/-  (2.18e-165, 2.37e-397j)
| (0.011838278727530527054 + 1.0195622115602654932e-1686j)  +/-  (7.07e-168, 7.69e-400j)
| (0.010606139776595415528 - 6.3402218395289890149e-1687j)  +/-  (7.84e-166, 8.52e-398j)
| (0.01031578495136801386 + 6.0075589512754066836e-1687j)  +/-  (4.63e-165, 5.04e-397j)
| (0.011888117840364167549 - 9.1252150958373120711e-1687j)  +/-  (4.81e-169, 5.23e-401j)
| (0.0096636297729686519674 + 1.3662102253416089623e-1686j)  +/-  (7.51e-166, 8.16e-398j)
| (0.0089285714285714285714 + 1.4313318625224405132e-1686j)  +/-  (2.21e-164, 2.4e-396j)
| (0.011838278727530527054 + 8.7693966799578689208e-1687j)  +/-  (1.8e-169, 1.95e-401j)
| (0.010001028201017377323 - 5.6798572948103421497e-1687j)  +/-  (7.75e-166, 8.43e-398j)
| (0.011493296122882168188 - 7.7114011061986801172e-1687j)  +/-  (1.34e-169, 1.45e-401j)
| (0.011315290880371542418 + 1.1612770528893443845e-1686j)  +/-  (7.54e-170, 8.2e-402j)
| (0.010606139776595415528 - 1.2652967979077491602e-1686j)  +/-  (3.33e-169, 3.63e-401j)
| (0.0116403143201555996 + 1.0907115106704529965e-1686j)  +/-  (3.08e-170, 3.35e-402j)
| (0.011315290880371542418 + 7.3634461999564371944e-1687j)  +/-  (2.54e-170, 2.76e-402j)
| (0.011107294070145468135 - 7.0186232044658236983e-1687j)  +/-  (3.53e-170, 3.84e-402j)
| (0.011888117840364167549 - 9.8387886446557586551e-1687j)  +/-  (1.26e-171, 1.37e-403j)
| (0.010870468894738064714 + 1.2309205622158813599e-1686j)  +/-  (4.69e-171, 5.1e-403j)
| (0.010001028201017377323 - 1.3329747570181642669e-1686j)  +/-  (4.5e-170, 4.9e-402j)
| (0.0116403143201555996 + 8.0620225045927164557e-1687j)  +/-  (5.19e-172, 5.64e-404j)
| (0.010870468894738064714 + 6.677395156147583489e-1687j)  +/-  (2.31e-171, 2.51e-403j)
| (0.011755523286796569089 - 8.4148435018054311355e-1687j)  +/-  (2.64e-172, 2.87e-404j)
| (0.011755523286796569089 - 1.0551879998902747616e-1686j)  +/-  (4.26e-173, 4.7e-405j)
| (0.011107294070145468135 - 1.1962344122679956991e-1686j)  +/-  (4.03e-173, 4.65e-405j)
| (0.011904761904761904762 + 9.4818333370045396531e-1687j)  +/-  (4.18e-173, 4.42e-405j)
