Starting with polynomial:
P : 2*t^2 - 1
Extension levels are: 2 3 72
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : 2*t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 72 Kronrod extension for:
P2 : 2*t^5 - 3*t^3 + 1*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^77 - 39*t^75 + 731/2*t^73 - 8769/4*t^71 + 1210195/128*t^69 - 7994777/256*t^67 + 21036191/256*t^65 - 22639903/128*t^63 + 1300017147/4096*t^61 - 3943973605/8192*t^59 + 10220947659/16384*t^57 - 22807046549/32768*t^55 + 5642807573529/8388608*t^53 - 9490989513891/16777216*t^51 + 1742058970275/4194304*t^49 - 8952821093895/33554432*t^47 + 322489165730865/2147483648*t^45 - 318199961380455/4294967296*t^43 + 275130067799895/8589934592*t^41 - 208244759201325/17179869184*t^39 + 2203661208153405/549755813888*t^37 - 1270245305056455/1099511627776*t^35 + 317986441828055/1099511627776*t^33 - 68842914507185/1099511627776*t^31 + 410268308308075/35184372088832*t^29 - 130597282505669/70368744177664*t^27 + 35249111410527/140737488355328*t^25 - 7990239579257/281474976710656*t^23 + 48115078418451/18014398509481984*t^21 - 7410623527505/36028797018963968*t^19 + 229488985407/18014398509481984*t^17 - 44730788399/72057594037927936*t^15 + 213414110077/9223372036854775808*t^13 - 11726954603/18446744073709551616*t^11 + 451512295/36893488147419103232*t^9 - 11323221/73786976294838206464*t^7 + 2641171/2361183241434822606848*t^5 - 18297/4722366482869645213696*t^3 + 19/4722366482869645213696*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:
| (0.99914575838730102919 - 8.8666113903333214535e-1832j)  +/-  (1.44e-481, 1.44e-481j)
| (-0.95842748245825270023 - 1.1458784426690752789e-1838j)  +/-  (1.65e-482, 1.65e-482j)
| (-0.93159108805127897294 + 6.6329943571532559906e-1857j)  +/-  (4.22e-483, 4.22e-483j)
| (-1 - 1.096234732413436228e-1875j)  +/-  (1.27e-481, 1.27e-481j)
| (0.94581724170063467902 - 9.7167535406614053018e-1909j)  +/-  (8.68e-483, 8.68e-483j)
| (0.89839098189197887157 - 1.2467185883328709903e-1909j)  +/-  (5.91e-484, 5.91e-484j)
| (0.83716647826252857481 - 5.4478709770582176166e-1913j)  +/-  (1.81e-485, 1.81e-485j)
| (-0.91577332665505743992 - 3.6090074847926120356e-1907j)  +/-  (1.61e-483, 1.61e-483j)
| (-0.87947375120648907139 + 2.7740941958521503175e-1928j)  +/-  (2.04e-484, 2.04e-484j)
| (-0.99658449300666984982 - 3.4814981757291574666e-1946j)  +/-  (1.25e-481, 1.25e-481j)
| (0.8590539543698851819 + 1.2949754578526293608e-1984j)  +/-  (6.69e-485, 6.69e-485j)
| (-0.99914575838730102919 - 7.1236773788121886453e-1978j)  +/-  (1.32e-481, 1.32e-481j)
| (-0.94581724170063467902 - 3.1346493540097411466e-1990j)  +/-  (8.4e-483, 8.4e-483j)
| (-0.8590539543698851819 - 1.5822847143252023135e-1993j)  +/-  (6.67e-485, 6.67e-485j)
| (1 - 1.3175958728170710972e-1987j)  +/-  (1.26e-481, 1.26e-481j)
| (0.87947375120648907139 - 2.5838549118319150415e-1994j)  +/-  (2.21e-484, 2.21e-484j)
| (0.95842748245825270023 - 7.1774857938039913941e-1993j)  +/-  (1.67e-482, 1.67e-482j)
| (-0.96940026593933041674 + 1.1730856762982636175e-1989j)  +/-  (2.98e-482, 2.98e-482j)
| (-0.78914050939639359922 - 9.9300065229355407508e-2002j)  +/-  (9.69e-487, 9.69e-487j)
| (0.9863613034027223736 - 9.1484898321428993462e-1997j)  +/-  (7.02e-482, 7.02e-482j)
| (0.96940026593933041674 - 2.8209524848177686331e-1999j)  +/-  (2.83e-482, 2.83e-482j)
| (0.76308406819980650614 + 1.4806489267215752268e-2003j)  +/-  (2.18e-487, 2.18e-487j)
| (0.99232057973704506275 + 1.7820536682043900681e-1996j)  +/-  (9.68e-482, 9.68e-482j)
| (-0.83716647826252857481 + 1.4768774243995516631e-2000j)  +/-  (1.77e-485, 1.77e-485j)
| (-0.76308406819980650614 + 7.845523805160672767e-2003j)  +/-  (2.38e-487, 2.38e-487j)
| (0.99658449300666984982 + 1.4977387471831188541e-1997j)  +/-  (1.26e-481, 1.26e-481j)
| (0.73572391067313162477 + 3.2872329282843635545e-2004j)  +/-  (4.81e-488, 4.81e-488j)
| (0.8138487172701949671 - 7.9869474267760758023e-2003j)  +/-  (4.66e-486, 4.66e-486j)
| (-0.89839098189197887157 + 1.2929967730184435226e-1999j)  +/-  (6.34e-484, 6.34e-484j)
| (-0.64629923786094089199 + 3.5738158526788097068e-2006j)  +/-  (1.41e-490, 1.41e-490j)
| (-0.9863613034027223736 - 4.8123183898902974844e-1995j)  +/-  (7.38e-482, 7.38e-482j)
| (0.78914050939639359922 - 4.2454658968916053974e-2025j)  +/-  (9.88e-487, 9.88e-487j)
| (0.67728157162574107476 - 1.3224622129520879265e-2028j)  +/-  (9.14e-490, 9.14e-490j)
| (-0.97871684532735448364 - 3.5624502518134918383e-2018j)  +/-  (4.86e-482, 4.86e-482j)
| (-0.73572391067313162477 - 1.5830917526703951524e-2051j)  +/-  (4.47e-488, 4.47e-488j)
| (-0.7071067811865475244 + 6.8429911769437347014e-2052j)  +/-  (8.06e-489, 8.06e-489j)
| (0.91577332665505743992 - 1.5137389868712577202e-2046j)  +/-  (1.67e-483, 1.67e-483j)
| (0.61421271268966781744 + 4.5777001706135362136e-2057j)  +/-  (1.86e-491, 1.86e-491j)
| (0.7071067811865475244 + 3.421337721080785238e-2053j)  +/-  (8.18e-489, 8.18e-489j)
| (0.97871684532735448364 - 5.0698614291856235104e-2047j)  +/-  (5.11e-482, 5.11e-482j)
| (-0.54694815812242687471 - 1.3194433520608001086e-2058j)  +/-  (2.35e-493, 2.35e-493j)
| (-0.99232057973704506275 - 1.175129149845562164e-2050j)  +/-  (9.73e-482, 9.73e-482j)
| (0.64629923786094089199 + 1.0338080727977745498e-2080j)  +/-  (1.43e-490, 1.43e-490j)
| (0.58107681540193828 + 5.1393647897522714407e-2081j)  +/-  (2.25e-492, 2.25e-492j)
| (-0.67728157162574107476 + 9.7074238830242740745e-2080j)  +/-  (9.51e-490, 9.51e-490j)
| (-0.58107681540193828 - 5.6429134789727944733e-2081j)  +/-  (2.02e-492, 2.02e-492j)
| (-0.8138487172701949671 - 1.1839328727173880463e-2074j)  +/-  (4.58e-486, 4.58e-486j)
| (0.20521534219563429132 + 9.6178082658368654571e-2093j)  +/-  (6.01e-504, 6.01e-504j)
| (0.47594739303707354443 - 6.6662492958197257838e-2084j)  +/-  (1.44e-495, 1.44e-495j)
| (-0.041324974248813211938 - 2.9205611396933797508e-2098j)  +/-  (1.59e-509, 1.59e-509j)
| (-0.43919658884737036545 - 4.5472381071567753583e-2086j)  +/-  (1.26e-496, 1.26e-496j)
| (-0.47594739303707354443 + 8.1581252738293748876e-2085j)  +/-  (1.42e-495, 1.42e-495j)
| (-0.16459459028073389414 - 6.1468097860626167687e-2094j)  +/-  (2.33e-505, 2.33e-505j)
| (0.54694815812242687471 - 5.7973531714323703666e-2082j)  +/-  (2.36e-493, 2.36e-493j)
| (0.51188504908960100217 + 4.1445362198349746128e-2083j)  +/-  (2.61e-494, 2.61e-494j)
| (0.93159108805127897294 - 2.1329619178590241587e-2089j)  +/-  (4.09e-483, 4.09e-483j)
| (-0.51188504908960100217 - 2.0931272791117578784e-2098j)  +/-  (2.5e-494, 2.5e-494j)
| (-0.61421271268966781744 + 1.7076511464828156197e-2103j)  +/-  (1.9e-491, 1.9e-491j)
| (0.0825793454723323246 + 7.6944198390240460054e-2121j)  +/-  (5.83e-508, 5.83e-508j)
| (0.43919658884737036545 - 3.9756605940691528013e-2109j)  +/-  (1.22e-496, 1.22e-496j)
| (0.12369263126934761602 - 9.6632962858661897154e-2119j)  +/-  (9.9e-507, 9.9e-507j)
| (-0.20521534219563429132 + 3.1296626347283547295e-2116j)  +/-  (5.82e-504, 5.82e-504j)
| (-0.40169542465296945752 + 3.8596910042190289877e-2110j)  +/-  (9.31e-498, 9.31e-498j)
| (-0.0825793454723323246 - 3.5797701617791019431e-2120j)  +/-  (5.83e-508, 5.83e-508j)
| (0.40169542465296945752 + 2.7865606884914263829e-2110j)  +/-  (9.62e-498, 9.62e-498j)
| (0.36350797056382984848 + 4.3622152766835125636e-2111j)  +/-  (7.03e-499, 7.03e-499j)
| (-0.12369263126934761602 + 1.0985306988041398395e-2118j)  +/-  (9.31e-507, 9.31e-507j)
| (-0.32469946920468348741 - 1.3835296998924920554e-2112j)  +/-  (3.68e-500, 3.68e-500j)
| (-0.24548548714079914892 - 1.4812195237520474499e-2115j)  +/-  (1.02e-502, 1.02e-502j)
| (0.16459459028073389414 + 4.047489167236391674e-2118j)  +/-  (2.22e-505, 2.22e-505j)
| (0.32469946920468348741 - 2.535499634874029784e-2113j)  +/-  (3.91e-500, 3.91e-500j)
| (0.041324974248813211938 - 9.8742403717063236006e-2122j)  +/-  (1.59e-509, 1.59e-509j)
| (-0.28533622424910530907 - 7.7165465068534115092e-2114j)  +/-  (2.15e-501, 2.15e-501j)
| (-0.36350797056382984848 + 1.2292421662358270471e-2111j)  +/-  (6.83e-499, 6.83e-499j)
| (2.5575055690988727772e-2159 - 3.099108355026200347e-2159j)  +/-  (3.09e-2157, 3.09e-2157j)
| (0.28533622424910530907 + 5.0529962515878815461e-2114j)  +/-  (2.17e-501, 2.17e-501j)
| (0.24548548714079914892 + 2.1723038516274142838e-2116j)  +/-  (1.01e-502, 1.01e-502j)
-------------------------------------------------
The weights are:
| (0.013157894736842105263 - 3.4128543346640889852e-1831j)  +/-  (6.55e-139, 1.53e-371j)
| (0.013157894736842105263 + 5.9597317043186507151e-1834j)  +/-  (3.14e-139, 7.33e-372j)
| (0.013157894736842105263 + 6.0425041779326126634e-1834j)  +/-  (2.51e-139, 5.86e-372j)
| (0.0065789473684210526316 - 2.9179129110246231917e-1834j)  +/-  (3.64e-140, 8.52e-373j)
| (0.013157894736842105263 - 2.1876839292141538361e-1832j)  +/-  (1.28e-140, 2.99e-373j)
| (0.013157894736842105263 + 1.1579196797064983726e-1832j)  +/-  (8.02e-141, 1.88e-373j)
| (0.013157894736842105263 - 7.2025223162188633858e-1833j)  +/-  (5.19e-141, 1.21e-373j)
| (0.013157894736842105263 - 6.0924382327227952669e-1834j)  +/-  (1.62e-140, 3.78e-373j)
| (0.013157894736842105263 - 6.2101761427126239214e-1834j)  +/-  (2.45e-141, 5.72e-374j)
| (0.013157894736842105263 - 5.8458164803165293947e-1834j)  +/-  (2.01e-141, 4.7e-374j)
| (0.013157894736842105263 + 8.3278203891087526111e-1833j)  +/-  (8.98e-144, 2.1e-376j)
| (0.013157894736842105263 + 5.8383213011507083166e-1834j)  +/-  (5.99e-141, 1.4e-373j)
| (0.013157894736842105263 - 5.9982433526774756699e-1834j)  +/-  (1.75e-141, 4.08e-374j)
| (0.013157894736842105263 + 6.2784240365591977948e-1834j)  +/-  (2.97e-143, 6.94e-376j)
| (0.0065789473684210526316 + 6.8286265629499332592e-1831j)  +/-  (1.49e-145, 3.49e-378j)
| (0.013157894736842105263 - 9.7488076880404881038e-1833j)  +/-  (6.5e-145, 1.52e-377j)
| (0.013157894736842105263 + 2.8651983995959253949e-1832j)  +/-  (5.2e-146, 1.22e-378j)
| (0.013157894736842105263 - 5.9266404148213577879e-1834j)  +/-  (9.83e-144, 2.3e-376j)
| (0.013157894736842105263 - 6.52388726439407328e-1834j)  +/-  (4.74e-147, 1.11e-379j)
| (0.013157894736842105263 - 9.1256091392324737285e-1832j)  +/-  (7.93e-147, 1.85e-379j)
| (0.013157894736842105263 - 3.9221384321648401701e-1832j)  +/-  (6.95e-147, 1.63e-379j)
| (0.013157894736842105263 + 4.9421800371907723876e-1833j)  +/-  (1.17e-150, 2.74e-383j)
| (0.013157894736842105263 + 1.7093463083103891579e-1831j)  +/-  (6.26e-147, 1.46e-379j)
| (0.013157894736842105263 - 6.3532611009545857176e-1834j)  +/-  (1.07e-149, 2.5e-382j)
| (0.013157894736842105263 + 6.6203511920368422274e-1834j)  +/-  (2.19e-151, 5.13e-384j)
| (0.013157894736842105263 - 4.5550117613344663074e-1831j)  +/-  (8.91e-147, 2.08e-379j)
| (0.013157894736842105263 - 4.4288633617330140044e-1833j)  +/-  (1.38e-152, 3.23e-385j)
| (0.013157894736842105263 + 6.2961576216630024134e-1833j)  +/-  (6.72e-151, 1.57e-383j)
| (0.013157894736842105263 + 6.1482584410386410538e-1834j)  +/-  (3.24e-149, 7.58e-382j)
| (0.013157894736842105263 + 7.0902315257766361531e-1834j)  +/-  (4.87e-155, 1.14e-387j)
| (0.013157894736842105263 - 5.8759302988117227613e-1834j)  +/-  (4.67e-150, 1.09e-382j)
| (0.013157894736842105263 - 5.5553819771284579452e-1833j)  +/-  (3.09e-152, 7.23e-385j)
| (0.013157894736842105263 - 3.624694550627214183e-1833j)  +/-  (1.6e-155, 3.75e-388j)
| (0.013157894736842105263 + 5.8986609539259006317e-1834j)  +/-  (6.52e-150, 1.52e-382j)
| (0.013157894736842105263 - 6.7247600193814869231e-1834j)  +/-  (1.2e-154, 2.82e-387j)
| (0.013157894736842105263 + 6.8375480345562820947e-1834j)  +/-  (1.6e-155, 3.73e-388j)
| (0.013157894736842105263 - 1.3993347231428643491e-1832j)  +/-  (3.92e-153, 9.15e-386j)
| (0.013157894736842105263 - 3.0308111231289393008e-1833j)  +/-  (5.91e-159, 1.38e-391j)
| (0.013157894736842105263 + 3.9948755409656274647e-1833j)  +/-  (2.12e-156, 4.97e-389j)
| (0.013157894736842105263 + 5.7108245967439773296e-1832j)  +/-  (4.8e-153, 1.12e-385j)
| (0.013157894736842105263 - 7.5458470827037126854e-1834j)  +/-  (1.25e-161, 2.92e-394j)
| (0.013157894736842105263 + 5.8583377994922862173e-1834j)  +/-  (4.71e-153, 1.1e-385j)
| (0.013157894736842105263 + 3.3064216095217372465e-1833j)  +/-  (2.57e-158, 6e-391j)
| (0.013157894736842105263 + 2.7905908154521730554e-1833j)  +/-  (1.2e-160, 2.82e-393j)
| (0.013157894736842105263 - 6.9591951499508478425e-1834j)  +/-  (8.42e-159, 1.97e-391j)
| (0.013157894736842105263 + 7.3828761936793811972e-1834j)  +/-  (2.49e-161, 5.81e-394j)
| (0.013157894736842105263 + 6.4349754974659743467e-1834j)  +/-  (2.03e-156, 4.74e-389j)
| (0.013157894736842105263 + 1.4694729749634728436e-1833j)  +/-  (5.98e-167, 1.4e-399j)
| (0.013157894736842105263 - 2.2298604424886935023e-1833j)  +/-  (3.02e-164, 7.06e-397j)
| (0.013157894736842105263 + 1.1212801915663950312e-1833j)  +/-  (8.81e-168, 2.06e-400j)
| (0.013157894736842105263 + 8.11113555854235381e-1834j)  +/-  (2.11e-165, 4.93e-398j)
| (0.013157894736842105263 - 7.9090526003492745575e-1834j)  +/-  (1.01e-164, 2.37e-397j)
| (0.013157894736842105263 - 1.0025081400415841467e-1833j)  +/-  (2.5e-168, 5.84e-401j)
| (0.013157894736842105263 - 2.5799768673936245209e-1833j)  +/-  (3.71e-164, 8.67e-397j)
| (0.013157894736842105263 + 2.3943226310617183993e-1833j)  +/-  (5.45e-165, 1.27e-397j)
| (0.013157894736842105263 + 1.7269855396714734011e-1832j)  +/-  (6.84e-160, 1.6e-392j)
| (0.013157894736842105263 + 7.7209470349499561283e-1834j)  +/-  (2.89e-165, 6.76e-398j)
| (0.013157894736842105263 - 7.2312428247913572626e-1834j)  +/-  (1.11e-163, 2.59e-396j)
| (0.013157894736842105263 - 1.2728584031399617906e-1833j)  +/-  (5.82e-171, 1.36e-403j)
| (0.013157894736842105263 + 2.0835093549956270115e-1833j)  +/-  (2.08e-168, 4.85e-401j)
| (0.013157894736842105263 + 1.3326347640419992838e-1833j)  +/-  (5.66e-171, 1.32e-403j)
| (0.013157894736842105263 + 9.6869547830667830323e-1834j)  +/-  (2.1e-171, 4.92e-404j)
| (0.013157894736842105263 - 8.328274669644088588e-1834j)  +/-  (8.94e-170, 2.09e-402j)
| (0.013157894736842105263 - 1.0785172712437922303e-1833j)  +/-  (1.21e-171, 2.82e-404j)
| (0.013157894736842105263 - 1.9527302293794125139e-1833j)  +/-  (8.96e-171, 2.09e-403j)
| (0.013157894736842105263 + 1.8354152999021880605e-1833j)  +/-  (1.2e-171, 2.79e-404j)
| (0.013157894736842105263 + 1.0390268104474542608e-1833j)  +/-  (2.44e-172, 5.71e-405j)
| (0.013157894736842105263 - 8.8126546380667866628e-1834j)  +/-  (5.95e-173, 1.39e-405j)
| (0.013157894736842105263 - 9.3735323971751562205e-1834j)  +/-  (5.06e-173, 1.18e-405j)
| (0.013157894736842105263 - 1.397948173828054479e-1833j)  +/-  (3.85e-174, 9e-407j)
| (0.013157894736842105263 - 1.7298031480434059252e-1833j)  +/-  (3.91e-174, 9.13e-407j)
| (0.013157894736842105263 + 1.2180350106565425885e-1833j)  +/-  (1.89e-174, 4.41e-407j)
| (0.013157894736842105263 + 9.0827206726901108712e-1834j)  +/-  (4.76e-174, 1.11e-406j)
| (0.013157894736842105263 + 8.5616692145160680482e-1834j)  +/-  (6.1e-174, 1.43e-406j)
| (0.013157894736842105263 - 1.1676566972260183796e-1833j)  +/-  (7.09e-175, 1.66e-407j)
| (0.013157894736842105263 + 1.6344126144839365597e-1833j)  +/-  (4.95e-176, 1.16e-408j)
| (0.013157894736842105263 - 1.5479909762920001605e-1833j)  +/-  (4.98e-176, 1.16e-408j)
