Starting with polynomial:
P : 2*t
Extension levels are: 1 76
-------------------------------------------------
Trying to find an order 76 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^77 - 2926*t^75 + 4059825/2*t^73 - 889101675*t^71 + 2209417662375/8*t^69 - 518329383593175/8*t^67 + 382008755708169975/32*t^65 - 3547224160147292625/2*t^63 + 6927728784767662496625/32*t^61 - 704319093118045687156875/32*t^59 + 241017993664995234145082625/128*t^57 - 8742379952030281674898906125/64*t^55 + 4327478076254989429074958531875/512*t^53 - 229356338041514439740972802189375/512*t^51 + 41775618714704415809962903255921875/2048*t^49 - 409401063404103274937636451908034375/512*t^47 + 442562549539835640207585004512585159375/16384*t^45 - 12886380118954037758985563366689979640625/16384*t^43 + 1292933471935055121818218191124561290609375/65536*t^41 - 13950071670878226314354459430554477082890625/32768*t^39 + 2067400621624153139787330887608173503684390625/262144*t^37 - 32783067000040142645199104074929608415566765625/262144*t^35 + 1773265896820353170353951538598465182478384140625/1048576*t^33 - 2544251069350941505290452207554319609642898984375/131072*t^31 + 394358915749395933320020092170919539494649342578125/2097152*t^29 - 3202194395885094978558563148427866660696552661734375/2097152*t^27 + 86459248688897564421081205007552399838806921866828125/8388608*t^25 - 240164579691382123391892236132089999552241449630078125/4194304*t^23 + 8680234094559953888306962248774109983816726679487109375/33554432*t^21 - 31428433790648108905939001245561432700026079356763671875/33554432*t^19 + 358284145213388441527704614199400332780297304667105859375/134217728*t^17 - 196478402213793661482934788431929214750485618688412890625/33554432*t^15 + 20630232232448334455708152785352567548800989962283353515625/2147483648*t^13 - 24381183547438940720382362382689398012219351773607599609375/2147483648*t^11 + 78880299712302455271825290061642170039533196914612822265625/8589934592*t^9 - 20283505640306345641326503158707986581594250635186154296875/4294967296*t^7 + 47328179827381473163095174036985302023719918148767693359375/34359738368*t^5 - 6395699976673172049066915410403419192394583533617255859375/34359738368*t^3 + 1009847364737869270905302433221592504062302663202724609375/137438953472*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:   77 out of 77
Indefinite weights: 0 out of 77
Negative weights:   0 out of 77
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-9.6654804081925358115 + 7.3364938990163792518e-1737j)  +/-  (2.49e-493, 2.49e-493j)
| (-10.529212793984576415 + 7.2400525344360579248e-1742j)  +/-  (6.51e-495, 6.51e-495j)
| (8.212098830473652194 - 5.6979788711089282445e-1743j)  +/-  (1.2e-491, 1.2e-491j)
| (-8.9073408793931364512 - 4.2140934886932222033e-1753j)  +/-  (2.58e-492, 2.58e-492j)
| (-6.0512072677740341637 - 4.2894387133426084726e-1756j)  +/-  (8.11e-492, 8.11e-492j)
| (-11.03366042947502918 + 1.1443134442943020435e-1762j)  +/-  (4.96e-496, 4.96e-496j)
| (-8.5533950218190300224 + 9.174616968037987383e-1758j)  +/-  (6.07e-492, 6.07e-492j)
| (9.2767169065128167569 + 1.0853145433939557433e-1762j)  +/-  (8.99e-493, 8.99e-493j)
| (10.079638983721910453 - 8.7509336104542510098e-1772j)  +/-  (5.19e-494, 5.19e-494j)
| (-6.3421458141623203165 - 3.8282932016055554331e-1776j)  +/-  (1.09e-491, 1.09e-491j)
| (-10.079638983721910453 + 5.3901080908577170325e-1779j)  +/-  (5.06e-494, 5.06e-494j)
| (5.4817016838558223381 + 1.5043793764575525038e-1775j)  +/-  (1.85e-492, 1.85e-492j)
| (-5.2023370059655709344 + 1.5037900958037324272e-1779j)  +/-  (8.85e-493, 8.85e-493j)
| (-4.3819377189728371832 + 1.7348498715628607146e-1781j)  +/-  (4.88e-494, 4.88e-494j)
| (11.643967905483197403 - 7.0133270221002746049e-1779j)  +/-  (2.06e-497, 2.06e-497j)
| (1.0104550177477930133 - 4.9919299772055290228e-1793j)  +/-  (7.27e-505, 7.27e-505j)
| (9.6654804081925358115 - 2.3371996706115540364e-1779j)  +/-  (2.47e-493, 2.47e-493j)
| (10.529212793984576415 + 9.7278616102354632658e-1785j)  +/-  (7.24e-495, 7.24e-495j)
| (-7.8814041633182295351 + 1.3906690835855191596e-1782j)  +/-  (1.2e-491, 1.2e-491j)
| (-4.6527327077376204463 + 4.5747872258401994005e-1785j)  +/-  (1.36e-493, 1.36e-493j)
| (3.320151226914721742 - 5.8637106629084186704e-1787j)  +/-  (1.46e-496, 1.46e-496j)
| (2.2838996982733863872 + 1.3524458546982112286e-1790j)  +/-  (8.75e-500, 8.75e-500j)
| (-5.4817016838558223381 + 2.5448591469462060305e-1784j)  +/-  (1.88e-492, 1.88e-492j)
| (-7.2458969961152931192 + 1.6931710462985323036e-1782j)  +/-  (1.99e-491, 1.99e-491j)
| (5.7645343514856854897 + 1.6675373428666892193e-1782j)  +/-  (4.64e-492, 4.64e-492j)
| (-3.320151226914721742 + 1.3791154683787423186e-1793j)  +/-  (1.54e-496, 1.54e-496j)
| (2.5411156130214038627 + 1.2149291233187055147e-1795j)  +/-  (7.03e-499, 7.03e-499j)
| (3.8471712777564734511 - 1.3876228517515421293e-1791j)  +/-  (2.91e-495, 2.91e-495j)
| (-7.5597467325857200812 + 5.8852565757646498598e-1789j)  +/-  (1.68e-491, 1.68e-491j)
| (-11.643967905483197403 - 2.1077194064263368214e-1794j)  +/-  (1.99e-497, 1.99e-497j)
| (5.2023370059655709344 - 2.2664266205542825516e-1788j)  +/-  (9.5e-493, 9.5e-493j)
| (4.6527327077376204463 - 2.8824931525182685855e-1793j)  +/-  (1.27e-493, 1.27e-493j)
| (8.9073408793931364512 + 1.6326022590645721319e-1800j)  +/-  (2.5e-492, 2.5e-492j)
| (-3.5827860282892380752 - 5.9848286127407124366e-1817j)  +/-  (7.35e-496, 7.35e-496j)
| (4.1134892401757891344 - 5.268859521090736615e-1815j)  +/-  (1.55e-494, 1.55e-494j)
| (1.772357411860218343 + 9.8688617913410681806e-1823j)  +/-  (1.15e-501, 1.15e-501j)
| (-9.2767169065128167569 + 2.030124781681155496e-1812j)  +/-  (8.58e-493, 8.58e-493j)
| (2.7994686133415088579 + 5.3345974438816565415e-1819j)  +/-  (3.43e-498, 3.43e-498j)
| (3.5827860282892380752 + 8.557963128471961456e-1817j)  +/-  (7.27e-496, 7.27e-496j)
| (11.03366042947502918 + 1.5955098416450305825e-1813j)  +/-  (4.85e-496, 4.85e-496j)
| (6.938865637103067435 - 1.8029671913520277863e-1812j)  +/-  (2.03e-491, 2.03e-491j)
| (6.0512072677740341637 - 1.6070130035599182088e-1817j)  +/-  (7.48e-492, 7.48e-492j)
| (-8.212098830473652194 - 6.6205811608111139706e-1826j)  +/-  (1.22e-491, 1.22e-491j)
| (-2.0276888921639607489 + 1.4164841490158607774e-1840j)  +/-  (1.43e-500, 1.43e-500j)
| (-2.5411156130214038627 - 1.8844231678959323872e-1838j)  +/-  (6.42e-499, 6.42e-499j)
| (-1.772357411860218343 + 2.1326972526452477545e-1841j)  +/-  (1.19e-501, 1.19e-501j)
| (-5.7645343514856854897 + 2.1097466951820116434e-1831j)  +/-  (4.97e-492, 4.97e-492j)
| (-3.0590979254933975941 - 2.6481511124419070686e-1847j)  +/-  (2.71e-497, 2.71e-497j)
| (3.0590979254933975941 + 1.1565779082940383777e-1847j)  +/-  (2.78e-497, 2.78e-497j)
| (2.0276888921639607489 - 5.7958492735002825853e-1854j)  +/-  (1.47e-500, 1.47e-500j)
| (8.5533950218190300224 - 9.2882763050080568814e-1843j)  +/-  (6.09e-492, 6.09e-492j)
| (-0.75747605237336063367 + 5.0545599850943166599e-1880j)  +/-  (4.64e-506, 4.64e-506j)
| (-4.1134892401757891344 - 2.9455139480892027807e-1865j)  +/-  (1.54e-494, 1.54e-494j)
| (6.3421458141623203165 - 5.1017677873866947886e-1880j)  +/-  (1.07e-491, 1.07e-491j)
| (7.5597467325857200812 + 2.4971326143065483112e-1914j)  +/-  (1.79e-491, 1.79e-491j)
| (-2.7994686133415088579 + 4.7451359663675668932e-1941j)  +/-  (4.03e-498, 4.03e-498j)
| (-1.263854750000140942 - 3.7590424678200567232e-1946j)  +/-  (8.77e-504, 8.77e-504j)
| (-2.2838996982733863872 + 3.120168197397658816e-1942j)  +/-  (1e-499, 1e-499j)
| (-1.3659657923266942885e-1991 - 2.2142413646830755426e-1991j)  +/-  (2e-1989, 2e-1989j)
| (0.75747605237336063367 - 7.1280017508674334813e-1949j)  +/-  (4.8e-506, 4.8e-506j)
| (4.3819377189728371832 + 6.4012230477600083945e-1934j)  +/-  (4.77e-494, 4.77e-494j)
| (-1.0104550177477930133 + 1.151514030338133708e-1949j)  +/-  (7.37e-505, 7.37e-505j)
| (-1.5177847328096994868 + 1.2569533193504293338e-1947j)  +/-  (1.37e-502, 1.37e-502j)
| (7.8814041633182295351 + 5.8589978891788940351e-1935j)  +/-  (1.2e-491, 1.2e-491j)
| (-6.6378409471161140341 + 1.2998643251265716138e-1947j)  +/-  (1.63e-491, 1.63e-491j)
| (7.2458969961152931192 - 8.5391005831689339716e-1949j)  +/-  (1.87e-491, 1.87e-491j)
| (1.5177847328096994868 - 9.6666002739199733564e-1975j)  +/-  (1.29e-502, 1.29e-502j)
| (-0.50481068435860236342 + 3.7319995415510558469e-1979j)  +/-  (3.7e-507, 3.7e-507j)
| (6.6378409471161140341 - 1.013498840455677127e-1965j)  +/-  (1.55e-491, 1.55e-491j)
| (-6.938865637103067435 + 6.3875708182322600012e-1978j)  +/-  (1.93e-491, 1.93e-491j)
| (4.9261115854472980118 + 6.058796332627284623e-1982j)  +/-  (3.82e-493, 3.82e-493j)
| (-4.9261115854472980118 + 6.0634701334012714588e-1987j)  +/-  (3.66e-493, 3.66e-493j)
| (-3.8471712777564734511 - 2.4537111496645398387e-1997j)  +/-  (2.76e-495, 2.76e-495j)
| (-0.25235344827118409097 - 3.0170503910065345595e-2011j)  +/-  (9.79e-509, 9.79e-509j)
| (1.263854750000140942 + 4.3442329368334915058e-2008j)  +/-  (8.74e-504, 8.74e-504j)
| (0.25235344827118409097 - 1.7549761265875494192e-2011j)  +/-  (9.35e-509, 9.35e-509j)
| (0.50481068435860236342 + 6.1452094043570488424e-2011j)  +/-  (4.36e-507, 4.36e-507j)
-------------------------------------------------
The weights are:
| (6.0433421504904167707e-42 + 4.2931167189507515983e-1777j)  +/-  (3.42e-163, 9.12e-408j)
| (1.8967886101450954632e-49 - 8.9632780560074544177e-1782j)  +/-  (2.84e-166, 7.56e-411j)
| (9.753928293773677805e-31 + 4.6637279533975073426e-1772j)  +/-  (1.11e-160, 2.97e-405j)
| (7.1094797815049000609e-36 + 6.4306797148806942675e-1775j)  +/-  (3.74e-161, 9.98e-406j)
| (2.0384881057776112456e-17 - 2.4311335766131527236e-1766j)  +/-  (7.87e-151, 2.1e-395j)
| (4.1204126561639811776e-54 + 2.616450435132298126e-1784j)  +/-  (1.24e-168, 3.31e-413j)
| (3.3022583246728153431e-33 - 9.5124265181995814833e-1774j)  +/-  (2.93e-160, 7.8e-405j)
| (9.0146830726145794649e-39 + 4.1147013308370077939e-1777j)  +/-  (1.62e-167, 4.32e-412j)
| (1.8224090828528017019e-45 + 8.9642983107765935647e-1781j)  +/-  (1.96e-170, 5.22e-415j)
| (5.6245234965401644635e-19 + 4.3599866400101476269e-1767j)  +/-  (1.11e-153, 2.95e-398j)
| (1.8224090828528017019e-45 + 1.8458838674860174222e-1779j)  +/-  (8.37e-166, 2.23e-410j)
| (1.4127196117968260555e-14 - 3.8649173444236141896e-1765j)  +/-  (4.59e-154, 1.22e-398j)
| (2.761775110176846291e-13 + 2.3441003951668722022e-1764j)  +/-  (2.05e-149, 5.46e-394j)
| (6.9673351711161180261e-10 - 1.0189669342880994367e-1762j)  +/-  (1.48e-145, 3.93e-390j)
| (5.2184705636769467762e-60 - 1.8124379775292721582e-1788j)  +/-  (5.19e-177, 1.38e-421j)
| (0.051453686366146929097 + 5.6045395769322960711e-1759j)  +/-  (4.52e-111, 1.2e-355j)
| (6.0433421504904167707e-42 - 7.2249508827202081944e-1779j)  +/-  (4.34e-170, 1.16e-414j)
| (1.8967886101450954632e-49 - 6.6876974512202381489e-1783j)  +/-  (3.65e-173, 9.74e-418j)
| (1.9395690716184472957e-28 - 1.456580383267058391e-1771j)  +/-  (1.19e-162, 3.17e-407j)
| (6.088264954292204719e-11 + 3.1486742474325400788e-1763j)  +/-  (3.87e-150, 1.03e-394j)
| (2.4100116625816924372e-06 - 3.9419467908318790896e-1761j)  +/-  (1.38e-146, 3.69e-391j)
| (0.00078608827064711509288 - 6.8932073534369912858e-1760j)  +/-  (1.81e-137, 4.83e-382j)
| (1.4127196117968260555e-14 - 5.6121801662719597623e-1765j)  +/-  (8.85e-154, 2.36e-398j)
| (2.7632652261350233683e-24 - 1.2995912222178513669e-1769j)  +/-  (3.34e-161, 8.91e-406j)
| (5.9463298287192859918e-16 + 8.4568838836629721762e-1766j)  +/-  (6.59e-161, 1.76e-405j)
| (2.4100116625816924372e-06 - 5.1700202366995778786e-1761j)  +/-  (1.86e-146, 4.97e-391j)
| (0.00022818530663290889431 + 3.7308898766140589699e-1760j)  +/-  (5.49e-142, 1.46e-386j)
| (5.5888323279589364922e-08 - 6.2032010326842294031e-1762j)  +/-  (8.26e-152, 2.2e-396j)
| (2.7129145316346265226e-26 + 1.46949156007438919e-1770j)  +/-  (2.3e-162, 6.12e-407j)
| (5.2184705636769467762e-60 - 2.0176639156876238595e-1787j)  +/-  (1.04e-177, 2.78e-422j)
| (2.761775110176846291e-13 + 1.620081816034343424e-1764j)  +/-  (3.47e-159, 9.25e-404j)
| (6.088264954292204719e-11 + 2.2164747346352833508e-1763j)  +/-  (3.37e-157, 8.99e-402j)
| (7.1094797815049000609e-36 - 1.8992874007540677401e-1775j)  +/-  (6.94e-173, 1.85e-417j)
| (3.9574516733997994766e-07 + 2.1653993120010626031e-1761j)  +/-  (1.05e-151, 2.81e-396j)
| (6.759211128150306357e-09 + 2.204927659035611591e-1762j)  +/-  (1.02e-154, 2.71e-399j)
| (0.0062175915613133015819 - 1.9324068476527290811e-1759j)  +/-  (1.99e-141, 5.31e-386j)
| (9.0146830726145794649e-39 - 4.4352566671367623459e-1776j)  +/-  (2.84e-170, 7.58e-415j)
| (5.7689061536278805487e-05 - 1.8886400551132553577e-1760j)  +/-  (2.52e-148, 6.71e-393j)
| (3.9574516733997994766e-07 + 1.6211176774109285894e-1761j)  +/-  (2.98e-152, 7.95e-397j)
| (4.1204126561639811776e-54 + 2.279811107024319824e-1785j)  +/-  (7.9e-181, 2.1e-425j)
| (2.1077291104141965554e-22 + 7.9936067440595944435e-1769j)  +/-  (6.76e-169, 1.8e-413j)
| (2.0384881057776112456e-17 - 1.6939033098673500097e-1766j)  +/-  (1.02e-164, 2.72e-409j)
| (9.753928293773677805e-31 + 1.259406438728905054e-1772j)  +/-  (1.78e-169, 4.75e-414j)
| (0.0023639069757304043772 + 1.4152855742780248514e-1759j)  +/-  (6.67e-151, 1.78e-395j)
| (0.00022818530663290889431 + 4.614588077825155624e-1760j)  +/-  (7.38e-154, 1.97e-398j)
| (0.0062175915613133015819 - 2.2461527587206673716e-1759j)  +/-  (9.52e-150, 2.54e-394j)
| (5.9463298287192859918e-16 + 1.2255933386745807501e-1765j)  +/-  (1.26e-163, 3.35e-408j)
| (1.2669609886617577466e-05 + 1.1494432283663088287e-1760j)  +/-  (6.5e-156, 1.73e-400j)
| (1.2669609886617577466e-05 + 8.9322060065608829816e-1761j)  +/-  (3.39e-155, 9.04e-400j)
| (0.0023639069757304043772 + 1.1923244257755438858e-1759j)  +/-  (1.97e-151, 5.25e-396j)
| (3.3022583246728153431e-33 + 8.9062518936079662771e-1774j)  +/-  (1.11e-175, 2.95e-420j)
| (0.080357177736003871144 - 7.5177915555804611533e-1759j)  +/-  (3.23e-148, 8.6e-393j)
| (6.759211128150306357e-09 + 3.0460713053445412767e-1762j)  +/-  (4.68e-161, 1.25e-405j)
| (5.6245234965401644635e-19 + 3.1019280218838248767e-1767j)  +/-  (3.01e-169, 8.02e-414j)
| (2.7129145316346265226e-26 + 1.5933014775119993005e-1770j)  +/-  (7.08e-174, 1.89e-418j)
| (5.7689061536278805487e-05 - 2.3832796359250709515e-1760j)  +/-  (1.2e-158, 3.2e-403j)
| (0.028969609809574659344 - 4.6645052504470374167e-1759j)  +/-  (3.28e-154, 8.75e-399j)
| (0.00078608827064711509288 - 8.3535820023642552204e-1760j)  +/-  (2.33e-157, 6.2e-402j)
| (0.14236543797973869594 + 9.6261260366177500643e-1759j)  +/-  (4.58e-154, 1.22e-398j)
| (0.080357177736003871144 - 7.0450274531252563353e-1759j)  +/-  (6.13e-154, 1.63e-398j)
| (6.9673351711161180261e-10 - 7.2671121061918247014e-1763j)  +/-  (8.65e-164, 2.3e-408j)
| (0.051453686366146929097 + 6.110899606495993027e-1759j)  +/-  (4.18e-155, 1.11e-399j)
| (0.014327962022984623326 + 3.3419277913506312426e-1759j)  +/-  (2.35e-156, 6.27e-401j)
| (1.9395690716184472957e-28 - 2.5130790839913870995e-1771j)  +/-  (4.69e-175, 1.25e-419j)
| (1.2319562570455697905e-20 - 7.0324243628172276483e-1768j)  +/-  (8.39e-172, 2.23e-416j)
| (2.7632652261350233683e-24 - 1.1454553038168086242e-1769j)  +/-  (2e-173, 5.34e-418j)
| (0.014327962022984623326 + 2.9366443567607420637e-1759j)  +/-  (9.05e-161, 2.41e-405j)
| (0.11043046816321127857 + 8.6878332222291420717e-1759j)  +/-  (6.86e-160, 1.83e-404j)
| (1.2319562570455697905e-20 - 5.195500866516608098e-1768j)  +/-  (1.1e-171, 2.94e-416j)
| (2.1077291104141965554e-22 + 1.0142316265842709517e-1768j)  +/-  (2.83e-173, 7.54e-418j)
| (4.4826264565655956756e-12 - 6.242782073294815449e-1764j)  +/-  (1.5e-167, 3.99e-412j)
| (4.4826264565655956756e-12 - 8.9638563216371089878e-1764j)  +/-  (1.95e-168, 5.2e-413j)
| (5.5888323279589364922e-08 - 8.4312834079284311819e-1762j)  +/-  (2.76e-166, 7.36e-411j)
| (0.1336093769597086214 - 9.4335799609870251381e-1759j)  +/-  (6.36e-163, 1.7e-407j)
| (0.028969609809574659344 - 4.1871967413579040976e-1759j)  +/-  (1.06e-163, 2.83e-408j)
| (0.1336093769597086214 - 9.2312713209495218352e-1759j)  +/-  (7.13e-164, 1.93e-408j)
| (0.11043046816321127857 + 8.3193753527161531021e-1759j)  +/-  (5.08e-164, 1.33e-408j)
