Starting with polynomial:
P : 4*t^2 - 1
Extension levels are: 2 78
-------------------------------------------------
Trying to find an order 78 Kronrod extension for:
P1 : 4*t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^80 - 79*t^78 + 3003/4*t^76 - 36575/8*t^74 + 1282975/64*t^72 - 8629695/128*t^70 + 92625393/512*t^68 - 407337153/1024*t^66 + 11969016345/16384*t^64 - 9309234935/8192*t^62 + 49588065527/32768*t^60 - 113988150627/65536*t^58 + 910253202833/524288*t^56 - 1585735217605/1048576*t^54 + 4838352017895/4194304*t^52 - 6480459369423/8388608*t^50 + 122131734269895/268435456*t^48 - 1012974972473835/4294967296*t^46 + 1849081298960175/17179869184*t^44 - 1484915881847475/34359738368*t^42 + 4191844505805495/274877906944*t^40 - 2594951360736735/549755813888*t^38 + 2810864108779545/2199023255552*t^36 - 1327469556620025/4398046511104*t^34 + 4355031703297275/70368744177664*t^32 - 771462758869803/70368744177664*t^30 + 469351468683027/281474976710656*t^28 - 121683714103007/562949953421312*t^26 + 106596245508025/4503599627370496*t^24 - 19509657665925/9007199254740992*t^22 + 5891151530495/36028797018963968*t^20 - 722141155351/72057594037927936*t^18 + 2254848913647/4611686018427387904*t^16 - 341643774795/18446744073709551616*t^14 + 38910617655/73786976294838206464*t^12 - 1595093643/147573952589676412928*t^10 + 177232627/1180591620717411303424*t^8 - 3048227/2361183241434822606848*t^6 + 55965/9444732965739290427392*t^4 - 205/18889465931478580854784*t^2 + 1/302231454903657293676544
-------------------------------------------------
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:
| (0.9969929411677920648 - 4.6108662725050111947e-1702j)  +/-  (2.77e-482, 2.77e-482j)
| (-0.95224788533841532593 - 4.5168789153569198968e-1701j)  +/-  (3.61e-482, 3.61e-482j)
| (-0.93969262078590838405 + 1.156261381571635713e-1718j)  +/-  (2.2e-482, 2.2e-482j)
| (-0.99323835774194298855 + 7.6719752814573192316e-1742j)  +/-  (5.08e-482, 5.08e-482j)
| (0.92572396926889039109 - 4.8267162546535153552e-1761j)  +/-  (1.3e-482, 1.3e-482j)
| (0.91036294096614665951 + 1.5241921113465803724e-1761j)  +/-  (6.27e-483, 6.27e-483j)
| (0.98125531062738467889 + 2.7571772628072041261e-1759j)  +/-  (7.29e-482, 7.29e-482j)
| (-0.89363264032341224819 - 2.5611457434350568115e-1763j)  +/-  (2.83e-483, 2.83e-483j)
| (-0.9879898494768089787 + 5.0606952047953993062e-1778j)  +/-  (6.76e-482, 6.76e-482j)
| (-0.99924795250423006929 - 3.6904203847018904156e-1813j)  +/-  (8.18e-483, 8.18e-483j)
| (0.85616689953026647765 - 8.2590306923354687303e-1843j)  +/-  (4.11e-484, 4.11e-484j)
| (-0.9969929411677920648 - 6.4195907268301993164e-1839j)  +/-  (2.74e-482, 2.74e-482j)
| (-0.92572396926889039109 - 1.5790731226314973095e-1851j)  +/-  (1.25e-482, 1.25e-482j)
| (-0.87555823130209085011 + 1.9166350938994813769e-1859j)  +/-  (1.11e-483, 1.11e-483j)
| (0.9879898494768089787 - 2.6436104572254369508e-1868j)  +/-  (7.15e-482, 7.15e-482j)
| (0.89363264032341224819 + 1.1648371950270882349e-1869j)  +/-  (2.76e-483, 2.76e-483j)
| (0.93969262078590838405 + 3.4325674210684217836e-1868j)  +/-  (2.21e-482, 2.21e-482j)
| (0.96337087861588033308 - 2.1104670630383935944e-1868j)  +/-  (5.29e-482, 5.29e-482j)
| (-0.7660444431189780352 - 1.3398316626846100407e-1871j)  +/-  (2.45e-486, 2.45e-486j)
| (-0.97304487057982383883 - 3.7282015923417229719e-1866j)  +/-  (6.42e-482, 6.42e-482j)
| (0.83548781141293641965 + 2.5003215190701502276e-1892j)  +/-  (1.2e-484, 1.2e-484j)
| (0.7660444431189780352 - 1.8006184369884790071e-1894j)  +/-  (2.44e-486, 2.44e-486j)
| (0.99924795250423006929 + 2.6048141748536537921e-1888j)  +/-  (7.8e-483, 7.8e-483j)
| (-0.81355207026296756371 - 3.3316284467526830393e-1893j)  +/-  (3.73e-485, 3.73e-485j)
| (-0.79039266951875929283 - 3.3911093493237610652e-1898j)  +/-  (9.58e-486, 9.58e-486j)
| (0.74054401310900458045 + 3.2936926725063239328e-1901j)  +/-  (5.39e-487, 5.39e-487j)
| (0.71392973455789904243 - 4.2010170810481924403e-1902j)  +/-  (1.14e-487, 1.14e-487j)
| (0.87555823130209085011 - 1.3170625279047629165e-1897j)  +/-  (1.12e-483, 1.12e-483j)
| (-0.96337087861588033308 - 8.4562025194501194066e-1894j)  +/-  (5.34e-482, 5.34e-482j)
| (-0.62781212467209856145 + 5.465768493868271785e-1917j)  +/-  (3.2e-490, 3.2e-490j)
| (-0.91036294096614665951 + 4.3035384643111220599e-1908j)  +/-  (6.13e-483, 6.13e-483j)
| (0.79039266951875929283 + 9.2129076200581085176e-1923j)  +/-  (9.39e-486, 9.39e-486j)
| (0.68624163786873358573 - 4.5197638223559597249e-1926j)  +/-  (1.41e-488, 1.41e-488j)
| (-0.98125531062738467889 + 1.2336051483830010301e-1918j)  +/-  (7.14e-482, 7.14e-482j)
| (-0.68624163786873358573 - 5.9887940115163883193e-1940j)  +/-  (1.4e-488, 1.4e-488j)
| (-0.74054401310900458045 - 1.0108895837558604742e-1938j)  +/-  (5.4e-487, 5.4e-487j)
| (0.17364817766693034885 + 3.0508692801062920481e-1956j)  +/-  (8.65e-505, 8.65e-505j)
| (0.59715859170278616485 + 7.8023048863084619943e-1942j)  +/-  (4.75e-491, 4.75e-491j)
| (0.99323835774194298855 - 2.2128811095291493159e-1930j)  +/-  (5.11e-482, 5.11e-482j)
| (-0.85616689953026647765 + 1.6505653501804888922e-1936j)  +/-  (4.17e-484, 4.17e-484j)
| (-0.56560687548653861053 + 6.2727060937247702294e-1945j)  +/-  (5.56e-492, 5.56e-492j)
| (0.97304487057982383883 - 1.3053409821499095761e-1933j)  +/-  (6.5e-482, 6.5e-482j)
| (0.65752136856906365554 - 8.3026304810365035773e-1945j)  +/-  (2.22e-489, 2.22e-489j)
| (0.56560687548653861053 - 4.4228790865647769325e-1948j)  +/-  (5.7e-492, 5.7e-492j)
| (-0.53320443280169124347 - 8.0268967050833751677e-1950j)  +/-  (6.85e-493, 6.85e-493j)
| (-0.59715859170278616485 - 1.1148026894723440651e-1948j)  +/-  (4.82e-491, 4.82e-491j)
| (-0.83548781141293641965 + 1.5612536480589450986e-1941j)  +/-  (1.19e-484, 1.19e-484j)
| (0.95224788533841532593 - 2.6919086218151628563e-1943j)  +/-  (3.6e-482, 3.6e-482j)
| (0.46604351970253882582 - 5.6195259050470467793e-1957j)  +/-  (4.59e-495, 4.59e-495j)
| (0.62781212467209856145 + 2.309605374131713423e-1951j)  +/-  (3.24e-490, 3.24e-490j)
| (-0.71392973455789904243 + 6.1005156476687290482e-1952j)  +/-  (1.13e-487, 1.13e-487j)
| (-0.5 + 4.0832794230197274205e-1958j)  +/-  (7.55e-494, 7.55e-494j)
| (-0.096810870703179095791 + 1.8011633799510786563e-1971j)  +/-  (3.27e-507, 3.27e-507j)
| (0.53320443280169124347 - 6.8206924530526626008e-1956j)  +/-  (6.6e-493, 6.6e-493j)
| (0.5 - 5.524411756418307885e-1956j)  +/-  (7.49e-494, 7.49e-494j)
| (-0.13533129975013109826 + 3.0897808119458101676e-1969j)  +/-  (6.11e-506, 6.11e-506j)
| (-0.46604351970253882582 - 2.7407501101188068966e-1959j)  +/-  (4.59e-495, 4.59e-495j)
| (-0.65752136856906365554 - 3.2412292183213546638e-1953j)  +/-  (2.27e-489, 2.27e-489j)
| (0.13533129975013109826 - 8.8400943552095956745e-1969j)  +/-  (6.55e-506, 6.55e-506j)
| (0.43138606568125345427 - 2.289363725329521785e-1958j)  +/-  (4.15e-496, 4.15e-496j)
| (0.81355207026296756371 + 1.0266393345157717295e-1964j)  +/-  (3.7e-485, 3.7e-485j)
| (-0.32373394205832102335 + 2.9946466652427510711e-1979j)  +/-  (1.25e-499, 1.25e-499j)
| (-0.43138606568125345427 - 6.9363726739072476705e-1976j)  +/-  (4.02e-496, 4.02e-496j)
| (-0.019391331771824372455 + 2.2687836802507325837e-1990j)  +/-  (1.03e-510, 1.03e-510j)
| (0.3960797660391568237 - 1.0991599972286139148e-1976j)  +/-  (3.2e-497, 3.2e-497j)
| (0.36017772480471041725 - 3.5895042319888561575e-1978j)  +/-  (2.56e-498, 2.56e-498j)
| (0.019391331771824372455 - 2.3240085362896805689e-1990j)  +/-  (1.03e-510, 1.03e-510j)
| (-0.3960797660391568237 - 1.7779088827536231716e-1976j)  +/-  (3.08e-497, 3.08e-497j)
| (-0.24944114405798129066 - 1.2981380682673760065e-1981j)  +/-  (3.68e-502, 3.68e-502j)
| (0.21170387222941074548 - 8.5729969439409450082e-1983j)  +/-  (2.47e-503, 2.47e-503j)
| (0.32373394205832102335 - 6.2301789439247836316e-1979j)  +/-  (1.19e-499, 1.19e-499j)
| (0.096810870703179095791 + 8.4282244207962204404e-1987j)  +/-  (3.34e-507, 3.34e-507j)
| (-0.21170387222941074548 + 1.2426356721493184249e-1982j)  +/-  (2.52e-503, 2.52e-503j)
| (-0.36017772480471041725 + 6.7070553443701471965e-1978j)  +/-  (2.75e-498, 2.75e-498j)
| (0.058144828910475828539 - 1.4274181384515849139e-1988j)  +/-  (8.62e-509, 8.62e-509j)
| (0.2868032327110902531 - 2.6383720103978180643e-1980j)  +/-  (7.96e-501, 7.96e-501j)
| (0.24944114405798129066 + 4.3604270004062742637e-1981j)  +/-  (3.58e-502, 3.58e-502j)
| (-0.058144828910475828539 + 1.3278536443729207074e-1988j)  +/-  (9.57e-509, 9.57e-509j)
| (-0.2868032327110902531 + 4.8945272246979884507e-1981j)  +/-  (7.93e-501, 7.93e-501j)
| (-0.17364817766693034885 - 3.5641453467338810351e-1985j)  +/-  (8.71e-505, 8.71e-505j)
-------------------------------------------------
The weights are:
| (7.4136731624635933938e-05 + 8.6847584133705371322e-1704j)  +/-  (9.06e-138, 5.26e-372j)
| (0.001150913146524891582 - 7.9923881744080558529e-1703j)  +/-  (4.41e-138, 2.56e-372j)
| (0.0014441701042038392889 + 5.1989811311821131203e-1702j)  +/-  (3.96e-138, 2.3e-372j)
| (0.00016638968777886519239 - 1.8296494646350605943e-1703j)  +/-  (3.94e-139, 2.29e-373j)
| (0.00176586583606235159 + 1.5671809345092786213e-1703j)  +/-  (1.09e-139, 6.34e-374j)
| (0.0021140656261168910152 - 1.6378739737755736712e-1703j)  +/-  (9.29e-140, 5.4e-374j)
| (0.00045849401685870128954 - 1.4504211860349123956e-1703j)  +/-  (2.25e-140, 1.31e-374j)
| (0.0024866753598593446614 - 1.9222915137088967244e-1702j)  +/-  (2.06e-140, 1.2e-374j)
| (0.00029476613988632514856 + 3.718250311070630066e-1703j)  +/-  (2.79e-140, 1.62e-374j)
| (1.8562091556839106173e-05 - 1.7795976852902829342e-1704j)  +/-  (4.07e-141, 2.37e-375j)
| (0.0032960276561571677418 + 1.90242040215937752e-1703j)  +/-  (1.57e-144, 9.1e-379j)
| (7.4136731624635933938e-05 + 7.4667369785827157349e-1704j)  +/-  (9.63e-141, 5.59e-375j)
| (0.00176586583606235159 - 3.0114083764612447641e-1702j)  +/-  (3.57e-142, 2.07e-376j)
| (0.002881454118508078744 + 1.7042183651980984621e-1702j)  +/-  (1.8e-143, 1.05e-377j)
| (0.00029476613988632514856 + 1.5782444448444169164e-1703j)  +/-  (6.32e-145, 3.67e-379j)
| (0.0024866753598593446614 + 1.7177877462800924329e-1703j)  +/-  (7.98e-145, 4.64e-379j)
| (0.0014441701042038392889 - 1.5068866336593543572e-1703j)  +/-  (5.36e-145, 3.12e-379j)
| (0.0008878586448748982861 - 1.4269427174345018046e-1703j)  +/-  (1.72e-145, 1e-379j)
| (0.0051009371748954916738 - 1.2507137007565386934e-1702j)  +/-  (3.45e-148, 2.01e-382j)
| (0.00065658863997893673955 + 1.4245023433995896789e-1702j)  +/-  (3.27e-144, 1.9e-378j)
| (0.0037279026787706368908 - 2.0061808878290388607e-1703j)  +/-  (4.06e-147, 2.36e-381j)
| (0.0051009371748954916738 + 2.3592820856054769904e-1703j)  +/-  (6.18e-149, 3.59e-383j)
| (1.8562091556839106173e-05 + 3.752464257538486385e-1704j)  +/-  (2.5e-146, 1.45e-380j)
| (0.0041744818391461665225 - 1.3701262057184537048e-1702j)  +/-  (1.57e-148, 9.1e-383j)
| (0.0046330793576667821564 + 1.3049010982839219675e-1702j)  +/-  (9.99e-149, 5.8e-383j)
| (0.0055752415388692648408 - 2.4900523057826650034e-1703j)  +/-  (3.47e-150, 2.02e-384j)
| (0.006053139927334417454 + 2.6269661009616736395e-1703j)  +/-  (5.65e-151, 3.28e-385j)
| (0.002881454118508078744 - 1.8061514780702344733e-1703j)  +/-  (9.47e-148, 5.5e-382j)
| (0.0008878586448748982861 - 3.6033710489334565667e-1702j)  +/-  (2.1e-147, 1.22e-381j)
| (0.0074796535322803132437 + 1.0625625245600702766e-1702j)  +/-  (2.04e-154, 1.18e-388j)
| (0.0021140656261168910152 + 2.2849222281794977358e-1702j)  +/-  (2.91e-148, 1.69e-382j)
| (0.0046330793576667821564 - 2.234884095535709207e-1703j)  +/-  (1.12e-150, 6.53e-385j)
| (0.0065317582031510853614 - 2.7698009897501690641e-1703j)  +/-  (6.84e-153, 3.97e-387j)
| (0.00045849401685870128954 - 7.1287336226617098249e-1703j)  +/-  (1.06e-147, 6.19e-382j)
| (0.0065317582031510853614 + 1.1270077126121793495e-1702j)  +/-  (1.55e-154, 8.99e-389j)
| (0.0055752415388692648408 + 1.2043192475433943165e-1702j)  +/-  (4.49e-153, 2.61e-387j)
| (0.011973411239419187556 + 5.4740335360806856944e-1703j)  +/-  (3.5e-160, 2.03e-394j)
| (0.007943229831549939834 + 3.2316441660703941192e-1703j)  +/-  (6.41e-157, 3.73e-391j)
| (0.00016638968777886519239 - 2.0820018275851358968e-1703j)  +/-  (3.45e-152, 2e-386j)
| (0.0032960276561571677418 - 1.5577018250554874352e-1702j)  +/-  (1.73e-152, 1e-386j)
| (0.0083961587950908050447 + 1.0056444757972452151e-1702j)  +/-  (7.8e-159, 4.53e-393j)
| (0.00065658863997893673955 + 1.4182101970608378317e-1703j)  +/-  (3.1e-152, 1.8e-386j)
| (0.0070082178996921672732 + 2.918337657089796395e-1703j)  +/-  (2.19e-156, 1.28e-390j)
| (0.0083961587950908050447 - 3.3959774913214522369e-1703j)  +/-  (1.05e-158, 6.1e-393j)
| (0.0088357164548225521868 - 9.7902810535186445333e-1703j)  +/-  (3.67e-160, 2.13e-394j)
| (0.007943229831549939834 - 1.0333855564926163716e-1702j)  +/-  (9.75e-159, 5.67e-393j)
| (0.0037279026787706368908 + 1.4515241902905614899e-1702j)  +/-  (8.2e-155, 4.76e-389j)
| (0.001150913146524891582 + 1.458948501411220983e-1703j)  +/-  (4.71e-154, 2.74e-388j)
| (0.0096642399721391272255 + 3.9170631109550218417e-1703j)  +/-  (1.97e-162, 1.15e-396j)
| (0.0074796535322803132437 - 3.0723580414734074191e-1703j)  +/-  (2.51e-158, 1.46e-392j)
| (0.006053139927334417454 - 1.1635734643889294312e-1702j)  +/-  (1.23e-157, 7.15e-392j)
| (0.0092592592592592592593 + 9.5329871284612004676e-1703j)  +/-  (4.14e-162, 2.41e-396j)
| (0.012229971053255460981 - 6.9732171818490232468e-1703j)  +/-  (2.25e-167, 1.31e-401j)
| (0.0088357164548225521868 + 3.5651386456055728544e-1703j)  +/-  (2.01e-161, 1.17e-395j)
| (0.0092592592592592592593 - 3.7389074406485171712e-1703j)  +/-  (2.93e-162, 1.7e-396j)
| (0.012119573324789384772 + 7.1946438627003438574e-1703j)  +/-  (1.83e-167, 1.06e-401j)
| (0.0096642399721391272255 - 9.2827347364106535722e-1703j)  +/-  (2.06e-164, 1.2e-398j)
| (0.0070082178996921672732 - 1.093586552863605442e-1702j)  +/-  (1.58e-160, 9.21e-395j)
| (0.012119573324789384772 - 5.6819744719325910287e-1703j)  +/-  (2.79e-168, 1.62e-402j)
| (0.01004822299180307754 - 4.0993847384556175423e-1703j)  +/-  (1.81e-165, 1.05e-399j)
| (0.0041744818391461665225 + 2.1170978311419978062e-1703j)  +/-  (2.4e-160, 1.39e-394j)
| (0.011051806601967649956 - 8.3283284405880936451e-1703j)  +/-  (2.33e-168, 1.35e-402j)
| (0.01004822299180307754 + 9.0381126507357093221e-1703j)  +/-  (3.03e-166, 1.76e-400j)
| (0.012341036743853272033 - 6.5353693017723018802e-1703j)  +/-  (9.89e-170, 5.75e-404j)
| (0.010408898999189713492 + 4.2856518388269174104e-1703j)  +/-  (2.01e-167, 1.17e-401j)
| (0.010744098846351880126 - 4.4756450970893324746e-1703j)  +/-  (2.03e-168, 1.18e-402j)
| (0.012341036743853272033 + 6.319068799289942561e-1703j)  +/-  (1.34e-170, 7.77e-405j)
| (0.010408898999189713492 - 8.7980308745830727903e-1703j)  +/-  (5.12e-169, 2.98e-403j)
| (0.011577519946309202778 - 7.8690541526247120124e-1703j)  +/-  (4.72e-171, 2.74e-405j)
| (0.011792363833124362096 - 5.2685879357117841623e-1703j)  +/-  (4.75e-171, 2.76e-405j)
| (0.011051806601967649956 + 4.6691472487204555801e-1703j)  +/-  (2.15e-170, 1.25e-404j)
| (0.012229971053255460981 + 5.8922336998155130743e-1703j)  +/-  (1.36e-171, 7.9e-406j)
| (0.011792363833124362096 + 7.6424902128331297556e-1703j)  +/-  (1.82e-172, 1.06e-406j)
| (0.010744098846351880126 + 8.5616500162024540352e-1703j)  +/-  (2.18e-171, 1.27e-405j)
| (0.012303940479888536966 - 6.1046476107223780157e-1703j)  +/-  (4.98e-172, 2.89e-406j)
| (0.011330171675388496418 - 4.8659441097222787114e-1703j)  +/-  (3.43e-172, 1.99e-406j)
| (0.011577519946309202778 + 5.0658257656077760543e-1703j)  +/-  (2.57e-172, 1.49e-406j)
| (0.012303940479888536966 + 6.753444408011421001e-1703j)  +/-  (1.85e-173, 1.07e-407j)
| (0.011330171675388496418 + 8.0975821820676138219e-1703j)  +/-  (5.34e-174, 3.15e-408j)
| (0.011973411239419187556 - 7.4177203716275396252e-1703j)  +/-  (5.55e-174, 3.2e-408j)
