Starting with polynomial:
P : t
Extension levels are: 1 78
-------------------------------------------------
Trying to find an order 78 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^79 - 79/4*t^77 + 1501/8*t^75 - 73075/64*t^73 + 640137/128*t^71 - 8598597/512*t^69 + 46055499/1024*t^67 - 1616328703/16384*t^65 + 1479737545/8192*t^63 - 9174372779/32768*t^61 + 24332032153/65536*t^59 - 222631588309/524288*t^57 + 441940317091/1048576*t^55 - 1529793405315/4194304*t^53 + 2316544299477/8388608*t^51 - 196906265455545/1073741824*t^49 + 459447952729605/4294967296*t^47 - 942434984631315/17179869184*t^45 + 849736461552825/34359738368*t^43 - 2692322893972635/274877906944*t^41 + 1870936248353865/549755813888*t^39 - 2276459376075885/2199023255552*t^37 + 1209028663848915/4398046511104*t^35 - 4468149409876425/70368744177664*t^33 + 893629881975285/70368744177664*t^31 - 615611696471863/281474976710656*t^29 + 181377611587501/562949953421312*t^27 - 181377611587501/4503599627370496*t^25 + 38104540249475/9007199254740992*t^23 - 13297170597403/36028797018963968*t^21 + 1899595799629/72057594037927936*t^19 - 3492805179963/2305843009213693952*t^17 + 1263355065093/18446744073709551616*t^15 - 174772439835/73786976294838206464*t^13 + 8909967521/147573952589676412928*t^11 - 1272852503/1180591620717411303424*t^9 + 29601221/2361183241434822606848*t^7 - 800033/9444732965739290427392*t^5 + 5135/18889465931478580854784*t^3 - 79/302231454903657293676544*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:   79 out of 79
Indefinite weights: 0 out of 79
Negative weights:   0 out of 79
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.97617631441905084005 + 4.2558803686021503649e-1674j)  +/-  (8.46e-482, 8.46e-482j)
| (-0.95585146140576079687 - 1.7727080171094066627e-1672j)  +/-  (3.94e-482, 3.94e-482j)
| (-0.91408381135403463748 - 2.6705795138886375404e-1693j)  +/-  (5.02e-483, 5.02e-483j)
| (-0.99822143678193302316 + 6.3095753729773351148e-1717j)  +/-  (7.64e-482, 7.64e-482j)
| (0.89723886061921225575 - 8.5406246483337574862e-1749j)  +/-  (2.14e-483, 2.14e-483j)
| (0.94341329972213454557 + 1.2176086326557750766e-1746j)  +/-  (2.28e-482, 2.28e-482j)
| (0.99032946647250187999 - 1.4192551296624152014e-1745j)  +/-  (1.2e-481, 1.2e-481j)
| (-0.89723886061921225575 - 8.0397989366205032674e-1747j)  +/-  (2.21e-483, 2.21e-483j)
| (-0.99980232977006556464 - 1.4779640608732058718e-1758j)  +/-  (2.66e-482, 2.66e-482j)
| (-0.99032946647250187999 + 8.6464020457529028281e-1788j)  +/-  (1.16e-481, 1.16e-481j)
| (0.87897519082243374142 - 8.3201950819388467073e-1805j)  +/-  (8.19e-484, 8.19e-484j)
| (0.98403086797842065357 + 9.9972775268246502512e-1801j)  +/-  (1.09e-481, 1.09e-481j)
| (-0.92948340769738705843 - 6.920628970204671423e-1801j)  +/-  (1.11e-482, 1.11e-482j)
| (-0.83830940613027654749 + 4.4968400114602374e-1811j)  +/-  (7.41e-485, 7.41e-485j)
| (0.99822143678193302316 + 5.5797524801835305019e-1808j)  +/-  (7.81e-482, 7.81e-482j)
| (0.85932168057966104712 + 1.8487872602841265501e-1811j)  +/-  (2.85e-484, 2.85e-484j)
| (0.91408381135403463748 + 6.1454671955799631574e-1810j)  +/-  (5.21e-483, 5.21e-483j)
| (0.99506215052242745345 - 7.4940099663750944685e-1809j)  +/-  (1.1e-481, 1.1e-481j)
| (-0.76746266869390795472 - 2.6677501586731149783e-1813j)  +/-  (1.14e-486, 1.14e-486j)
| (-0.94341329972213454557 + 3.1113837461287610155e-1808j)  +/-  (2.2e-482, 2.2e-482j)
| (0.92948340769738705843 + 5.4933360149361281095e-1818j)  +/-  (1.14e-482, 1.14e-482j)
| (0.74136826169861817122 + 5.7247900900634988345e-1824j)  +/-  (2.47e-487, 2.47e-487j)
| (0.99980232977006556464 + 2.2358553048555464769e-1817j)  +/-  (2.76e-482, 2.76e-482j)
| (-0.85932168057966104712 + 1.9229968978735284742e-1817j)  +/-  (2.78e-484, 2.78e-484j)
| (-0.79234355946157430788 + 1.1582203595619475042e-1820j)  +/-  (5.1e-486, 5.1e-486j)
| (0.19752739717795267046 - 7.4533393385639417246e-1840j)  +/-  (5.42e-504, 5.42e-504j)
| (0.76746266869390795472 - 5.6799975966531022454e-1823j)  +/-  (1.16e-486, 1.16e-486j)
| (0.79234355946157430788 + 3.4422243366715564697e-1822j)  +/-  (5.26e-486, 5.26e-486j)
| (0.96677822545803712702 - 8.3376090276449225024e-1818j)  +/-  (5.92e-482, 5.92e-482j)
| (-0.6562257492703756164 - 5.2253531279290785558e-1825j)  +/-  (9.98e-490, 9.98e-490j)
| (-0.87897519082243374142 + 2.0793238401426542511e-1816j)  +/-  (7.8e-484, 7.8e-484j)
| (0.81597159219916099773 + 2.3330975612898075748e-1838j)  +/-  (2.29e-485, 2.29e-485j)
| (0.6562257492703756164 + 2.2816670789900753421e-1843j)  +/-  (1.02e-489, 1.02e-489j)
| (-0.98403086797842065357 - 2.504666148050107132e-1832j)  +/-  (1.04e-481, 1.04e-481j)
| (-0.71410159909674973691 + 4.218997879837939122e-1865j)  +/-  (5e-488, 5e-488j)
| (-0.74136826169861817122 + 4.408953129977202849e-1864j)  +/-  (2.76e-487, 2.76e-487j)
| (0.95585146140576079687 + 2.7486751045556550144e-1860j)  +/-  (3.81e-482, 3.81e-482j)
| (0.62570807566055991493 + 2.1480711915573370019e-1868j)  +/-  (1.37e-490, 1.37e-490j)
| (0.83830940613027654749 + 1.1286183207580731039e-1862j)  +/-  (7.56e-485, 7.56e-485j)
| (-0.97617631441905084005 - 4.1242557350383468043e-1857j)  +/-  (8.58e-482, 8.58e-482j)
| (-0.59420102897171050501 - 1.1676711213881729036e-1889j)  +/-  (1.83e-491, 1.83e-491j)
| (-0.99506215052242745345 - 7.9677595815481539051e-1882j)  +/-  (1.04e-481, 1.04e-481j)
| (0.56175442832077085463 - 5.6124172602417280386e-1910j)  +/-  (2.29e-492, 2.29e-492j)
| (0.59420102897171050501 + 1.9868659494239639934e-1910j)  +/-  (1.73e-491, 1.73e-491j)
| (-0.81597159219916099773 + 2.1209774154130818199e-1903j)  +/-  (2.2e-485, 2.2e-485j)
| (-0.56175442832077085463 + 4.8667218530318188005e-1913j)  +/-  (2.16e-492, 2.16e-492j)
| (-0.68570579508641317533 + 2.9081668916912954435e-1908j)  +/-  (6.37e-489, 6.37e-489j)
| (-0.96677822545803712702 + 3.8406230817262836764e-1912j)  +/-  (6.15e-482, 6.15e-482j)
| (0.49424918861672287801 + 8.1901250207082581931e-1933j)  +/-  (1.47e-494, 1.47e-494j)
| (0.71410159909674973691 + 2.8370812905422072639e-1925j)  +/-  (5.38e-488, 5.38e-488j)
| (-0.62570807566055991493 - 1.0836857649461266106e-1930j)  +/-  (1.33e-490, 1.33e-490j)
| (-0.45929728922297789714 + 7.1308347418138568542e-1936j)  +/-  (1.49e-495, 1.49e-495j)
| (-0.1190181918019047783 - 1.0571963341879347476e-1946j)  +/-  (1.02e-506, 1.02e-506j)
| (0.45929728922297789714 + 1.072161083975585823e-1934j)  +/-  (1.5e-495, 1.5e-495j)
| (0.5284195784526194879 + 3.6814879806360934389e-1933j)  +/-  (2.46e-493, 2.46e-493j)
| (-0.15839802440721497568 + 3.2429527388115188396e-1945j)  +/-  (2.28e-505, 2.28e-505j)
| (-0.49424918861672287801 - 6.702368212672265106e-1935j)  +/-  (1.49e-494, 1.49e-494j)
| (-0.5284195784526194879 - 1.3278478875332852222e-1934j)  +/-  (2.47e-493, 2.47e-493j)
| (0.68570579508641317533 + 2.7180572216895308336e-1940j)  +/-  (6.56e-489, 6.56e-489j)
| (0.4236191464085280675 - 1.5962111466101983929e-1948j)  +/-  (1.25e-496, 1.25e-496j)
| (0.15839802440721497568 + 2.4656930590885550298e-1957j)  +/-  (2.21e-505, 2.21e-505j)
| (-0.4236191464085280675 - 1.7571043212932076487e-1947j)  +/-  (1.27e-496, 1.27e-496j)
| (-0.38727117465064103737 + 4.5034398234338271296e-1949j)  +/-  (8.89e-498, 8.89e-498j)
| (0.039756515096925630625 + 1.0551175316619982781e-1960j)  +/-  (1.61e-509, 1.61e-509j)
| (0.35031084756382428487 + 4.0284590179292722831e-1951j)  +/-  (4.71e-499, 4.71e-499j)
| (0.38727117465064103737 - 2.1359631530292508195e-1949j)  +/-  (8.54e-498, 8.54e-498j)
| (3.7934347310887670526e-1996 - 5.404790539078556375e-1997j)  +/-  (3.03e-1994, 3.03e-1994j)
| (-0.35031084756382428487 + 3.5966628417941314685e-1950j)  +/-  (4.83e-499, 4.83e-499j)
| (-0.19752739717795267046 - 8.0489452252523229659e-1955j)  +/-  (5.45e-504, 5.45e-504j)
| (0.1190181918019047783 - 7.3662500888579930336e-1958j)  +/-  (9.87e-507, 9.87e-507j)
| (0.31279660702222714473 - 3.0171835963164455405e-1952j)  +/-  (3.27e-500, 3.27e-500j)
| (0.079450166971714371773 - 8.0046718126574773751e-1959j)  +/-  (6.83e-508, 6.83e-508j)
| (-0.23634443853290489424 - 2.4329472931002648996e-1953j)  +/-  (1.06e-502, 1.06e-502j)
| (-0.31279660702222714473 + 3.127017528382796606e-1951j)  +/-  (3.47e-500, 3.47e-500j)
| (-0.039756515096925630625 + 4.5219847654993566312e-1960j)  +/-  (1.36e-509, 1.36e-509j)
| (0.27478777075102532008 - 1.0477107033525445988e-1952j)  +/-  (2.18e-501, 2.18e-501j)
| (0.23634443853290489424 + 5.2651076550474316527e-1954j)  +/-  (1.06e-502, 1.06e-502j)
| (-0.079450166971714371773 - 7.0254702386498489135e-1960j)  +/-  (5.84e-508, 5.84e-508j)
| (-0.27478777075102532008 - 1.2838783936824924085e-1952j)  +/-  (2.25e-501, 2.25e-501j)
-------------------------------------------------
The weights are:
| (0.012658227848101265823 - 1.4161098834934685988e-1674j)  +/-  (4.97e-141, 8.63e-374j)
| (0.012658227848101265823 - 1.2457668823174942625e-1673j)  +/-  (2.17e-141, 3.78e-374j)
| (0.012658227848101265823 + 7.4194864600474749692e-1673j)  +/-  (1.69e-141, 2.93e-374j)
| (0.012658227848101265823 + 1.0736905766403086827e-1673j)  +/-  (2.58e-142, 4.48e-375j)
| (0.012658227848101265823 - 3.2083378309399551704e-1674j)  +/-  (2.08e-142, 3.61e-375j)
| (0.012658227848101265823 + 3.8463806779239575154e-1674j)  +/-  (3.04e-142, 5.29e-375j)
| (0.012658227848101265823 + 1.8894071071522037509e-1674j)  +/-  (5.99e-143, 1.04e-375j)
| (0.012658227848101265823 - 5.7585088330596684522e-1673j)  +/-  (1.28e-142, 2.22e-375j)
| (0.012658227848101265823 - 3.4519662350148850382e-1674j)  +/-  (7.85e-143, 1.36e-375j)
| (0.012658227848101265823 + 3.0710151182073651268e-1673j)  +/-  (3.02e-143, 5.24e-376j)
| (0.012658227848101265823 + 3.2027304227481217953e-1674j)  +/-  (6.35e-144, 1.1e-376j)
| (0.012658227848101265823 - 4.9258144305522640434e-1674j)  +/-  (2.04e-143, 3.55e-376j)
| (0.012658227848101265823 - 1.0687286702111551628e-1672j)  +/-  (8.68e-144, 1.51e-376j)
| (0.012658227848101265823 + 3.5494100194381255084e-1673j)  +/-  (4.12e-146, 7.16e-379j)
| (0.012658227848101265823 + 4.3844191796658621885e-1675j)  +/-  (1.03e-144, 1.78e-377j)
| (0.012658227848101265823 - 3.2382271769583715175e-1674j)  +/-  (7.21e-146, 1.25e-378j)
| (0.012658227848101265823 + 3.2775831324300541206e-1674j)  +/-  (3.26e-145, 5.67e-378j)
| (0.012658227848101265823 - 9.1633410533888706849e-1675j)  +/-  (1.1e-144, 1.91e-377j)
| (0.012658227848101265823 - 2.6077944604232173927e-1673j)  +/-  (2.89e-150, 5.03e-383j)
| (0.012658227848101265823 + 2.0363811754653475123e-1672j)  +/-  (3.03e-147, 5.26e-380j)
| (0.012658227848101265823 - 3.4554115575236338617e-1674j)  +/-  (1.11e-145, 1.93e-378j)
| (0.012658227848101265823 + 3.7290876430408427944e-1674j)  +/-  (1.88e-150, 3.26e-383j)
| (0.012658227848101265823 - 1.3130384423869092703e-1675j)  +/-  (2.95e-145, 5.12e-378j)
| (0.012658227848101265823 - 4.0528031626275605127e-1673j)  +/-  (2.41e-149, 4.19e-382j)
| (0.012658227848101265823 + 2.8578020079649302018e-1673j)  +/-  (1.53e-150, 2.66e-383j)
| (0.012658227848101265823 + 6.8029561177336242028e-1674j)  +/-  (1.84e-154, 3.2e-387j)
| (0.012658227848101265823 - 3.6034355092816852725e-1674j)  +/-  (2.28e-150, 3.96e-383j)
| (0.012658227848101265823 + 3.4888375423411411406e-1674j)  +/-  (3.34e-150, 5.79e-383j)
| (0.012658227848101265823 + 7.768226409205032017e-1674j)  +/-  (6.44e-147, 1.12e-379j)
| (0.012658227848101265823 - 1.9345744499838091807e-1673j)  +/-  (2.91e-155, 5.06e-388j)
| (0.012658227848101265823 + 4.7432299608359819058e-1673j)  +/-  (5.46e-151, 9.48e-384j)
| (0.012658227848101265823 - 3.3874131597396748723e-1674j)  +/-  (2.38e-150, 4.13e-383j)
| (0.012658227848101265823 - 4.1598724387940955733e-1674j)  +/-  (1.12e-154, 1.94e-387j)
| (0.012658227848101265823 - 4.8212983173786603305e-1673j)  +/-  (1.51e-152, 2.62e-385j)
| (0.012658227848101265823 - 2.2215535594265607081e-1673j)  +/-  (3.62e-155, 6.29e-388j)
| (0.012658227848101265823 + 2.3990356763286998893e-1673j)  +/-  (1.77e-154, 3.08e-387j)
| (0.012658227848101265823 - 4.7633685537727092515e-1674j)  +/-  (9.41e-149, 1.64e-381j)
| (0.012658227848101265823 + 4.3190025663609538815e-1674j)  +/-  (1.87e-156, 3.25e-389j)
| (0.012658227848101265823 + 3.302292036264233226e-1674j)  +/-  (7.06e-151, 1.23e-383j)
| (0.012658227848101265823 + 8.1494237159440896141e-1673j)  +/-  (1.22e-153, 2.12e-386j)
| (0.012658227848101265823 - 1.7110463565742733346e-1673j)  +/-  (6.64e-160, 1.15e-392j)
| (0.012658227848101265823 - 1.9317268486659641215e-1673j)  +/-  (2.73e-153, 4.74e-386j)
| (0.012658227848101265823 + 4.6584854463426866157e-1674j)  +/-  (8.35e-160, 1.45e-392j)
| (0.012658227848101265823 - 4.4852589825737440371e-1674j)  +/-  (7.5e-159, 1.3e-391j)
| (0.012658227848101265823 - 3.1639271651264811623e-1673j)  +/-  (1.04e-155, 1.8e-388j)
| (0.012658227848101265823 + 1.616401936278395576e-1673j)  +/-  (1e-161, 1.74e-394j)
| (0.012658227848101265823 + 2.0683992115517392229e-1673j)  +/-  (1.29e-158, 2.25e-391j)
| (0.012658227848101265823 - 1.7860850846587374861e-1672j)  +/-  (7.69e-155, 1.34e-387j)
| (0.012658227848101265823 + 5.0257546264568511963e-1674j)  +/-  (1.94e-163, 3.36e-396j)
| (0.012658227848101265823 - 3.8643335518053689734e-1674j)  +/-  (5.22e-159, 9.08e-392j)
| (0.012658227848101265823 + 1.81638697201704736e-1673j)  +/-  (1.9e-160, 3.29e-393j)
| (0.012658227848101265823 - 1.3814200070115891115e-1673j)  +/-  (2.9e-165, 5.04e-398j)
| (0.012658227848101265823 + 9.2854845998192784572e-1674j)  +/-  (8.18e-169, 1.42e-401j)
| (0.012658227848101265823 - 5.21996804686037665e-1674j)  +/-  (3.14e-165, 5.45e-398j)
| (0.012658227848101265823 - 4.8386355073098002238e-1674j)  +/-  (1.96e-163, 3.4e-396j)
| (0.012658227848101265823 - 9.6710574479392227471e-1674j)  +/-  (3.99e-169, 6.94e-402j)
| (0.012658227848101265823 + 1.4528010231644482006e-1673j)  +/-  (1.08e-165, 1.88e-398j)
| (0.012658227848101265823 - 1.530767512482697395e-1673j)  +/-  (6.68e-165, 1.16e-397j)
| (0.012658227848101265823 + 4.0081607159733106997e-1674j)  +/-  (4.96e-163, 8.62e-396j)
| (0.012658227848101265823 + 5.4214728295557998118e-1674j)  +/-  (9.2e-168, 1.6e-400j)
| (0.012658227848101265823 - 7.0665804050269963342e-1674j)  +/-  (4.09e-171, 7.1e-404j)
| (0.012658227848101265823 + 1.3157409886806980373e-1673j)  +/-  (1.29e-168, 2.23e-401j)
| (0.012658227848101265823 - 1.2550352167663921944e-1673j)  +/-  (1.19e-169, 2.07e-402j)
| (0.012658227848101265823 + 7.9288709861242102379e-1674j)  +/-  (5.66e-173, 9.84e-406j)
| (0.012658227848101265823 + 5.8474772609439158073e-1674j)  +/-  (3.25e-171, 5.65e-404j)
| (0.012658227848101265823 - 5.6305330190306568497e-1674j)  +/-  (2.29e-170, 3.98e-403j)
| (0.012658227848101265823 - 8.2433630533252538142e-1674j)  +/-  (7.97e-174, 1.38e-406j)
| (0.012658227848101265823 + 1.198695810069906818e-1673j)  +/-  (1.15e-172, 2e-405j)
| (0.012658227848101265823 + 1.007895711116196945e-1673j)  +/-  (5.57e-174, 9.68e-407j)
| (0.012658227848101265823 + 7.3415137589436263357e-1674j)  +/-  (4.13e-174, 7.18e-407j)
| (0.012658227848101265823 - 6.0726984358773984423e-1674j)  +/-  (8.95e-174, 1.55e-406j)
| (0.012658227848101265823 - 7.6286198017514122951e-1674j)  +/-  (2.68e-174, 4.65e-407j)
| (0.012658227848101265823 - 1.0511547438648986686e-1673j)  +/-  (2.58e-175, 4.48e-408j)
| (0.012658227848101265823 - 1.1462130096873595359e-1673j)  +/-  (4.35e-175, 7.55e-408j)
| (0.012658227848101265823 + 8.5733325091783682313e-1674j)  +/-  (9.34e-176, 1.62e-408j)
| (0.012658227848101265823 + 6.3066550418939788867e-1674j)  +/-  (9.21e-176, 1.6e-408j)
| (0.012658227848101265823 - 6.5498741829759910353e-1674j)  +/-  (7.22e-176, 1.25e-408j)
| (0.012658227848101265823 - 8.9201777432325972161e-1674j)  +/-  (1.86e-176, 3.26e-409j)
| (0.012658227848101265823 + 1.0971552866525059574e-1673j)  +/-  (1.62e-176, 2.77e-409j)
