Starting with polynomial:
P : t
Extension levels are: 1 6 70
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 70 Kronrod extension for:
P2 : t^7 - 7/4*t^5 + 7/8*t^3 - 7/64*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^77 - 77/4*t^75 + 2849/16*t^73 - 16863/16*t^71 + 574035/128*t^69 - 14963179/1024*t^67 + 155322013/4096*t^65 - 41207881/512*t^63 + 1166362197/8192*t^61 - 6975303335/32768*t^59 + 35626101511/131072*t^57 - 39159268603/131072*t^55 + 298212891669/1048576*t^53 - 15805283258457/67108864*t^51 + 45695546835675/268435456*t^49 - 14445688999665/134217728*t^47 + 255996554239965/4294967296*t^45 - 496934487642285/17179869184*t^43 + 845069382939705/68719476736*t^41 - 314408754088275/68719476736*t^39 + 817462760629515/549755813888*t^37 - 1851803396528085/4398046511104*t^35 + 1821195075924315/17592186044416*t^33 - 96778482295495/4398046511104*t^31 + 283031410486825/70368744177664*t^29 - 176785773319463/281474976710656*t^27 + 93592468227951/1125899906842624*t^25 - 10399163136439/1125899906842624*t^23 + 7670519747869/9007199254740992*t^21 - 9257523833635/144115188075855872*t^19 + 2245441951137/576460752303423488*t^17 - 53537886633/288230376151711744*t^15 + 124921735477/18446744073709551616*t^13 - 13421343481/73786976294838206464*t^11 + 1009813805/295147905179352825856*t^9 - 12365067/295147905179352825856*t^7 + 703703/2361183241434822606848*t^5 - 19019/18889465931478580854784*t^3 + 77/75557863725914323419136*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:
| (0.99480253285700401983 + 3.8906544976489383304e-1789j)  +/-  (1.96e-482, 1.96e-482j)
| (-0.89193080800269382063 - 6.3336589961378216081e-1790j)  +/-  (3.19e-484, 3.19e-484j)
| (-0.9258191900208980879 - 1.4094758332319648852e-1821j)  +/-  (1.81e-483, 1.81e-483j)
| (-0.99480253285700401983 + 8.680097796875719766e-1846j)  +/-  (1.92e-482, 1.92e-482j)
| (0.95354639807892763896 - 1.5625450298927764324e-1874j)  +/-  (6.71e-483, 6.71e-483j)
| (0.94046545001381151853 - 3.4997399969529980838e-1876j)  +/-  (3.54e-483, 3.54e-483j)
| (0.85210677361545651595 + 3.234818782383706217e-1880j)  +/-  (3.91e-485, 3.91e-485j)
| (-0.90963199535451837141 + 7.4686579409960632904e-1876j)  +/-  (8.44e-484, 8.44e-484j)
| (0.96504026226913991517 + 2.5829956047446245951e-1886j)  +/-  (1.03e-482, 1.03e-482j)
| (-0.99812787319336687828 + 3.1686454913518311159e-1892j)  +/-  (1.42e-482, 1.42e-482j)
| (0.87274508984485613497 + 1.5593547534926080293e-1919j)  +/-  (1.14e-484, 1.14e-484j)
| (-0.99979192818920649537 - 1.3271480603592146229e-1914j)  +/-  (5.12e-483, 5.12e-483j)
| (-0.94046545001381151853 + 5.1356222316841290912e-1929j)  +/-  (3.5e-483, 3.5e-483j)
| (-0.87274508984485613497 - 4.2282649643588039914e-1936j)  +/-  (1.17e-484, 1.17e-484j)
| (0.99812787319336687828 + 6.6987797460276298609e-1934j)  +/-  (1.4e-482, 1.4e-482j)
| (0.8066121092375300603 - 2.8614221566712580387e-1939j)  +/-  (3.03e-486, 3.03e-486j)
| (0.90963199535451837141 - 1.8576572643340058705e-1936j)  +/-  (7.94e-484, 7.94e-484j)
| (-0.98319289079950297361 + 8.3118863097330942081e-1933j)  +/-  (1.91e-482, 1.91e-482j)
| (-0.8066121092375300603 - 2.6460297180527122649e-1945j)  +/-  (2.77e-486, 2.77e-486j)
| (-0.95354639807892763896 - 7.9488965845406434458e-1940j)  +/-  (6.47e-483, 6.47e-483j)
| (0.98982144188093273238 - 1.8666551821243951861e-1954j)  +/-  (1.99e-482, 1.99e-482j)
| (0.78183148246802980871 + 3.6681773262484313723e-1959j)  +/-  (6.65e-487, 6.65e-487j)
| (0.97492791218182360702 - 1.3682786430138874523e-1955j)  +/-  (1.53e-482, 1.53e-482j)
| (-0.83005020975508058805 + 1.6355327029818764468e-1955j)  +/-  (1.06e-485, 1.06e-485j)
| (-0.78183148246802980871 - 1.0008688916322746131e-1958j)  +/-  (6.36e-487, 6.36e-487j)
| (0.89193080800269382063 + 7.4342189932534991267e-1957j)  +/-  (3.16e-484, 3.16e-484j)
| (0.75574957435425828377 - 5.4738836133601057581e-1961j)  +/-  (1.47e-487, 1.47e-487j)
| (0.83005020975508058805 - 6.0789020856934055865e-1958j)  +/-  (1.03e-485, 1.03e-485j)
| (0.99979192818920649537 - 6.4673953369412696621e-1956j)  +/-  (5.19e-483, 5.19e-483j)
| (-0.63930828993555148636 - 1.6297803085360058408e-1963j)  +/-  (1.12e-490, 1.12e-490j)
| (-0.96504026226913991517 - 8.6857123294878672375e-1953j)  +/-  (1.02e-482, 1.02e-482j)
| (0.9258191900208980879 + 1.4434061495100037594e-1982j)  +/-  (1.86e-483, 1.86e-483j)
| (0.6701406618375595239 - 1.2248114685637787615e-1988j)  +/-  (6.65e-490, 6.65e-490j)
| (-0.98982144188093273238 - 6.8642726620138283762e-1981j)  +/-  (2.21e-482, 2.21e-482j)
| (-0.75574957435425828377 - 1.0421460008015576867e-2011j)  +/-  (1.45e-487, 1.45e-487j)
| (-0.72840979565826910527 + 1.1746623025762615938e-2014j)  +/-  (2.98e-488, 2.98e-488j)
| (0.98319289079950297361 + 1.0820597765100552432e-2009j)  +/-  (1.77e-482, 1.77e-482j)
| (0.57450443793646331994 - 2.727873751746787222e-2021j)  +/-  (1.76e-492, 1.76e-492j)
| (0.72840979565826910527 + 3.6850818448465791313e-2017j)  +/-  (2.95e-488, 2.95e-488j)
| (-0.97492791218182360702 + 2.044142426848175407e-2018j)  +/-  (1.41e-482, 1.41e-482j)
| (-0.57450443793646331994 + 1.1737466264059865096e-2039j)  +/-  (1.73e-492, 1.73e-492j)
| (-0.12209431687415986496 + 1.0083496979384591939e-2052j)  +/-  (9.24e-507, 9.24e-507j)
| (0.63930828993555148636 + 8.7715011222973768724e-2037j)  +/-  (1.12e-490, 1.12e-490j)
| (0.60741185247774751451 - 8.2206329708742536481e-2038j)  +/-  (1.35e-491, 1.35e-491j)
| (-0.54064081745559758211 - 1.0844378537741462672e-2038j)  +/-  (1.95e-493, 1.95e-493j)
| (-0.60741185247774751451 - 7.3474313095574598471e-2036j)  +/-  (1.49e-491, 1.49e-491j)
| (-0.6701406618375595239 + 1.500537683680093899e-2034j)  +/-  (6.41e-490, 6.41e-490j)
| (0.69985765074356179589 - 1.0763666858746919811e-2035j)  +/-  (3.99e-489, 3.99e-489j)
| (0.47027190699273680067 + 8.6524237748168137589e-2042j)  +/-  (1.25e-495, 1.25e-495j)
| (0.24236173709321233675 + 2.7342747263661552341e-2048j)  +/-  (9.35e-503, 9.35e-503j)
| (-0.69985765074356179589 + 4.0645793984825622469e-2036j)  +/-  (4.01e-489, 4.01e-489j)
| (-0.50587735368946824748 + 8.1254943340885233918e-2042j)  +/-  (2.12e-494, 2.12e-494j)
| (-0.85210677361545651595 - 1.9657703295014721108e-2049j)  +/-  (3.95e-485, 3.95e-485j)
| (0.54064081745559758211 - 2.5387818513816979927e-2059j)  +/-  (1.96e-493, 1.96e-493j)
| (0.50587735368946824748 - 7.1882605889809635909e-2063j)  +/-  (2.12e-494, 2.12e-494j)
| (-0.081509283547063164483 - 2.3561253518822578907e-2075j)  +/-  (6.07e-508, 6.07e-508j)
| (-0.47027190699273680067 - 3.1726163579513255333e-2062j)  +/-  (1.32e-495, 1.32e-495j)
| (-0.43388373911755812048 + 4.9637439030023167685e-2065j)  +/-  (1.09e-496, 1.09e-496j)
| (0.12209431687415986496 - 1.6412283240616933803e-2074j)  +/-  (9.53e-507, 9.53e-507j)
| (0.43388373911755812048 + 1.2020561642772377377e-2066j)  +/-  (1.06e-496, 1.06e-496j)
| (0.081509283547063164483 + 1.5556163489391198114e-2075j)  +/-  (5.89e-508, 5.89e-508j)
| (-0.39677341457824251103 - 1.4339675662937901565e-2065j)  +/-  (8.1e-498, 8.1e-498j)
| (-0.35900269984759869364 + 1.1390349413222929807e-2066j)  +/-  (6.55e-499, 6.55e-499j)
| (-0.040788586061585571552 - 6.2402259626892753721e-2077j)  +/-  (1.32e-509, 1.32e-509j)
| (0.39677341457824251103 + 3.3997694470100462613e-2067j)  +/-  (7.55e-498, 7.55e-498j)
| (0.35900269984759869364 + 1.0946701245188949017e-2067j)  +/-  (6.18e-499, 6.18e-499j)
| (-0.16247613626020580153 - 6.0794802423787720897e-2073j)  +/-  (2.11e-505, 2.11e-505j)
| (-0.32063446055273549838 + 1.2647257336107792993e-2068j)  +/-  (3.55e-500, 3.55e-500j)
| (-0.20258753015208096744 + 1.6995801580976747451e-2071j)  +/-  (6.08e-504, 6.08e-504j)
| (0.20258753015208096744 - 4.3356400795815294539e-2072j)  +/-  (5.84e-504, 5.84e-504j)
| (0.32063446055273549838 + 3.6602237608971138564e-2069j)  +/-  (3.46e-500, 3.46e-500j)
| (5.6252913505541695539e-2116 + 2.9724336903478896043e-2116j)  +/-  (4.9e-2114, 4.9e-2114j)
| (-0.24236173709321233675 - 2.1946820758326317447e-2070j)  +/-  (9.69e-503, 9.69e-503j)
| (-0.28173255684142969771 - 6.9733242905262325918e-2070j)  +/-  (2.28e-501, 2.28e-501j)
| (0.040788586061585571552 + 4.7189360234233999348e-2077j)  +/-  (1.37e-509, 1.37e-509j)
| (0.28173255684142969771 + 9.8610269433890750502e-2071j)  +/-  (2.15e-501, 2.15e-501j)
| (0.16247613626020580153 - 1.0593786412449467974e-2073j)  +/-  (2.19e-505, 2.19e-505j)
-------------------------------------------------
The weights are:
| (0.012987012987012987013 - 2.4230994641418727077e-1789j)  +/-  (9.26e-140, 6.96e-374j)
| (0.012987012987012987013 + 1.0098517574450577858e-1790j)  +/-  (4.42e-140, 3.32e-374j)
| (0.012987012987012987013 + 3.0054688808915334278e-1790j)  +/-  (3.69e-140, 2.77e-374j)
| (0.012987012987012987013 - 4.3401692313412934376e-1791j)  +/-  (4.93e-141, 3.7e-375j)
| (0.012987012987012987013 + 3.620454379873102242e-1789j)  +/-  (2.61e-141, 1.96e-375j)
| (0.012987012987012987013 - 3.100665565938327774e-1789j)  +/-  (1.61e-141, 1.21e-375j)
| (0.012987012987012987013 + 1.8145863033870126877e-1789j)  +/-  (1.61e-142, 1.21e-376j)
| (0.012987012987012987013 - 5.3515737671872624748e-1790j)  +/-  (1.22e-141, 9.18e-376j)
| (0.012987012987012987013 - 4.3675171453585586628e-1789j)  +/-  (8.34e-142, 6.27e-376j)
| (0.012987012987012987013 + 2.5705828444996652324e-1791j)  +/-  (5.89e-143, 4.42e-377j)
| (0.012987012987012987013 - 1.9796839938943011463e-1789j)  +/-  (1.17e-143, 8.76e-378j)
| (0.012987012987012987013 - 8.5152209689367580165e-1792j)  +/-  (3.38e-143, 2.54e-377j)
| (0.012987012987012987013 - 2.1454616947997847823e-1790j)  +/-  (1.18e-143, 8.88e-378j)
| (0.012987012987012987013 + 3.3315463340730384576e-1790j)  +/-  (2.59e-144, 1.94e-378j)
| (0.012987012987012987013 - 9.1276144669337825014e-1789j)  +/-  (2.23e-145, 1.68e-379j)
| (0.012987012987012987013 + 1.5522732416368069179e-1789j)  +/-  (3.77e-146, 2.83e-380j)
| (0.012987012987012987013 - 2.4161594766033868202e-1789j)  +/-  (7.65e-145, 5.75e-379j)
| (0.012987012987012987013 - 8.2193985555670289979e-1791j)  +/-  (3.73e-145, 2.8e-379j)
| (0.012987012987012987013 + 3.6797512918371864158e-1791j)  +/-  (2.32e-147, 1.75e-381j)
| (0.012987012987012987013 + 1.6566452540759834809e-1790j)  +/-  (4.68e-145, 3.52e-379j)
| (0.012987012987012987013 + 1.4176521276377111231e-1788j)  +/-  (6.73e-146, 5.06e-380j)
| (0.012987012987012987013 - 1.4459870492630911647e-1789j)  +/-  (2.23e-148, 1.68e-382j)
| (0.012987012987012987013 + 5.5537792126064997504e-1789j)  +/-  (7.93e-146, 5.96e-380j)
| (0.012987012987012987013 + 1.2292131929244394179e-1791j)  +/-  (6.87e-148, 5.16e-382j)
| (0.012987012987012987013 - 7.1131506555421015964e-1791j)  +/-  (3.9e-149, 2.93e-383j)
| (0.012987012987012987013 + 2.1765797525179749207e-1789j)  +/-  (5.77e-147, 4.33e-381j)
| (0.012987012987012987013 + 1.3521502216724980258e-1789j)  +/-  (3.68e-150, 2.77e-384j)
| (0.012987012987012987013 - 1.6738652233438754296e-1789j)  +/-  (3.84e-148, 2.88e-382j)
| (0.012987012987012987013 + 2.0289867439985629955e-1789j)  +/-  (2.28e-147, 1.72e-381j)
| (0.012987012987012987013 + 1.7813711059523122158e-1790j)  +/-  (4.76e-155, 3.58e-389j)
| (0.012987012987012987013 - 1.3158069815912950666e-1790j)  +/-  (5.9e-150, 4.43e-384j)
| (0.012987012987012987013 + 2.715131133463140925e-1789j)  +/-  (1.79e-147, 1.35e-381j)
| (0.012987012987012987013 - 1.1258333972421414086e-1789j)  +/-  (5.3e-154, 3.98e-388j)
| (0.012987012987012987013 + 6.2030843758491769046e-1791j)  +/-  (4.63e-150, 3.48e-384j)
| (0.012987012987012987013 + 9.8158432386637517213e-1791j)  +/-  (2.6e-153, 1.95e-387j)
| (0.012987012987012987013 - 1.2108059409051936481e-1790j)  +/-  (2.91e-154, 2.18e-388j)
| (0.012987012987012987013 - 7.8018516208362259093e-1789j)  +/-  (2.64e-148, 1.99e-382j)
| (0.012987012987012987013 + 9.5622695319423726794e-1790j)  +/-  (1.91e-157, 1.44e-391j)
| (0.012987012987012987013 - 1.2685827229838755361e-1789j)  +/-  (1.44e-153, 1.08e-387j)
| (0.012987012987012987013 + 1.0483137130920652398e-1790j)  +/-  (6.27e-151, 4.71e-385j)
| (0.012987012987012987013 + 2.1191299004736165765e-1790j)  +/-  (9.16e-159, 6.89e-393j)
| (0.012987012987012987013 + 4.1751953713756002965e-1790j)  +/-  (2.53e-162, 1.9e-396j)
| (0.012987012987012987013 + 1.0642409828373826223e-1789j)  +/-  (1.59e-156, 1.19e-390j)
| (0.012987012987012987013 - 1.0079431905166131926e-1789j)  +/-  (2.72e-157, 2.04e-391j)
| (0.012987012987012987013 - 2.2831784800819515433e-1790j)  +/-  (3.99e-160, 3e-394j)
| (0.012987012987012987013 - 1.9524506695591559282e-1790j)  +/-  (6.41e-159, 4.82e-393j)
| (0.012987012987012987013 - 1.6034382519817986357e-1790j)  +/-  (2.9e-158, 2.18e-392j)
| (0.012987012987012987013 + 1.1935899394282350852e-1789j)  +/-  (7.33e-157, 5.5e-391j)
| (0.012987012987012987013 - 8.2312639357729377112e-1790j)  +/-  (6.57e-163, 4.94e-397j)
| (0.012987012987012987013 - 6.2427681939211908898e-1790j)  +/-  (9.85e-166, 7.4e-400j)
| (0.012987012987012987013 + 1.4150813111467026366e-1790j)  +/-  (9.9e-159, 7.44e-393j)
| (0.012987012987012987013 + 2.445931852372955137e-1790j)  +/-  (6.31e-163, 4.74e-397j)
| (0.012987012987012987013 - 9.8448260414922876256e-1791j)  +/-  (3.21e-157, 2.41e-391j)
| (0.012987012987012987013 - 9.0850161671980570175e-1790j)  +/-  (2.83e-162, 2.12e-396j)
| (0.012987012987012987013 + 8.6427346774847677404e-1790j)  +/-  (4.12e-163, 3.09e-397j)
| (0.012987012987012987013 - 4.3714401586741306099e-1790j)  +/-  (1.28e-168, 9.64e-403j)
| (0.012987012987012987013 - 2.6084413780536283791e-1790j)  +/-  (2.88e-165, 2.16e-399j)
| (0.012987012987012987013 + 2.7715689390036296623e-1790j)  +/-  (2.09e-166, 1.57e-400j)
| (0.012987012987012987013 + 5.4655392073438222932e-1790j)  +/-  (2.31e-170, 1.74e-404j)
| (0.012987012987012987013 + 7.8470700826368101968e-1790j)  +/-  (1.28e-167, 9.6e-402j)
| (0.012987012987012987013 - 5.2291198044502767076e-1790j)  +/-  (1.54e-170, 1.16e-404j)
| (0.012987012987012987013 - 2.9360489514028068505e-1790j)  +/-  (1.57e-168, 1.18e-402j)
| (0.012987012987012987013 + 3.1025305594762849536e-1790j)  +/-  (1.57e-169, 1.18e-403j)
| (0.012987012987012987013 + 4.5742538599831775328e-1790j)  +/-  (1.51e-171, 1.14e-405j)
| (0.012987012987012987013 - 7.4871307882999102693e-1790j)  +/-  (3.32e-170, 2.49e-404j)
| (0.012987012987012987013 + 7.1488442180776280452e-1790j)  +/-  (4.9e-171, 3.68e-405j)
| (0.012987012987012987013 - 3.9848920217217975219e-1790j)  +/-  (1.38e-172, 1.04e-406j)
| (0.012987012987012987013 - 3.2716074230763185978e-1790j)  +/-  (3.19e-172, 2.4e-406j)
| (0.012987012987012987013 + 3.7999385152354784239e-1790j)  +/-  (4.39e-173, 3.3e-407j)
| (0.012987012987012987013 + 5.9712317008226801328e-1790j)  +/-  (3.43e-174, 2.57e-408j)
| (0.012987012987012987013 - 6.8299567098602632763e-1790j)  +/-  (1.49e-173, 1.12e-407j)
| (0.012987012987012987013 - 4.7843090784686487408e-1790j)  +/-  (2.67e-174, 2e-408j)
| (0.012987012987012987013 - 3.6197700903543279244e-1790j)  +/-  (4.77e-174, 3.59e-408j)
| (0.012987012987012987013 + 3.4438395681304941379e-1790j)  +/-  (5.55e-174, 4.17e-408j)
| (0.012987012987012987013 + 5.0023333423411709102e-1790j)  +/-  (3.92e-175, 2.94e-409j)
| (0.012987012987012987013 + 6.528504778178568323e-1790j)  +/-  (1.18e-175, 8.96e-410j)
| (0.012987012987012987013 - 5.712553517911548435e-1790j)  +/-  (1.25e-175, 9.32e-410j)
