Starting with polynomial:
P : t
Extension levels are: 1 30 32
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 32 Kronrod extension for:
P2 : t^31 - 31/4*t^29 + 217/8*t^27 - 3627/64*t^25 + 10075/128*t^23 - 39215/512*t^21 + 54901/1024*t^19 - 447051/16384*t^17 + 330429/32768*t^15 - 350455/131072*t^13 + 130169/262144*t^11 - 130169/2097152*t^9 + 20553/4194304*t^7 - 3689/16777216*t^5 + 155/33554432*t^3 - 31/1073741824*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^63 - 16*t^61 + 1951/16*t^59 - 9425/16*t^57 + 259217/128*t^55 - 337491/64*t^53 + 44268939/4096*t^51 - 73264815/4096*t^49 + 797362475/32768*t^47 - 225761445/8192*t^45 + 13747006735/524288*t^43 - 11058073285/524288*t^41 + 60419672509/4194304*t^39 - 17561974645/2097152*t^37 + 1113356771979/268435456*t^35 - 469578464931/268435456*t^33 + 1346790732573/2147483648*t^31 - 51138429529/268435456*t^29 + 1676887120055/34359738368*t^27 - 360026437953/34359738368*t^25 + 514057545105/274877906944*t^23 - 37743692415/137438953472*t^21 + 288075375705/8796093022208*t^19 - 27444469725/8796093022208*t^17 + 16361903385/70368744177664*t^15 - 232041789/17592186044416*t^13 + 618457161/1125899906842624*t^11 - 17988091/1125899906842624*t^9 + 2719475/9007199254740992*t^7 - 14911/4503599627370496*t^5 + 19871/1152921504606846976*t^3 - 31/1152921504606846976*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
Sufficient bits for target precision reached
Positive weights:   63 out of 63
Indefinite weights: 0 out of 63
Negative weights:   0 out of 63
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.97952994125249449394 - 6.5201944644805926855e-804j)  +/-  (1.37e-232, 1.37e-232j)
| (-0.96807711886620430515 - 5.5989901930658113851e-800j)  +/-  (7.31e-233, 7.31e-233j)
| (-0.95413925640004885148 + 2.0280839236505781133e-803j)  +/-  (4.22e-233, 4.22e-233j)
| (-0.98846832432811139916 - 1.2702984075188387491e-815j)  +/-  (1.82e-232, 1.82e-232j)
| (0.91895781162023062913 - 4.4677401294393602384e-837j)  +/-  (7.81e-234, 7.81e-234j)
| (0.93775213214708045843 - 8.3993501118475126662e-836j)  +/-  (2.08e-233, 2.08e-233j)
| (0.99871650717105280715 - 2.0533654982712623734e-832j)  +/-  (3.02e-232, 3.02e-232j)
| (-0.89780453957074165714 + 4.1266127257104735445e-832j)  +/-  (3.17e-234, 3.17e-234j)
| (0.99486932339189514632 + 2.1151552030566779562e-846j)  +/-  (2.63e-232, 2.63e-232j)
| (-0.99871650717105280715 + 1.9026162799654952295e-844j)  +/-  (2.85e-232, 2.85e-232j)
| (0.89780453957074165714 + 1.9303543574032086101e-868j)  +/-  (2.98e-234, 2.98e-234j)
| (0.98846832432811139916 + 1.8974957208227652173e-866j)  +/-  (2.14e-232, 2.14e-232j)
| (-0.93775213214708045843 + 1.4154068827091654083e-864j)  +/-  (2.27e-233, 2.27e-233j)
| (-0.87434661614458211883 + 3.342513727179071403e-872j)  +/-  (1.06e-234, 1.06e-234j)
| (-0.99486932339189514632 - 4.4021623211335131822e-872j)  +/-  (2.45e-232, 2.45e-232j)
| (0.82076344120727632636 + 2.8105072878069258511e-899j)  +/-  (8.71e-236, 8.71e-236j)
| (0.84864425749475095046 + 5.101003022458915201e-899j)  +/-  (3.41e-235, 3.41e-235j)
| (-1 - 3.4081055528365124196e-896j)  +/-  (1.57e-232, 1.57e-232j)
| (-0.72479278722911995887 + 1.4462605096072561344e-912j)  +/-  (7.94e-238, 7.94e-238j)
| (-0.91895781162023062913 + 1.4118363895641036877e-907j)  +/-  (9.48e-234, 9.48e-234j)
| (0.95413925640004885148 - 2.5604588184665212879e-905j)  +/-  (4.3e-233, 4.3e-233j)
| (0.79077573693769858208 - 5.3542590133956579751e-911j)  +/-  (1.96e-236, 1.96e-236j)
| (0.96807711886620430515 - 4.8838836074173335551e-906j)  +/-  (7.45e-233, 7.45e-233j)
| (-0.84864425749475095046 + 9.2089779839179322616e-911j)  +/-  (2.98e-235, 2.98e-235j)
| (-0.82076344120727632636 - 7.6674574331663170714e-912j)  +/-  (8.9e-236, 8.9e-236j)
| (0.87434661614458211883 - 1.6805910733434947487e-911j)  +/-  (9.97e-235, 9.97e-235j)
| (0.75875812269279090191 + 3.1292221057462430718e-914j)  +/-  (4.62e-237, 4.62e-237j)
| (0.72479278722911995887 + 6.091241727196154327e-916j)  +/-  (7.43e-238, 7.43e-238j)
| (-0.48530196253108102521 + 1.24208830742924016e-920j)  +/-  (1.91e-243, 1.91e-243j)
| (-0.6889669190756865678 - 4.8025425479758039111e-915j)  +/-  (1.17e-238, 1.17e-238j)
| (1 - 4.2406615917915215082e-911j)  +/-  (1.64e-232, 1.64e-232j)
| (0.6889669190756865678 - 3.4536896671357299425e-918j)  +/-  (1.27e-238, 1.27e-238j)
| (0.65137248272222220745 - 8.0121908277519320776e-919j)  +/-  (1.74e-239, 1.74e-239j)
| (-0.97952994125249449394 - 1.1352109803928350862e-915j)  +/-  (1.31e-232, 1.31e-232j)
| (-0.65137248272222220745 - 1.2265025286744724088e-925j)  +/-  (1.58e-239, 1.58e-239j)
| (-0.75875812269279090191 + 3.1084306238903741806e-921j)  +/-  (4.09e-237, 4.09e-237j)
| (0.25065253225872053931 - 1.3296066343480756943e-938j)  +/-  (2.38e-249, 2.38e-249j)
| (0.61210598254766284415 + 8.7168256866963765284e-929j)  +/-  (2.18e-240, 2.18e-240j)
| (0.29936312297335795401 + 6.8556885911858194539e-936j)  +/-  (4.67e-248, 4.67e-248j)
| (-0.79077573693769858208 + 2.0789761511355294683e-930j)  +/-  (2.41e-236, 2.41e-236j)
| (-0.52896401032696245737 + 9.9264962803170801311e-937j)  +/-  (2.23e-242, 2.23e-242j)
| (-0.15142777750457666366 + 3.0106258434662469712e-947j)  +/-  (5.46e-252, 5.46e-252j)
| (0.57126821509479227916 + 5.3396101780385715826e-938j)  +/-  (2.37e-241, 2.37e-241j)
| (0.52896401032696245737 - 7.6476466231134948574e-941j)  +/-  (2.51e-242, 2.51e-242j)
| (-7.3378893873161709237e-985 - 1.4597258096780455482e-984j)  +/-  (1.03e-982, 1.03e-982j)
| (-0.57126821509479227916 - 1.1140677108504127582e-934j)  +/-  (2.44e-241, 2.44e-241j)
| (-0.61210598254766284415 - 2.2895983788403361092e-940j)  +/-  (1.88e-240, 1.88e-240j)
| (0.050649168838712712279 - 4.8540416570949242007e-956j)  +/-  (1.45e-254, 1.45e-254j)
| (0.48530196253108102521 - 1.516701142974102454e-944j)  +/-  (2e-243, 2e-243j)
| (0.20129852008866007914 + 1.3919448802793439612e-952j)  +/-  (1.19e-250, 1.19e-250j)
| (-0.20129852008866007914 + 6.6103371442220397353e-952j)  +/-  (1.18e-250, 1.18e-250j)
| (-0.44039415155763430952 - 3.082090472719932567e-945j)  +/-  (1.53e-244, 1.53e-244j)
| (-0.050649168838712712279 + 2.5759261429433830191e-956j)  +/-  (8.97e-255, 8.97e-255j)
| (0.34730525284482028554 - 2.1116961254956485722e-948j)  +/-  (7.17e-247, 7.17e-247j)
| (0.44039415155763430952 - 4.0680402706265236469e-946j)  +/-  (1.57e-244, 1.57e-244j)
| (-0.10116832198743217779 - 1.0244752097536305343e-954j)  +/-  (2.77e-253, 2.77e-253j)
| (-0.3943558551133185801 + 1.2682156356181650567e-946j)  +/-  (1.13e-245, 1.13e-245j)
| (-0.25065253225872053931 - 1.1378032948114192508e-950j)  +/-  (2.06e-249, 2.06e-249j)
| (0.15142777750457666366 - 8.8321867027406840192e-955j)  +/-  (6.01e-252, 6.01e-252j)
| (0.3943558551133185801 + 1.6696453841334988567e-946j)  +/-  (1.12e-245, 1.12e-245j)
| (0.10116832198743217779 + 3.7493083297135902765e-956j)  +/-  (2.96e-253, 2.96e-253j)
| (-0.29936312297335795401 + 4.2370101417665141132e-949j)  +/-  (4.7e-248, 4.7e-248j)
| (-0.34730525284482028554 + 3.4764943797166318674e-948j)  +/-  (7.95e-247, 7.95e-247j)
-------------------------------------------------
The weights are:
| (0.016129032258064516129 + 4.6257627738596051796e-802j)  +/-  (1.03e-35, 6.95e-146j)
| (0.016129032258064516129 + 6.9809243071556592547e-801j)  +/-  (4.95e-36, 3.34e-146j)
| (0.016129032258064516129 + 6.4790381183486545145e-800j)  +/-  (3.81e-36, 2.57e-146j)
| (0.016129032258064516129 + 4.4296358419866641099e-800j)  +/-  (1.15e-36, 7.74e-147j)
| (0.016129032258064516129 + 4.8047267485382739235e-802j)  +/-  (1.72e-37, 1.16e-147j)
| (0.016129032258064516129 - 4.7653265261612005859e-802j)  +/-  (1.91e-37, 1.29e-147j)
| (0.016129032258064516129 - 4.5384125642803112884e-802j)  +/-  (7.44e-39, 5.02e-149j)
| (0.016129032258064516129 - 1.28567205180879991e-800j)  +/-  (2.2e-40, 1.48e-150j)
| (0.016129032258064516129 + 4.5336678991928428667e-802j)  +/-  (9.1e-39, 6.14e-149j)
| (0.016129032258064516129 + 2.9481206677054663493e-800j)  +/-  (2.04e-40, 1.38e-150j)
| (0.016129032258064516129 - 4.8545068389658268507e-802j)  +/-  (2.25e-40, 1.52e-150j)
| (0.016129032258064516129 - 4.4996280836853300199e-802j)  +/-  (5.85e-39, 3.95e-149j)
| (0.016129032258064516129 - 2.9799516021425601944e-800j)  +/-  (1.15e-40, 7.76e-151j)
| (0.016129032258064516129 + 9.6388312641546294025e-801j)  +/-  (6.67e-42, 4.5e-152j)
| (0.016129032258064516129 - 3.371416037570596694e-800j)  +/-  (1.66e-40, 1.12e-150j)
| (0.016129032258064516129 + 5.0567810981490011256e-802j)  +/-  (7.98e-44, 5.38e-154j)
| (0.016129032258064516129 - 4.9806882345803988824e-802j)  +/-  (2.42e-43, 1.63e-153j)
| (0.0080645161290322580645 - 1.414798574338642803e-800j)  +/-  (7.86e-41, 5.3e-151j)
| (0.016129032258064516129 - 3.7134530181849553009e-801j)  +/-  (2.12e-46, 1.43e-156j)
| (0.016129032258064516129 + 1.8394444217656002091e-800j)  +/-  (1.43e-42, 9.63e-153j)
| (0.016129032258064516129 + 4.7411622276118077189e-802j)  +/-  (1.56e-42, 1.06e-152j)
| (0.016129032258064516129 - 5.1418320732414002532e-802j)  +/-  (1.23e-45, 8.3e-156j)
| (0.016129032258064516129 - 4.757735444927978228e-802j)  +/-  (1.83e-42, 1.23e-152j)
| (0.016129032258064516129 - 7.5644183852110646533e-801j)  +/-  (3.14e-45, 2.12e-155j)
| (0.016129032258064516129 + 6.1327152212379588397e-801j)  +/-  (4.02e-46, 2.71e-156j)
| (0.016129032258064516129 + 4.9132814217512992964e-802j)  +/-  (1.2e-44, 8.1e-155j)
| (0.016129032258064516129 + 5.2362568286239465132e-802j)  +/-  (1.25e-47, 8.44e-158j)
| (0.016129032258064516129 - 5.3405854342798066861e-802j)  +/-  (7.89e-49, 5.32e-159j)
| (0.016129032258064516129 - 1.8713357908683577535e-801j)  +/-  (1.22e-53, 8.24e-164j)
| (0.016129032258064516129 + 3.2368033519765148633e-801j)  +/-  (2.57e-51, 1.74e-161j)
| (0.0080645161290322580645 + 2.2694268966694612886e-802j)  +/-  (1e-44, 6.75e-155j)
| (0.016129032258064516129 + 5.4554528311359007406e-802j)  +/-  (3.54e-50, 2.39e-160j)
| (0.016129032258064516129 - 5.5815992518401113843e-802j)  +/-  (2.04e-51, 1.38e-161j)
| (0.016129032258064516129 - 7.886351824618926391e-800j)  +/-  (3.31e-47, 2.23e-157j)
| (0.016129032258064516129 - 2.8525806759647139955e-801j)  +/-  (6.6e-53, 4.45e-163j)
| (0.016129032258064516129 + 4.3160251087978194615e-801j)  +/-  (1.74e-51, 1.18e-161j)
| (0.016129032258064516129 + 7.4140287776540689125e-802j)  +/-  (9.53e-57, 6.43e-167j)
| (0.016129032258064516129 + 5.7198766159757001748e-802j)  +/-  (3.33e-53, 2.25e-163j)
| (0.016129032258064516129 - 7.1292485287526260675e-802j)  +/-  (1.29e-56, 8.69e-167j)
| (0.016129032258064516129 - 5.0954396170201945639e-801j)  +/-  (2.34e-51, 1.58e-161j)
| (0.016129032258064516129 + 2.0574001617399742874e-801j)  +/-  (1.13e-55, 7.63e-166j)
| (0.016129032258064516129 + 1.1063153014467940588e-801j)  +/-  (5.67e-59, 3.83e-169j)
| (0.016129032258064516129 - 5.8712592596523436157e-802j)  +/-  (5.32e-55, 3.59e-165j)
| (0.016129032258064516129 + 6.0368584291313650675e-802j)  +/-  (4.88e-56, 3.29e-166j)
| (0.016129032258064516129 - 9.3329213164215615762e-802j)  +/-  (8.42e-60, 5.68e-170j)
| (0.016129032258064516129 - 2.276735357761507279e-801j)  +/-  (1.81e-56, 1.22e-166j)
| (0.016129032258064516129 + 2.5379217649803579586e-801j)  +/-  (6.31e-56, 4.26e-166j)
| (0.016129032258064516129 + 8.8690154506986647626e-802j)  +/-  (1.65e-60, 1.11e-170j)
| (0.016129032258064516129 - 6.2179405306938647497e-802j)  +/-  (2.4e-58, 1.62e-168j)
| (0.016129032258064516129 - 7.7267901024577300966e-802j)  +/-  (3.45e-60, 2.33e-170j)
| (0.016129032258064516129 - 1.1782597888579520768e-801j)  +/-  (1.28e-61, 8.66e-172j)
| (0.016129032258064516129 + 1.7120848257845310258e-801j)  +/-  (1.73e-60, 1.17e-170j)
| (0.016129032258064516129 + 9.8480621312777725358e-802j)  +/-  (1.91e-61, 1.29e-171j)
| (0.016129032258064516129 + 6.869579282568620455e-802j)  +/-  (5.1e-61, 3.44e-171j)
| (0.016129032258064516129 + 6.4159494834923154158e-802j)  +/-  (1.36e-60, 9.19e-171j)
| (0.016129032258064516129 - 1.0421854678076451048e-801j)  +/-  (4.73e-62, 3.19e-172j)
| (0.016129032258064516129 - 1.5747056314653225076e-801j)  +/-  (8.33e-63, 5.62e-173j)
| (0.016129032258064516129 + 1.2593070725455093462e-801j)  +/-  (3e-63, 2.03e-173j)
| (0.016129032258064516129 + 8.0708565228409581147e-802j)  +/-  (4.07e-63, 2.75e-173j)
| (0.016129032258064516129 - 6.632533799691389458e-802j)  +/-  (1.09e-62, 7.37e-173j)
| (0.016129032258064516129 - 8.4500933927992831595e-802j)  +/-  (2.88e-63, 1.95e-173j)
| (0.016129032258064516129 - 1.3510289931785332776e-801j)  +/-  (1.6e-64, 1.08e-174j)
| (0.016129032258064516129 + 1.4553603495578619909e-801j)  +/-  (1.52e-64, 1.02e-174j)
