Starting with polynomial:
P : 1073741824*t^30 - 7784628224*t^28 + 25367150592*t^26 - 49073356800*t^24 + 62704844800*t^22 - 55710842880*t^20 + 35283533824*t^18 - 16066609152*t^16 + 5239111680*t^14 - 1203937280*t^12 + 189190144*t^10 - 19348992*t^8 + 1188096*t^6 - 38080*t^4 + 480*t^2 - 1
Extension levels are: 30 31
-------------------------------------------------
Trying to find an order 31 Kronrod extension for:
P1 : 1073741824*t^30 - 7784628224*t^28 + 25367150592*t^26 - 49073356800*t^24 + 62704844800*t^22 - 55710842880*t^20 + 35283533824*t^18 - 16066609152*t^16 + 5239111680*t^14 - 1203937280*t^12 + 189190144*t^10 - 19348992*t^8 + 1188096*t^6 - 38080*t^4 + 480*t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1073741824*t^61 - 16106127360*t^59 + 114823266304*t^57 - 517677776896*t^55 + 1656792023040*t^53 - 4005367382016*t^51 + 7599469363200*t^49 - 11606462300160*t^47 + 14521511280640*t^45 - 15069492838400*t^43 + 13084376954880*t^41 - 9562557132800*t^39 + 5904879029504*t^37 - 3086851988736*t^35 + 1366575099180*t^33 - 511738760544*t^31 + 323313211485/2*t^29 - 85794224747/2*t^27 + 304179524103/32*t^25 - 27923456925/16*t^23 + 67282234305/256*t^21 - 8205150525/256*t^19 + 25510558905/8192*t^17 - 483477705/2048*t^15 + 890616825/65536*t^13 - 37550331/65536*t^11 + 17651865/1048576*t^9 - 168113/524288*t^7 + 29667/8388608*t^5 - 155/8388608*t^3 + 31/1073741824*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: 1
  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
-------------------------------------------------
The nodes are:
| (-0.97952994125249449394 + 2.8234672187905385385e-861j)  +/-  (2.36e-234, 2.36e-234j)
| (-0.99486932339189514632 + 6.890133363891005222e-876j)  +/-  (1.26e-234, 1.26e-234j)
| (-0.91895781162023062913 - 1.4923682929441599351e-887j)  +/-  (7.15e-235, 7.15e-235j)
| (-0.99871650717105280715 - 2.8948790103843756092e-892j)  +/-  (3.86e-235, 3.86e-235j)
| (0.97952994125249449394 + 7.003362481533116018e-898j)  +/-  (2.4e-234, 2.4e-234j)
| (0.93775213214708045843 + 1.1469190528878914909e-898j)  +/-  (1.19e-234, 1.19e-234j)
| (0.99871650717105280715 - 4.5368650692616839277e-898j)  +/-  (3.95e-235, 3.95e-235j)
| (-0.89780453957074165714 - 3.9739142379445137853e-900j)  +/-  (3.15e-235, 3.15e-235j)
| (-0.98846832432811139916 - 1.2328601979785530455e-906j)  +/-  (2.12e-234, 2.12e-234j)
| (0.99486932339189514632 + 1.3898934471737377975e-913j)  +/-  (1.15e-234, 1.15e-234j)
| (0.89780453957074165714 - 3.2152653839358132141e-917j)  +/-  (2.9e-235, 2.9e-235j)
| (0.84864425749475095046 + 4.28900195728254804e-920j)  +/-  (4.37e-236, 4.37e-236j)
| (-0.84864425749475095046 - 1.5963425282640491734e-917j)  +/-  (4.38e-236, 4.38e-236j)
| (-0.87434661614458211883 + 6.6094433897629340995e-919j)  +/-  (1.17e-235, 1.17e-235j)
| (0.79077573693769858208 - 1.541168893075892246e-928j)  +/-  (4.51e-237, 4.51e-237j)
| (0.87434661614458211883 - 3.1482502167669905531e-926j)  +/-  (1.27e-235, 1.27e-235j)
| (0.96807711886620430515 - 2.2009473334352045032e-926j)  +/-  (2.54e-234, 2.54e-234j)
| (-0.96807711886620430515 - 5.1182989337032789837e-926j)  +/-  (2.65e-234, 2.65e-234j)
| (-0.75875812269279090191 + 1.9348550574519197392e-945j)  +/-  (1.06e-237, 1.06e-237j)
| (-0.95413925640004885148 - 5.4707207822926406451e-941j)  +/-  (1.95e-234, 1.95e-234j)
| (0.29936312297335795401 + 8.298144106758838244e-973j)  +/-  (3.56e-248, 3.56e-248j)
| (0.75875812269279090191 - 8.46785425375690895e-962j)  +/-  (1.24e-237, 1.24e-237j)
| (-0.93775213214708045843 - 6.1017363628042508776e-959j)  +/-  (1.24e-234, 1.24e-234j)
| (-0.82076344120727632636 - 2.9834739183326939704e-967j)  +/-  (1.97e-236, 1.97e-236j)
| (-0.72479278722911995887 + 2.615470632744582193e-970j)  +/-  (2.52e-238, 2.52e-238j)
| (0.82076344120727632636 - 1.7345822624692870432e-967j)  +/-  (1.48e-236, 1.48e-236j)
| (0.72479278722911995887 - 3.0042854375765324034e-969j)  +/-  (1.98e-238, 1.98e-238j)
| (0.25065253225872053931 - 2.2018324433014280618e-981j)  +/-  (1.6e-249, 1.6e-249j)
| (0.61210598254766284415 + 2.958875939690754741e-972j)  +/-  (8.19e-241, 8.19e-241j)
| (-0.65137248272222220745 + 7.8370845065626440006e-972j)  +/-  (6.45e-240, 6.45e-240j)
| (0.95413925640004885148 - 2.3791530449179805436e-964j)  +/-  (1.77e-234, 1.77e-234j)
| (0.91895781162023062913 - 8.6368513443013938143e-969j)  +/-  (6.66e-235, 6.66e-235j)
| (0.6889669190756865678 - 1.0876181335315530039e-975j)  +/-  (3.85e-239, 3.85e-239j)
| (-0.57126821509479227916 - 1.0655614369399286229e-979j)  +/-  (1.03e-241, 1.03e-241j)
| (-0.6889669190756865678 + 6.8688782810923725781e-977j)  +/-  (4.17e-239, 4.17e-239j)
| (-0.61210598254766284415 - 1.9415992145234164525e-978j)  +/-  (9.26e-241, 9.26e-241j)
| (0.44039415155763430952 - 9.6893113858802849281e-982j)  +/-  (1.07e-244, 1.07e-244j)
| (0.57126821509479227916 - 1.3461198629689980299e-978j)  +/-  (1.02e-241, 1.02e-241j)
| (0.98846832432811139916 - 1.0681039465150199045e-978j)  +/-  (1.97e-234, 1.97e-234j)
| (-0.20129852008866007914 - 1.305875136548645623e-995j)  +/-  (1.06e-250, 1.06e-250j)
| (-0.52896401032696245737 - 3.6599968201815373129e-987j)  +/-  (1.31e-242, 1.31e-242j)
| (-0.79077573693769858208 + 7.2893254408408778686e-989j)  +/-  (4.64e-237, 4.64e-237j)
| (0.65137248272222220745 - 2.0386046047010032611e-996j)  +/-  (6.13e-240, 6.13e-240j)
| (0.52896401032696245737 + 8.0793386433383930429e-1000j)  +/-  (1.39e-242, 1.39e-242j)
| (-0.050649168838712712279 + 1.3776762541908719886e-1011j)  +/-  (1.09e-254, 1.09e-254j)
| (-0.48530196253108102521 - 2.7290423311063307726e-1001j)  +/-  (1.33e-243, 1.33e-243j)
| (-0.34730525284482028554 + 1.5986817219779668265e-1007j)  +/-  (6.17e-247, 6.17e-247j)
| (-1.6730419490651318013e-1019 + 2.102840573325230674e-1019j)  +/-  (1.64e-1017, 1.64e-1017j)
| (0.48530196253108102521 + 1.2729694660652088714e-1002j)  +/-  (1.26e-243, 1.26e-243j)
| (0.15142777750457666366 - 2.3099271246574090259e-1011j)  +/-  (4.61e-252, 4.61e-252j)
| (-0.29936312297335795401 + 4.5791043639968128703e-1007j)  +/-  (3.85e-248, 3.85e-248j)
| (-0.44039415155763430952 + 1.1404684209362923606e-1003j)  +/-  (1.09e-244, 1.09e-244j)
| (-0.15142777750457666366 + 9.8392302302129485831e-1011j)  +/-  (5.72e-252, 5.72e-252j)
| (0.20129852008866007914 + 5.7491726263735390248e-1010j)  +/-  (1.07e-250, 1.07e-250j)
| (0.34730525284482028554 + 9.34109612881889739e-1006j)  +/-  (5.11e-247, 5.11e-247j)
| (-0.10116832198743217779 + 1.936361907592964006e-1012j)  +/-  (2.68e-253, 2.68e-253j)
| (-0.3943558551133185801 - 2.08927212744713836e-1006j)  +/-  (9.09e-246, 9.09e-246j)
| (-0.25065253225872053931 - 1.9108791492104975195e-1009j)  +/-  (1.92e-249, 1.92e-249j)
| (0.10116832198743217779 - 5.5072900680963634072e-1013j)  +/-  (2.68e-253, 2.68e-253j)
| (0.3943558551133185801 - 4.5846458795736449371e-1006j)  +/-  (9.24e-246, 9.24e-246j)
| (0.050649168838712712279 + 3.1137731214703692316e-1014j)  +/-  (1.18e-254, 1.18e-254j)
-------------------------------------------------
The weights are:
| (0.00065356603532072073285 + 6.6911387393957718548e-863j)  +/-  (2.15e-45, 1.61e-156j)
| (0.00016508111893149601663 - 3.0385912777224178185e-863j)  +/-  (9.51e-46, 7.12e-157j)
| (0.0025083312977767212274 + 1.1692161454674315847e-862j)  +/-  (1.06e-46, 7.94e-158j)
| (4.1376424258910110312e-05 + 6.0888945954004258588e-864j)  +/-  (3.84e-46, 2.87e-157j)
| (0.00065356603532072073285 + 9.4194276169006251437e-865j)  +/-  (2.79e-47, 2.09e-158j)
| (0.0019454990105420088555 - 2.8650206230296365887e-864j)  +/-  (1.36e-47, 1.02e-158j)
| (4.1376424258910110312e-05 - 5.9054814742065986679e-866j)  +/-  (5.83e-48, 4.36e-159j)
| (0.0031281775600994931924 - 1.0807296891474480219e-862j)  +/-  (2.39e-47, 1.78e-158j)
| (0.00036984470645121893971 + 1.1682699162411447064e-862j)  +/-  (6.25e-46, 4.67e-157j)
| (0.00016508111893149601663 + 2.3607237709759382875e-865j)  +/-  (8.25e-48, 6.17e-159j)
| (0.0031281775600994931924 - 4.7047059997662356274e-864j)  +/-  (3.33e-49, 2.49e-160j)
| (0.0045129503906642394394 - 6.9698869488476661421e-864j)  +/-  (5.22e-50, 3.9e-161j)
| (0.0045129503906642394394 - 9.7353408885061518325e-863j)  +/-  (8.52e-50, 6.37e-161j)
| (0.0037986773360728834083 + 1.0196902334244196347e-862j)  +/-  (2.97e-49, 2.22e-160j)
| (0.0060431247398490279088 - 9.6382024936332794555e-864j)  +/-  (3.09e-51, 2.31e-162j)
| (0.0037986773360728834083 + 5.7854126750614765348e-864j)  +/-  (7.11e-50, 5.32e-161j)
| (0.0010133337407694990417 - 1.469040987447798397e-864j)  +/-  (8.49e-50, 6.35e-161j)
| (0.0010133337407694990417 - 2.4981742510754578138e-862j)  +/-  (1.72e-49, 1.29e-160j)
| (0.0068433243749630914221 + 8.7519784754743680317e-863j)  +/-  (1.62e-53, 1.21e-164j)
| (0.0014454561192961586584 + 1.6073603342131960309e-862j)  +/-  (4.43e-50, 3.31e-161j)
| (0.014683576138768357471 - 3.2417562532895184388e-863j)  +/-  (2.98e-57, 2.23e-168j)
| (0.0068433243749630914221 + 1.1115477601799126164e-863j)  +/-  (1.14e-54, 8.5e-166j)
| (0.0019454990105420088555 - 1.3148254535307714342e-862j)  +/-  (2.43e-50, 1.82e-161j)
| (0.0052636673157675783424 + 9.3607858789204278301e-863j)  +/-  (6.23e-53, 4.66e-164j)
| (0.0076560550900103813526 - 8.4858530569573995814e-863j)  +/-  (4.65e-55, 3.48e-166j)
| (0.0052636673157675783424 + 8.2552056578595349786e-864j)  +/-  (1.15e-54, 8.61e-166j)
| (0.0076560550900103813526 - 1.2683408025167342188e-863j)  +/-  (2.08e-56, 1.56e-167j)
| (0.015115698517295017087 + 3.4692966427077168962e-863j)  +/-  (8.52e-60, 6.37e-171j)
| (0.01008590751821548822 + 1.7891798509701192764e-863j)  +/-  (1.42e-58, 1.06e-169j)
| (0.0092857078831014247069 - 7.989424323501468875e-863j)  +/-  (7.15e-59, 5.35e-170j)
| (0.0014454561192961586584 + 2.1105978075192161734e-864j)  +/-  (1.11e-55, 8.33e-167j)
| (0.0025083312977767212274 + 3.7304381776613490914e-864j)  +/-  (1.44e-55, 1.07e-166j)
| (0.0084729771680541347764 + 1.433815900310180205e-863j)  +/-  (3.74e-58, 2.8e-169j)
| (0.010865364942296937787 - 7.514297757836161538e-863j)  +/-  (1.2e-60, 8.95e-172j)
| (0.0084729771680541347764 + 8.2333853428205048592e-863j)  +/-  (9.83e-59, 7.35e-170j)
| (0.01008590751821548822 + 7.750509615599560156e-863j)  +/-  (4.97e-60, 3.72e-171j)
| (0.013000854697965022937 + 2.5851724920954487113e-863j)  +/-  (2.29e-62, 1.72e-173j)
| (0.010865364942296937787 - 1.9782072611583229889e-863j)  +/-  (4.01e-61, 3e-172j)
| (0.00036984470645121893971 - 5.3061246189673449349e-865j)  +/-  (3.75e-58, 2.81e-169j)
| (0.015475466222743795396 - 5.6145858914399737905e-863j)  +/-  (1.47e-65, 1.1e-176j)
| (0.01161608186740027669 + 7.2792069067495959959e-863j)  +/-  (1.69e-62, 1.26e-173j)
| (0.0060431247398490279088 - 9.03956797357990482e-863j)  +/-  (4.24e-59, 3.17e-170j)
| (0.0092857078831014247069 - 1.607569614576050736e-863j)  +/-  (2.2e-60, 1.64e-171j)
| (0.01161608186740027669 + 2.1741967429867015468e-863j)  +/-  (3.25e-62, 2.43e-173j)
| (0.016087655833805606019 + 4.8900752629316311444e-863j)  +/-  (5.86e-67, 4.38e-178j)
| (0.012330354921991632721 - 7.0441890012706438078e-863j)  +/-  (2.42e-64, 1.81e-175j)
| (0.014183533247522507273 + 6.3342577259783422151e-863j)  +/-  (2.18e-66, 1.63e-177j)
| (0.016129032258064516129 - 4.6491477119351848825e-863j)  +/-  (2.05e-67, 1.53e-178j)
| (0.012330354921991632721 - 2.3766790461330464291e-863j)  +/-  (1.13e-64, 8.48e-176j)
| (0.015759187551613297189 + 3.9343247505002253249e-863j)  +/-  (1.48e-67, 1.11e-178j)
| (0.014683576138768357471 - 6.0953570165801794968e-863j)  +/-  (1.97e-67, 1.48e-178j)
| (0.013000854697965022937 + 6.8085791664357848058e-863j)  +/-  (1.42e-66, 1.06e-177j)
| (0.015759187551613297189 + 5.3731956508082555269e-863j)  +/-  (3.16e-68, 2.37e-179j)
| (0.015475466222743795396 - 3.7003233751488674197e-863j)  +/-  (1.98e-68, 1.48e-179j)
| (0.014183533247522507273 + 3.0182151746623353296e-863j)  +/-  (2.88e-68, 2.16e-179j)
| (0.015963951139133020112 - 5.1315644644662259897e-863j)  +/-  (1.01e-68, 7.53e-180j)
| (0.013620700960287794902 - 6.5719934578878219975e-863j)  +/-  (2.59e-68, 1.94e-179j)
| (0.015115698517295017087 + 5.8553988264805571419e-863j)  +/-  (9.98e-69, 7.47e-180j)
| (0.015963951139133020112 - 4.1707934820386789405e-863j)  +/-  (3.9e-70, 2.93e-181j)
| (0.013620700960287794902 - 2.7991848201683938622e-863j)  +/-  (3.22e-70, 2.58e-181j)
| (0.016087655833805606019 + 4.4092302424879368995e-863j)  +/-  (3.87e-70, 2.86e-181j)
