Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 27
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Trying to find an order 27 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^31 - 6935573019906972/2131629896939*t^29 + 14028659586556851864/49027487629597*t^27 - 703432775795215778325/49027487629597*t^25 + 22329286500781131063075/49027487629597*t^23 - 81958994450919132378975/8526519587756*t^21 + 293986041775374683559825/2131629896939*t^19 - 46137771541636426411434675/34106078351024*t^17 + 307091726299187887869937125/34106078351024*t^15 - 5439345752883001170870784125/136424313404096*t^13 + 7745935158254298069970030125/68212156702048*t^11 - 107806127340207725167962848625/545697253616384*t^9 + 106195135331703505454470978875/545697253616384*t^7 - 212700560299676707590815608125/2182789014465536*t^5 + 5860305021723339953159769375/272848626808192*t^3 - 14114684606831488089300515625/8731156057862144*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 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
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (-3.8490777396411562868 - 1.0400873649406500807e-452j)  +/-  (1.56e-120, 1.56e-120j)
| (-5.9994860514270239881 - 3.4812118179166041722e-463j)  +/-  (3.08e-121, 3.08e-121j)
| (-5.3902144856779369673 - 1.3364372376524422989e-471j)  +/-  (8.99e-121, 8.99e-121j)
| (-4.332196053102100055 - 3.7961836844147959005e-479j)  +/-  (1.82e-120, 1.82e-120j)
| (-4.8420040089838206934 + 5.1891155323197083595e-489j)  +/-  (1.78e-120, 1.78e-120j)
| (-6.7291534459076522115 - 2.0981073615973375203e-496j)  +/-  (5.09e-122, 5.09e-122j)
| (6.7291534459076522115 - 1.1276811010352312366e-496j)  +/-  (4.44e-122, 4.44e-122j)
| (2.4998662838577144537 + 7.1552478943798370941e-496j)  +/-  (1.06e-121, 1.06e-121j)
| (5.3902144856779369673 - 2.6880241824813121957e-495j)  +/-  (9.15e-121, 9.15e-121j)
| (5.9994860514270239881 + 1.143642496822472393e-495j)  +/-  (3.39e-121, 3.39e-121j)
| (1.235219087218314021 - 2.1401564707243854597e-498j)  +/-  (6.01e-124, 6.01e-124j)
| (1.6506801238857845559 - 1.7395427106291121238e-498j)  +/-  (4.62e-123, 4.62e-123j)
| (4.8420040089838206934 + 9.206097729806517957e-495j)  +/-  (1.58e-120, 1.58e-120j)
| (-2.0717581302219017374 - 3.1511113619211076109e-497j)  +/-  (2.49e-122, 2.49e-122j)
| (4.332196053102100055 - 7.6915939932595209488e-495j)  +/-  (1.88e-120, 1.88e-120j)
| (0.39778986989463982746 - 1.9150255492214181954e-501j)  +/-  (1.04e-125, 1.04e-125j)
| (3.8490777396411562868 - 4.2286561126773590535e-495j)  +/-  (1.39e-120, 1.39e-120j)
| (-3.385572050594827248 - 2.338711082302120409e-496j)  +/-  (7.47e-121, 7.47e-121j)
| (-1.235219087218314021 + 2.9572692197235236758e-508j)  +/-  (6.21e-124, 6.21e-124j)
| (3.385572050594827248 + 1.6865435097457015505e-503j)  +/-  (7.99e-121, 7.99e-121j)
| (-1.6506801238857845559 - 1.0670014702351627972e-506j)  +/-  (4.6e-123, 4.6e-123j)
| (0.52464762327529031788 + 1.479754585980642612e-509j)  +/-  (3.53e-125, 3.53e-125j)
| (2.9369593765407853686 - 8.5631502247952038766e-506j)  +/-  (3.41e-121, 3.41e-121j)
| (-2.9369593765407853686 - 5.3604496601575966412e-508j)  +/-  (3.34e-121, 3.34e-121j)
| (-0.82557225692136375447 - 1.892790706113315405e-517j)  +/-  (9.64e-125, 9.64e-125j)
| (2.0717581302219017374 - 7.4716901046732340447e-517j)  +/-  (2.49e-122, 2.49e-122j)
| (0.82557225692136375447 + 1.1229021140554529988e-519j)  +/-  (1.09e-124, 1.09e-124j)
| (-0.39778986989463982746 - 1.1775078040302137758e-519j)  +/-  (1.04e-125, 1.04e-125j)
| (-1.3132027110259375241e-524 + 6.5473006504088770211e-525j)  +/-  (4.55e-523, 4.55e-523j)
| (-0.52464762327529031788 + 1.3839896033555798816e-519j)  +/-  (3.43e-125, 3.43e-125j)
| (-2.4998662838577144537 + 2.465195174002409403e-519j)  +/-  (1.05e-121, 1.05e-121j)
-------------------------------------------------
The weights are:
| (9.8054158030513546973e-08 - 4.4649823037191005035e-459j)  +/-  (1.21e-25, 1.76e-85j)
| (8.6034356314582456041e-17 + 5.721427561082359483e-465j)  +/-  (8.16e-32, 1.18e-91j)
| (7.7936194952903647602e-14 - 2.9819398270162655854e-463j)  +/-  (1.74e-30, 2.52e-90j)
| (1.973474960791750349e-09 - 2.355108095561901838e-460j)  +/-  (3.13e-28, 4.54e-88j)
| (1.9532944113100896835e-11 + 9.1001886077779618056e-462j)  +/-  (1.62e-29, 2.36e-89j)
| (1.0229428869096476246e-20 - 3.6971104607821237083e-467j)  +/-  (1.42e-34, 2.06e-94j)
| (1.0229428869096476246e-20 + 1.0065915401838344641e-467j)  +/-  (4.52e-39, 6.56e-99j)
| (0.00047107697496390811923 + 2.7066228207429361582e-458j)  +/-  (1.5e-28, 2.18e-88j)
| (7.7936194952903647602e-14 + 4.9739492266428992806e-464j)  +/-  (7.25e-37, 1.05e-96j)
| (8.6034356314582456041e-17 - 1.2492588405418908368e-465j)  +/-  (4.97e-38, 7.21e-98j)
| (0.050657811396955657652 - 1.6610470607978468464e-456j)  +/-  (3.21e-24, 4.66e-84j)
| (0.015465096170868635779 + 4.3533025842996484175e-457j)  +/-  (8.37e-27, 1.21e-86j)
| (1.9532944113100896835e-11 - 1.0396653242923629134e-462j)  +/-  (2.39e-36, 3.47e-96j)
| (0.0032736799701021821704 - 3.7868634585323610626e-457j)  +/-  (7.88e-31, 1.14e-90j)
| (1.973474960791750349e-09 + 1.3907319079766071322e-461j)  +/-  (8.43e-36, 1.22e-95j)
| (0.17727807746996343241 + 4.1498626277001256686e-455j)  +/-  (6.7e-28, 9.74e-88j)
| (9.8054158030513546973e-08 - 1.324796454448059679e-460j)  +/-  (2.7e-35, 3.92e-95j)
| (2.7033300344645108418e-06 + 1.5012425032216216511e-458j)  +/-  (5.54e-35, 7.91e-95j)
| (0.050657811396955657652 - 3.2309537061809551218e-456j)  +/-  (5.91e-30, 8.58e-90j)
| (2.7033300344645108418e-06 + 9.6180805022585274903e-460j)  +/-  (7.19e-35, 1.05e-94j)
| (0.015465096170868635779 + 1.0890709646301903412e-456j)  +/-  (5.08e-32, 7.27e-92j)
| (0.023303279751052575817 - 3.7847061936907103309e-455j)  +/-  (5.77e-30, 8.71e-90j)
| (4.4782254838661495228e-05 - 5.588952779825695212e-459j)  +/-  (2.94e-34, 4.31e-94j)
| (4.4782254838661495228e-05 - 4.158105191037781581e-458j)  +/-  (2.68e-35, 3.65e-95j)
| (0.115453252736303778 + 1.2672003733253824023e-455j)  +/-  (1.29e-31, 2.03e-91j)
| (0.0032736799701021821704 - 1.1367426544114717709e-457j)  +/-  (4.03e-33, 6.16e-93j)
| (0.115453252736303778 + 8.1960944226225569791e-456j)  +/-  (5.29e-31, 8.19e-91j)
| (0.17727807746996343241 + 5.1064755658580214569e-455j)  +/-  (8.39e-32, 1.31e-91j)
| (0.22810027979534549277 - 2.2050090729470365062e-455j)  +/-  (7.15e-32, 1.05e-91j)
| (0.023303279751052575817 - 4.9792791218686799951e-455j)  +/-  (5.81e-32, 9.52e-92j)
| (0.00047107697496390811923 + 1.2736474114536196348e-457j)  +/-  (5.27e-35, 5.6e-95j)
