Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 27
-------------------------------------------------
Trying to find an order 27 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^31 - 1733893254976743/4263259793878*t^29 + 3507164896639212966/49027487629597*t^27 - 703432775795215778325/98054975259194*t^25 + 22329286500781131063075/49027487629597*t^23 - 81958994450919132378975/4263259793878*t^21 + 1175944167101498734239300/2131629896939*t^19 - 46137771541636426411434675/4263259793878*t^17 + 307091726299187887869937125/2131629896939*t^15 - 5439345752883001170870784125/4263259793878*t^13 + 15491870316508596139940060250/2131629896939*t^11 - 107806127340207725167962848625/4263259793878*t^9 + 106195135331703505454470978875/2131629896939*t^7 - 212700560299676707590815608125/4263259793878*t^5 + 46882440173786719625278155000/2131629896939*t^3 - 14114684606831488089300515625/4263259793878*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
  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:   31 out of 31
Indefinite weights: 0 out of 31
Negative weights:   0 out of 31
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-8.4845545411963053184 - 3.6927427709130360932e-651j)  +/-  (9.78e-249, 9.78e-249j)
| (-9.5164600664922489904 - 4.5826649389185514398e-654j)  +/-  (1.43e-249, 1.43e-249j)
| (-5.4434179420289000812 - 2.9483289313246015386e-652j)  +/-  (4.86e-248, 4.86e-248j)
| (-4.7879219103424950306 - 1.3710726259756341892e-652j)  +/-  (2.91e-248, 2.91e-248j)
| (-6.1266504131561829663 - 9.0782626074255323322e-652j)  +/-  (5.94e-248, 5.94e-248j)
| (-6.8476277385698167852 - 1.7347171242153778756e-652j)  +/-  (5.61e-248, 5.61e-248j)
| (-7.62291442974565556 - 1.843309445037535995e-653j)  +/-  (2.62e-248, 2.62e-248j)
| (1.1675354824571579106 - 2.0976675685662843637e-656j)  +/-  (3.13e-252, 3.13e-252j)
| (9.5164600664922489904 + 4.2655174445557482203e-652j)  +/-  (1.45e-249, 1.45e-249j)
| (2.9299084457165382071 + 1.8924166872562944473e-665j)  +/-  (8.06e-250, 8.06e-250j)
| (8.4845545411963053184 - 1.0692905792113561294e-676j)  +/-  (9.49e-249, 9.49e-249j)
| (-1.7468635856462546689 + 8.6401348459616811864e-695j)  +/-  (2.03e-251, 2.03e-251j)
| (5.4434179420289000812 - 4.9003333748617393605e-711j)  +/-  (4.98e-248, 4.98e-248j)
| (6.1266504131561829663 + 6.6910565941191123129e-741j)  +/-  (6.05e-248, 6.05e-248j)
| (3.5353448027508091919 + 6.2550701239685845445e-764j)  +/-  (3.68e-249, 3.68e-249j)
| (-0.56255982897962858603 + 7.1365808571057900448e-780j)  +/-  (3.61e-253, 3.61e-253j)
| (-4.1534877824428083163 - 4.2388566108085951002e-783j)  +/-  (1.12e-248, 1.12e-248j)
| (4.7879219103424950306 + 3.6390830921411916887e-807j)  +/-  (2.82e-248, 2.82e-248j)
| (0.56255982897962858603 + 3.1867337730991050256e-826j)  +/-  (4.13e-253, 4.13e-253j)
| (-3.5353448027508091919 + 8.2511252781251508968e-822j)  +/-  (3.36e-249, 3.36e-249j)
| (-1.1675354824571579106 - 1.3067894884549302634e-826j)  +/-  (3.17e-252, 3.17e-252j)
| (0.74196378430272585765 + 7.9771390976336446659e-828j)  +/-  (9.8e-253, 9.8e-253j)
| (7.6028320194617947924e-830 + 8.644069934759986287e-830j)  +/-  (3.57e-828, 3.57e-828j)
| (-2.3344142183389772393 + 7.6827215370843840339e-825j)  +/-  (1.39e-250, 1.39e-250j)
| (-2.9299084457165382071 + 3.0772357118690210171e-835j)  +/-  (7.46e-250, 7.46e-250j)
| (7.62291442974565556 + 2.5325777705086205695e-858j)  +/-  (2.95e-248, 2.95e-248j)
| (2.3344142183389772393 - 6.6622716579087027067e-878j)  +/-  (1.27e-250, 1.27e-250j)
| (1.7468635856462546689 + 1.9375326223377608269e-879j)  +/-  (1.96e-251, 1.96e-251j)
| (6.8476277385698167852 + 1.6390890816872251145e-882j)  +/-  (4.93e-248, 4.93e-248j)
| (-0.74196378430272585765 - 2.2070878987828319088e-906j)  +/-  (9.58e-253, 9.58e-253j)
| (4.1534877824428083163 + 2.1585342573578765046e-892j)  +/-  (1.09e-248, 1.09e-248j)
-------------------------------------------------
The weights are:
| (8.6034356314582456041e-17 - 1.4349471638682302515e-664j)  +/-  (2.71e-93, 1.69e-217j)
| (1.0229428869096476246e-20 + 9.3620697166165602613e-667j)  +/-  (6.89e-95, 4.3e-219j)
| (9.8054158030513546973e-08 - 1.4915723384683583268e-658j)  +/-  (1.18e-88, 7.36e-213j)
| (2.7033300344645108418e-06 - 8.2532483318934952995e-658j)  +/-  (1.53e-87, 9.57e-212j)
| (1.973474960791750349e-09 - 6.2136575033035864927e-660j)  +/-  (2.46e-90, 1.54e-214j)
| (1.9532944113100896835e-11 - 2.6138975513400558438e-661j)  +/-  (5.26e-92, 3.28e-216j)
| (7.7936194952903647602e-14 + 7.2826074466642898805e-663j)  +/-  (2.02e-93, 1.26e-217j)
| (0.115453252736303778 - 2.5111931982417297777e-655j)  +/-  (1.19e-78, 7.42e-203j)
| (1.0229428869096476246e-20 - 3.0017697312525518439e-667j)  +/-  (4.1e-102, 2.56e-226j)
| (0.0032736799701021821704 + 3.5338541671363171485e-657j)  +/-  (1.2e-89, 7.5e-214j)
| (8.6034356314582456041e-17 + 3.7385204214210975282e-665j)  +/-  (6.8e-101, 4.25e-225j)
| (0.050657811396955657652 + 1.1269287672228901289e-655j)  +/-  (2.06e-85, 1.29e-209j)
| (9.8054158030513546973e-08 + 4.0243393128088332247e-660j)  +/-  (9.07e-97, 5.66e-221j)
| (1.973474960791750349e-09 - 4.2071560537776622035e-661j)  +/-  (4.9e-98, 3.06e-222j)
| (0.00047107697496390811923 - 8.3532283279036371894e-658j)  +/-  (2.08e-93, 1.3e-217j)
| (0.17727807746996343241 - 1.6794711604674274865e-654j)  +/-  (5.67e-86, 3.54e-210j)
| (4.4782254838661495228e-05 + 2.6475725043209518755e-657j)  +/-  (1.59e-93, 9.9e-218j)
| (2.7033300344645108418e-06 - 2.9351609454145093187e-659j)  +/-  (3.82e-96, 2.39e-220j)
| (0.17727807746996343241 - 1.3098167009061278393e-654j)  +/-  (3.65e-87, 2.28e-211j)
| (0.00047107697496390811923 - 5.7763856888407923972e-657j)  +/-  (3.89e-93, 2.43e-217j)
| (0.115453252736303778 - 4.2767672724503826274e-655j)  +/-  (1.23e-88, 7.69e-213j)
| (0.023303279751052575817 + 1.1821794516531203506e-654j)  +/-  (1.54e-87, 9.58e-212j)
| (0.22810027979534549277 + 7.1090533458999131747e-655j)  +/-  (7.98e-88, 4.98e-212j)
| (0.015465096170868635779 - 3.9839789427593718566e-656j)  +/-  (7.27e-92, 4.53e-216j)
| (0.0032736799701021821704 + 1.4942421767989303999e-656j)  +/-  (9.76e-93, 6.09e-217j)
| (7.7936194952903647602e-14 - 1.4936386484715673998e-663j)  +/-  (3.17e-102, 1.97e-226j)
| (0.015465096170868635779 - 1.3662476788860987064e-656j)  +/-  (9.57e-95, 5.95e-219j)
| (0.050657811396955657652 + 5.2968464623057695306e-656j)  +/-  (5.54e-94, 3.45e-218j)
| (1.9532944113100896835e-11 + 3.1331889985775188849e-662j)  +/-  (3.31e-101, 2.08e-225j)
| (0.023303279751052575817 + 1.6491631262259028947e-654j)  +/-  (3.11e-93, 2.49e-217j)
| (4.4782254838661495228e-05 + 1.7144901170061918411e-658j)  +/-  (2.13e-97, 1.31e-221j)
