Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 3 24
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Trying to find an order 3 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 24 Kronrod extension for:
P2 : t^5 - 7*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^29 - 293504355204580288329551/829570297882516527293*t^27 + 44457440150973753657746208/829570297882516527293*t^25 - 3795164987273268928693815150/829570297882516527293*t^23 + 18395770014616372306411917825/75415481625683320663*t^21 - 641917168208195722603803492975/75415481625683320663*t^19 + 14945879575468433049267357963450/75415481625683320663*t^17 - 232627175297949900309923422763100/75415481625683320663*t^15 + 2391230172076488456036847814453625/75415481625683320663*t^13 - 15818354765348533415077536257110875/75415481625683320663*t^11 + 64594315567092858516905952141625500/75415481625683320663*t^9 - 153039484173841278348092467652192250/75415481625683320663*t^7 + 191887681368368217566498305930527375/75415481625683320663*t^5 - 109350010828228492423578956203895625/75415481625683320663*t^3 + 19552927818001434867300796120046250/75415481625683320663*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: 1
  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
Positive weights:   29 out of 29
Indefinite weights: 0 out of 29
Negative weights:   0 out of 29
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (3.0616148149006608712 + 1.0752760668286526289e-431j)  +/-  (2.69e-122, 2.69e-122j)
| (8.0862842271994863271 + 9.7888334031814368478e-431j)  +/-  (2.08e-121, 2.08e-121j)
| (-7.2128136825561928083 + 2.4790105546824580708e-430j)  +/-  (5.97e-121, 5.97e-121j)
| (-8.0862842271994863271 + 5.9017775990649555495e-435j)  +/-  (2.17e-121, 2.17e-121j)
| (7.2128136825561928083 - 1.0015605110274997865e-434j)  +/-  (5.76e-121, 5.76e-121j)
| (-6.4262452739510430589 + 3.6478491323734862383e-439j)  +/-  (8.24e-121, 8.24e-121j)
| (-5.6942383474675584026 - 4.5974857762643893088e-442j)  +/-  (8.36e-121, 8.36e-121j)
| (5.6942383474675584026 + 6.0106780027193577104e-448j)  +/-  (9.12e-121, 9.12e-121j)
| (-3.6891371873822652854 - 9.3544719548254224868e-458j)  +/-  (1.06e-121, 1.06e-121j)
| (9.1314208922544435709 + 3.7608402540493493542e-458j)  +/-  (3.64e-122, 3.64e-122j)
| (-3.0616148149006608712 - 4.4656749700907727148e-462j)  +/-  (3.04e-122, 3.04e-122j)
| (-9.1314208922544435709 + 4.097181830433944754e-464j)  +/-  (3.06e-122, 3.06e-122j)
| (4.33391182001406842 - 3.006098257388069633e-464j)  +/-  (2.91e-121, 2.91e-121j)
| (-1.856685160477125348 + 1.6195179143512500065e-474j)  +/-  (1.29e-123, 1.29e-123j)
| (-2.4494897427831780982 + 3.2832547478656740745e-474j)  +/-  (7.25e-123, 7.25e-123j)
| (1 + 8.859905313579719532e-476j)  +/-  (9.81e-125, 9.81e-125j)
| (1.856685160477125348 + 2.646944501107599328e-473j)  +/-  (1.29e-123, 1.29e-123j)
| (-5.0001217438068530231 + 9.0635813401552295243e-472j)  +/-  (5.71e-121, 5.71e-121j)
| (-1 + 1.1435571102212644727e-479j)  +/-  (8.67e-125, 8.67e-125j)
| (2.4494897427831780982 + 1.4845436939758974102e-476j)  +/-  (6.98e-123, 6.98e-123j)
| (1.3261218731917758015 - 9.496038009821526973e-482j)  +/-  (3.05e-124, 3.05e-124j)
| (6.4262452739510430589 + 1.3235897790287239206e-478j)  +/-  (7.49e-121, 7.49e-121j)
| (0.55970255803352463976 - 1.3551675497326579897e-491j)  +/-  (5.65e-126, 5.65e-126j)
| (-1.3261218731917758015 - 1.2637320939242809147e-489j)  +/-  (3.45e-124, 3.45e-124j)
| (-0.55970255803352463976 + 1.4418471345174449818e-491j)  +/-  (5.65e-126, 5.65e-126j)
| (5.0001217438068530231 - 1.9726952080810534818e-487j)  +/-  (6.29e-121, 6.29e-121j)
| (3.6891371873822652854 - 2.3192686825258624286e-494j)  +/-  (1.1e-121, 1.1e-121j)
| (-1.2908971866924668312e-501 + 8.8257569805572471427e-503j)  +/-  (3.75e-500, 3.75e-500j)
| (-4.33391182001406842 - 4.0420547229620169457e-496j)  +/-  (2.63e-121, 2.63e-121j)
-------------------------------------------------
The weights are:
| (0.0022788350211459970844 - 5.5575295523104900131e-434j)  +/-  (1.35e-31, 2.31e-92j)
| (2.363272863856645507e-15 - 6.4183734674637273474e-442j)  +/-  (1.42e-43, 2.44e-104j)
| (1.6557711917857177188e-12 - 8.8622140751087455245e-441j)  +/-  (7.29e-43, 1.25e-103j)
| (2.363272863856645507e-15 + 3.0253353511723580958e-442j)  +/-  (2.02e-44, 3.46e-105j)
| (1.6557711917857177188e-12 + 2.5924683486056463518e-440j)  +/-  (1.44e-43, 2.46e-104j)
| (3.2493466059030466616e-10 + 1.9174307182234755044e-439j)  +/-  (4.83e-42, 8.27e-103j)
| (2.5817801301378272091e-08 - 2.4364900005739283007e-438j)  +/-  (2.88e-41, 4.93e-102j)
| (2.5817801301378272091e-08 + 8.2935183661076535456e-438j)  +/-  (1.58e-42, 2.71e-103j)
| (0.00028105499340925742472 + 8.3762554090349291147e-436j)  +/-  (1.32e-38, 2.27e-99j)
| (3.7526238500899498197e-19 + 5.221610598013340806e-444j)  +/-  (9.25e-48, 1.58e-108j)
| (0.0022788350211459970844 - 3.9790669142698828858e-435j)  +/-  (1.67e-37, 2.86e-98j)
| (3.7526238500899498197e-19 - 2.6596703303194505446e-444j)  +/-  (2.22e-47, 3.8e-108j)
| (2.1790708869926374973e-05 + 8.8265428915820190621e-436j)  +/-  (2.32e-41, 3.97e-102j)
| (0.041086577679225594329 - 7.2780043906817321571e-434j)  +/-  (2.01e-35, 3.43e-96j)
| (0.011998385899606411933 + 1.7093922599439682502e-434j)  +/-  (7.23e-37, 1.24e-97j)
| (0.074485877885500490895 - 1.0581675470915909817e-432j)  +/-  (3.38e-33, 5.79e-94j)
| (0.041086577679225594329 - 2.9797552030614834059e-433j)  +/-  (6.83e-37, 1.17e-97j)
| (1.0086517687465756514e-06 + 2.1856034474805479264e-437j)  +/-  (1.36e-41, 2.33e-102j)
| (0.074485877885500490895 - 5.3627692400995764017e-433j)  +/-  (8.18e-35, 1.4e-95j)
| (0.011998385899606411933 + 1.5455094410733125839e-433j)  +/-  (1.41e-38, 2.42e-99j)
| (0.073308062718859666683 + 7.9300613371699984081e-433j)  +/-  (2.55e-36, 4.37e-97j)
| (3.2493466059030466616e-10 - 5.6745263735155882508e-439j)  +/-  (4.84e-45, 8.29e-106j)
| (0.18305891132117019061 + 7.6643341442272274412e-433j)  +/-  (1.12e-36, 1.92e-97j)
| (0.073308062718859666683 + 3.1300503856446369191e-433j)  +/-  (1.62e-37, 2.77e-98j)
| (0.18305891132117019061 + 5.290633053359923895e-433j)  +/-  (2.48e-37, 4.25e-98j)
| (1.0086517687465756514e-06 - 9.2240427151474716909e-437j)  +/-  (2.71e-43, 4.65e-104j)
| (0.00028105499340925742472 - 9.0798901339322003738e-435j)  +/-  (1.19e-41, 2.04e-102j)
| (0.22695893795209924256 - 5.4082357939704173282e-433j)  +/-  (4.16e-39, 7.43e-100j)
| (2.1790708869926374973e-05 - 1.5028494599917665631e-436j)  +/-  (1.54e-42, 2.6e-103j)
