Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 7 16
-------------------------------------------------
Trying to find an order 7 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 16 Kronrod extension for:
P2 : t^9 - 173/5*t^7 + 1743/5*t^5 - 1113*t^3 + 798*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^25 - 1998271118619436701/8668431607928285*t^23 + 1110940457535288120331/50276903325984053*t^21 - 3193129745837663521251159/2765229682929122915*t^19 + 501641788199872874368428992/13826148414645614575*t^17 - 9866485266684488257413190502/13826148414645614575*t^15 + 24556924537063223375525157066/2765229682929122915*t^13 - 191331382580401935250738474206/2765229682929122915*t^11 + 16445562475294184528223386277/50276903325984053*t^9 - 222571687427214277786313843709/251384516629920265*t^7 + 312026495095950148930485331899/251384516629920265*t^5 - 1300279447112577931849497921/1733686321585657*t^3 + 6437953764527756999871721014/50276903325984053*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:   25 out of 25
Indefinite weights: 0 out of 25
Negative weights:   0 out of 25
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-4.4288667337963182986 + 2.4759772925126113634e-372j)  +/-  (7.7e-122, 7.7e-122j)
| (6.8692708804302950813 + 1.5651523948581283567e-382j)  +/-  (2.95e-122, 2.95e-122j)
| (-7.9484973427633864962 + 4.1147402260242217748e-390j)  +/-  (5.52e-123, 5.52e-123j)
| (-5.9698675612085715968 + 2.5903426149004250716e-410j)  +/-  (6.47e-122, 6.47e-122j)
| (7.9484973427633864962 + 9.6530253001020775385e-422j)  +/-  (5.41e-123, 5.41e-123j)
| (5.1657019829608286981 - 3.996571299678679234e-419j)  +/-  (8.27e-122, 8.27e-122j)
| (4.4288667337963182986 - 1.8716774876582567192e-419j)  +/-  (7.21e-122, 7.21e-122j)
| (-3.1397980296785904718 - 1.3236821237843814114e-420j)  +/-  (2.53e-122, 2.53e-122j)
| (-3.7524558804224923398 - 1.2000104577823423631e-422j)  +/-  (4.69e-122, 4.69e-122j)
| (-2.5791182567429707587 + 2.7466059672142235484e-428j)  +/-  (7.48e-123, 7.48e-123j)
| (2.0314545988278380851 + 1.6648905704202141583e-431j)  +/-  (1.78e-123, 1.78e-123j)
| (1.4932295159471496162 + 2.2088876322078793414e-435j)  +/-  (2.92e-124, 2.92e-124j)
| (-1 - 1.3578339232318735134e-434j)  +/-  (4.15e-125, 4.15e-125j)
| (-2.0314545988278380851 + 1.3302278434687668651e-433j)  +/-  (1.89e-123, 1.89e-123j)
| (-5.1657019829608286981 - 5.2947805859191457245e-445j)  +/-  (9.02e-122, 9.02e-122j)
| (2.5791182567429707587 - 7.39346025061332948e-454j)  +/-  (7.93e-123, 7.93e-123j)
| (1 + 1.1470712133081415028e-458j)  +/-  (4.26e-125, 4.26e-125j)
| (-9.5340337390845962579e-460 - 1.7308959425352887549e-459j)  +/-  (4.94e-458, 4.94e-458j)
| (-0.52057712965949371644 - 4.9454169786722535855e-459j)  +/-  (2.68e-126, 2.68e-126j)
| (3.7524558804224923398 - 5.3396864058991391547e-461j)  +/-  (5.2e-122, 5.2e-122j)
| (-6.8692708804302950813 - 8.602771291053303307e-480j)  +/-  (3.04e-122, 3.04e-122j)
| (0.52057712965949371644 + 2.903782470558506643e-490j)  +/-  (2.68e-126, 2.68e-126j)
| (5.9698675612085715968 + 7.694828309365497069e-486j)  +/-  (7e-122, 7e-122j)
| (3.1397980296785904718 + 2.3728216719847294611e-489j)  +/-  (2.27e-122, 2.27e-122j)
| (-1.4932295159471496162 - 9.5135398814884782957e-496j)  +/-  (3.07e-124, 3.07e-124j)
-------------------------------------------------
The weights are:
| (1.5518305760138097596e-05 + 1.235442383289811912e-376j)  +/-  (8.62e-42, 1.68e-102j)
| (2.1845618237296597331e-11 - 5.9509311569480953317e-382j)  +/-  (5.46e-47, 1.06e-107j)
| (9.4575638266566189924e-15 - 2.1455960494605601018e-383j)  +/-  (1.98e-48, 3.85e-109j)
| (6.1458425088199552694e-09 - 1.3362305813027915732e-379j)  +/-  (2.46e-45, 4.79e-106j)
| (9.4575638266566189924e-15 + 6.1012227509882504417e-384j)  +/-  (6.19e-49, 1.21e-109j)
| (4.918268049132682992e-07 - 3.6093354363942188374e-379j)  +/-  (2.58e-45, 5.02e-106j)
| (1.5518305760138097596e-05 + 4.3377883090540929466e-378j)  +/-  (3.05e-44, 5.95e-105j)
| (0.0016777607854465190957 + 1.2929961075734615098e-375j)  +/-  (3.26e-42, 6.35e-103j)
| (0.00022538916494692615419 - 4.4719947069239819662e-376j)  +/-  (2.08e-43, 4.05e-104j)
| (0.0078586825637522553702 - 3.4185090230224918898e-375j)  +/-  (2.1e-41, 4.08e-102j)
| (0.027763539503184092054 + 2.8298893618208450366e-375j)  +/-  (1.11e-41, 2.17e-102j)
| (0.068077547275039627752 - 7.4122372120125826576e-375j)  +/-  (5.69e-40, 1.11e-100j)
| (0.11412012223317357634 + 2.3245087742690699543e-374j)  +/-  (1.32e-38, 2.56e-99j)
| (0.027763539503184092054 + 7.6257203951158840028e-375j)  +/-  (2.82e-41, 5.48e-102j)
| (4.918268049132682992e-07 + 4.6998317338207311838e-378j)  +/-  (1.08e-46, 2.1e-107j)
| (0.0078586825637522553702 - 9.023109877761022799e-376j)  +/-  (6.12e-44, 1.19e-104j)
| (0.11412012223317357634 + 1.4681573888879124314e-374j)  +/-  (5.59e-41, 1.09e-101j)
| (0.21215277758531269322 + 2.4542577057375097477e-374j)  +/-  (3.44e-41, 6.69e-102j)
| (0.17418455338153802063 - 2.6485823762168633092e-374j)  +/-  (3.82e-41, 7.43e-102j)
| (0.00022538916494692615419 - 3.6973309801283943614e-377j)  +/-  (2.45e-46, 4.76e-107j)
| (2.1845618237296597331e-11 + 2.7550534707602372296e-381j)  +/-  (8.7e-51, 1.68e-111j)
| (0.17418455338153802063 - 2.0914323411362216675e-374j)  +/-  (1.54e-42, 3.02e-103j)
| (6.1458425088199552694e-09 + 1.9801760223862153178e-380j)  +/-  (8.07e-50, 1.56e-110j)
| (0.0016777607854465190957 + 2.2021860776079077912e-376j)  +/-  (1.24e-45, 2.43e-106j)
| (0.068077547275039627752 - 1.4952795232516121426e-374j)  +/-  (3.81e-44, 6.06e-105j)
