Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 9 18
-------------------------------------------------
Trying to find an order 9 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P2 : t^11 - 619/7*t^9 + 15354/7*t^7 - 19566*t^5 + 59445*t^3 - 41985*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^29 - 1021756589425959955765938581/2850224919301609318221683*t^27 + 22525821539178627681014146092/407174988471658474031669*t^25 - 151620348062466494230739924936430/31352474112317702500438513*t^23 + 41592892484187154753690246367848443/156762370561588512502192565*t^21 - 214420888020936329369418966738563943/22394624365941216071741795*t^19 + 5191816660652832223273260124557362958/22394624365941216071741795*t^17 - 84600042386791542941118914897094812124/22394624365941216071741795*t^15 + 183605529121517298860656872021148360473/4478924873188243214348359*t^13 - 117761403601833167872513315908748990197/407174988471658474031669*t^11 + 518747118222095370706942641325194258696/407174988471658474031669*t^9 - 1337180070411216499248694591054847140086/407174988471658474031669*t^7 + 1811229591549404416703024650011408191493/407174988471658474031669*t^5 - 24566974753529111223411036510323895045/9469185778410662186783*t^3 + 166100845302103913621419931053394347530/407174988471658474031669*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:
| (5.7898698002819304955 + 3.4108424348264697808e-480j)  +/-  (9.63e-121, 9.63e-121j)
| (8.8571133130148536045 + 3.1999643968362559539e-487j)  +/-  (1.04e-121, 1.04e-121j)
| (6.5560462636330533108 + 2.6879109118970982235e-490j)  +/-  (1.09e-120, 1.09e-120j)
| (-8.8571133130148536045 + 2.2080287743897730234e-499j)  +/-  (1.01e-121, 1.01e-121j)
| (7.3693356610308432189 + 2.9146713267651583776e-497j)  +/-  (7.61e-121, 7.61e-121j)
| (-7.3693356610308432189 - 1.0314432708147098502e-505j)  +/-  (7.96e-121, 7.96e-121j)
| (-8.1462872336954129028 + 5.2293348321412969054e-508j)  +/-  (4.34e-121, 4.34e-121j)
| (5.0690355465806323091 - 3.2559058618304732229e-506j)  +/-  (6.11e-121, 6.11e-121j)
| (-4.3862249342620953383 - 3.9213891569568565135e-512j)  +/-  (3.26e-121, 3.26e-121j)
| (-5.0690355465806323091 + 2.7167737537206897219e-512j)  +/-  (6.4e-121, 6.4e-121j)
| (1.5167131566735577311 - 2.0332752681680985352e-516j)  +/-  (4.42e-124, 4.42e-124j)
| (-6.5560462636330533108 + 2.0033607479206297774e-513j)  +/-  (1.04e-120, 1.04e-120j)
| (8.1462872336954129028 + 5.7570183570550656911e-515j)  +/-  (3.8e-121, 3.8e-121j)
| (-5.7898698002819304955 - 3.9816054602821828249e-515j)  +/-  (9.46e-121, 9.46e-121j)
| (2.5558390227137815367 - 3.2487459806004912942e-515j)  +/-  (1.42e-122, 1.42e-122j)
| (4.3862249342620953383 - 1.2488953845409530422e-518j)  +/-  (3.24e-121, 3.24e-121j)
| (-3.7378435769604270701 + 2.7274424117001777229e-527j)  +/-  (1.41e-121, 1.41e-121j)
| (-2.0281536517888087075 - 9.8597175431337201383e-529j)  +/-  (3.02e-123, 3.02e-123j)
| (-1.5167131566735577311 + 6.3246282892754330572e-529j)  +/-  (3.92e-124, 3.92e-124j)
| (-3.1255538604259774764 + 2.7217677541213957257e-527j)  +/-  (5.33e-122, 5.33e-122j)
| (0.49000685851585938765 + 6.14055602050527252e-531j)  +/-  (2.91e-126, 2.91e-126j)
| (2.0281536517888087075 - 4.5643483060792959189e-527j)  +/-  (3.11e-123, 3.11e-123j)
| (1 - 4.7059006556563761886e-530j)  +/-  (4.22e-125, 4.22e-125j)
| (-0.49000685851585938765 - 1.173140776598701421e-531j)  +/-  (2.91e-126, 2.91e-126j)
| (-1 + 1.7234555732433604783e-530j)  +/-  (4.46e-125, 4.46e-125j)
| (3.7378435769604270701 - 1.0347308287687697626e-528j)  +/-  (1.42e-121, 1.42e-121j)
| (8.4714398275024111568e-543 - 5.3779665146385085273e-543j)  +/-  (2.91e-541, 2.91e-541j)
| (3.1255538604259774764 - 1.35806147983666354e-539j)  +/-  (4.71e-122, 4.71e-122j)
| (-2.5558390227137815367 - 7.7956043040809582407e-546j)  +/-  (1.38e-122, 1.38e-122j)
-------------------------------------------------
The weights are:
| (1.5561200081563432617e-08 - 1.6638896292844923603e-487j)  +/-  (3.98e-33, 2.09e-93j)
| (3.3559369409544793223e-18 + 1.8841353068409314382e-493j)  +/-  (8.12e-39, 4.26e-99j)
| (1.4651807012365342102e-10 - 6.008444138496707547e-489j)  +/-  (6.51e-35, 3.41e-95j)
| (3.3559369409544793223e-18 - 3.9455919028027527419e-494j)  +/-  (6.31e-41, 3.3e-101j)
| (5.3141913765609518586e-13 + 1.8882117165538736655e-490j)  +/-  (7.62e-37, 3.99e-97j)
| (5.3141913765609518586e-13 - 2.2663723527736758279e-491j)  +/-  (2.63e-39, 1.38e-99j)
| (1.0591795842534912471e-15 + 1.185952499892229208e-492j)  +/-  (3.56e-40, 1.87e-100j)
| (7.3604860149091675773e-07 + 6.373705013416979191e-487j)  +/-  (4.21e-35, 2.2e-95j)
| (1.7631979696833869749e-05 - 3.0457924517090776692e-487j)  +/-  (1.02e-35, 5.36e-96j)
| (7.3604860149091675773e-07 + 4.2309834646210143333e-488j)  +/-  (5.33e-37, 2.79e-97j)
| (0.064861888077064088239 + 3.1960751103080893635e-484j)  +/-  (4.84e-29, 2.54e-89j)
| (1.4651807012365342102e-10 + 3.728786471830860505e-490j)  +/-  (2.45e-39, 1.28e-99j)
| (1.0591795842534912471e-15 - 7.0138762507761143569e-492j)  +/-  (8.73e-42, 4.58e-102j)
| (1.5561200081563432617e-08 - 4.5835919809534626015e-489j)  +/-  (1.96e-38, 1.03e-98j)
| (0.0083216262077528910262 + 8.0537508565234305433e-485j)  +/-  (9.66e-35, 5.06e-95j)
| (1.7631979696833869749e-05 - 2.2081278021759662506e-486j)  +/-  (1.72e-37, 9e-98j)
| (0.00023288668402424852538 + 1.7662292191310589179e-486j)  +/-  (7.99e-37, 4.18e-97j)
| (0.026201340903880275248 - 8.7475108768643905796e-485j)  +/-  (4.54e-35, 2.37e-95j)
| (0.064861888077064088239 + 1.869181486275979528e-484j)  +/-  (4.29e-34, 2.25e-94j)
| (0.0017868039638507563832 - 8.346485775298015014e-486j)  +/-  (1.08e-36, 5.69e-97j)
| (0.17685024772481942771 + 5.8822323932775544868e-484j)  +/-  (5.13e-34, 2.72e-94j)
| (0.026201340903880275248 - 1.8180065290144323121e-484j)  +/-  (8.17e-36, 4.32e-96j)
| (0.12512343130845383693 - 4.6710380468679257577e-484j)  +/-  (1.68e-34, 8.85e-95j)
| (0.17685024772481942771 + 4.9642735311227112557e-484j)  +/-  (5.69e-35, 3.02e-95j)
| (0.12512343130845383693 - 3.2951536236715279384e-484j)  +/-  (4.68e-35, 2.47e-95j)
| (0.00023288668402424852538 + 8.2007362124105036758e-486j)  +/-  (1.2e-38, 6.36e-99j)
| (0.1932067827872110356 - 6.0870949230952493167e-484j)  +/-  (1.14e-35, 6.5e-96j)
| (0.0017868039638507563832 - 2.792929158729209774e-485j)  +/-  (6.31e-38, 3.35e-98j)
| (0.0083216262077528910262 + 3.1208946654215913475e-485j)  +/-  (1.82e-37, 7.95e-98j)
