Starting with polynomial:
P : t
Extension levels are: 1 4 8 14
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Trying to find an order 4 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P2 : t^5 - 10*t^3 + 15*t
Solvable: 1
-------------------------------------------------
Trying to find an order 14 Kronrod extension for:
P3 : t^13 - 170/3*t^11 + 3251/3*t^9 - 8652*t^7 + 29631*t^5 - 41790*t^3 + 19215*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^27 - 90241522318027534903/375814988811315009*t^25 + 27380734788980366551220/1127444966433945027*t^23 - 1534816087842443410443152/1127444966433945027*t^21 + 17606211387194407209146089/375814988811315009*t^19 - 389462550966169308065806627/375814988811315009*t^17 + 5637850523975265918167980792/375814988811315009*t^15 - 17789116633714730956551281200/125271662937105003*t^13 + 9842432068968480385513453435/11388332994282273*t^11 - 37213821308029265617366690405/11388332994282273*t^9 + 27512798187638179150922749380/3796110998094091*t^7 - 32601173250838664085191148480/3796110998094091*t^5 + 17551931606509521536927327625/3796110998094091*t^3 - 2989529438334911095439436075/3796110998094091*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
-------------------------------------------------
The nodes are:
| (4.4953732788803620681 + 1.2653193355431063501e-483j)  +/-  (2.39e-121, 2.39e-121j)
| (-4.4953732788803620681 + 7.5191610094248603554e-484j)  +/-  (2.48e-121, 2.48e-121j)
| (6.8646569731360898879 + 4.6344173280951747288e-494j)  +/-  (4.52e-122, 4.52e-122j)
| (5.1842688974446196437 - 1.7514901350318315527e-491j)  +/-  (1.78e-121, 1.78e-121j)
| (-5.9716165958155659137 + 1.8584333100649795157e-491j)  +/-  (1.27e-121, 1.27e-121j)
| (7.9414317245184430624 - 7.0147890409568475799e-499j)  +/-  (7.78e-123, 7.78e-123j)
| (-5.1842688974446196437 + 6.3169998450287053841e-496j)  +/-  (1.99e-121, 1.99e-121j)
| (-6.8646569731360898879 - 3.2492597328379770877e-499j)  +/-  (4.75e-122, 4.75e-122j)
| (-2.3315704814142589935 + 2.2836832227600404748e-501j)  +/-  (1.07e-122, 1.07e-122j)
| (2.3315704814142589935 - 2.0290032055059543982e-505j)  +/-  (9.65e-123, 9.65e-123j)
| (1.3556261799742658658 + 1.1746753089720125721e-507j)  +/-  (3.53e-124, 3.53e-124j)
| (5.9716165958155659137 - 3.6506342371629003571e-507j)  +/-  (1.27e-121, 1.27e-121j)
| (-3.4145186036662132826 - 4.6408663898857572833e-512j)  +/-  (1.12e-121, 1.12e-121j)
| (-1.8550647122034955328 + 1.6407525285560507691e-520j)  +/-  (2.27e-123, 2.27e-123j)
| (3.4145186036662132826 - 4.1218904985676397371e-520j)  +/-  (1.1e-121, 1.1e-121j)
| (1.8550647122034955328 - 6.951166992097161047e-527j)  +/-  (2.01e-123, 2.01e-123j)
| (-7.9414317245184430624 + 2.4831532119654591688e-525j)  +/-  (7.7e-123, 7.7e-123j)
| (-3.9309600114055574643 - 6.4101835018362290666e-532j)  +/-  (1.98e-121, 1.98e-121j)
| (-0.9467370109606977334 + 1.4969976205627070675e-542j)  +/-  (6.09e-125, 6.09e-125j)
| (-2.8569700138728056542 + 4.0441146402382448493e-541j)  +/-  (3.79e-122, 3.79e-122j)
| (3.9309600114055574643 + 1.6319286370125254369e-545j)  +/-  (2e-121, 2e-121j)
| (0.54948825854010391233 + 2.2594687320354963227e-553j)  +/-  (6.38e-126, 6.38e-126j)
| (2.8569700138728056542 + 1.9982614172108857056e-550j)  +/-  (3.67e-122, 3.67e-122j)
| (-0.54948825854010391233 + 1.9382502459230556043e-553j)  +/-  (6.38e-126, 6.38e-126j)
| (-1.3556261799742658658 + 6.3519712523138741693e-552j)  +/-  (3.36e-124, 3.36e-124j)
| (9.7792200601463023502e-565 - 8.6627319689287111902e-564j)  +/-  (2.35e-562, 2.35e-562j)
| (0.9467370109606977334 + 7.3591851307494158399e-553j)  +/-  (5.47e-125, 5.47e-125j)
-------------------------------------------------
The weights are:
| (1.0276723732373045114e-05 - 5.2448568825210825288e-488j)  +/-  (3.16e-40, 2.29e-100j)
| (1.0276723732373045114e-05 + 3.0232000487928494098e-488j)  +/-  (4.08e-41, 2.95e-101j)
| (2.2459170251320789295e-11 - 3.4628223497142956524e-493j)  +/-  (1.62e-45, 1.17e-105j)
| (4.3113041391985869169e-07 - 1.2420169050036815572e-489j)  +/-  (3.47e-42, 2.52e-102j)
| (6.0111838527093500604e-09 - 1.6234696429508935119e-491j)  +/-  (3.18e-45, 2.3e-105j)
| (9.9925057616981490956e-15 + 1.9179376495149277268e-495j)  +/-  (8.42e-48, 6.1e-108j)
| (4.3113041391985869169e-07 + 7.9292752403800227637e-490j)  +/-  (8.1e-44, 5.87e-104j)
| (2.2459170251320789295e-11 + 2.473444184719160216e-493j)  +/-  (3.44e-47, 2.49e-107j)
| (0.012862918224136025067 + 9.64779910088918671e-487j)  +/-  (1.35e-38, 9.76e-99j)
| (0.012862918224136025067 - 2.8238974581364086015e-486j)  +/-  (4.67e-39, 3.38e-99j)
| (0.077890037144891157525 - 1.0378740947546366509e-485j)  +/-  (1.72e-35, 1.25e-95j)
| (6.0111838527093500604e-09 + 2.3929882406702849653e-491j)  +/-  (1.67e-45, 1.21e-105j)
| (0.00063442992302376718552 + 2.0961784415876365861e-487j)  +/-  (4.32e-42, 3.13e-102j)
| (0.034664049638753941034 - 1.3385141379900537479e-486j)  +/-  (9.51e-39, 6.89e-99j)
| (0.00063442992302376718552 - 4.208801388857281661e-487j)  +/-  (1.74e-42, 1.26e-102j)
| (0.034664049638753941034 + 5.6465447975991028565e-486j)  +/-  (4.35e-39, 3.15e-99j)
| (9.9925057616981490956e-15 - 1.4348995054552313815e-495j)  +/-  (2.4e-50, 1.74e-110j)
| (9.0143547419970170231e-05 - 9.7810803923747768771e-488j)  +/-  (2.91e-43, 2.11e-103j)
| (0.085365110532132688707 + 1.3186475872280252257e-486j)  +/-  (7.95e-40, 5.75e-100j)
| (0.0037510272845906561077 - 4.7294699349024778049e-487j)  +/-  (6.58e-42, 4.76e-102j)
| (9.0143547419970170231e-05 + 1.7812105788651864358e-487j)  +/-  (5.62e-44, 4.07e-104j)
| (0.17058533411147067239 - 1.0989598378124015728e-485j)  +/-  (4.95e-41, 3.56e-101j)
| (0.0037510272845906561077 + 1.104759711535144105e-486j)  +/-  (1.25e-42, 9.05e-103j)
| (0.17058533411147067239 - 3.8584439774282118076e-486j)  +/-  (2.96e-41, 2.16e-101j)
| (0.077890037144891157525 + 8.7820140909984310149e-487j)  +/-  (1.24e-41, 9.04e-102j)
| (0.22829247141156362689 + 6.1338829046860895999e-486j)  +/-  (1.25e-41, 9.07e-102j)
| (0.085365110532132688707 + 1.3968935674229423419e-485j)  +/-  (7.33e-42, 4.95e-102j)
