Starting with polynomial:
P : t^16 - 120*t^14 + 5460*t^12 - 120120*t^10 + 1351350*t^8 - 7567560*t^6 + 18918900*t^4 - 16216200*t^2 + 2027025
Extension levels are: 16 25
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Trying to find an order 25 Kronrod extension for:
P1 : t^16 - 120*t^14 + 5460*t^12 - 120120*t^10 + 1351350*t^8 - 7567560*t^6 + 18918900*t^4 - 16216200*t^2 + 2027025
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^41 - 248054953244/408408193*t^39 + 202411153785854/1225224579*t^37 - 10896701130176420/408408193*t^35 + 1168326885794833765/408408193*t^33 - 88100064328183027120/408408193*t^31 + 4829881900863762582840/408408193*t^29 - 196305899121812340740880/408408193*t^27 + 5979351243855464607582450/408408193*t^25 - 137094302135218919287797000/408408193*t^23 + 2364173128625785876032133500/408408193*t^21 - 30492012440248769076541875000/408408193*t^19 + 291021402143092545730877321250/408408193*t^17 - 2022098444553556847182174470000/408408193*t^15 + 9991374953853472107355221795000/408408193*t^13 - 33962761969004744357650057890000/408408193*t^11 + 75753940895289273032147104498125/408408193*t^9 - 103398360408377630918290145677500/408408193*t^7 + 77345027955580891543033953206250/408408193*t^5 - 26007998459469469863402845362500/408408193*t^3 + 2470336694583616570015044365625/408408193*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
Sufficient bits for target precision reached
Positive weights:   41 out of 41
Indefinite weights: 0 out of 41
Negative weights:   0 out of 41
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-9.4987822264271850052 - 7.6616222768435624279e-470j)  +/-  (9.25e-120, 9.25e-120j)
| (9.4987822264271850052 + 4.5057093355060352375e-476j)  +/-  (9.66e-120, 9.66e-120j)
| (7.2654225115862398378 - 1.9252132201158892953e-474j)  +/-  (1.98e-118, 1.98e-118j)
| (-8.6772611853438965473 - 2.1794232675122768489e-476j)  +/-  (4.44e-119, 4.44e-119j)
| (-7.9428132535551561096 + 1.6501250980076964551e-483j)  +/-  (1.06e-118, 1.06e-118j)
| (-6.6308781983931284802 - 1.5516577047275558104e-482j)  +/-  (2.81e-118, 2.81e-118j)
| (6.6308781983931284802 + 1.8009579763470070632e-483j)  +/-  (2.8e-118, 2.8e-118j)
| (5.4722257059493430884 - 1.0088568795108883241e-489j)  +/-  (2.69e-118, 2.69e-118j)
| (4.4929553025200112427 - 3.4347954557055078199e-505j)  +/-  (1.44e-118, 1.44e-118j)
| (-6.032969628636979794 - 3.1260332820783349175e-510j)  +/-  (2.97e-118, 2.97e-118j)
| (-10.488082730031421184 + 2.0799192679677663263e-521j)  +/-  (1.04e-120, 1.04e-120j)
| (4.0515226652221296048 + 7.0795276593418471706e-518j)  +/-  (6.97e-119, 6.97e-119j)
| (-7.2654225115862398378 - 9.1917169970321017345e-522j)  +/-  (1.97e-118, 1.97e-118j)
| (-5.4722257059493430884 + 1.064713495237824864e-523j)  +/-  (2.99e-118, 2.99e-118j)
| (8.6772611853438965473 + 4.6203463823596126842e-528j)  +/-  (4.11e-119, 4.11e-119j)
| (2.3689608750868280748 + 1.8451783214558008004e-529j)  +/-  (3.99e-121, 3.99e-121j)
| (-2.3689608750868280748 - 2.8376300876814255843e-529j)  +/-  (4.28e-121, 4.28e-121j)
| (3.6008736241715482882 + 3.6720369554424150098e-527j)  +/-  (2.36e-119, 2.36e-119j)
| (-1.9519803457163334645 + 5.347440932573686333e-530j)  +/-  (5.7e-122, 5.7e-122j)
| (-4.9569018166016545024 + 9.0323386421807464731e-528j)  +/-  (2.57e-118, 2.57e-118j)
| (4.9569018166016545024 + 4.2655406151241043708e-527j)  +/-  (2.18e-118, 2.18e-118j)
| (1.1638291005549647742 - 1.8473844167055842975e-532j)  +/-  (7.17e-124, 7.17e-124j)
| (-3.6008736241715482882 - 2.3246745731114134239e-526j)  +/-  (2.36e-119, 2.36e-119j)
| (-4.0515226652221296048 - 2.1506394300748461446e-527j)  +/-  (7.49e-119, 7.49e-119j)
| (-0.38676060450055734772 - 2.0819940973198024179e-535j)  +/-  (4.24e-126, 4.24e-126j)
| (7.9428132535551561096 + 2.2174978876206064447e-529j)  +/-  (1.18e-118, 1.18e-118j)
| (-3.1605163033526521288 + 5.1882212484279703482e-529j)  +/-  (7.16e-120, 7.16e-120j)
| (3.1605163033526521288 - 1.8474718134351713226e-531j)  +/-  (7.98e-120, 7.98e-120j)
| (-1.5420352676670267927 - 6.4611611772136868443e-534j)  +/-  (6.37e-123, 6.37e-123j)
| (-2.7602450476307016168 - 1.9289843382060626609e-530j)  +/-  (2.25e-120, 2.25e-120j)
| (6.032969628636979794 + 2.300997377755260386e-532j)  +/-  (3.17e-118, 3.17e-118j)
| (0.38676060450055734772 - 5.5271693869299042132e-537j)  +/-  (5.4e-126, 5.4e-126j)
| (0.78279746198315079883 + 3.7688043931598902338e-536j)  +/-  (6.51e-125, 6.51e-125j)
| (-1.1638291005549647742 - 4.8611827553578853443e-535j)  +/-  (7.38e-124, 7.38e-124j)
| (-4.4929553025200112427 - 1.8969339767797132598e-535j)  +/-  (1.53e-118, 1.53e-118j)
| (10.488082730031421184 - 4.7941415977185885031e-537j)  +/-  (9.62e-121, 9.62e-121j)
| (2.7602450476307016168 + 1.1841717014514094558e-536j)  +/-  (2e-120, 2e-120j)
| (1.5420352676670267927 - 7.7945949569697766334e-538j)  +/-  (7.11e-123, 7.11e-123j)
| (1.9519803457163334645 + 4.9729488707975468037e-538j)  +/-  (5.55e-122, 5.55e-122j)
| (-5.1497854742802204531e-560 - 2.2017238935127567667e-559j)  +/-  (9.27e-558, 9.27e-558j)
| (-0.78279746198315079883 + 6.8323122178606139852e-541j)  +/-  (5.73e-125, 5.73e-125j)
-------------------------------------------------
The weights are:
| (9.0069131129305274326e-21 - 3.8541641812460628401e-489j)  +/-  (6.19e-33, 3.92e-92j)
| (9.0069131129305274326e-21 - 2.7584888659207711747e-491j)  +/-  (1.69e-33, 1.07e-92j)
| (9.0016996517721351695e-13 + 1.1964546838405565951e-485j)  +/-  (5.78e-29, 3.66e-88j)
| (1.3734238323301985635e-17 + 6.7629638542463741181e-488j)  +/-  (8.65e-32, 5.48e-91j)
| (5.600341077096992537e-15 - 1.4821950810165425479e-486j)  +/-  (1.02e-30, 6.47e-90j)
| (6.9606938425697316209e-11 - 4.142997745835093738e-484j)  +/-  (1.36e-28, 8.63e-88j)
| (6.9606938425697316209e-11 - 1.2590435138307071111e-484j)  +/-  (1.8e-29, 1.14e-88j)
| (6.7731154740389069669e-08 - 1.7569579729932178945e-482j)  +/-  (3.06e-27, 1.94e-86j)
| (7.3326831921565277973e-06 - 1.0370208113970507871e-480j)  +/-  (6.77e-25, 4.29e-84j)
| (2.8901146546405692346e-09 + 5.1474986780029528068e-483j)  +/-  (5.77e-29, 3.65e-88j)
| (5.9151241563286707448e-25 - 2.5879938846755098616e-492j)  +/-  (7.94e-38, 5.03e-97j)
| (4.8415202807225876696e-05 + 4.9528719805443060193e-480j)  +/-  (5.47e-25, 3.47e-84j)
| (9.0016996517721351695e-13 + 2.7546882379444379163e-485j)  +/-  (3.82e-31, 2.42e-90j)
| (6.7731154740389069669e-08 - 5.3315779661353376136e-482j)  +/-  (1.03e-28, 6.53e-88j)
| (1.3734238323301985635e-17 + 1.9406346725729004304e-489j)  +/-  (1.54e-36, 9.78e-96j)
| (0.0097795525436463073138 + 5.7522638700372574877e-478j)  +/-  (1.49e-21, 9.42e-81j)
| (0.0097795525436463073138 + 9.147940635298723208e-478j)  +/-  (2.73e-22, 1.73e-81j)
| (0.00027564890177900821702 - 2.0990792211945915355e-479j)  +/-  (2.34e-25, 1.48e-84j)
| (0.02500298562127015431 - 1.7912862889380310697e-477j)  +/-  (1.07e-20, 6.78e-80j)
| (9.0061447168698941439e-07 + 4.3834024116652210615e-481j)  +/-  (6.85e-29, 4.34e-88j)
| (9.0061447168698941439e-07 + 1.6043607982246586556e-481j)  +/-  (5.44e-29, 3.44e-88j)
| (0.07529078130274632338 - 4.2640218775986909321e-477j)  +/-  (1.57e-18, 9.93e-78j)
| (0.00027564890177900821702 - 4.2990089634900603041e-479j)  +/-  (3.1e-27, 1.97e-86j)
| (4.8415202807225876696e-05 + 1.1157382989759340023e-479j)  +/-  (3.74e-28, 2.37e-87j)
| (0.14576487077905268667 - 7.8372151577668180441e-477j)  +/-  (5.37e-21, 3.4e-80j)
| (5.600341077096992537e-15 - 3.5803108178083698175e-488j)  +/-  (7.07e-37, 4.48e-96j)
| (0.0011413810996321096008 + 1.5305360653832368738e-478j)  +/-  (8.69e-27, 5.51e-86j)
| (0.0011413810996321096008 + 8.1908313529543884072e-479j)  +/-  (6.6e-28, 4.18e-87j)
| (0.047765412202719329036 + 3.386050584596259222e-477j)  +/-  (4.59e-24, 2.91e-83j)
| (0.0034003375751887076264 - 4.267527087083092981e-478j)  +/-  (3.04e-26, 1.92e-85j)
| (2.8901146546405692346e-09 + 1.5467627504349908793e-483j)  +/-  (1.98e-33, 1.25e-92j)
| (0.14576487077905268667 - 7.272680701206473321e-477j)  +/-  (2.03e-24, 1.28e-83j)
| (0.11527243428116445993 + 5.8841758754241503988e-477j)  +/-  (1.21e-24, 7.68e-84j)
| (0.07529078130274632338 - 5.3432404443763753368e-477j)  +/-  (2.67e-25, 1.69e-84j)
| (7.3326831921565277973e-06 - 2.5669665455184663231e-480j)  +/-  (1.12e-29, 7.12e-89j)
| (5.9151241563286707448e-25 + 1.0578759811774787544e-493j)  +/-  (1.4e-43, 8.88e-103j)
| (0.0034003375751887076264 - 2.4792181684361478457e-478j)  +/-  (1.46e-28, 9.25e-88j)
| (0.047765412202719329036 + 2.5092585223886698443e-477j)  +/-  (7.75e-28, 4.9e-87j)
| (0.02500298562127015431 - 1.2241979543554032288e-477j)  +/-  (3e-28, 1.9e-87j)
| (0.15249975300109545403 + 8.1072242503493598082e-477j)  +/-  (1.25e-27, 8.4e-87j)
| (0.11527243428116445993 + 6.8465658775892522459e-477j)  +/-  (5.45e-28, 3.1e-87j)
