Starting with polynomial:
P : 65536*t^16 - 3932160*t^14 + 89456640*t^12 - 984023040*t^10 + 5535129600*t^8 - 15498362880*t^6 + 19372953600*t^4 - 8302694400*t^2 + 518918400
Extension levels are: 16 25
-------------------------------------------------
Trying to find an order 25 Kronrod extension for:
P1 : 65536*t^16 - 3932160*t^14 + 89456640*t^12 - 984023040*t^10 + 5535129600*t^8 - 15498362880*t^6 + 19372953600*t^4 - 8302694400*t^2 + 518918400
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 65536*t^41 - 8128264707899392/408408193*t^39 + 3316304343627431936/1225224579*t^37 - 89265775658405232640/408408193*t^35 + 4785466924215639101440/408408193*t^33 - 180428931744118839541760/408408193*t^31 + 4945799066484492884828160/408408193*t^29 - 100508620350367918459330560/408408193*t^27 + 1530713918426998939541107200/408408193*t^25 - 17548070673308021668838016000/408408193*t^23 + 151307080232050296066056544000/408408193*t^21 - 975744398087960610449340000000/408408193*t^19 + 4656342434289480731694037140000/408408193*t^17 - 16176787556428454777457395760000/408408193*t^15 + 39965499815413888429420887180000/408408193*t^13 - 67925523938009488715300115780000/408408193*t^11 + 75753940895289273032147104498125/408408193*t^9 - 51699180204188815459145072838750/408408193*t^7 + 38672513977790445771516976603125/816816386*t^5 - 6501999614867367465850711340625/816816386*t^3 + 2470336694583616570015044365625/6534531088*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:
| (5.1374295261280278388 + 1.5446987509158440893e-426j)  +/-  (1.58e-118, 1.58e-118j)
| (-4.2659537351016957487 + 3.179909762532383984e-428j)  +/-  (2e-118, 2e-118j)
| (5.6164171132872353918 - 4.9566982582340453199e-435j)  +/-  (7.83e-119, 7.83e-119j)
| (-5.6164171132872353918 + 1.0696693687052168739e-435j)  +/-  (7.92e-119, 7.92e-119j)
| (-6.1357502262834886583 - 1.129512583552861139e-440j)  +/-  (3.26e-119, 3.26e-119j)
| (6.1357502262834886583 + 1.5887137457960941901e-441j)  +/-  (3.3e-119, 3.3e-119j)
| (6.7166533253209142291 - 1.1555029631473894458e-444j)  +/-  (6.69e-120, 6.69e-120j)
| (-7.4161944200507361316 + 1.4135390425365232202e-448j)  +/-  (7.33e-121, 7.33e-121j)
| (-5.1374295261280278388 + 6.5994149643181152286e-445j)  +/-  (1.42e-118, 1.42e-118j)
| (4.6887389393058183647 + 3.0090612660039269585e-450j)  +/-  (1.99e-118, 1.99e-118j)
| (1.0903835945961675569 - 3.1324901280359471991e-458j)  +/-  (5.19e-123, 5.19e-123j)
| (7.4161944200507361316 - 3.6274575454804519134e-456j)  +/-  (6.83e-121, 6.83e-121j)
| (-2.2348225101512998469 + 5.1699986527963336973e-455j)  +/-  (5.2e-120, 5.2e-120j)
| (0.27348104613815245216 - 3.3873959013765951797e-461j)  +/-  (3.62e-126, 3.62e-126j)
| (1.6751082991395138822 - 2.2630324554928354999e-456j)  +/-  (3.12e-121, 3.12e-121j)
| (2.5462021578474813622 + 2.5679657005737976905e-454j)  +/-  (1.66e-119, 1.66e-119j)
| (3.505058888194946037 + 1.7691326055382378951e-453j)  +/-  (1.47e-118, 1.47e-118j)
| (-3.8694479048601226987 + 3.2349284009460296916e-457j)  +/-  (1.82e-118, 1.82e-118j)
| (-0.82295144914465589258 + 2.8996793962160812125e-468j)  +/-  (5.65e-124, 5.65e-124j)
| (-1.6751082991395138822 - 2.1571760452680702642e-465j)  +/-  (3.01e-121, 3.01e-121j)
| (3.1769991619799560268 + 1.9488638795255754204e-463j)  +/-  (9.9e-119, 9.9e-119j)
| (2.2348225101512998469 + 1.5069535305661174383e-465j)  +/-  (4.88e-120, 4.88e-120j)
| (-2.5462021578474813622 + 1.0476850473422088627e-462j)  +/-  (1.77e-119, 1.77e-119j)
| (-6.7166533253209142291 + 5.9442005030229086062e-466j)  +/-  (7.31e-120, 7.31e-120j)
| (-1.3802585391988807964 + 1.163521217814411079e-469j)  +/-  (3.83e-122, 3.83e-122j)
| (-4.6887389393058183647 + 5.9615917602532845432e-465j)  +/-  (1.87e-118, 1.87e-118j)
| (3.8694479048601226987 - 2.3490533164999547529e-468j)  +/-  (1.82e-118, 1.82e-118j)
| (1.9517879909162539774 - 5.1817645628571102937e-472j)  +/-  (1.4e-120, 1.4e-120j)
| (4.2659537351016957487 - 7.1407835468314338988e-470j)  +/-  (2.04e-118, 2.04e-118j)
| (-0.55352139366390456624 - 6.3875351927017416184e-477j)  +/-  (5.14e-125, 5.14e-125j)
| (-3.505058888194946037 - 6.9726052009511040322e-469j)  +/-  (1.47e-118, 1.47e-118j)
| (1.3802585391988807964 - 2.5647152479611011028e-478j)  +/-  (4.06e-122, 4.06e-122j)
| (0.82295144914465589258 + 1.7003626855429052491e-480j)  +/-  (5.53e-124, 5.53e-124j)
| (2.864859150709562238 - 2.7836746134516266449e-476j)  +/-  (4.81e-119, 4.81e-119j)
| (-1.9517879909162539774 + 1.5417974422356540926e-475j)  +/-  (1.52e-120, 1.52e-120j)
| (-0.27348104613815245216 - 3.2758669742116669253e-482j)  +/-  (3.62e-126, 3.62e-126j)
| (-2.864859150709562238 + 1.1177145328595066176e-477j)  +/-  (4.69e-119, 4.69e-119j)
| (0.55352139366390456624 + 1.26099349287430157e-492j)  +/-  (5.05e-125, 5.05e-125j)
| (1.1741441795935134064e-498 + 4.7680370717744711069e-500j)  +/-  (4.82e-497, 4.82e-497j)
| (-3.1769991619799560268 - 1.3013882329103111367e-490j)  +/-  (9.8e-119, 9.8e-119j)
| (-1.0903835945961675569 - 1.4538179815716708136e-497j)  +/-  (4.93e-123, 4.93e-123j)
-------------------------------------------------
The weights are:
| (9.0016996517721351695e-13 - 9.3961639481083517107e-438j)  +/-  (7.34e-32, 3.25e-89j)
| (2.8901146546405692346e-09 + 5.459886404657195231e-436j)  +/-  (1.89e-29, 8.36e-87j)
| (5.600341077096992537e-15 - 1.1018826530201484685e-439j)  +/-  (1.31e-33, 5.8e-91j)
| (5.600341077096992537e-15 + 1.3690794628236381908e-440j)  +/-  (1.6e-34, 7.11e-92j)
| (1.3734238323301985635e-17 - 2.6568987532169826875e-442j)  +/-  (3.68e-36, 1.63e-93j)
| (1.3734238323301985635e-17 + 1.2891604639863126985e-441j)  +/-  (3.35e-36, 1.48e-93j)
| (9.0069131129305274326e-21 - 1.0245136202708997526e-443j)  +/-  (2.91e-38, 1.29e-95j)
| (5.9151241563286707448e-25 - 8.8611453407266680673e-447j)  +/-  (3.23e-41, 1.43e-98j)
| (9.0016996517721351695e-13 - 5.0009274330326365988e-439j)  +/-  (1.84e-34, 8.16e-92j)
| (6.9606938425697316209e-11 + 5.9077422929209610338e-437j)  +/-  (1.59e-33, 7.07e-91j)
| (0.047765412202719329036 - 1.2189833176896624346e-430j)  +/-  (5.81e-17, 2.58e-74j)
| (5.9151241563286707448e-25 + 2.66835617951142457e-446j)  +/-  (6.46e-41, 2.87e-98j)
| (0.0011413810996321096008 - 4.9986401313744000088e-433j)  +/-  (1.54e-26, 6.83e-84j)
| (0.14576487077905268667 + 2.4343955745468795802e-430j)  +/-  (2.43e-17, 1.08e-74j)
| (0.0097795525436463073138 - 3.6304471331800485844e-431j)  +/-  (9.7e-23, 4.3e-80j)
| (0.00027564890177900821702 + 1.9973443897614878949e-432j)  +/-  (8.1e-28, 3.59e-85j)
| (9.0061447168698941439e-07 - 2.6081577917074560331e-434j)  +/-  (1.49e-31, 6.59e-89j)
| (6.7731154740389069669e-08 - 2.2485349876334209109e-435j)  +/-  (5.47e-34, 2.42e-91j)
| (0.07529078130274632338 + 9.9696329306000756264e-431j)  +/-  (8.98e-22, 3.98e-79j)
| (0.0097795525436463073138 - 8.4908329673162600306e-432j)  +/-  (3.99e-26, 1.77e-83j)
| (7.3326831921565277973e-06 + 1.3816377500166633815e-433j)  +/-  (1.03e-30, 4.57e-88j)
| (0.0011413810996321096008 - 6.6969959773028286973e-432j)  +/-  (1.77e-27, 7.85e-85j)
| (0.00027564890177900821702 - 1.5792906448682824586e-434j)  +/-  (2.03e-30, 9.02e-88j)
| (9.0069131129305274326e-21 + 2.7826810458478569689e-444j)  +/-  (4.96e-42, 2.2e-99j)
| (0.02500298562127015431 + 2.225583619394312163e-431j)  +/-  (6.83e-27, 3.03e-84j)
| (6.9606938425697316209e-11 + 1.7228312491055407587e-437j)  +/-  (2.62e-36, 1.16e-93j)
| (6.7731154740389069669e-08 + 3.6734460411753418996e-435j)  +/-  (3.96e-34, 1.75e-91j)
| (0.0034003375751887076264 + 1.7753425260644099277e-431j)  +/-  (2.4e-29, 1.06e-86j)
| (2.8901146546405692346e-09 - 4.5052086829052072085e-436j)  +/-  (3.25e-35, 1.44e-92j)
| (0.11527243428116445993 - 1.5001395444120431061e-430j)  +/-  (6.24e-28, 2.77e-85j)
| (9.0061447168698941439e-07 + 8.2621811354085689399e-435j)  +/-  (3.38e-35, 1.5e-92j)
| (0.02500298562127015431 + 6.7682090882810007699e-431j)  +/-  (6.46e-29, 2.85e-86j)
| (0.07529078130274632338 + 1.8375897209459630187e-430j)  +/-  (1.11e-28, 4.9e-86j)
| (4.8415202807225876696e-05 - 5.5528472912259680476e-433j)  +/-  (1.99e-32, 8.76e-90j)
| (0.0034003375751887076264 + 2.7078733717942650555e-432j)  +/-  (1.56e-31, 6.87e-89j)
| (0.14576487077905268667 + 2.000282371009819702e-430j)  +/-  (1.1e-29, 4.82e-87j)
| (4.8415202807225876696e-05 + 5.1996506958876508156e-434j)  +/-  (4.03e-34, 1.77e-91j)
| (0.11527243428116445993 - 2.2438105627945961666e-430j)  +/-  (5.22e-30, 2.26e-87j)
| (0.15249975300109545403 - 2.3778841491656705633e-430j)  +/-  (3.96e-30, 1.71e-87j)
| (7.3326831921565277973e-06 - 2.5842492335920635354e-434j)  +/-  (4.12e-35, 1.86e-92j)
| (0.047765412202719329036 - 5.2822751809560404109e-431j)  +/-  (3.16e-31, 1.3e-88j)
