Starting with polynomial:
P : t^12 - 66*t^10 + 1485*t^8 - 13860*t^6 + 51975*t^4 - 62370*t^2 + 10395
Extension levels are: 12 19
-------------------------------------------------
Trying to find an order 19 Kronrod extension for:
P1 : t^12 - 66*t^10 + 1485*t^8 - 13860*t^6 + 51975*t^4 - 62370*t^2 + 10395
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^31 - 2116422576/6191363*t^29 + 312315913191/6191363*t^27 - 26259673964598/6191363*t^25 + 1398913205740875/6191363*t^23 - 49690386691151220/6191363*t^21 + 1206619116618088215/6191363*t^19 - 20214059593797457290/6191363*t^17 + 232994755858705193745/6191363*t^15 - 1822790280084794080200/6191363*t^13 + 9432838402471077518925/6191363*t^11 - 30971150712054099196650/6191363*t^9 + 60404032344599956037025/6191363*t^7 - 62796054487194584255700/6191363*t^5 + 28569575948565113587125/6191363*t^3 - 3613936658267491305750/6191363*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:   31 out of 31
Indefinite weights: 0 out of 31
Negative weights:   0 out of 31
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (4.8585313031016765169 - 2.8243379456039013542e-435j)  +/-  (1.72e-120, 1.72e-120j)
| (7.8267518736097742965 + 1.2209604521975643304e-436j)  +/-  (2.94e-121, 2.94e-121j)
| (-6.9662752197869389118 - 2.9471897654072431903e-435j)  +/-  (9.18e-121, 9.18e-121j)
| (2.2594644510007991239 + 1.9980438503648003225e-438j)  +/-  (2.19e-122, 2.19e-122j)
| (-8.8640582179674461365 - 9.9147045501851773663e-438j)  +/-  (4.28e-122, 4.28e-122j)
| (-7.8267518736097742965 + 3.7147863680136555071e-436j)  +/-  (2.93e-121, 2.93e-121j)
| (-3.2237098287700974717 + 1.8930512460191526677e-436j)  +/-  (2.84e-121, 2.84e-121j)
| (-1.8019134732470272895 - 6.9607855160882902479e-446j)  +/-  (3.65e-123, 3.65e-123j)
| (3.7339958339931289716 + 2.7121234816315336222e-442j)  +/-  (6.8e-121, 6.8e-121j)
| (5.5009017044677476008 + 1.517936753100232692e-442j)  +/-  (1.89e-120, 1.89e-120j)
| (0.88615220755582252043 - 9.6802429323758466131e-451j)  +/-  (4.54e-125, 4.54e-125j)
| (-1.6378008808504279831e-450 - 2.5424336154466374501e-449j)  +/-  (7.9e-448, 7.9e-448j)
| (-3.7339958339931289716 + 1.1701666539444847793e-445j)  +/-  (6.91e-121, 6.91e-121j)
| (-5.5009017044677476008 + 1.8151381336023526048e-458j)  +/-  (1.9e-120, 1.9e-120j)
| (-6.2003189329012795746 + 1.4927835441016489343e-471j)  +/-  (1.4e-120, 1.4e-120j)
| (6.9662752197869389118 - 1.2640162288289818736e-474j)  +/-  (8.68e-121, 8.68e-121j)
| (3.2237098287700974717 + 2.8157318004633649856e-475j)  +/-  (3.02e-121, 3.02e-121j)
| (-1.3403751971516167215 + 7.8383616459430441014e-479j)  +/-  (5.11e-124, 5.11e-124j)
| (4.271825847932281723 + 7.4523848736539993365e-475j)  +/-  (1.26e-120, 1.26e-120j)
| (-4.271825847932281723 + 9.7003011149246614725e-482j)  +/-  (1.35e-120, 1.35e-120j)
| (1.3403751971516167215 + 1.7051459617508798054e-492j)  +/-  (4.55e-124, 4.55e-124j)
| (0.4444030019441389453 + 3.9374444096121113419e-495j)  +/-  (4.21e-126, 4.21e-126j)
| (6.2003189329012795746 + 3.1810333709656660623e-489j)  +/-  (1.59e-120, 1.59e-120j)
| (-2.2594644510007991239 - 2.8005023230007356988e-489j)  +/-  (2.38e-122, 2.38e-122j)
| (-2.7298260491038105662 - 3.477820178196928474e-490j)  +/-  (9.46e-122, 9.46e-122j)
| (2.7298260491038105662 - 1.687342408114393493e-495j)  +/-  (9.04e-122, 9.04e-122j)
| (-4.8585313031016765169 + 8.6175488899432728164e-497j)  +/-  (1.75e-120, 1.75e-120j)
| (1.8019134732470272895 - 8.2055447686278052653e-503j)  +/-  (3.98e-123, 3.98e-123j)
| (-0.88615220755582252043 - 1.464450504862222065e-504j)  +/-  (4.54e-125, 4.54e-125j)
| (-0.4444030019441389453 - 5.8533633478367359186e-507j)  +/-  (4.21e-126, 4.21e-126j)
| (8.8640582179674461365 + 2.8043266080454216719e-503j)  +/-  (4.74e-122, 4.74e-122j)
-------------------------------------------------
The weights are:
| (1.834761036627671056e-06 + 1.9655851883372004916e-440j)  +/-  (3.38e-35, 8.85e-95j)
| (1.8433210889435411775e-14 - 7.4373654219371646005e-447j)  +/-  (1.68e-41, 4.4e-101j)
| (9.3197556417967358002e-12 - 2.5862566996122442421e-445j)  +/-  (5.96e-41, 1.56e-100j)
| (0.014283768373208966543 - 4.0696504141247515769e-438j)  +/-  (1.27e-27, 3.32e-87j)
| (4.1402184411429285131e-18 - 1.2910679151951896518e-449j)  +/-  (1.86e-44, 4.87e-104j)
| (1.8433210889435411775e-14 + 1.881303143983851827e-447j)  +/-  (1.2e-42, 3.15e-102j)
| (0.0011104297325818600254 + 4.3066704248017299606e-439j)  +/-  (4.64e-34, 1.21e-93j)
| (0.036128080110526805915 + 6.6673236462683796354e-439j)  +/-  (2.29e-28, 6e-88j)
| (0.00019469316340377817102 + 2.2223904081772495457e-439j)  +/-  (5.78e-36, 1.51e-95j)
| (7.1830807896505041659e-08 + 6.9376468893143541858e-442j)  +/-  (5.28e-40, 1.38e-99j)
| (0.12017683474287501966 + 1.5430349213106637299e-437j)  +/-  (4.56e-29, 1.19e-88j)
| (0.17818064467804792109 + 1.5918609437245437945e-437j)  +/-  (3.42e-29, 8.95e-89j)
| (0.00019469316340377817102 + 1.2488697291562866567e-439j)  +/-  (3.38e-36, 8.85e-96j)
| (7.1830807896505041659e-08 - 8.6293606389832441313e-443j)  +/-  (2.13e-40, 5.59e-100j)
| (1.3068916756587821913e-09 + 4.9399112086309429261e-444j)  +/-  (2.34e-41, 6.13e-101j)
| (9.3197556417967358002e-12 + 5.0036942971274905751e-445j)  +/-  (1.14e-44, 2.99e-104j)
| (0.0011104297325818600254 - 6.6715990016717871581e-439j)  +/-  (1.43e-37, 3.74e-97j)
| (0.074908499447635291641 - 3.1831311885191803313e-438j)  +/-  (1.1e-32, 2.87e-92j)
| (2.4338602941354416663e-05 - 7.2975599977445360672e-440j)  +/-  (1.8e-39, 4.71e-99j)
| (2.4338602941354416663e-05 - 1.2820287428744757304e-440j)  +/-  (5.76e-40, 1.5e-99j)
| (0.074908499447635291641 - 1.1486340570071326259e-437j)  +/-  (1.58e-34, 4.14e-94j)
| (0.1594393119189018652 - 1.7273657958610686453e-437j)  +/-  (1.88e-33, 4.91e-93j)
| (1.3068916756587821913e-09 - 2.007518257541304795e-443j)  +/-  (1.4e-43, 3.66e-103j)
| (0.014283768373208966543 + 4.9576313693779161287e-439j)  +/-  (5.16e-37, 1.34e-96j)
| (0.0046418136608267050564 - 9.4751996304120415629e-439j)  +/-  (5.9e-38, 1.53e-97j)
| (0.0046418136608267050564 + 1.7715634654444980192e-438j)  +/-  (2.17e-38, 5.65e-98j)
| (1.834761036627671056e-06 + 1.1844191481205236423e-441j)  +/-  (1.41e-41, 3.63e-101j)
| (0.036128080110526805915 + 7.4498161645854212209e-438j)  +/-  (1.79e-37, 4.52e-97j)
| (0.12017683474287501966 + 7.3207359810501174468e-438j)  +/-  (7.21e-37, 1.67e-96j)
| (0.1594393119189018652 - 1.2139539780324513463e-437j)  +/-  (9.7e-37, 2.17e-96j)
| (4.1402184411429285131e-18 + 3.7308806066900298157e-449j)  +/-  (7.38e-50, 2.05e-109j)
