Starting with polynomial:
P : 4096*t^12 - 135168*t^10 + 1520640*t^8 - 7096320*t^6 + 13305600*t^4 - 7983360*t^2 + 665280
Extension levels are: 12 19
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Trying to find an order 19 Kronrod extension for:
P1 : 4096*t^12 - 135168*t^10 + 1520640*t^8 - 7096320*t^6 + 13305600*t^4 - 7983360*t^2 + 665280
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4096*t^31 - 4334433435648/6191363*t^29 + 319811495107584/6191363*t^27 - 13444953069874176/6191363*t^25 + 358121780669664000/6191363*t^23 - 6360369496467356160/6191363*t^21 + 77223623463557645760/6191363*t^19 - 646849907001518633280/6191363*t^17 + 3727916093739283099920/6191363*t^15 - 14582322240678352641600/6191363*t^13 + 37731353609884310075700/6191363*t^11 - 61942301424108198393300/6191363*t^9 + 60404032344599956037025/6191363*t^7 - 31398027243597292127850/6191363*t^5 + 28569575948565113587125/24765452*t^3 - 1806968329133745652875/24765452*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:
| (-4.3842875629738329382 + 4.7242034080889257829e-437j)  +/-  (9.77e-121, 9.77e-121j)
| (-2.2795070805010599002 - 5.0152476450082041344e-437j)  +/-  (2.08e-121, 2.08e-121j)
| (-6.2678356747571253171 - 8.7871784356466898e-439j)  +/-  (2.84e-122, 2.84e-122j)
| (4.3842875629738329382 - 1.8533375692614699199e-436j)  +/-  (1.11e-120, 1.11e-120j)
| (3.8897248978697819193 - 3.9169289661989533862e-445j)  +/-  (1.34e-120, 1.34e-120j)
| (6.2678356747571253171 + 1.2043574791290345003e-451j)  +/-  (3.05e-122, 3.05e-122j)
| (-4.9259004475231512763 - 4.0375292311924147217e-454j)  +/-  (5.91e-121, 5.91e-121j)
| (2.6403337751388594822 - 4.6045226233916800166e-452j)  +/-  (4.76e-121, 4.76e-121j)
| (-1.5976826351526047967 + 1.0127737163671546381e-462j)  +/-  (1.55e-122, 1.55e-122j)
| (3.4355004310303087844 + 1.4692989732034585372e-463j)  +/-  (1.35e-120, 1.35e-120j)
| (1.5976826351526047967 - 4.2593549611853551569e-471j)  +/-  (1.55e-122, 1.55e-122j)
| (4.9259004475231512763 + 2.3070299845903500519e-473j)  +/-  (5.61e-121, 5.61e-121j)
| (5.5343493244939875391 + 1.7933422077065518153e-481j)  +/-  (2.29e-121, 2.29e-121j)
| (-1.2741452360443775821 - 3.0290950535935266357e-488j)  +/-  (2.75e-123, 2.75e-123j)
| (3.0206370251208897717 - 7.2111533870625229675e-485j)  +/-  (8.91e-121, 8.91e-121j)
| (0.9477883912401637437 + 5.9272599551396562307e-493j)  +/-  (3.26e-124, 3.26e-124j)
| (-3.8897248978697819193 - 2.6046729413046511515e-489j)  +/-  (1.35e-120, 1.35e-120j)
| (1.2741452360443775821 - 1.104129153444445987e-490j)  +/-  (2.76e-123, 2.76e-123j)
| (-1.8801814011292474548e-497 - 1.8899657573604012131e-498j)  +/-  (5.86e-496, 5.86e-496j)
| (-5.5343493244939875391 + 3.3420784142720089507e-489j)  +/-  (2.08e-121, 2.08e-121j)
| (1.9302785107809857158 - 2.1370122906516263471e-489j)  +/-  (6.89e-122, 6.89e-122j)
| (0.31424037625435911128 + 4.8285584634720065365e-496j)  +/-  (3.28e-126, 3.28e-126j)
| (-3.0206370251208897717 - 7.5914951984080407006e-492j)  +/-  (8.42e-121, 8.42e-121j)
| (-3.4355004310303087844 - 4.0270529661241912435e-491j)  +/-  (1.22e-120, 1.22e-120j)
| (-2.6403337751388594822 - 8.9014022694289243707e-493j)  +/-  (4.89e-121, 4.89e-121j)
| (-1.9302785107809857158 - 1.0652451139138989049e-497j)  +/-  (6.13e-122, 6.13e-122j)
| (0.62660423512615104079 - 1.1291908636001321091e-500j)  +/-  (3.58e-125, 3.58e-125j)
| (2.2795070805010599002 + 9.8193615944223429593e-501j)  +/-  (1.94e-121, 1.94e-121j)
| (-0.9477883912401637437 + 4.3946141911875138296e-506j)  +/-  (3.26e-124, 3.26e-124j)
| (-0.62660423512615104079 + 3.1974275840034469808e-507j)  +/-  (3.88e-125, 3.88e-125j)
| (-0.31424037625435911128 - 5.5937595368036509749e-508j)  +/-  (2.76e-126, 2.76e-126j)
-------------------------------------------------
The weights are:
| (1.3068916756587821913e-09 - 2.1485948278798057398e-445j)  +/-  (8.4e-35, 1.39e-94j)
| (0.0011104297325818600254 - 2.2055252923248117442e-439j)  +/-  (8.39e-27, 1.39e-86j)
| (4.1402184411429285131e-18 + 1.7829622885139181695e-450j)  +/-  (1.2e-39, 2e-99j)
| (1.3068916756587821913e-09 + 1.6341131019054995619e-444j)  +/-  (1.73e-36, 2.87e-96j)
| (7.1830807896505041659e-08 - 1.1793892423668570854e-443j)  +/-  (3.45e-35, 5.73e-95j)
| (4.1402184411429285131e-18 - 1.4534693719850460851e-451j)  +/-  (7.25e-42, 1.2e-101j)
| (9.3197556417967358002e-12 + 2.2148972269135769731e-446j)  +/-  (2.24e-38, 3.73e-98j)
| (0.00019469316340377817102 + 3.9914008372901306276e-441j)  +/-  (2.3e-32, 3.83e-92j)
| (0.014283768373208966543 - 8.3601610597322568468e-439j)  +/-  (5.8e-28, 9.64e-88j)
| (1.834761036627671056e-06 + 9.6005459557721573651e-443j)  +/-  (1.28e-34, 2.12e-94j)
| (0.014283768373208966543 - 1.841688787003900313e-439j)  +/-  (3.92e-29, 6.51e-89j)
| (9.3197556417967358002e-12 + 1.0184276907027162434e-446j)  +/-  (5.78e-39, 9.6e-99j)
| (1.8433210889435411775e-14 - 3.2512828678056888074e-449j)  +/-  (1.05e-40, 1.74e-100j)
| (0.036128080110526805915 + 1.2651038294371889746e-438j)  +/-  (6.95e-30, 1.15e-89j)
| (2.4338602941354416663e-05 - 7.0572225690707245054e-442j)  +/-  (1.57e-34, 2.61e-94j)
| (0.074908499447635291641 - 8.3653033764643257269e-439j)  +/-  (1.89e-30, 3.14e-90j)
| (7.1830807896505041659e-08 + 1.0726717742048618039e-443j)  +/-  (2.02e-39, 3.35e-99j)
| (0.036128080110526805915 + 4.2519806047158103902e-439j)  +/-  (1.8e-31, 3e-91j)
| (0.17818064467804792109 + 2.4828747648399589452e-438j)  +/-  (2.81e-31, 4.66e-91j)
| (1.8433210889435411775e-14 - 3.3892545348901904334e-448j)  +/-  (3.39e-43, 5.63e-103j)
| (0.0046418136608267050564 + 6.3701328532387097136e-440j)  +/-  (1.3e-33, 2.16e-93j)
| (0.1594393119189018652 - 2.0493141821023145068e-438j)  +/-  (1.11e-31, 1.85e-91j)
| (2.4338602941354416663e-05 + 2.7228695799430924094e-441j)  +/-  (3.17e-38, 5.26e-98j)
| (1.834761036627671056e-06 - 1.993113253592216549e-442j)  +/-  (4.61e-39, 7.65e-99j)
| (0.00019469316340377817102 - 3.4035393947633189511e-440j)  +/-  (1.2e-37, 1.99e-97j)
| (0.0046418136608267050564 + 5.7580301957220630173e-439j)  +/-  (1.98e-36, 3.29e-96j)
| (0.12017683474287501966 + 1.4297041516893745617e-438j)  +/-  (9.74e-35, 1.62e-94j)
| (0.0011104297325818600254 - 1.7624420685402950485e-440j)  +/-  (3.86e-37, 6.44e-97j)
| (0.074908499447635291641 - 1.790534802654236199e-438j)  +/-  (5.02e-36, 8.34e-96j)
| (0.12017683474287501966 + 2.3196075338861013674e-438j)  +/-  (4.18e-36, 6.91e-96j)
| (0.1594393119189018652 - 2.5991216638235926353e-438j)  +/-  (6.22e-36, 1.03e-95j)
