Starting with polynomial:
P : t
Extension levels are: 1 12 14
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Trying to find an order 12 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 14 Kronrod extension for:
P2 : t^13 - 78/25*t^11 + 429/115*t^9 - 1716/805*t^7 + 1287/2185*t^5 - 2574/37145*t^3 + 429/185725*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^27 - 4887/725*t^25 + 12109122/599633*t^23 - 2062690074/58216543*t^21 + 5736590789607/142056681569*t^19 - 4274902113141375/136381890973691*t^17 + 17422711867822224708/1031343926935576111*t^15 - 7757714083455663571260/1226267929126399995979*t^13 + 152903247596126139465/94328302240492307383*t^11 - 11781946181505952413/42876501018405594265*t^9 + 200572021320761302578/6903116663963300676665*t^7 - 8535217413360695202/4930797617116643340475*t^5 + 899612877850981029/18737030945043244693805*t^3 - 125817983821378791/318529526065735159794685*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:
| (-0.34183246302180637632 + 1.1903380018406875529e-428j)  +/-  (3.02e-124, 3.02e-124j)
| (0.11597108974493355031 - 2.7084093015874070911e-427j)  +/-  (8.3e-127, 8.3e-127j)
| (-0.91759839922297796521 - 1.0795221991112866508e-422j)  +/-  (6.79e-119, 6.79e-119j)
| (0.99736617699482494478 + 8.0325709577071408215e-422j)  +/-  (4.54e-119, 4.54e-119j)
| (0.98418305471858814947 - 7.5235836032159134375e-438j)  +/-  (1.11e-118, 1.11e-118j)
| (0.86533316026634446208 + 7.1442746684361532676e-449j)  +/-  (2.95e-119, 2.95e-119j)
| (-0.44849275103644685288 + 1.5333447243065988904e-459j)  +/-  (4e-123, 4e-123j)
| (-0.86533316026634446208 + 2.032072202152931721e-455j)  +/-  (3.18e-119, 3.18e-119j)
| (-0.98418305471858814947 - 1.6002659227572280436e-454j)  +/-  (1.12e-118, 1.12e-118j)
| (-0.23045831595513479407 + 1.5692225475471038812e-462j)  +/-  (1.48e-125, 1.48e-125j)
| (0.80157809073330991279 - 4.1429118849774552597e-456j)  +/-  (9.08e-120, 9.08e-120j)
| (-0.99736617699482494478 - 1.0902180497148230059e-457j)  +/-  (4.92e-119, 4.92e-119j)
| (-0.95755246838608118226 - 3.8532070098156160248e-459j)  +/-  (1.14e-118, 1.14e-118j)
| (-0.80157809073330991279 - 8.7788715647782517532e-461j)  +/-  (9.08e-120, 9.08e-120j)
| (0.44849275103644685288 - 3.0048346642277565684e-461j)  +/-  (3.89e-123, 3.89e-123j)
| (0.91759839922297796521 + 1.6171479952741369205e-459j)  +/-  (6.13e-119, 6.13e-119j)
| (0.54907995795653685794 - 5.7888217836427872398e-471j)  +/-  (3.87e-122, 3.87e-122j)
| (0.95755246838608118226 - 1.847528789676094461e-474j)  +/-  (1.07e-118, 1.07e-118j)
| (-0.72694884932063203807 - 7.3539840293717901386e-485j)  +/-  (2.4e-120, 2.4e-120j)
| (-0.11597108974493355031 + 1.055680714985297922e-490j)  +/-  (7.43e-127, 7.43e-127j)
| (0.23045831595513479407 + 2.6521485516436344104e-489j)  +/-  (1.64e-125, 1.64e-125j)
| (0.64234933944034022064 - 4.4669287648064018601e-486j)  +/-  (3.75e-121, 3.75e-121j)
| (0.34183246302180637632 - 2.669433569913729798e-490j)  +/-  (3.68e-124, 3.68e-124j)
| (-0.54907995795653685794 - 8.6713832169996651077e-488j)  +/-  (4.01e-122, 4.01e-122j)
| (-0.64234933944034022064 - 3.6947209770239092029e-489j)  +/-  (3.53e-121, 3.53e-121j)
| (2.841992762909821862e-496 - 2.6098261444006257655e-496j)  +/-  (1.04e-494, 1.04e-494j)
| (0.72694884932063203807 - 9.4641403262554303963e-492j)  +/-  (2.11e-120, 2.11e-120j)
-------------------------------------------------
The weights are:
| (0.10926635109528501905 - 4.485599078038741748e-423j)  +/-  (4.22e-33, 1.05e-90j)
| (0.11548879909128642565 - 9.3073151881461714811e-423j)  +/-  (2.61e-33, 6.48e-91j)
| (0.046279017973830715737 + 4.3112945808344078189e-424j)  +/-  (7.42e-34, 1.84e-91j)
| (0.0070878463512486450452 - 8.5270865013470973254e-422j)  +/-  (2.61e-34, 6.46e-92j)
| (0.019753746382705915616 + 1.2619216423387717354e-421j)  +/-  (2.2e-34, 5.45e-92j)
| (0.058115210423114584633 - 3.5000691369233487629e-422j)  +/-  (6.05e-35, 1.5e-92j)
| (0.10383060116903996335 + 3.3612102160891461602e-423j)  +/-  (2.49e-34, 6.16e-92j)
| (0.058115210423114584633 + 9.6117151835996218822e-423j)  +/-  (3.4e-35, 8.42e-93j)
| (0.019753746382705915616 + 4.2332894676850951946e-423j)  +/-  (5.51e-36, 1.36e-93j)
| (0.11321025917152986688 + 5.6039289058448961879e-423j)  +/-  (2.47e-35, 6.12e-93j)
| (0.069303633247781497752 + 2.8101354827051079364e-422j)  +/-  (7.51e-37, 1.86e-94j)
| (0.0070878463512486450452 - 1.2537728304441743198e-423j)  +/-  (2.28e-36, 5.65e-94j)
| (0.033443589989552415197 - 1.0496354215372540622e-422j)  +/-  (4.58e-36, 1.14e-93j)
| (0.069303633247781497752 - 3.4284513480525749425e-423j)  +/-  (8.3e-37, 2.06e-94j)
| (0.10383060116903996335 + 1.4388444157567264276e-422j)  +/-  (4.05e-39, 1e-96j)
| (0.046279017973830715737 + 4.589091173422972616e-422j)  +/-  (6.92e-39, 1.72e-96j)
| (0.097141734876078608438 - 1.6684499473428387806e-422j)  +/-  (1.07e-39, 2.65e-97j)
| (0.033443589989552415197 - 6.7279389552763220162e-422j)  +/-  (6.75e-39, 1.67e-96j)
| (0.079805962169476289804 + 8.4424665515428027777e-424j)  +/-  (1.98e-39, 4.9e-97j)
| (0.11548879909128642565 - 6.7621573048811677366e-423j)  +/-  (7.66e-40, 1.9e-97j)
| (0.11321025917152986688 + 1.0770136789527748808e-422j)  +/-  (4e-40, 9.91e-98j)
| (0.089168441877539610227 + 1.9510392468895464115e-422j)  +/-  (1.21e-40, 2.99e-98j)
| (0.10926635109528501905 - 1.2443566435394167807e-422j)  +/-  (2.56e-40, 6.36e-98j)
| (0.097141734876078608438 - 2.1729887525882965756e-423j)  +/-  (4.35e-41, 1.08e-98j)
| (0.089168441877539610227 + 8.3585207727472013934e-424j)  +/-  (4.06e-41, 1.01e-98j)
| (0.11620961236306088522 + 7.9878962805859073873e-423j)  +/-  (2.48e-41, 6.27e-99j)
| (0.079805962169476289804 - 2.317702189365166019e-422j)  +/-  (1.09e-41, 2.5e-99j)
