Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 5 14
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Trying to find an order 5 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
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Trying to find an order 14 Kronrod extension for:
P2 : 16*t^9 - 168*t^7 + 432*t^5 - 270*t^3 + 45*t
Solvable: 1
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Ending with final polynomial:
P : 16*t^23 - 1297379011493152/910428501785*t^21 + 46587422190452784/910428501785*t^19 - 878796263976985038/910428501785*t^17 + 9529093728525786696/910428501785*t^15 - 12254430548564146215/182085700357*t^13 + 8497918703745057951/33106490974*t^11 - 9412546414531352274/16553245487*t^9 + 186327422204203087353/264851927792*t^7 - 121470447834989743581/264851927792*t^5 + 76217320752581838375/529703855584*t^3 - 35261234801507861055/2118815422336*t
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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:
| (1.2614180201606563782 - 2.164953765034012645e-439j)  +/-  (4.15e-124, 4.15e-124j)
| (-5.2393200219725625871 + 4.5184838195562820474e-440j)  +/-  (1.12e-123, 1.12e-123j)
| (4.4515873701510676755 + 1.2889532579859411322e-446j)  +/-  (5.14e-123, 5.14e-123j)
| (-3.1932874374350604599 + 1.3190333321482562509e-453j)  +/-  (1.02e-122, 1.02e-122j)
| (3.7903340392764448866 + 3.5447686800147428385e-459j)  +/-  (8.47e-123, 8.47e-123j)
| (-2.6384291054842239697 + 3.01084622767982714e-464j)  +/-  (6.57e-123, 6.57e-123j)
| (-3.7903340392764448866 + 3.845855936323580714e-466j)  +/-  (9.52e-123, 9.52e-123j)
| (-1.2614180201606563782 + 4.6540000463998063938e-467j)  +/-  (4.11e-124, 4.11e-124j)
| (-4.4515873701510676755 + 5.366195590163432452e-467j)  +/-  (4.97e-123, 4.97e-123j)
| (5.2393200219725625871 - 1.9387545358009820472e-467j)  +/-  (1.12e-123, 1.12e-123j)
| (0.73395630342256598469 - 7.9089369229664284275e-472j)  +/-  (2.59e-124, 2.59e-124j)
| (3.1932874374350604599 - 6.0756794930201160652e-474j)  +/-  (9.65e-123, 9.65e-123j)
| (-1.6506801238857845559 + 8.5825294762508249463e-479j)  +/-  (1.29e-123, 1.29e-123j)
| (-0.80571881261920597446 - 7.8268350569582994793e-480j)  +/-  (3.47e-124, 3.47e-124j)
| (2.1195715314737654489 - 1.4231410685056466356e-485j)  +/-  (2.99e-123, 2.99e-123j)
| (0.80571881261920597446 + 6.9876816311093472948e-488j)  +/-  (3.45e-124, 3.45e-124j)
| (0.52464762327529031788 - 2.8277488615100775923e-489j)  +/-  (1.74e-125, 1.74e-125j)
| (-0.52464762327529031788 - 1.4964028049354069866e-487j)  +/-  (1.73e-125, 1.73e-125j)
| (-0.73395630342256598469 - 2.2975459499769380438e-490j)  +/-  (2.5e-124, 2.5e-124j)
| (-2.1195715314737654489 - 1.3535694747919355156e-493j)  +/-  (3.24e-123, 3.24e-123j)
| (2.6384291054842239697 - 3.0529629910042381342e-498j)  +/-  (6.18e-123, 6.18e-123j)
| (4.360322074869529509e-508 + 1.7441288299478118036e-507j)  +/-  (4.13e-506, 4.13e-506j)
| (1.6506801238857845559 + 7.8136971581661968801e-505j)  +/-  (1.19e-123, 1.19e-123j)
-------------------------------------------------
The weights are:
| (0.042150126675066029845 + 3.5497138458596953715e-440j)  +/-  (2.04e-36, 1.06e-97j)
| (6.1056972409052184424e-13 - 9.3969765474482910899e-450j)  +/-  (2.28e-50, 1.18e-111j)
| (9.8828858144380079229e-10 - 1.5466400248362501941e-447j)  +/-  (3.61e-49, 1.87e-110j)
| (1.2068119560454270888e-05 + 5.0731929702890279371e-445j)  +/-  (2.8e-46, 1.45e-107j)
| (2.0279481479290354915e-07 + 5.5219039795269338604e-446j)  +/-  (5.03e-48, 2.61e-109j)
| (0.00028718145427405634799 - 6.6417440586029875882e-444j)  +/-  (3.9e-45, 2.02e-106j)
| (2.0279481479290354915e-07 - 2.7596551246522902362e-446j)  +/-  (4.65e-48, 2.41e-109j)
| (0.042150126675066029845 + 3.6160650677408524778e-441j)  +/-  (6.72e-42, 3.49e-103j)
| (9.8828858144380079229e-10 + 8.6074576967365873575e-448j)  +/-  (1.24e-49, 6.43e-111j)
| (6.1056972409052184424e-13 + 1.5631155695988729061e-449j)  +/-  (1.33e-52, 6.89e-114j)
| (-0.36321087293675927651 + 5.1777216395045261576e-439j)  +/-  (2.42e-42, 1.27e-103j)
| (1.2068119560454270888e-05 - 1.1710800297766382401e-444j)  +/-  (1.03e-48, 5.32e-110j)
| (0.015933695113129631616 - 6.2962855824142645095e-442j)  +/-  (1.1e-44, 5.74e-106j)
| (0.36591663023632685868 - 9.7960733670878935458e-440j)  +/-  (2.55e-43, 1.34e-104j)
| (0.0031495732523168322476 - 2.7964643232320125761e-442j)  +/-  (6.67e-47, 3.48e-108j)
| (0.36591663023632685868 - 4.444453013865344635e-439j)  +/-  (9.48e-43, 5.02e-104j)
| (0.29555701041663664253 - 1.2859565403640527017e-439j)  +/-  (3.59e-43, 1.9e-104j)
| (0.29555701041663664253 - 5.3041117017382804684e-440j)  +/-  (4.36e-44, 2.32e-105j)
| (-0.36321087293675927651 + 1.368475154609241807e-439j)  +/-  (1.21e-43, 6.32e-105j)
| (0.0031495732523168322476 + 7.0941284615550845842e-443j)  +/-  (1.07e-47, 6.34e-109j)
| (0.00028718145427405634799 + 1.8824135722563457445e-443j)  +/-  (7.78e-49, 3.85e-110j)
| (0.2804087677714696538 + 2.6424599243928408727e-440j)  +/-  (9.32e-46, 9.17e-107j)
| (0.015933695113129631616 + 4.7121120617478538251e-441j)  +/-  (7.44e-47, 3.42e-108j)
