Starting with polynomial:
P : 128*t^7 - 1344*t^5 + 3360*t^3 - 1680*t
Extension levels are: 7 12
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Trying to find an order 12 Kronrod extension for:
P1 : 128*t^7 - 1344*t^5 + 3360*t^3 - 1680*t
Solvable: 1
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Ending with final polynomial:
P : 128*t^19 - 141824/17*t^17 + 3605808/17*t^15 - 46240440/17*t^13 + 323646180/17*t^11 - 1252495530/17*t^9 + 2593221345/17*t^7 - 5249048805/34*t^5 + 4234455225/68*t^3 - 46621575/8*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: 1
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   19 out of 19
Indefinite weights: 0 out of 19
Negative weights:   0 out of 19
Extension rule has valid weights: 1
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The nodes are:
| (2.6519613568352334924 - 2.6145114374730871814e-236j)  +/-  (1.4e-59, 1.4e-59j)
| (-3.928763082007146568 - 2.5194906473446600041e-239j)  +/-  (8.83e-60, 8.83e-60j)
| (-4.7358707020660293007 + 2.7884987633371888066e-241j)  +/-  (2.42e-60, 2.42e-60j)
| (2.1173675140549681161 + 4.3204156259688587077e-243j)  +/-  (8.64e-60, 8.64e-60j)
| (4.7358707020660293007 + 3.4416870240768874451e-243j)  +/-  (2.42e-60, 2.42e-60j)
| (3.2536029059107203817 - 4.0275060920048682869e-244j)  +/-  (1.69e-59, 1.69e-59j)
| (0.36182369793669724678 + 4.1333425447067007632e-245j)  +/-  (6.97e-63, 6.97e-63j)
| (-2.1173675140549681161 - 1.0801039064922146769e-242j)  +/-  (7.67e-60, 7.67e-60j)
| (-1.673551628767471445 - 2.2025423940651623444e-245j)  +/-  (3.62e-60, 3.62e-60j)
| (-3.2536029059107203817 + 6.0605924751878611229e-255j)  +/-  (1.48e-59, 1.48e-59j)
| (0.81628788285896466304 - 4.1030451376059377957e-260j)  +/-  (9.18e-62, 9.18e-62j)
| (3.928763082007146568 - 2.6676144857499905173e-259j)  +/-  (9.16e-60, 9.16e-60j)
| (-0.36182369793669724678 + 1.6156534162206043758e-261j)  +/-  (6.39e-63, 6.39e-63j)
| (-1.2699316830802473781 - 1.7987343389628507488e-259j)  +/-  (8.79e-61, 8.79e-61j)
| (1.673551628767471445 - 6.7801868179478925649e-261j)  +/-  (3.73e-60, 3.73e-60j)
| (1.2699316830802473781 + 1.0494800292710621176e-262j)  +/-  (8.94e-61, 8.94e-61j)
| (2.8531962970726275065e-263 - 2.9772483099888287024e-263j)  +/-  (7.83e-262, 7.83e-262j)
| (-2.6519613568352334924 + 8.2136000739437901214e-266j)  +/-  (1.43e-59, 1.43e-59j)
| (-0.81628788285896466304 + 1.0906262341224954367e-271j)  +/-  (9.48e-62, 9.48e-62j)
-------------------------------------------------
The weights are:
| (0.00028385521789333570391 + 2.9764928621342798887e-239j)  +/-  (4.26e-18, 5.23e-48j)
| (8.0887172413281458375e-08 + 4.9176744007638860761e-243j)  +/-  (1.49e-21, 1.83e-51j)
| (9.4940453455990014675e-11 - 8.207039875684631634e-245j)  +/-  (5.11e-23, 6.27e-53j)
| (0.0031451265939855343999 - 1.0484392246459576886e-238j)  +/-  (1.49e-17, 1.83e-47j)
| (9.4940453455990014675e-11 + 2.9079230845363956277e-244j)  +/-  (4.58e-24, 5.62e-54j)
| (9.0415880608410985259e-06 + 1.073020936886422177e-240j)  +/-  (7.59e-21, 9.37e-51j)
| (0.20884223855008832032 - 9.0577377058612839633e-238j)  +/-  (1.38e-17, 1.58e-47j)
| (0.0031451265939855343999 - 1.1750195938927179207e-239j)  +/-  (8.2e-20, 1.02e-49j)
| (0.013750281835550528794 + 5.4673302176946812304e-239j)  +/-  (8.02e-19, 9.85e-49j)
| (9.0415880608410985259e-06 - 1.0925521021765594528e-241j)  +/-  (3.05e-22, 3.69e-52j)
| (0.13573035088023066203 + 6.0151358748555409346e-238j)  +/-  (3.71e-18, 4.25e-48j)
| (8.0887172413281458375e-08 - 2.5396424134283665699e-242j)  +/-  (2.54e-23, 2.98e-53j)
| (0.20884223855008832032 - 6.8827303465083770128e-238j)  +/-  (3.67e-18, 4.08e-48j)
| (0.048063556171494640814 - 1.4563005772927753466e-238j)  +/-  (5.18e-19, 5.94e-49j)
| (0.013750281835550528794 + 2.417338072379731822e-238j)  +/-  (1.42e-19, 1.66e-49j)
| (0.048063556171494640814 - 4.1329615073077394234e-238j)  +/-  (3.51e-19, 4.12e-49j)
| (0.18035093636116654019 + 1.0211844764140675387e-237j)  +/-  (2.28e-18, 2.56e-48j)
| (0.00028385521789333570391 + 1.3988601583918692503e-240j)  +/-  (5.26e-22, 7.8e-52j)
| (0.13573035088023066203 + 3.1835467430741928464e-238j)  +/-  (3.34e-19, 3.2e-49j)
