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 28
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Trying to find an order 28 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
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Ending with final polynomial:
P : 4096*t^40 - 11830521452376901066752/9396449026283357*t^38 + 1631005004112580176012288/9396449026283357*t^36 - 2540600920330923788915512320/178532531499383783*t^34 + 138469970751756794829744468480/178532531499383783*t^32 - 90329943840795383329275873269760/3035053035489524311*t^30 + 2521252356197929608962609243717760/3035053035489524311*t^28 - 52146918479145724644425470101440640/3035053035489524311*t^26 + 806724652400671297185967255717536000/3035053035489524311*t^24 - 492455918936050942983980382008496000/159739633446817069*t^22 + 81060038732864811797507731634080848000/3035053035489524311*t^20 - 581796360820051218891127184982876000/3398715605251427*t^18 + 7506479316035115741256426248979475250/9396449026283357*t^16 - 24911941860890296834672590361231410000/9396449026283357*t^14 + 113699988539685466795883627544907108125/18792898052566714*t^12 - 170042198777491480540770827920173035625/18792898052566714*t^10 + 1241840605512032198616835133456170831875/150343184420533712*t^8 - 309303659339975729837082893720368741875/75171592210266856*t^6 + 551325444213682517849984922389390784375/601372737682134848*t^4 - 35270458110888257916875217134724215625/601372737682134848*t^2 + 32511654524837328076382995958484375/300686368841067424
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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: 0
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   38 out of 40
Indefinite weights: 0 out of 40
Negative weights:   2 out of 40
Extension rule has valid weights: 0
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*** EXTENSION WITH INVALID WEIGHTS ***
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