Starting with polynomial:
P : t^16 - 120*t^14 + 5460*t^12 - 120120*t^10 + 1351350*t^8 - 7567560*t^6 + 18918900*t^4 - 16216200*t^2 + 2027025
Extension levels are: 16 29
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Trying to find an order 29 Kronrod extension for:
P1 : t^16 - 120*t^14 + 5460*t^12 - 120120*t^10 + 1351350*t^8 - 7567560*t^6 + 18918900*t^4 - 16216200*t^2 + 2027025
Solvable: 1
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Ending with final polynomial:
P : t^45 - 40673026117210/54781808743*t^43 + 780890100414867695/3122563098351*t^41 - 475301711137281015260/9367689295053*t^39 + 368598525047330277275485/53083572671967*t^37 - 36109560277349411480277650/53083572671967*t^35 + 154281011254783803186521725/3122563098351*t^33 - 48117582578412088809961093200/17694524223989*t^31 + 2033700966701239790827109887650/17694524223989*t^29 - 66497469656383924808915742176700/17694524223989*t^27 + 1686773053182286842506113508978850/17694524223989*t^25 - 33151407096148806289521051019665000/17694524223989*t^23 + 502290276868032859682746921889988750/17694524223989*t^21 - 5814688355653503084785698450936657500/17694524223989*t^19 + 2670961648898939981914095253593356250/931290748631*t^17 - 1014709706077812781558631018339430000/54781808743*t^15 + 4727477031459026498823808831038721875/54781808743*t^13 - 15343153668396050083574240565293231250/54781808743*t^11 + 33031731022332477284369275096387921875/54781808743*t^9 - 43907269985768209862439333904681012500/54781808743*t^7 + 32188792549970940351820893609333890625/54781808743*t^5 - 10645534828058559223751383147376906250/54781808743*t^3 + 1003682319559068824048192135332640625/54781808743*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: 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:   43 out of 45
Indefinite weights: 0 out of 45
Negative weights:   2 out of 45
Extension rule has valid weights: 0
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*** EXTENSION WITH INVALID WEIGHTS ***
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