Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 18
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Trying to find an order 18 Kronrod extension for:
P1 : 35/8*t^4 - 15/4*t^2 + 3/8
Solvable: 1
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Ending with final polynomial:
P : 35/8*t^22 - 4464152121/191548568*t^20 + 113408704076613/2119101807784*t^18 - 5141152044847599/74168563272440*t^16 + 412630972878933/7416856327244*t^14 - 72312906879441/2526621386204*t^12 + 691191914990115/73272020199916*t^10 - 141675704352963/73272020199916*t^8 + 844966842584733/3663601009995800*t^6 - 711697261325501/50557693937942040*t^4 + 39461412446203/117967952521864760*t^2 - 154908650299/117967952521864760
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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
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The nodes are:
| (0.99402078285642610617 - 1.4610251601730419054e-461j)  +/-  (3.42e-121, 3.42e-121j)
| (-0.86113631159405257522 + 3.8884112921093205889e-471j)  +/-  (4.34e-121, 4.34e-121j)
| (-0.92396019027290009586 + 8.8122999621906323901e-472j)  +/-  (8.29e-121, 8.29e-121j)
| (-0.99402078285642610617 - 1.1006626976563842552e-471j)  +/-  (3.97e-121, 3.97e-121j)
| (0.58258021317866156543 + 2.9042387308509055683e-474j)  +/-  (6.45e-123, 6.45e-123j)
| (0.96869901960587075322 + 6.5324924512286231813e-476j)  +/-  (8.79e-121, 8.79e-121j)
| (-0.46584324601871858403 - 1.5983817711110927594e-490j)  +/-  (6.98e-124, 6.98e-124j)
| (-0.96869901960587075322 + 8.763137265028224615e-489j)  +/-  (7.57e-121, 7.57e-121j)
| (-0.78200094102074097978 + 5.9207008163529549083e-489j)  +/-  (1.73e-121, 1.73e-121j)
| (0.92396019027290009586 - 4.3106282193439109208e-487j)  +/-  (8.65e-121, 8.65e-121j)
| (0.86113631159405257522 + 9.9532964006589599733e-498j)  +/-  (5.02e-121, 5.02e-121j)
| (0.20702313934899688624 - 1.1289146371966891244e-505j)  +/-  (3.19e-126, 3.19e-126j)
| (-0.3399810435848562648 + 8.808162853885040525e-506j)  +/-  (6.42e-125, 6.42e-125j)
| (-0.58258021317866156543 + 4.2524229102442078793e-507j)  +/-  (6.42e-123, 6.42e-123j)
| (0.069528472770917187352 - 2.0068974051821697467e-508j)  +/-  (2.05e-127, 2.05e-127j)
| (0.78200094102074097978 - 2.9880980593934996461e-506j)  +/-  (1.61e-121, 1.61e-121j)
| (0.46584324601871858403 + 8.0242719686983062976e-512j)  +/-  (7.84e-124, 7.84e-124j)
| (-0.069528472770917187352 - 2.1539701602561979879e-511j)  +/-  (2.05e-127, 2.05e-127j)
| (-0.68852261044466735796 - 3.6610822074513640887e-511j)  +/-  (4.02e-122, 4.02e-122j)
| (-0.20702313934899688624 + 8.162129922192253351e-514j)  +/-  (3.48e-126, 3.48e-126j)
| (0.3399810435848562648 + 5.1741941424236483104e-515j)  +/-  (6.32e-125, 6.32e-125j)
| (0.68852261044466735796 - 4.1995903789345747466e-530j)  +/-  (3.72e-122, 3.72e-122j)
-------------------------------------------------
The weights are:
| (0.015321323838185624643 + 1.8928047184998894691e-461j)  +/-  (1.11e-40, 3.75e-99j)
| (0.07130120571061019342 + 1.3992744857097882242e-462j)  +/-  (5.61e-41, 1.89e-99j)
| (0.054046835395753910489 - 8.3145031152676308815e-463j)  +/-  (3.81e-41, 1.28e-99j)
| (0.015321323838185624643 - 1.1259744397450187018e-463j)  +/-  (5.95e-42, 2e-100j)
| (0.11160575414355543773 + 1.4990545472996736814e-461j)  +/-  (4.3e-43, 1.45e-101j)
| (0.03520593419684023844 - 3.1380025065728878625e-461j)  +/-  (5.65e-43, 1.9e-101j)
| (0.12159703195223641235 + 4.8937752656540721633e-462j)  +/-  (5.94e-43, 2e-101j)
| (0.03520593419684023844 + 4.0484513818263580639e-463j)  +/-  (7.17e-42, 2.41e-100j)
| (0.086636132523921421458 - 2.115778126762655859e-462j)  +/-  (2.18e-42, 7.34e-101j)
| (0.054046835395753910489 + 2.276180976210732972e-461j)  +/-  (1.77e-43, 5.95e-102j)
| (0.07130120571061019342 - 1.9534818191848850286e-461j)  +/-  (6.38e-44, 2.15e-102j)
| (0.13569487432329231884 - 1.0510019123601919132e-461j)  +/-  (6.83e-45, 2.3e-103j)
| (0.1297921003902492838 - 5.8808938409078333023e-462j)  +/-  (1.42e-44, 4.79e-103j)
| (0.11160575414355543773 - 3.9120351877870478114e-462j)  +/-  (3.31e-44, 1.11e-102j)
| (0.1387940108197643105 + 9.157934661552849522e-462j)  +/-  (1.38e-45, 4.66e-104j)
| (0.086636132523921421458 + 1.7723189837320123802e-461j)  +/-  (6.97e-46, 2.34e-104j)
| (0.12159703195223641235 - 1.3526221723270750129e-461j)  +/-  (3.35e-46, 1.13e-104j)
| (0.1387940108197643105 - 7.9605529565189160903e-462j)  +/-  (4.97e-46, 1.67e-104j)
| (0.10000479670559084831 + 2.967630099903823095e-462j)  +/-  (7.1e-46, 2.39e-104j)
| (0.13569487432329231884 + 6.8868091597987013037e-462j)  +/-  (3.7e-46, 1.24e-104j)
| (0.1297921003902492838 + 1.1994872255659970748e-461j)  +/-  (7.33e-47, 2.56e-105j)
| (0.10000479670559084831 - 1.6344341351956809697e-461j)  +/-  (5.58e-47, 1.77e-105j)
