Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 8 9
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Trying to find an order 8 Kronrod extension for:
P1 : 35/8*t^4 - 15/4*t^2 + 3/8
Solvable: 1
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Trying to find an order 9 Kronrod extension for:
P2 : 35/8*t^12 - 87219/8284*t^10 + 102069/11336*t^8 - 891429/269230*t^6 + 24664563/47599864*t^4 - 792603/23799932*t^2 + 30429/47599864
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 35/8*t^21 - 1293446949/57540664*t^19 + 802951151159049/16271079433336*t^17 - 1075397492446125607711/17800479544672417320*t^15 + 4174928113335324976987859873/92449281989043135334097556*t^13 - 704402512054425406268155115/33186921739656510119932456*t^11 + 7372678859239421647130446532/1182284086975263173022593745*t^9 - 38286064931065468066090893/34645687530410642432896520*t^7 + 168469102792805459195567951/1531339388844150395534026184*t^5 - 178906677587990549728641/33289986714003269468131004*t^3 + 11150881316753074980201/123648522080583572310200872*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:
| (-0.9732162594524303742 - 4.3104700354727291536e-268j)  +/-  (3.34e-121, 3.34e-121j)
| (0.9732162594524303742 - 5.1019490610952734314e-267j)  +/-  (3.11e-121, 3.11e-121j)
| (-0.99900152771046987452 + 5.332325668340842504e-269j)  +/-  (1.48e-121, 1.48e-121j)
| (-0.18035397587349104032 - 2.1771413618980613312e-267j)  +/-  (2.08e-126, 2.08e-126j)
| (0.86113631159405257522 - 2.0452132973576734493e-266j)  +/-  (2.3e-121, 2.3e-121j)
| (0.78641193364718379371 + 5.9575402583370086661e-267j)  +/-  (6.85e-122, 6.85e-122j)
| (0.99900152771046987452 - 1.1724210354484315566e-269j)  +/-  (1.44e-121, 1.44e-121j)
| (-0.86113631159405257522 + 1.732669667930774987e-269j)  +/-  (2.19e-121, 2.19e-121j)
| (-0.78641193364718379371 - 4.5176011689729399344e-270j)  +/-  (6.37e-122, 6.37e-122j)
| (0.91887309143310793072 + 5.4612184414163516199e-271j)  +/-  (3.57e-121, 3.57e-121j)
| (-0.35241611849142175407 + 1.0191925264362730926e-269j)  +/-  (6e-124, 6e-124j)
| (-0.52029226136447175936 - 4.9841642366924927699e-272j)  +/-  (8.97e-124, 8.97e-124j)
| (4.7885885754141092012e-270 - 8.9080132580276364565e-270j)  +/-  (2.12e-268, 2.12e-268j)
| (-0.91887309143310793072 + 3.4789077822226327938e-274j)  +/-  (3.95e-121, 3.95e-121j)
| (-0.6674742407002819824 + 5.5781716002753373454e-275j)  +/-  (9.23e-123, 9.23e-123j)
| (-0.3399810435848562648 + 1.5223852913396934238e-273j)  +/-  (4.71e-124, 4.71e-124j)
| (0.18035397587349104032 - 9.0735590986343728504e-291j)  +/-  (2.08e-126, 2.08e-126j)
| (0.35241611849142175407 + 1.5108527449825319321e-318j)  +/-  (6.5e-124, 6.5e-124j)
| (0.6674742407002819824 - 3.3208614272156620341e-336j)  +/-  (7.9e-123, 7.9e-123j)
| (0.52029226136447175936 - 1.5250185166763730734e-357j)  +/-  (9.88e-124, 9.88e-124j)
| (0.3399810435848562648 - 1.4781193912741529178e-377j)  +/-  (4.66e-124, 4.66e-124j)
-------------------------------------------------
The weights are:
| (0.042226292359851276752 + 1.5355272821769153132e-268j)  +/-  (6.3e-38, 4.35e-96j)
| (0.042226292359851276752 - 1.1840371504919590332e-267j)  +/-  (1.69e-38, 1.16e-96j)
| (0.0082149123737693243824 - 3.1281457896714429702e-268j)  +/-  (2.62e-38, 1.81e-96j)
| (0.17906145995789873992 + 7.8365856019046091166e-267j)  +/-  (3.05e-39, 2.11e-97j)
| (0.055643787458841919315 + 6.7923592170770288595e-268j)  +/-  (7.68e-39, 5.3e-97j)
| (0.099290990584903489758 - 1.7023829531727196705e-266j)  +/-  (4.78e-39, 3.3e-97j)
| (0.0082149123737693243824 + 3.553496447941517697e-267j)  +/-  (2.45e-39, 1.69e-97j)
| (0.055643787458841919315 + 1.0239141426544109164e-267j)  +/-  (3.7e-40, 2.55e-98j)
| (0.099290990584903489758 - 1.3978743234879342475e-267j)  +/-  (2.57e-40, 1.77e-98j)
| (0.061805220892338986228 + 5.8981677188393003308e-267j)  +/-  (1.16e-39, 7.99e-98j)
| (0.21503846936137162488 + 7.316980085246827906e-266j)  +/-  (7.12e-41, 4.91e-99j)
| (0.15761712468507115222 - 3.346542621757612765e-267j)  +/-  (1.85e-41, 1.28e-99j)
| (0.18100892252540159184 - 3.6619246186030919506e-267j)  +/-  (2.6e-42, 1.79e-100j)
| (0.061805220892338986228 - 1.6759685660782459311e-268j)  +/-  (1.64e-41, 1.14e-99j)
| (0.13522796341151460729 + 1.6813743869137506357e-267j)  +/-  (9.1e-42, 6.28e-100j)
| (-0.044630682348261916663 - 7.7340456303639417816e-266j)  +/-  (4.26e-41, 2.94e-99j)
| (0.17906145995789873992 + 8.3095203055773107926e-267j)  +/-  (4.91e-44, 3.39e-102j)
| (0.21503846936137162488 + 1.1825124181474225833e-265j)  +/-  (5.59e-45, 3.85e-103j)
| (0.13522796341151460729 + 1.2975866557585958708e-266j)  +/-  (4.32e-46, 2.88e-104j)
| (0.15761712468507115222 - 1.1295968190533665373e-266j)  +/-  (3.24e-46, 2.12e-104j)
| (-0.044630682348261916663 - 1.1780171230273694323e-265j)  +/-  (4.95e-45, 3.45e-103j)
