Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 8
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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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Ending with final polynomial:
P : 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
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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
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The nodes are:
| (0.9732162594524303742 - 6.0881362148396272271e-159j)  +/-  (2.11e-61, 2.11e-61j)
| (-0.86113631159405257522 + 4.9105186293624331764e-158j)  +/-  (3.26e-61, 3.26e-61j)
| (-0.9732162594524303742 + 4.4899726739598565166e-160j)  +/-  (2.05e-61, 2.05e-61j)
| (-0.18035397587349104032 + 4.3245994229981667518e-158j)  +/-  (5.21e-63, 5.21e-63j)
| (0.6674742407002819824 - 7.3938203031577589629e-165j)  +/-  (1.55e-61, 1.55e-61j)
| (0.35241611849142175407 - 1.246217760642003435e-176j)  +/-  (3.62e-61, 3.62e-61j)
| (-0.3399810435848562648 + 1.1068510122619142448e-183j)  +/-  (3.3e-61, 3.3e-61j)
| (-0.6674742407002819824 - 2.1260550685381509486e-191j)  +/-  (1.74e-61, 1.74e-61j)
| (-0.35241611849142175407 - 2.6137326486925206249e-191j)  +/-  (3.66e-61, 3.66e-61j)
| (0.3399810435848562648 - 1.2837747097013666986e-202j)  +/-  (3.4e-61, 3.4e-61j)
| (0.86113631159405257522 + 4.3512532797893367543e-215j)  +/-  (3.16e-61, 3.16e-61j)
| (0.18035397587349104032 + 2.1756266398946683771e-215j)  +/-  (5.21e-63, 5.21e-63j)
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The weights are:
| (0.068470605297872075792 + 9.6517169907115427224e-159j)  +/-  (2.4e-19, 9.94e-49j)
| (0.15438611119178875381 + 4.4507651467506214111e-158j)  +/-  (1.05e-19, 4.37e-49j)
| (0.068470605297872075792 + 1.602357618629801712e-158j)  +/-  (5.97e-20, 2.48e-49j)
| (0.43620250740301438705 + 3.5256403509145382163e-157j)  +/-  (3.24e-20, 1.34e-49j)
| (0.23191943772574034729 + 3.7762238962389251688e-158j)  +/-  (7.39e-21, 3.06e-50j)
| (2.7735455210981224144 - 3.1593436985127879389e-156j)  +/-  (1.08e-20, 4.47e-50j)
| (-2.6645241827165379783 - 4.3665848411458107888e-156j)  +/-  (1.19e-20, 4.93e-50j)
| (0.23191943772574034729 - 1.2847778091461662353e-157j)  +/-  (2.68e-22, 1.11e-51j)
| (2.7735455210981224144 + 4.1915209539248931243e-156j)  +/-  (1.04e-20, 4.33e-50j)
| (-2.6645241827165379783 + 3.445220596512646522e-156j)  +/-  (1.34e-21, 5.44e-51j)
| (0.15438611119178875381 - 2.1062717891880570377e-158j)  +/-  (4.23e-24, 1.54e-53j)
| (0.43620250740301438705 - 4.2178173067080257204e-157j)  +/-  (1.33e-22, 5.68e-52j)
