Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 5 10
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Trying to find an order 5 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 10 Kronrod extension for:
P2 : 35/8*t^9 - 855/88*t^7 + 45297/6292*t^5 - 24885/12584*t^3 + 1845/12584*t
Solvable: 1
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Ending with final polynomial:
P : 35/8*t^19 - 253168212362648541839565/11708192433819507315404*t^17 + 2198478180054710631324137587/48682664139821511417449832*t^15 - 1560698298959239597472769455/30136887324651411829849896*t^13 + 1890462290846455170733824875/53319108343614036314349816*t^11 - 1501265945999485834157880623/101791025019626796600122376*t^9 + 1051375538808820972670179/290002920283837027350776*t^7 - 3926436962744550026756171/8078652779335460047628760*t^5 + 12055752003614008885037/403932638966773002381438*t^3 - 79715227995217817572411/147031480583905372866843432*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
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The nodes are:
| (-0.86113631159405257522 - 1.7995713917990458477e-321j)  +/-  (6.41e-122, 6.41e-122j)
| (-0.97656025073757311153 - 7.5030573368378102258e-322j)  +/-  (2.72e-121, 2.72e-121j)
| (-0.93255859254079555751 - 1.3384418976528980031e-321j)  +/-  (1.86e-121, 1.86e-121j)
| (-0.99634525995846133169 + 1.4996926172228346766e-322j)  +/-  (1.49e-121, 1.49e-121j)
| (0.97656025073757311153 + 2.1008072689507049071e-319j)  +/-  (2.77e-121, 2.77e-121j)
| (-0.17239110194761708419 - 2.3027338490817709876e-327j)  +/-  (7.84e-127, 7.84e-127j)
| (-2.3566248004702183424e-328 - 5.7130298193217414361e-329j)  +/-  (4.61e-327, 4.61e-327j)
| (0.93255859254079555751 + 2.8228367753408034923e-337j)  +/-  (1.88e-121, 1.88e-121j)
| (0.6402862174963099824 + 1.5942171346619649941e-347j)  +/-  (2.65e-123, 2.65e-123j)
| (0.17239110194761708419 + 3.439231074381421528e-353j)  +/-  (7.84e-127, 7.84e-127j)
| (0.86113631159405257522 + 2.2811334197814140235e-361j)  +/-  (7.31e-122, 7.31e-122j)
| (0.99634525995846133169 - 1.2553614234617968364e-368j)  +/-  (1.38e-121, 1.38e-121j)
| (-0.49769353776163459836 - 1.5126774519218181688e-375j)  +/-  (2.4e-124, 2.4e-124j)
| (-0.6402862174963099824 + 2.0070845590932079877e-380j)  +/-  (2.36e-123, 2.36e-123j)
| (-0.3399810435848562648 - 1.5898943239160456497e-376j)  +/-  (1.84e-125, 1.84e-125j)
| (0.7628055005750890492 + 1.1925825222874493026e-390j)  +/-  (1.68e-122, 1.68e-122j)
| (0.49769353776163459836 - 5.9225062013528076963e-418j)  +/-  (2.86e-124, 2.86e-124j)
| (0.3399810435848562648 + 1.5046918475530513225e-434j)  +/-  (1.65e-125, 1.65e-125j)
| (-0.7628055005750890492 + 8.6960990540594421155e-444j)  +/-  (1.72e-122, 1.72e-122j)
-------------------------------------------------
The weights are:
| (0.085181971033446352657 - 3.2718100534004055813e-321j)  +/-  (1.21e-40, 9.88e-100j)
| (0.030951648991194363374 - 3.881552981837113663e-321j)  +/-  (5.29e-41, 4.3e-100j)
| (0.057551573903254285293 + 2.9947666042448119823e-321j)  +/-  (4.22e-41, 3.44e-100j)
| (0.010029269618355209388 + 1.0317834294416533621e-321j)  +/-  (2.48e-41, 2.02e-100j)
| (0.030951648991194363374 - 1.3881742338223424631e-322j)  +/-  (8.24e-44, 6.71e-103j)
| (0.17080948918625406787 + 6.8294680110228638751e-321j)  +/-  (8.13e-43, 6.62e-102j)
| (0.17317826409068164515 - 7.9987706766240737653e-321j)  +/-  (4.97e-43, 4.05e-102j)
| (0.057551573903254285293 + 1.8054365609414523416e-319j)  +/-  (3.78e-44, 3.08e-103j)
| (0.13332971847796348901 - 2.2995479727250832017e-320j)  +/-  (7.81e-45, 6.36e-104j)
| (0.17080948918625406787 + 9.6403637420326885161e-321j)  +/-  (1.33e-44, 1.08e-103j)
| (0.085181971033446352657 - 7.0089190772208627295e-320j)  +/-  (1.06e-44, 8.65e-104j)
| (0.010029269618355209388 - 1.3352712529208880344e-319j)  +/-  (1.22e-44, 9.92e-104j)
| (0.1510206249799015245 + 5.467188377656976507e-321j)  +/-  (1.28e-45, 1.04e-104j)
| (0.13332971847796348901 - 5.2685687471366894716e-321j)  +/-  (7.44e-46, 6.06e-105j)
| (0.16352228159564932938 - 5.9989733156656279429e-321j)  +/-  (1.3e-45, 1.06e-104j)
| (0.11101429016864055596 + 3.6975879993535125171e-320j)  +/-  (1.99e-46, 1.62e-105j)
| (0.1510206249799015245 + 1.6004031849403008192e-320j)  +/-  (4.63e-47, 3.77e-106j)
| (0.16352228159564932938 - 1.2074789294083511382e-320j)  +/-  (4.07e-47, 3.32e-106j)
| (0.11101429016864055596 + 5.7579401821955570446e-321j)  +/-  (2.33e-47, 1.79e-106j)
