Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 31
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Trying to find an order 31 Kronrod extension for:
P1 : 35/8*t^4 - 15/4*t^2 + 3/8
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 35/8*t^35 - 13196487110802315195/360426259637619992*t^33 + 1146082747469936923713/8199697406755854818*t^31 - 483660613910242558218935/1500544625436321431694*t^29 + 1056558649694078055122840/2107907926208165820713*t^27 - 1711884574264171025346705/3080788507535011584119*t^25 + 2789383063552812193871175/6161577015070023168238*t^23 - 89938799242675009973068635/326563581798711227916614*t^21 + 82211756326633739109662325/653127163597422455833228*t^19 - 72664552947943316684129025/1684380579803878965043588*t^17 + 434808645773440452330601125/39582943625391155678524318*t^15 - 11548757581920821896402275/5654706232198736525503474*t^13 + 76808961453518368722115/284721742370662377747833*t^11 - 121059047987851157166280650/4984623543683186247231312331*t^9 + 13938136027931415470670225/9969247087366372494462624662*t^7 - 222417104948381517305472825/4795207849023225169836522462422*t^5 + 98385401445466022208448875/134265819772650304755422628947816*t^3 - 11525705591235381694305/3274776092015861091595673876776*t
-------------------------------------------------
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:
| (-0.96747705708751225209 - 3.5585176760067041552e-400j)  +/-  (2.71e-116, 2.71e-116j)
| (-0.99747414768780994855 - 2.5678580109041342381e-414j)  +/-  (6.97e-117, 6.97e-117j)
| (-0.93993485103340813409 - 1.6060230149639920998e-429j)  +/-  (2.09e-116, 2.09e-116j)
| (0.99747414768780994855 - 1.7188627698819575872e-437j)  +/-  (7.36e-117, 7.36e-117j)
| (0.69084710727910547761 - 3.5415736519111636228e-442j)  +/-  (1.47e-118, 1.47e-118j)
| (0.90436597695790938265 - 1.0722090807193415245e-439j)  +/-  (1.24e-116, 1.24e-116j)
| (0.98671823704325100043 - 1.2320285809512892228e-438j)  +/-  (2.11e-116, 2.11e-116j)
| (-0.86113631159405257522 - 1.8564182853077310096e-440j)  +/-  (5.76e-117, 5.76e-117j)
| (-0.98671823704325100043 + 9.2151167444204434638e-443j)  +/-  (2.02e-116, 2.02e-116j)
| (0.93993485103340813409 + 1.3804189830308135875e-447j)  +/-  (1.93e-116, 1.93e-116j)
| (0.81071368758631269101 - 3.0926867524482217123e-450j)  +/-  (2.1e-117, 2.1e-117j)
| (0.96747705708751225209 + 2.2472133654437058679e-450j)  +/-  (2.61e-116, 2.61e-116j)
| (-0.90436597695790938265 + 6.1136928032287751611e-453j)  +/-  (1.28e-116, 1.28e-116j)
| (-0.81071368758631269101 - 6.3869583274004598095e-460j)  +/-  (2.22e-117, 2.22e-117j)
| (-0.41173028206842991385 + 2.5844333277525434203e-466j)  +/-  (9.23e-122, 9.23e-122j)
| (0.86113631159405257522 - 3.5367574061499830096e-461j)  +/-  (6.15e-117, 6.15e-117j)
| (0.6232665175461617044 - 1.0128333857341981262e-463j)  +/-  (2.59e-119, 2.59e-119j)
| (-0.3399810435848562648 + 4.3141822496296499339e-468j)  +/-  (8.55e-123, 8.55e-123j)
| (-0.75369204844473473557 - 1.2694434757699036886e-462j)  +/-  (5.75e-118, 5.75e-118j)
| (-0.089475455211244527566 + 5.7713640436569300561e-474j)  +/-  (8.2e-127, 8.2e-127j)
| (0.26166269092503151735 - 1.8912036519499525282e-470j)  +/-  (4.77e-124, 4.77e-124j)
| (0.75369204844473473557 - 8.0748670293832635002e-465j)  +/-  (6.06e-118, 6.06e-118j)
| (0.17735342420098148371 + 6.1242734105619817915e-475j)  +/-  (2.06e-125, 2.06e-125j)
| (-0.6232665175461617044 + 1.0162189955155715427e-464j)  +/-  (2.56e-119, 2.56e-119j)
| (-0.55263157057652185396 + 5.6380803751880867182e-466j)  +/-  (4.71e-120, 4.71e-120j)
| (0.089475455211244527566 + 7.9187450131368010539e-475j)  +/-  (8.2e-127, 8.2e-127j)
| (0.55263157057652185396 - 1.205089693875593351e-467j)  +/-  (4.08e-120, 4.08e-120j)
| (0.3399810435848562648 + 1.4155917238467117698e-470j)  +/-  (8.51e-123, 8.51e-123j)
| (-0.17735342420098148371 + 8.6119440178710215943e-472j)  +/-  (2.13e-125, 2.13e-125j)
| (-0.69084710727910547761 + 7.3750062865029291632e-469j)  +/-  (1.44e-118, 1.44e-118j)
| (-0.26166269092503151735 - 1.0983140922830393978e-474j)  +/-  (4.37e-124, 4.37e-124j)
| (0.41173028206842991385 + 1.9637634274777187931e-474j)  +/-  (8.61e-122, 8.61e-122j)
| (0.48150288822001325531 - 5.6110743413715945578e-474j)  +/-  (7.36e-121, 7.36e-121j)
| (9.771271135803671562e-485 + 5.3163064160603023888e-485j)  +/-  (3.89e-483, 3.89e-483j)
| (-0.48150288822001325531 + 8.4964279549362504763e-473j)  +/-  (6.95e-121, 6.95e-121j)
-------------------------------------------------
The weights are:
| (0.023430050119617134825 - 1.4616059152782860712e-400j)  +/-  (1.25e-22, 3.68e-77j)
| (0.0064790961373520076458 + 3.8232480144108976526e-401j)  +/-  (3.38e-23, 9.92e-78j)
| (0.031608686527391782839 + 5.07679533674378293e-400j)  +/-  (8.08e-23, 2.37e-77j)
| (0.0064790961373520076458 - 5.8365987306446692532e-403j)  +/-  (1.64e-24, 4.82e-79j)
| (0.065430807880805121806 - 5.5020815454305137772e-401j)  +/-  (1.7e-24, 5.01e-79j)
| (0.039468242490993713135 - 1.1432604623550064726e-401j)  +/-  (1.51e-24, 4.44e-79j)
| (0.015021303516903771544 + 2.0955429679728693428e-402j)  +/-  (9.77e-25, 2.87e-79j)
| (0.046913481544056580382 + 2.939337977430103727e-400j)  +/-  (1.7e-25, 4.99e-80j)
| (0.015021303516903771544 - 2.1282999359089988912e-400j)  +/-  (3.79e-24, 1.12e-78j)
| (0.031608686527391782839 + 7.3306737083791405034e-402j)  +/-  (2.79e-25, 8.21e-80j)
| (0.053833611525084217623 - 2.5125746245744313419e-401j)  +/-  (1.89e-26, 5.55e-81j)
| (0.023430050119617134825 - 4.3089521808081509985e-402j)  +/-  (3.37e-25, 9.92e-80j)
| (0.039468242490993713135 - 3.3908532830750387956e-400j)  +/-  (7.09e-26, 2.08e-80j)
| (0.053833611525084217623 - 2.8500516140579427642e-400j)  +/-  (5.24e-27, 1.54e-81j)
| (0.069718831277266862455 - 6.3924793922627757182e-400j)  +/-  (2.05e-29, 6.02e-84j)
| (0.046913481544056580382 + 1.7093355934640296632e-401j)  +/-  (8.69e-27, 2.55e-81j)
| (0.069458006095491714081 + 8.3795575132341060818e-401j)  +/-  (1.12e-28, 3.3e-83j)
| (0.074712180086149632124 + 5.8767628019254911353e-400j)  +/-  (6.33e-30, 1.86e-84j)
| (0.060082342698525319138 + 2.9736696180980502641e-400j)  +/-  (5.45e-29, 1.6e-83j)
| (0.088961231121495719621 - 3.1773325630060562439e-400j)  +/-  (5.55e-31, 1.63e-85j)
| (0.081714511130467846333 - 2.7374396640539027225e-400j)  +/-  (1.72e-31, 5.05e-86j)
| (0.060082342698525319138 + 3.693570741901437856e-401j)  +/-  (2.46e-29, 7.23e-84j)
| (0.086471955771853138042 + 2.6279780362872639583e-400j)  +/-  (9.35e-32, 2.75e-86j)
| (0.069458006095491714081 + 3.8725505878500703987e-400j)  +/-  (2.68e-31, 7.87e-86j)
| (0.071372238027452227635 - 4.7589460712150753484e-400j)  +/-  (1.85e-31, 5.42e-86j)
| (0.088961231121495719621 - 2.6393835556014187501e-400j)  +/-  (3.3e-32, 9.69e-87j)
| (0.071372238027452227635 - 1.2987409335519660815e-400j)  +/-  (3.03e-32, 8.89e-87j)
| (0.074712180086149632124 + 2.8204691443745317759e-400j)  +/-  (7.83e-33, 2.3e-87j)
| (0.086471955771853138042 + 3.8077450602346436549e-400j)  +/-  (6.21e-33, 1.82e-87j)
| (0.065430807880805121806 - 3.2983539155548621843e-400j)  +/-  (6.87e-33, 2.01e-87j)
| (0.081714511130467846333 - 4.7671116658741851531e-400j)  +/-  (5.7e-33, 1.67e-87j)
| (0.069718831277266862455 - 2.5758272202931646947e-400j)  +/-  (1.5e-33, 4.42e-88j)
| (0.070458601405895768526 + 1.9541649093376644227e-400j)  +/-  (1.24e-33, 3.65e-88j)
| (0.089729645286394884489 + 2.8103011542828622558e-400j)  +/-  (5.19e-34, 1.57e-88j)
| (0.070458601405895768526 + 5.8265355338793630108e-400j)  +/-  (3.53e-34, 9.47e-89j)
