Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 19
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Trying to find an order 19 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^23 - 78773570205/3381024574*t^21 + 9405110609961/175813277848*t^19 - 225413970227853/3252545640188*t^17 + 6337990954094679/113839097406580*t^15 - 23342273091342/813136410047*t^13 + 73745497559067/7756070372756*t^11 - 221435557932501/112463020404962*t^9 + 107980305524487/449852081619848*t^7 - 129872348385527/8434726530372150*t^5 + 939848410523/2249260408099240*t^3 - 22415950321/7872411428347340*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:
| (0.9688907824185387614 + 3.0661891922532255609e-385j)  +/-  (8.81e-121, 8.81e-121j)
| (-0.6863131463334647897 + 5.0113426825059952464e-384j)  +/-  (4.06e-122, 4.06e-122j)
| (-0.86113631159405257522 - 1.683161835153996039e-386j)  +/-  (4.69e-121, 4.69e-121j)
| (-0.9688907824185387614 - 5.5451922979189053029e-388j)  +/-  (9.9e-121, 9.9e-121j)
| (0.86113631159405257522 - 7.5698100699687034551e-392j)  +/-  (4.57e-121, 4.57e-121j)
| (0.46243244489479936378 + 4.3965732620263529718e-394j)  +/-  (7.75e-124, 7.75e-124j)
| (-0.99406644087377638794 - 3.7894351310739324036e-389j)  +/-  (3.71e-121, 3.71e-121j)
| (-0.92422643201342944583 - 1.2852611296903392439e-395j)  +/-  (9.6e-121, 9.6e-121j)
| (0.99406644087377638794 + 9.7432566936000399492e-402j)  +/-  (3.93e-121, 3.93e-121j)
| (-0.3399810435848562648 + 1.1893739382088398344e-403j)  +/-  (8.33e-125, 8.33e-125j)
| (0.78116192286098361242 + 1.3171847857161050395e-412j)  +/-  (1.54e-121, 1.54e-121j)
| (0.21640280502393991398 + 2.0850460106394404062e-415j)  +/-  (5.51e-126, 5.51e-126j)
| (-0.46243244489479936378 + 2.5356757448204373297e-418j)  +/-  (8.53e-124, 8.53e-124j)
| (-0.57907424174813289938 + 9.2293929867728058409e-431j)  +/-  (6.74e-123, 6.74e-123j)
| (0.099639517754412514008 - 9.2683042145029632289e-437j)  +/-  (3.67e-127, 3.67e-127j)
| (0.57907424174813289938 + 7.9935223749555459811e-439j)  +/-  (6.44e-123, 6.44e-123j)
| (0.92422643201342944583 - 3.2836568874745292786e-436j)  +/-  (8.41e-121, 8.41e-121j)
| (-0.21640280502393991398 + 6.3199261735676719584e-437j)  +/-  (5.51e-126, 5.51e-126j)
| (-0.78116192286098361242 + 2.3368532800667289202e-443j)  +/-  (1.61e-121, 1.61e-121j)
| (-0.099639517754412514008 + 9.9613397243836312065e-449j)  +/-  (3.67e-127, 3.67e-127j)
| (0.3399810435848562648 + 8.8961881159078921958e-453j)  +/-  (8.29e-125, 8.29e-125j)
| (0.6863131463334647897 - 6.5891805464106875847e-451j)  +/-  (3.98e-122, 3.98e-122j)
| (-7.8800898747593274505e-506 + 2.0160954031137462272e-506j)  +/-  (1.87e-504, 1.87e-504j)
-------------------------------------------------
The weights are:
| (0.035055689603089052602 - 1.5501377461142809782e-385j)  +/-  (1.06e-41, 1.37e-99j)
| (0.10149826489410487006 + 1.7586877926126838373e-384j)  +/-  (5.54e-42, 7.15e-100j)
| (0.071828231271709343271 - 1.2069147432817428693e-384j)  +/-  (3.22e-42, 4.15e-100j)
| (0.035055689603089052602 - 2.0516918557220651006e-385j)  +/-  (7.89e-43, 1.02e-100j)
| (0.071828231271709343271 - 2.2684422614448818795e-385j)  +/-  (7.3e-44, 9.43e-102j)
| (0.12020720347115528736 + 5.9732954358983395969e-385j)  +/-  (5.86e-44, 7.57e-102j)
| (0.01520980668293562999 + 5.2013495037243983224e-386j)  +/-  (2.5e-43, 3.23e-101j)
| (0.054094989293311677821 + 5.0185310890383590734e-385j)  +/-  (6.18e-43, 7.98e-101j)
| (0.01520980668293562999 - 1.2754934850012533769e-385j)  +/-  (1.13e-44, 1.46e-102j)
| (0.1239440828209593487 - 5.2360384911230218596e-384j)  +/-  (1.5e-44, 1.93e-102j)
| (0.08778564649679938922 + 1.0638395448549578837e-385j)  +/-  (1.71e-44, 2.2e-102j)
| (0.12198368686923757637 + 2.6837532780084191477e-384j)  +/-  (3.51e-45, 4.53e-103j)
| (0.12020720347115528736 + 5.2138695073017798441e-384j)  +/-  (8.84e-45, 1.14e-102j)
| (0.11248295422199284356 - 7.1565986555730263347e-384j)  +/-  (8.87e-45, 1.15e-102j)
| (0.10912487298651785018 - 5.337484088605602599e-384j)  +/-  (7.64e-46, 9.8e-104j)
| (0.11248295422199284356 - 2.3699920832864893985e-385j)  +/-  (1.52e-46, 1.94e-104j)
| (0.054094989293311677821 + 4.2712213808432535593e-385j)  +/-  (9.6e-47, 1.24e-104j)
| (0.12198368686923757637 + 6.1711275068575338065e-384j)  +/-  (2.75e-46, 3.59e-104j)
| (0.08778564649679938922 + 3.5323257575061247207e-384j)  +/-  (1.41e-46, 1.8e-104j)
| (0.10912487298651785018 - 7.731235725250627377e-384j)  +/-  (1.1e-46, 1.43e-104j)
| (0.1239440828209593487 - 1.2850869888392738098e-384j)  +/-  (2.94e-47, 3.44e-105j)
| (0.10149826489410487006 + 3.0383478820013102979e-386j)  +/-  (8.71e-48, 9.13e-106j)
| (0.093569142776374261723 + 7.8300848746229024687e-384j)  +/-  (6.38e-47, 8.82e-105j)
