Starting with polynomial:
P : 8*t^3 - 12*t
Extension levels are: 3 6 26
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Trying to find an order 6 Kronrod extension for:
P1 : 8*t^3 - 12*t
Solvable: 1
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P2 : 8*t^9 - 117*t^7 + 945/2*t^5 - 2205/4*t^3 + 945/8*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 8*t^35 - 290697708258522989004080931821/149908590829531287591787323*t^33 + 3765175490117101671802713294925/18170738282367428799004524*t^31 - 5163604061077454135245186661266739/399756242212083433578099528*t^29 + 1256805400737228573606089585726811031/2398537453272500601468597168*t^27 - 2596188494765740681609590180974264125/177669440983148192701377568*t^25 + 102526940774678510281832126147751403275/355338881966296385402755136*t^23 - 264506466412973194947735213321176239525/64607069448417524618682752*t^21 + 13310989224423175302394787916432742725/317479456748980464956672*t^19 - 79724345682880297261467398447163295305975/258428277793670098474731008*t^17 + 831694491688574974955376740619163680561375/516856555587340196949462016*t^15 - 6006479197812439372482655158331641183061875/1033713111174680393898924032*t^13 + 2631069359300418656618132235241130357742375/187947838395396435254349824*t^11 - 8003658380864455962810141255411397948065375/375895676790792870508699648*t^9 + 155676040108256963714564075056674000041554875/8269704889397443151191392256*t^7 - 141080780245798380617120080422583950881784375/16539409778794886302382784512*t^5 + 53751834892663314539541725817696059768255625/33078819557589772604765569024*t^3 - 6038866703595855320517922290826257435001875/66157639115179545209531138048*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:
| (6.2775611814676562083 + 2.8080584381979091148e-464j)  +/-  (1.1e-120, 1.1e-120j)
| (5.1360391493668126951 + 4.4760463671548543918e-464j)  +/-  (9.76e-120, 9.76e-120j)
| (-5.676486726712922865 - 7.4917530821307489173e-464j)  +/-  (4.15e-120, 4.15e-120j)
| (4.6336630214801841354 + 4.1214955495259775896e-466j)  +/-  (1.46e-119, 1.46e-119j)
| (-4.6336630214801841354 - 1.8770038746513291962e-465j)  +/-  (1.68e-119, 1.68e-119j)
| (-6.9980445823281482591 - 7.6424442368096994162e-470j)  +/-  (1.24e-121, 1.24e-121j)
| (-6.2775611814676562083 + 1.9568807928778280444e-469j)  +/-  (1.25e-120, 1.25e-120j)
| (6.9980445823281482591 + 6.0070764515823791351e-473j)  +/-  (1.48e-121, 1.48e-121j)
| (-2.9116706428390185702 - 1.0138971304149490487e-467j)  +/-  (5.24e-119, 5.24e-119j)
| (5.676486726712922865 - 3.1391108391678321138e-482j)  +/-  (4.06e-120, 4.06e-120j)
| (1.6194722422732588159 + 2.9324032184859296729e-484j)  +/-  (1.23e-122, 1.23e-122j)
| (4.157403431789769276 + 2.9350370643768558561e-480j)  +/-  (1.69e-119, 1.69e-119j)
| (-4.157403431789769276 + 1.4206074055257336061e-484j)  +/-  (1.67e-119, 1.67e-119j)
| (-0.84508857109212636298 + 1.8619434497107776155e-488j)  +/-  (1.58e-124, 1.58e-124j)
| (2.0232301911005156592 + 2.8163822327234730541e-483j)  +/-  (1.03e-121, 1.03e-121j)
| (2.9592107790638377223 - 5.9470800238580676048e-481j)  +/-  (6.22e-119, 6.22e-119j)
| (-2.9592107790638377223 + 3.7459715687663549236e-495j)  +/-  (7.15e-119, 7.15e-119j)
| (-2.4374631237360168735 - 9.1842832141127998429e-507j)  +/-  (8.6e-121, 8.6e-121j)
| (1.2378472225608442467e-521 + 7.9349964804591950984e-522j)  +/-  (5.15e-520, 5.15e-520j)
| (-5.1360391493668126951 - 1.530549251010778607e-505j)  +/-  (1.01e-119, 1.01e-119j)
| (-0.52403354748695764515 + 4.7981112578877490932e-511j)  +/-  (1.87e-125, 1.87e-125j)
| (0.84508857109212636298 + 1.716626762905810299e-510j)  +/-  (1.51e-124, 1.51e-124j)
| (2.9116706428390185702 - 3.7013057216750456124e-503j)  +/-  (5.62e-119, 5.62e-119j)
| (3.6988746353322762466 + 8.1501913134378797195e-511j)  +/-  (1.74e-119, 1.74e-119j)
| (-3.24082442498230135 - 1.8472038537031928365e-511j)  +/-  (2.2e-119, 2.2e-119j)
| (3.24082442498230135 - 3.875118042576868544e-519j)  +/-  (2.17e-119, 2.17e-119j)
| (1.2247448713915890491 - 2.122191128798244182e-525j)  +/-  (1.34e-123, 1.34e-123j)
| (0.52403354748695764515 + 1.0659699990786588981e-527j)  +/-  (2.05e-125, 2.05e-125j)
| (-0.30599436522045932431 - 4.466087762877208497e-528j)  +/-  (3.55e-126, 3.55e-126j)
| (-1.6194722422732588159 + 6.8517990058053513934e-523j)  +/-  (1.15e-122, 1.15e-122j)
| (-2.0232301911005156592 - 2.4383939136527245104e-522j)  +/-  (9.98e-122, 9.98e-122j)
| (0.30599436522045932431 + 4.304083502550752115e-529j)  +/-  (3.14e-126, 3.14e-126j)
| (2.4374631237360168735 - 7.1359076817290583216e-524j)  +/-  (8.46e-121, 8.46e-121j)
| (-3.6988746353322762466 - 5.5042591533676052469e-526j)  +/-  (1.49e-119, 1.49e-119j)
| (-1.2247448713915890491 + 1.378713936462939971e-532j)  +/-  (1.29e-123, 1.29e-123j)
-------------------------------------------------
The weights are:
| (2.7945234817478016139e-18 + 2.4744562305094383673e-479j)  +/-  (3.04e-38, 1.56e-97j)
| (1.0239418363555538088e-12 - 2.8426466252803388906e-475j)  +/-  (2.13e-35, 1.1e-94j)
| (3.2344547438137483459e-15 - 1.0364717142635774929e-477j)  +/-  (2.4e-38, 1.23e-97j)
| (1.3031218253409162963e-10 + 1.4172671746154199582e-474j)  +/-  (1.65e-34, 8.5e-94j)
| (1.3031218253409162963e-10 - 1.4767029400000523443e-474j)  +/-  (5.75e-36, 2.96e-95j)
| (2.5206930227669382445e-22 + 5.1361537497775205386e-482j)  +/-  (4.55e-42, 2.34e-101j)
| (2.7945234817478016139e-18 - 1.4462898899233745106e-479j)  +/-  (3.8e-40, 1.96e-99j)
| (2.5206930227669382445e-22 - 9.2187467507323759877e-482j)  +/-  (1.57e-42, 8.09e-102j)
| (0.00013419580653569417939 + 3.3044270892155940925e-470j)  +/-  (6.99e-33, 3.59e-92j)
| (3.2344547438137483459e-15 - 2.8775876389369853596e-477j)  +/-  (4.8e-39, 2.47e-98j)
| (0.016362625292532630859 + 3.3739008687865851414e-470j)  +/-  (6.96e-28, 3.58e-87j)
| (8.1942839338835597637e-09 - 1.1234884006809983029e-473j)  +/-  (2.29e-36, 1.18e-95j)
| (8.1942839338835597637e-09 + 7.8328484259371678589e-474j)  +/-  (1.57e-37, 8.05e-97j)
| (0.10079998887025106139 + 7.9802853149467723065e-470j)  +/-  (1.34e-28, 6.91e-88j)
| (0.003842428125723104143 - 1.5821592302004604635e-470j)  +/-  (7.71e-31, 3.96e-90j)
| (-7.1985946479245359385e-05 + 2.6014952459583236682e-470j)  +/-  (2.35e-34, 1.21e-93j)
| (-7.1985946479245359385e-05 - 3.364330572005304033e-470j)  +/-  (2.15e-34, 1.11e-93j)
| (0.00062595633386444252 - 3.3315606208373076662e-472j)  +/-  (4.09e-34, 2.1e-93j)
| (0.1895932991656172421 - 4.9846746670903675505e-469j)  +/-  (9.43e-30, 4.84e-89j)
| (1.0239418363555538088e-12 - 1.5938564022387099645e-476j)  +/-  (3.74e-40, 1.92e-99j)
| (0.10824852053183729943 - 2.8557540918550033401e-469j)  +/-  (1.26e-29, 6.5e-89j)
| (0.10079998887025106139 + 1.9552924739569669051e-469j)  +/-  (1.74e-30, 8.96e-90j)
| (0.00013419580653569417939 - 2.7627748197016273982e-470j)  +/-  (1.41e-34, 7.25e-94j)
| (2.9200953023317313234e-07 + 1.0374646556751221202e-472j)  +/-  (1.65e-37, 8.51e-97j)
| (7.5952910672124218751e-06 + 7.8281986750712200637e-472j)  +/-  (2.8e-37, 1.45e-96j)
| (7.5952910672124218751e-06 - 1.6754097476980902255e-471j)  +/-  (2.98e-36, 1.53e-95j)
| (0.04900738654460969911 - 7.6727846553275585385e-470j)  +/-  (4.9e-33, 2.52e-92j)
| (0.10824852053183729943 - 4.8732994056259452409e-469j)  +/-  (1.19e-32, 6.09e-92j)
| (0.12624633923209595158 + 4.5128696314604502202e-469j)  +/-  (2.78e-32, 1.42e-91j)
| (0.016362625292532630859 + 3.8378171799326383793e-471j)  +/-  (1.22e-35, 6.25e-95j)
| (0.003842428125723104143 - 2.1990483206850586781e-472j)  +/-  (3.27e-36, 1.68e-95j)
| (0.12624633923209595158 + 6.1370418750299703072e-469j)  +/-  (2.57e-33, 1.32e-92j)
| (0.00062595633386444252 + 8.4013193286461427472e-471j)  +/-  (2.29e-36, 1.17e-95j)
| (2.9200953023317313234e-07 - 5.1283452212921142344e-473j)  +/-  (2.9e-39, 1.53e-98j)
| (0.04900738654460969911 - 1.8770357173529221609e-470j)  +/-  (1.26e-35, 6.03e-95j)
