Starting with polynomial:
P : 231/16*t^6 - 315/16*t^4 + 105/16*t^2 - 5/16
Extension levels are: 6 8 14
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Trying to find an order 8 Kronrod extension for:
P1 : 231/16*t^6 - 315/16*t^4 + 105/16*t^2 - 5/16
Solvable: 1
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Trying to find an order 14 Kronrod extension for:
P2 : 231/16*t^14 - 3731/80*t^12 + 1182181/20400*t^10 - 200960617/5814000*t^8 + 14859361517/1482570000*t^6 - 123220867/98838000*t^4 + 4422019/98838000*t^2 - 22771/889542000
Solvable: 1
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Ending with final polynomial:
P : 231/16*t^28 - 66692493727151796794988446333257645296440476866860128033/663597268983353931807422985370501093993478178076901520*t^26 + 816847678131405704218368149283385868396031002842444010203039/2622868205656706415468839349676905574009222498848953257800*t^24 - 52902511698294444121244888611741925564991533881986676818448256/93439679826520166051077401832239761074078551521493959809125*t^22 + 7405854545331890169733841168915974072331836896857761098165302200709/11055782917073866047163478184790608530284974216023165324615670000*t^20 - 4720850890743672091813865876576510941755530915498890165728681135959/8728249671374104774076430145887322523909190170544604203643950000*t^18 + 268734920441836360320773975048366904677094383108487189898188337031/884234443832017150314932465759826791637859134924453367035825000*t^16 - 2821882549790272258728578066926496162659998811357899308972650177126/23719588955793860057198063394007353685685571294348461570736005625*t^14 + 65496969198730063814468456227107829860149419790124725879878070747987/2049372485780589508941912677242235358443233359831707079711590886000*t^12 - 97367264164004178962048425403998904508921817226742092674526672010679/17078104048171579241182605643685294653693611331930892330929924050000*t^10 + 3024693700013173972320540179681507292631323504966042350929983260741/4743917791158772011439612678801470737137114258869692314147201125000*t^8 - 72059093464365348661379919420964637532658646403937856563781448194/1778969171684539504289854754550551526426417847076134617805200421875*t^6 + 131903547531475184411735058229049663392298788239108160198163257037/108161325638420001860823169076673532806726205102228984762556185650000*t^4 - 12805183013790677239764371321010257567344108179919607456444457877/1103245521511884018980396324582070034628607292042735644578073093630000*t^2 + 52503378606980613389131885508938840451296119842593790874174029/8274341411339130142352972434365525259714554690320517334335548202225000
-------------------------------------------------
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:
| (0.98851944675836295466 - 4.6352432467154321984e-451j)  +/-  (4.04e-118, 4.04e-118j)
| (-0.02411517758027983534 + 2.3975028682954114792e-459j)  +/-  (9.02e-128, 9.02e-128j)
| (-0.96712689960799772045 - 1.1687988662941482735e-453j)  +/-  (3.28e-118, 3.28e-118j)
| (-0.883971622760591045 + 2.2427514394656385247e-458j)  +/-  (6.17e-119, 6.17e-119j)
| (0.93246951420315202781 + 1.0828184562429794351e-464j)  +/-  (1.64e-118, 1.64e-118j)
| (0.82190330787833020415 + 1.1812002782407355495e-464j)  +/-  (1.6e-119, 1.6e-119j)
| (-0.99824878303530830282 + 1.8699282972391287513e-461j)  +/-  (1.81e-118, 1.81e-118j)
| (-0.82190330787833020415 - 2.174831468051597973e-475j)  +/-  (1.61e-119, 1.61e-119j)
| (-0.98851944675836295466 - 9.7353222083551761012e-485j)  +/-  (3.83e-118, 3.83e-118j)
| (0.99824878303530830282 + 5.6935765693852099426e-493j)  +/-  (1.85e-118, 1.85e-118j)
| (0.883971622760591045 - 2.9139497206701772177e-497j)  +/-  (6.23e-119, 6.23e-119j)
| (0.46194088448213480754 - 2.1429167786819965029e-502j)  +/-  (5.11e-123, 5.11e-123j)
| (-0.93246951420315202781 - 5.9927089135633715804e-499j)  +/-  (1.6e-118, 1.6e-118j)
| (-0.74719594328349307383 + 3.0896451124344474738e-507j)  +/-  (3.2e-120, 3.2e-120j)
| (-0.12393098358550430843 + 3.2076758757327217229e-513j)  +/-  (1.26e-126, 1.26e-126j)
| (0.74719594328349307383 - 2.5832525517174166299e-510j)  +/-  (3.33e-120, 3.33e-120j)
| (0.96712689960799772045 - 4.5767238400646439771e-514j)  +/-  (3.24e-118, 3.24e-118j)
| (-0.23861918608319690863 - 5.9436303335409531424e-519j)  +/-  (2.24e-125, 2.24e-125j)
| (-0.66120938646626451366 - 1.1701482289759636178e-517j)  +/-  (5.15e-121, 5.15e-121j)
| (-0.35227159046255040751 - 8.4977424005664314188e-522j)  +/-  (3.46e-124, 3.46e-124j)
| (0.23861918608319690863 + 1.484216253932967539e-522j)  +/-  (2.41e-125, 2.41e-125j)
| (0.66120938646626451366 - 6.3172214763955621128e-519j)  +/-  (4.73e-121, 4.73e-121j)
| (0.12393098358550430843 - 1.3162127501828030837e-525j)  +/-  (1.25e-126, 1.25e-126j)
| (-0.46194088448213480754 + 1.7320233843440066528e-521j)  +/-  (4.73e-123, 4.73e-123j)
| (-0.56554411429006911123 - 1.1085236599419961384e-523j)  +/-  (5.56e-122, 5.56e-122j)
| (0.02411517758027983534 - 8.9504506686268620369e-528j)  +/-  (9.02e-128, 9.02e-128j)
| (0.56554411429006911123 - 8.2400244603037545181e-522j)  +/-  (5.46e-122, 5.46e-122j)
| (0.35227159046255040751 + 2.3315787273087444204e-526j)  +/-  (3.79e-124, 3.79e-124j)
-------------------------------------------------
The weights are:
| (0.015181351770776718175 + 2.125414581736977638e-452j)  +/-  (2.87e-32, 8.39e-89j)
| (0.067846995655740786727 - 1.7242253855148664463e-451j)  +/-  (1.76e-32, 5.13e-89j)
| (0.027853873086645363612 + 4.7373156557557232104e-453j)  +/-  (4.39e-33, 1.28e-89j)
| (0.055391083310313640126 + 4.7928590536993467788e-453j)  +/-  (3.47e-33, 1.01e-89j)
| (0.041556257510727588074 + 1.7077107514803503511e-451j)  +/-  (1.17e-33, 3.41e-90j)
| (0.068586224017537774476 + 6.0627507697250993111e-452j)  +/-  (7.62e-34, 2.23e-90j)
| (0.0048777762970791671871 + 1.7241234756451387631e-453j)  +/-  (3.84e-34, 1.12e-90j)
| (0.068586224017537774476 - 5.3294962745503034426e-453j)  +/-  (1.35e-34, 3.94e-91j)
| (0.015181351770776718175 - 4.7508882401870958772e-453j)  +/-  (5.35e-34, 1.56e-90j)
| (0.0048777762970791671871 + 2.8595313890971302333e-451j)  +/-  (2.21e-35, 6.46e-92j)
| (0.055391083310313640126 - 9.3446835657458231868e-452j)  +/-  (3.31e-35, 9.68e-92j)
| (0.10696115249450570458 + 3.4173262302592839132e-452j)  +/-  (1.2e-36, 3.51e-93j)
| (0.041556257510727588074 - 3.9826537853334423875e-453j)  +/-  (2.21e-34, 6.45e-91j)
| (0.080598635476815757465 + 6.0655937257213798569e-453j)  +/-  (6.14e-36, 1.8e-92j)
| (0.11323574468301810746 + 6.248041022235691129e-452j)  +/-  (2.22e-37, 6.48e-94j)
| (0.080598635476815757465 - 4.4887637278055491675e-452j)  +/-  (2.3e-37, 6.71e-94j)
| (0.027853873086645363612 - 4.2009362640424992655e-451j)  +/-  (2.19e-36, 6.39e-93j)
| (0.11483537820841878804 - 2.9785472906786827659e-452j)  +/-  (6.54e-38, 1.91e-94j)
| (0.091106045427594798695 - 7.2334623857923730074e-453j)  +/-  (6.71e-38, 1.96e-94j)
| (0.11203517015535906561 + 1.7993285073441199867e-452j)  +/-  (1.78e-38, 5.19e-95j)
| (0.11483537820841878804 + 4.8929763420726313748e-452j)  +/-  (1.24e-39, 3.62e-96j)
| (0.091106045427594798695 + 3.715784156014555111e-452j)  +/-  (1.18e-39, 3.44e-96j)
| (0.11323574468301810746 - 8.0546589688369819896e-452j)  +/-  (1.59e-39, 4.65e-96j)
| (0.10696115249450570458 - 1.2293724484384108685e-452j)  +/-  (5.8e-40, 1.7e-96j)
| (0.099934311905466739783 + 9.12579395214069474e-453j)  +/-  (3.87e-40, 1.14e-96j)
| (0.067846995655740786727 + 1.8111190973970838694e-451j)  +/-  (2.41e-39, 7.04e-96j)
| (0.099934311905466739783 - 3.3971981049255087209e-452j)  +/-  (4.49e-41, 1.33e-97j)
| (0.11203517015535906561 - 3.815311904839296048e-452j)  +/-  (7.68e-41, 2.22e-97j)
