Starting with polynomial:
P : 64*t^6 - 480*t^4 + 720*t^2 - 120
Extension levels are: 6 9 16
-------------------------------------------------
Trying to find an order 9 Kronrod extension for:
P1 : 64*t^6 - 480*t^4 + 720*t^2 - 120
Solvable: 1
-------------------------------------------------
Trying to find an order 16 Kronrod extension for:
P2 : 64*t^15 - 443040/191*t^13 + 5766480/191*t^11 - 34180440/191*t^9 + 97309620/191*t^7 - 129077550/191*t^5 + 68923575/191*t^3 - 18129825/382*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 64*t^31 - 1824323754501142631098863532500221108960/127678172195960946379309627115979517*t^29 + 164127716959105517589673680303217944307120/127678172195960946379309627115979517*t^27 - 24216086299404409078777124405117714234420920/383034516587882839137928881347938551*t^25 + 734965092199631214437839217619863065211165900/383034516587882839137928881347938551*t^23 - 14626520347829850321478887895851467434568457250/383034516587882839137928881347938551*t^21 + 197042092115289485868836481827746087311830959525/383034516587882839137928881347938551*t^19 - 3646561598011138324056834849627177832302053512075/766069033175765678275857762695877102*t^17 + 46446025834352566579721941475075622655427691161125/1532138066351531356551715525391754204*t^15 - 134489432478225917549691005099173615145785246235125/1021425377567687571034477016927836136*t^13 + 780492772593427554317977809703175091245115100816625/2042850755135375142068954033855672272*t^11 - 265690651878126795786194982639169187580326050571125/371427410024613662194355278882849504*t^9 + 608079922581907564869728793471397218483337468364625/742854820049227324388710557765699008*t^7 - 781520970338406505246184963233696013614138600216875/1485709640098454648777421115531398016*t^5 + 486096311613285833355945554098452142978708378284375/2971419280196909297554842231062796032*t^3 - 100252484253233875494515769323786003044777611875625/5942838560393818595109684462125592064*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:
| (-3.9268135162497144207 + 1.5076637823887615134e-479j)  +/-  (8.76e-121, 8.76e-121j)
| (-5.0978627626970569145 + 2.8060867133130328071e-483j)  +/-  (1.84e-121, 1.84e-121j)
| (3.4418485129732912657 - 4.807927130930201261e-486j)  +/-  (1.19e-120, 1.19e-120j)
| (3.0701613138889128067 - 1.4625614586066868451e-487j)  +/-  (1.26e-120, 1.26e-120j)
| (5.8418208952559505971 - 2.9363668190811027082e-490j)  +/-  (3.48e-122, 3.48e-122j)
| (-4.4776499798886559811 + 6.9505019701524555339e-488j)  +/-  (4.5e-121, 4.5e-121j)
| (2.0169355714010175893 - 1.417238091351168693e-496j)  +/-  (9.82e-122, 9.82e-122j)
| (-3.0701613138889128067 + 8.6167963936988597061e-501j)  +/-  (1.2e-120, 1.2e-120j)
| (-9.0963154716553218072 + 5.9970874713429447067e-513j)  +/-  (5.45e-124, 5.45e-124j)
| (-5.8418208952559505971 - 1.1541298460704056582e-509j)  +/-  (3.25e-122, 3.25e-122j)
| (1.7281759088743055938 - 1.44761764747043129e-512j)  +/-  (2.56e-122, 2.56e-122j)
| (5.0978627626970569145 - 4.5920060455905254911e-511j)  +/-  (1.75e-121, 1.75e-121j)
| (1.3358490740136969497 + 5.7537062129131276567e-513j)  +/-  (3.38e-123, 3.38e-123j)
| (-2.743319980252235728 - 5.3581431746850500965e-510j)  +/-  (7.29e-121, 7.29e-121j)
| (3.9268135162497144207 - 1.5590505399389678005e-518j)  +/-  (8.33e-121, 8.33e-121j)
| (-2.3506049736744922228 + 1.6371798213911647235e-521j)  +/-  (2.58e-121, 2.58e-121j)
| (4.4776499798886559811 - 4.0658978847078992754e-531j)  +/-  (4.54e-121, 4.54e-121j)
| (-3.4418485129732912657 + 1.0094886949352191409e-531j)  +/-  (1.23e-120, 1.23e-120j)
| (-0.95452011014285350763 + 1.0544658519166557849e-540j)  +/-  (7.2e-124, 7.2e-124j)
| (-1.7281759088743055938 + 2.9606002687778364045e-538j)  +/-  (2.68e-122, 2.68e-122j)
| (2.743319980252235728 + 4.0401213708949570109e-537j)  +/-  (7.84e-121, 7.84e-121j)
| (0.95452011014285350763 - 1.4488176012750235029e-543j)  +/-  (7.3e-124, 7.3e-124j)
| (9.0963154716553218072 - 4.8131967406745050406e-544j)  +/-  (6.27e-124, 6.27e-124j)
| (-1.3358490740136969497 - 3.824929722705729796e-543j)  +/-  (3.4e-123, 3.4e-123j)
| (2.3506049736744922228 - 1.9633187008598826746e-541j)  +/-  (2.72e-121, 2.72e-121j)
| (0.81615604951984204935 - 9.9861152011526093903e-545j)  +/-  (2.56e-124, 2.56e-124j)
| (5.1604992899560011788e-550 + 4.9609659244649791796e-551j)  +/-  (1.61e-548, 1.61e-548j)
| (-2.0169355714010175893 + 5.4936647657426865908e-544j)  +/-  (1.09e-121, 1.09e-121j)
| (0.43607741192761650868 + 1.6398523940041733988e-549j)  +/-  (6.18e-126, 6.18e-126j)
| (-0.43607741192761650868 - 8.9940857876450720101e-550j)  +/-  (6.18e-126, 6.18e-126j)
| (-0.81615604951984204935 - 1.768185126223266693e-548j)  +/-  (2.69e-124, 2.69e-124j)
-------------------------------------------------
The weights are:
| (5.909066538854108414e-08 + 5.5157614700374873882e-486j)  +/-  (8.44e-37, 1.19e-96j)
| (1.9437026168870552438e-12 - 5.6923210600173282586e-490j)  +/-  (2.79e-40, 3.94e-100j)
| (1.7772237638594821766e-06 - 2.3797167468568877668e-486j)  +/-  (1.81e-36, 2.56e-96j)
| (1.4157759110993614805e-05 + 2.1650945941527504733e-485j)  +/-  (3.92e-35, 5.55e-95j)
| (7.2800734358633311592e-16 - 5.3496882130233787652e-493j)  +/-  (6.88e-44, 9.73e-104j)
| (6.4375282105519273713e-10 + 5.7007323202993065298e-488j)  +/-  (1.13e-39, 1.6e-99j)
| (0.0026195598259236324481 - 1.8091489389633578178e-483j)  +/-  (4.7e-32, 6.65e-92j)
| (1.4157759110993614805e-05 + 1.76841764606537507e-484j)  +/-  (1.52e-36, 2.15e-96j)
| (3.2905401909146598397e-28 - 2.0975688891198630736e-499j)  +/-  (1.72e-50, 2.44e-110j)
| (7.2800734358633311592e-16 + 2.7289592540829706377e-492j)  +/-  (9.03e-44, 1.28e-103j)
| (0.0098723629195113989633 + 3.7711585505222626889e-483j)  +/-  (1.55e-32, 2.19e-92j)
| (1.9437026168870552438e-12 + 7.3869312635239878958e-491j)  +/-  (8.89e-44, 1.26e-103j)
| (0.039394271031786253877 - 8.491669181827704694e-483j)  +/-  (4.55e-32, 6.44e-92j)
| (0.00011258756003930748774 - 5.5454200501470299633e-484j)  +/-  (1.25e-37, 1.77e-97j)
| (5.909066538854108414e-08 + 1.1343826457957067468e-487j)  +/-  (6.5e-41, 9.2e-101j)
| (0.00087467731670125053947 + 1.9237073477449062711e-483j)  +/-  (1.65e-37, 2.33e-97j)
| (6.4375282105519273713e-10 - 3.7363820276411240005e-489j)  +/-  (1.52e-42, 2.15e-102j)
| (1.7772237638594821766e-06 - 3.6158607474359200556e-485j)  +/-  (1.24e-39, 1.75e-99j)
| (0.056721656032873121616 + 6.0348263701659326484e-482j)  +/-  (4.55e-35, 6.44e-95j)
| (0.0098723629195113989633 + 9.6995792895912866794e-483j)  +/-  (3.41e-37, 4.82e-97j)
| (0.00011258756003930748774 - 9.8393223446342700907e-485j)  +/-  (1.6e-38, 2.27e-98j)
| (0.056721656032873121616 + 3.6746672574357513069e-482j)  +/-  (7.18e-36, 1.02e-95j)
| (3.2905401909146598397e-28 + 8.3262347459076318242e-500j)  +/-  (1.07e-53, 1.51e-113j)
| (0.039394271031786253877 - 1.724793395784181818e-482j)  +/-  (2.05e-37, 2.9e-97j)
| (0.00087467731670125053947 + 4.8302704137417317951e-484j)  +/-  (5.41e-38, 7.65e-98j)
| (0.065776673463915747378 - 4.2078011010019549879e-482j)  +/-  (3.13e-36, 4.43e-96j)
| (0.24714650662959283198 - 1.7168580375173953399e-482j)  +/-  (2.49e-37, 3.53e-97j)
| (0.0026195598259236324481 - 5.6302695553008166153e-483j)  +/-  (1.07e-38, 1.51e-98j)
| (0.20103896381521537838 + 1.9600819331087761419e-482j)  +/-  (2.42e-37, 3.43e-97j)
| (0.20103896381521537838 + 2.4498051068589261198e-482j)  +/-  (4.59e-38, 6.49e-98j)
| (0.065776673463915747378 - 6.4158367021172082979e-482j)  +/-  (7.19e-38, 1e-97j)
