Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 10 24
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 24 Kronrod extension for:
P2 : 4*t^12 - 8477/76*t^10 + 155745/152*t^8 - 563535/152*t^6 + 1500975/304*t^4 - 2132865/1216*t^2 + 110565/2432
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^36 - 619179436373860848095672558382032774976633302247114653/641549688605694251299955452916483418969722860603852*t^34 + 2250012651262999248254419438345249194038905076552240006661/21812689412593604544198485399160436244970577260530968*t^32 - 35265080163156161422753858254839628099475959769361266036991/5453172353148401136049621349790109061242644315132742*t^30 + 723804960193785572280560014466693353301329271715931729789250/2726586176574200568024810674895054530621322157566371*t^28 - 658047079296742342877958970451276742993869462002591221387020385/87250757650374418176793941596641744979882309042123872*t^26 + 26671837959354889968758453624558739116213570884047305426794403745/174501515300748836353587883193283489959764618084247744*t^24 - 391584749778064160214509649201853884119107532940533438135549267685/174501515300748836353587883193283489959764618084247744*t^22 + 8374466589973009560107383134525589744140227735311179990879461120055/349003030601497672707175766386566979919529236168495488*t^20 - 427866407228848240678176261358408511236497144884807238002870490225/2296072569746695215178787936753730131049534448476944*t^18 + 561899764584178924424939300013268565523371908935798272365107614325/540252369352163580042067749824407089658713987876928*t^16 - 8850125497449793651555407244695249384582192631289727731422383663975/2161009477408654320168270999297628358634855951507712*t^14 + 95614816945912870365488742479853548694499967173410908523127218018075/8644037909634617280673083997190513434539423806030848*t^12 - 1360751389525879788793994468898987466701880000942475305333139691413025/69152303277076938245384671977524107476315390448246784*t^10 + 3007555328531040215462578388397362345811577617267378700123982664656625/138304606554153876490769343955048214952630780896493568*t^8 - 1893801866888139972066605487381974553746554365611084074856445832297875/138304606554153876490769343955048214952630780896493568*t^6 + 1187035703232164479346694431861135612920224311378783104330414810960875/276609213108307752981538687910096429905261561792987136*t^4 - 1157672053069521303911573171855782067033878191696522519905202205241625/2212873704866462023852309503280771439242092494343897088*t^2 + 51343280423676617037392209644506418116345669675531636300087968388625/4425747409732924047704619006561542878484184988687794176
-------------------------------------------------
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: 0
  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:
| (-4.5415399294236798253 - 3.1629919551230711123e-353j)  +/-  (3.62e-119, 3.62e-119j)
| (3.6970277052027912255 + 4.024191304203840014e-353j)  +/-  (1.1e-117, 1.1e-117j)
| (5.5801306123700395621 + 3.9066036169891907017e-365j)  +/-  (6.9e-120, 6.9e-120j)
| (2.4080748281550112364 - 5.5373901452526380274e-364j)  +/-  (9.05e-121, 9.05e-121j)
| (6.1802820771320259652 - 2.4990121097648213715e-364j)  +/-  (1.65e-120, 1.65e-120j)
| (-5.5801306123700395621 - 5.609099357058589402e-361j)  +/-  (6.36e-120, 6.36e-120j)
| (-3.6970277052027912255 + 6.7247980676766325619e-359j)  +/-  (1.09e-117, 1.09e-117j)
| (-6.9006044482884539405 + 5.7101310156086959367e-385j)  +/-  (1.63e-121, 1.63e-121j)
| (4.5415399294236798253 - 1.5854987327957085457e-382j)  +/-  (3.67e-119, 3.67e-119j)
| (-4.0660189859399418034 - 2.2521122686719411266e-381j)  +/-  (8.72e-119, 8.72e-119j)
| (0.16761481870756104368 - 7.0267982504319630616e-404j)  +/-  (9.06e-127, 9.06e-127j)
| (1.6968539710945151274 - 5.4339612369564314849e-399j)  +/-  (3.52e-122, 3.52e-122j)
| (-3.6783246397895513046 - 4.1331832923024418221e-396j)  +/-  (1.04e-117, 1.04e-117j)
| (-6.1802820771320259652 + 1.8658162051433937611e-414j)  +/-  (1.57e-120, 1.57e-120j)
| (-2.0436541275856649452 - 4.870394135525716242e-414j)  +/-  (2.13e-121, 2.13e-121j)
| (5.0414181487850290386 + 2.9215574260611673565e-412j)  +/-  (1.76e-119, 1.76e-119j)
| (-2.7962452403682858841 - 3.6494002010462447038e-412j)  +/-  (3.75e-120, 3.75e-120j)
| (4.0660189859399418034 - 2.0047127065851088192e-411j)  +/-  (7.9e-119, 7.9e-119j)
| (-0.7071067811865475244 - 1.8071056308134934545e-418j)  +/-  (1.12e-124, 1.12e-124j)
| (-3.207204485323931896 + 6.2337431942113455214e-412j)  +/-  (1.68e-119, 1.68e-119j)
| (-5.0414181487850290386 - 2.9076103630761024222e-415j)  +/-  (1.92e-119, 1.92e-119j)
| (2.0436541275856649452 - 1.3924177289151395363e-415j)  +/-  (2.04e-121, 2.04e-121j)
| (6.9006044482884539405 - 7.2336585218255304666e-417j)  +/-  (1.68e-121, 1.68e-121j)
| (3.207204485323931896 - 7.871130283194949803e-413j)  +/-  (1.65e-119, 1.65e-119j)
| (-1.6968539710945151274 + 1.9179624204313000975e-418j)  +/-  (3.87e-122, 3.87e-122j)
| (-1.3532153932168790075 + 1.2338786573467510108e-419j)  +/-  (5.71e-123, 5.71e-123j)
| (0.46529879999714272574 - 3.6171012601581686638e-422j)  +/-  (1.41e-125, 1.41e-125j)
| (3.6783246397895513046 + 2.2820971358892900358e-415j)  +/-  (1.12e-117, 1.12e-117j)
| (-0.16761481870756104368 + 1.1549359137923311907e-428j)  +/-  (9.06e-127, 9.06e-127j)
| (-0.46529879999714272574 + 4.0479150682471665937e-428j)  +/-  (1.36e-125, 1.36e-125j)
| (2.7962452403682858841 + 1.4369330116443550763e-422j)  +/-  (3.59e-120, 3.59e-120j)
| (0.7071067811865475244 - 1.0195501579012471757e-426j)  +/-  (1.13e-124, 1.13e-124j)
| (1.0114179437023830862 + 3.6969199562705302217e-425j)  +/-  (8.99e-124, 8.99e-124j)
| (1.3532153932168790075 - 1.9163931408371493537e-425j)  +/-  (5.78e-123, 5.78e-123j)
| (-1.0114179437023830862 + 9.5009375673998257785e-426j)  +/-  (7.67e-124, 7.67e-124j)
| (-2.4080748281550112364 + 5.8847286323131149545e-423j)  +/-  (9.33e-121, 9.33e-121j)
-------------------------------------------------
The weights are:
| (3.0178700528007697843e-10 - 6.6411007294915821346e-362j)  +/-  (6.97e-30, 4.59e-87j)
| (-8.2322919008771080579e-07 + 1.900773233738951638e-357j)  +/-  (4.14e-27, 2.73e-84j)
| (9.5465162341759625623e-15 - 3.2506182408054683595e-366j)  +/-  (1.55e-33, 1.02e-90j)
| (0.00064345617488860534854 + 1.4267075393698302693e-358j)  +/-  (3.38e-22, 2.23e-79j)
| (9.3811883844987815954e-18 + 3.3480362432099997226e-368j)  +/-  (3.4e-35, 2.24e-92j)
| (9.5465162341759625623e-15 + 7.5666135088169882679e-366j)  +/-  (3.11e-35, 2.05e-92j)
| (-8.2322919008771080579e-07 - 4.8680259010614278831e-359j)  +/-  (9.48e-30, 6.25e-87j)
| (9.7681123113622605111e-22 + 2.009067285640142501e-370j)  +/-  (9.09e-40, 5.99e-97j)
| (3.0178700528007697843e-10 - 8.9812925757100989822e-363j)  +/-  (1.38e-33, 9.08e-91j)
| (1.7588741279823888306e-08 + 6.829399700502613575e-361j)  +/-  (9.61e-32, 6.33e-89j)
| (0.18081464048486998905 - 1.3233724024886989845e-356j)  +/-  (7.03e-24, 4.63e-81j)
| (0.010870983217056281114 + 9.7503276152293118049e-358j)  +/-  (7.02e-24, 4.63e-81j)
| (1.2515959066247975738e-06 + 5.1379694143618308417e-359j)  +/-  (8.98e-30, 5.92e-87j)
| (9.3811883844987815954e-18 - 6.5953711843487426445e-368j)  +/-  (2.99e-38, 1.97e-95j)
| (0.0030617016553561312368 + 3.1765656540141622264e-358j)  +/-  (1.29e-27, 8.47e-85j)
| (2.6710910364125884577e-12 + 1.8630058073985083543e-364j)  +/-  (9.37e-37, 6.18e-94j)
| (9.0661548179143062404e-05 + 3.2420592787653591773e-359j)  +/-  (3.16e-30, 2.08e-87j)
| (1.7588741279823888306e-08 + 7.0509757809456549354e-361j)  +/-  (1.44e-34, 9.5e-92j)
| (0.08996073165593997355 + 1.0527173264623937389e-356j)  +/-  (2.87e-28, 1.89e-85j)
| (8.1350397881003759255e-06 - 1.1074845887900065828e-359j)  +/-  (5.27e-31, 3.47e-88j)
| (2.6710910364125884577e-12 - 6.36445235078391851e-364j)  +/-  (9.86e-36, 6.5e-93j)
| (0.0030617016553561312368 - 3.9420469341919666323e-358j)  +/-  (2.88e-30, 1.9e-87j)
| (9.7681123113622605111e-22 - 1.1202277237820684091e-370j)  +/-  (3e-43, 1.98e-100j)
| (8.1350397881003759255e-06 + 2.4484376851799328224e-359j)  +/-  (5.99e-34, 3.95e-91j)
| (0.010870983217056281114 - 8.3304956962314859492e-358j)  +/-  (5.3e-31, 3.49e-88j)
| (0.03116665821565554345 + 1.9844150259028180482e-357j)  +/-  (1.81e-30, 1.19e-87j)
| (0.11574574598361531631 + 1.4530465163181454006e-356j)  +/-  (1.38e-29, 9.07e-87j)
| (1.2515959066247975738e-06 - 1.911454165999797929e-357j)  +/-  (1.3e-33, 8.57e-91j)
| (0.18081464048486998905 + 1.3075699117399307884e-356j)  +/-  (1.31e-29, 8.63e-87j)
| (0.11574574598361531631 - 1.4046299378452020226e-356j)  +/-  (6.78e-30, 4.47e-87j)
| (9.0661548179143062404e-05 - 5.1240531049065644511e-359j)  +/-  (1.66e-33, 1.09e-90j)
| (0.08996073165593997355 - 1.1097642289396411005e-356j)  +/-  (1.21e-30, 7.94e-88j)
| (0.067636839764725447372 + 5.1662261294467528315e-357j)  +/-  (1.01e-31, 6.64e-89j)
| (0.03116665821565554345 - 2.2233939576692647709e-357j)  +/-  (2.49e-32, 1.64e-89j)
| (0.067636839764725447372 - 4.7737013187327644607e-357j)  +/-  (1.83e-32, 1.36e-89j)
| (0.00064345617488860534854 - 1.0524384419768063517e-358j)  +/-  (1.73e-34, 9.91e-92j)
