Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 6 23
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 23 Kronrod extension for:
P2 : 3/2*t^8 - 161/52*t^6 + 105/52*t^4 - 245/572*t^2 + 25/1716
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^31 - 8173315889517809953573279867891468303/705229703423670368169904435795320868*t^29 + 364011172940591415287076692503292293687/8991678718651797194166281556390341067*t^27 - 1500327531475534437313599362645026506950/17752801572722779075661632816462981081*t^25 + 391936535850957127758349899072329154421175/3337526695671882466224386969495040443228*t^23 - 11165170166163258384547217490342938850890/97525130717684877259803515342387545419*t^21 + 449612600799726971093794637284620208114415/5591440827813932962895401546296885937356*t^19 - 1157924149289402094914428053094208515104415/28153395045308750181596144627845723930196*t^17 + 4662229358245220118750589977354324298300/304656605651232313285862830323524759511*t^15 - 12588417408976628048806925767038464914425/3075580971336250019838234287075583286492*t^13 + 636209965648939680248132386264355650955/828041030744375005341063077289580115594*t^11 - 8942766824321485383821463352932451378945/91912554412625625592858001579143392830934*t^9 + 68290665724167403358613134601257313415/8753576610726250056462666817061275507708*t^7 - 1560791818662669086901785798409483175/4376788305363125028231333408530637753854*t^5 + 1812357952997487761588512376630972648725/236582915058098360276016496064715093146824116*t^3 - 3880906273048084901684029661853138625/78860971686032786758672165354905031048941372*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:
| (-0.99659184789930772401 + 6.5741880418615541627e-446j)  +/-  (5.61e-118, 5.61e-118j)
| (-0.98219129046748981137 - 6.8067468921241051438e-444j)  +/-  (1.64e-117, 1.64e-117j)
| (-0.88848227691311736826 + 2.3281084873433014722e-443j)  +/-  (2.23e-117, 2.23e-117j)
| (0.98219129046748981137 + 2.1109803426438126487e-441j)  +/-  (1.71e-117, 1.71e-117j)
| (0.85110112875893547946 + 8.1073279744384833243e-449j)  +/-  (1.01e-117, 1.01e-117j)
| (0.79851078578936840599 + 2.436107599337524849e-453j)  +/-  (2.59e-118, 2.59e-118j)
| (0.99659184789930772401 - 7.879931021598743869e-451j)  +/-  (5.84e-118, 5.84e-118j)
| (-0.9235173672435537034 + 6.2091441077583461302e-461j)  +/-  (2.93e-117, 2.93e-117j)
| (-0.95704103125552124278 + 4.7859373613902848523e-461j)  +/-  (2.72e-117, 2.72e-117j)
| (0.9235173672435537034 + 1.2426963277847257013e-459j)  +/-  (2.9e-117, 2.9e-117j)
| (0.88848227691311736826 - 9.1706426709862324246e-473j)  +/-  (2.06e-117, 2.06e-117j)
| (0.95704103125552124278 - 1.4164643775943236877e-489j)  +/-  (2.73e-117, 2.73e-117j)
| (-0.85110112875893547946 + 1.3202477151204249151e-499j)  +/-  (1.01e-117, 1.01e-117j)
| (-0.79851078578936840599 - 9.0510662878824617207e-502j)  +/-  (2.51e-118, 2.51e-118j)
| (7.2210220402997012363e-510 - 1.0304540758614055654e-509j)  +/-  (3.9e-508, 3.9e-508j)
| (0.73315618267263425483 + 2.7438325843365417541e-503j)  +/-  (4.22e-119, 4.22e-119j)
| (0.49030793160413410634 + 5.1003968190951658723e-507j)  +/-  (7.55e-122, 7.55e-122j)
| (-0.10278397627077407171 + 1.9497885828091250079e-513j)  +/-  (1.04e-126, 1.04e-126j)
| (-0.73315618267263425483 - 6.9204891021544770893e-505j)  +/-  (4.73e-119, 4.73e-119j)
| (-0.39866002823183718606 - 1.6583901657817357573e-509j)  +/-  (5.32e-123, 5.32e-123j)
| (0.39866002823183718606 - 7.6231459766874487011e-509j)  +/-  (5.94e-123, 5.94e-123j)
| (0.65876972049695109442 + 6.8337184408699467039e-506j)  +/-  (6.51e-120, 6.51e-120j)
| (0.10278397627077407171 - 1.3369598267712087048e-515j)  +/-  (9.88e-127, 9.88e-127j)
| (-0.49030793160413410634 - 3.2227914641191927971e-508j)  +/-  (7.87e-122, 7.87e-122j)
| (-0.57735026918962576451 - 2.6580041019085769358e-506j)  +/-  (7.83e-121, 7.83e-121j)
| (0.2041968861768067152 - 2.568796651946977803e-514j)  +/-  (2.32e-125, 2.32e-125j)
| (0.57735026918962576451 - 8.8519721028520064614e-509j)  +/-  (7.74e-121, 7.74e-121j)
| (0.30309200782089397844 - 2.9101103066576240244e-513j)  +/-  (3.64e-124, 3.64e-124j)
| (-0.30309200782089397844 - 6.3519932866830497146e-512j)  +/-  (3.42e-124, 3.42e-124j)
| (-0.65876972049695109442 - 1.3531996604500528139e-510j)  +/-  (6.59e-120, 6.59e-120j)
| (-0.2041968861768067152 - 2.1136809283552266001e-517j)  +/-  (2.32e-125, 2.32e-125j)
-------------------------------------------------
The weights are:
| (0.0087304963366449257261 + 2.8735059840107863477e-444j)  +/-  (4.05e-24, 3.69e-80j)
| (0.019969428699184200705 - 2.6085764523309805532e-443j)  +/-  (2.79e-24, 2.54e-80j)
| (0.033715009140322122152 + 2.5521705344079198874e-442j)  +/-  (4.51e-25, 4.1e-81j)
| (0.019969428699184200705 - 1.6365655070288200574e-441j)  +/-  (2.55e-25, 2.32e-81j)
| (0.044332940522736482526 - 3.6687548777868116306e-441j)  +/-  (1.34e-25, 1.22e-81j)
| (0.059845091373062869939 + 2.1647816559799996544e-441j)  +/-  (9.95e-26, 9.05e-82j)
| (0.0087304963366449257261 - 7.2999822051076652913e-442j)  +/-  (3.58e-26, 3.25e-82j)
| (0.035853973850455632121 - 1.3163139599900738314e-442j)  +/-  (1.09e-25, 9.95e-82j)
| (0.029995528673349264726 + 6.6541558185916791585e-443j)  +/-  (1.6e-25, 1.45e-81j)
| (0.035853973850455632121 - 4.2414165040620889512e-441j)  +/-  (7.43e-27, 6.75e-83j)
| (0.033715009140322122152 + 4.6506454605820527697e-441j)  +/-  (7.06e-27, 6.42e-83j)
| (0.029995528673349264726 + 4.274685199239271998e-441j)  +/-  (5.14e-27, 4.67e-83j)
| (0.044332940522736482526 - 2.9741382908292056557e-442j)  +/-  (1.05e-28, 9.58e-85j)
| (0.059845091373062869939 + 2.3822297330496025639e-442j)  +/-  (1.6e-29, 1.45e-85j)
| (0.10302060801496324268 - 3.4889981708767117819e-442j)  +/-  (4.77e-32, 4.34e-88j)
| (0.070283800364489465942 - 1.3795086635687850497e-441j)  +/-  (3.4e-30, 3.1e-86j)
| (0.089482616899046668844 + 6.7352883217036113938e-442j)  +/-  (7.05e-32, 6.41e-88j)
| (0.10231485895942029446 + 3.1696436416249511275e-442j)  +/-  (1.26e-32, 1.15e-88j)
| (0.070283800364489465942 - 2.0862477419488289157e-442j)  +/-  (7.21e-32, 6.56e-88j)
| (0.093703310675853696163 - 2.4813168500732068253e-442j)  +/-  (1.54e-33, 1.4e-89j)
| (0.093703310675853696163 - 5.810073797231576662e-442j)  +/-  (6.27e-33, 5.7e-89j)
| (0.078172442918420411708 + 1.0044133403582840161e-441j)  +/-  (4.44e-32, 4.04e-88j)
| (0.10231485895942029446 + 3.901725515062553236e-442j)  +/-  (1.86e-33, 1.7e-89j)
| (0.089482616899046668844 + 2.2829970246735266324e-442j)  +/-  (3.45e-34, 3.14e-90j)
| (0.084432772040461359137 - 2.1213221808740203973e-442j)  +/-  (2.94e-34, 2.68e-90j)
| (0.10031755971141102857 - 4.4240608946601392953e-442j)  +/-  (2.12e-34, 1.93e-90j)
| (0.084432772040461359137 - 8.0094056461242076406e-442j)  +/-  (5.34e-34, 4.85e-90j)
| (0.097339865827659955935 + 5.0581932342263232195e-442j)  +/-  (1.56e-34, 1.42e-90j)
| (0.097339865827659955935 + 2.6922982052670018334e-442j)  +/-  (1.11e-35, 1.02e-91j)
| (0.078172442918420411708 + 2.0359322830427984031e-442j)  +/-  (9.86e-36, 9.58e-92j)
| (0.10031755971141102857 - 2.9147127889398572177e-442j)  +/-  (1.07e-35, 9.55e-92j)
