Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 33
-------------------------------------------------
Trying to find an order 33 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^37 - 9134304935260641295446/14621279200179974225*t^35 + 73663421852791440917593839/424017096805219252525*t^33 - 12070827216270748819949668272/424017096805219252525*t^31 + 260123066842126161408383207988/84803419361043850505*t^29 - 671607228356725724751671903304/2924255840035994845*t^27 + 7202505671893855049258845957644/584851168007198969*t^25 - 280960070147509082431349484027792/584851168007198969*t^23 + 8020315682162644742727639006699486/584851168007198969*t^21 - 167225984335980066691345813612930980/584851168007198969*t^19 + 2523634650034666582245735892843264410/584851168007198969*t^17 - 27105009079613817325768306811354175120/584851168007198969*t^15 + 201825202397053493754592492321599694020/584851168007198969*t^13 - 1001883022312106603977297836718776264360/584851168007198969*t^11 + 3126390144699966311954540112714254799900/584851168007198969*t^9 - 5588572146330625437403210995690602914800/584851168007198969*t^7 + 4858918359874475236023799959776897389425/584851168007198969*t^5 - 1423459534853812900560622316969909300550/584851168007198969*t^3 + 1753871587251565821518467554878587275/584851168007198969*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: 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:
| (-6.8661093267213166766 - 2.6965187093091837436e-354j)  +/-  (1.12e-118, 1.12e-118j)
| (9.7596551584701694959 - 5.7440461313244605698e-369j)  +/-  (7.11e-120, 7.11e-120j)
| (-7.513039545508909414 - 3.1698662973059083461e-368j)  +/-  (9.21e-119, 9.21e-119j)
| (6.2474016878308504767 + 1.0490831459872008963e-379j)  +/-  (8.52e-119, 8.52e-119j)
| (10.748739400200513146 - 1.6057743473685888425e-382j)  +/-  (7.97e-121, 7.97e-121j)
| (4.5053195701668340841 - 4.5372732959106977622e-381j)  +/-  (1.03e-119, 1.03e-119j)
| (-5.6505366116111088271 + 8.5706284717851499016e-379j)  +/-  (5.53e-119, 5.53e-119j)
| (-3.4055037163133810311 + 2.3680921588632985881e-392j)  +/-  (7.01e-121, 7.01e-121j)
| (-9.7596551584701694959 - 9.9409705775708058228e-395j)  +/-  (6.79e-120, 6.79e-120j)
| (7.513039545508909414 + 1.4355637217607433042e-410j)  +/-  (9.16e-119, 9.16e-119j)
| (-10.748739400200513146 - 5.1447358844611092491e-416j)  +/-  (7.45e-121, 7.45e-121j)
| (3.9508922481250141714 + 5.9066622794874149332e-427j)  +/-  (3.23e-120, 3.23e-120j)
| (5.0709770653452262295 - 1.3545787715915264268e-424j)  +/-  (2.67e-119, 2.67e-119j)
| (-2.8672634260021402262 - 1.1232143453382148016e-431j)  +/-  (1.37e-121, 1.37e-121j)
| (-8.9363640954970245108 + 2.3890419576650273145e-434j)  +/-  (2.56e-119, 2.56e-119j)
| (1.2765791540346675058 - 2.6907524098378976464e-452j)  +/-  (2.15e-124, 2.15e-124j)
| (5.6505366116111088271 - 2.1902577352882543072e-446j)  +/-  (5.16e-119, 5.16e-119j)
| (8.1978041013062817335 - 1.0778724202236416528e-446j)  +/-  (6.03e-119, 6.03e-119j)
| (-1.8050799145110928448 + 5.8496613764726412443e-450j)  +/-  (2.33e-123, 2.33e-123j)
| (-3.9508922481250141714 - 7.8089704510231304476e-447j)  +/-  (3.27e-120, 3.27e-120j)
| (3.1972535582942629163e-467 + 1.1845389912863282471e-467j)  +/-  (1.26e-465, 1.26e-465j)
| (1.8050799145110928448 - 3.0774622474329628586e-450j)  +/-  (2.52e-123, 2.52e-123j)
| (3.4055037163133810311 + 7.3657661191166631626e-449j)  +/-  (7.14e-121, 7.14e-121j)
| (-4.5053195701668340841 + 3.7555087369128176525e-446j)  +/-  (1.08e-119, 1.08e-119j)
| (-1.2765791540346675058 + 5.997638062907277187e-452j)  +/-  (2.28e-124, 2.28e-124j)
| (0.035175810154686648468 + 8.2659650995745133196e-454j)  +/-  (1.78e-127, 1.78e-127j)
| (0.74196378430272585765 - 8.9717486706168302755e-453j)  +/-  (1.46e-125, 1.46e-125j)
| (-5.0709770653452262295 - 4.6862911888494873384e-445j)  +/-  (2.61e-119, 2.61e-119j)
| (-8.1978041013062817335 - 1.2377449065171556331e-447j)  +/-  (6.04e-119, 6.04e-119j)
| (-2.3344142183389772393 - 1.7450943235407768494e-462j)  +/-  (2.08e-122, 2.08e-122j)
| (6.8661093267213166766 - 2.6111889810234127107e-459j)  +/-  (1.06e-118, 1.06e-118j)
| (2.8672634260021402262 - 3.218342658432919281e-461j)  +/-  (1.41e-121, 1.41e-121j)
| (2.3344142183389772393 - 5.8067803280735424807e-462j)  +/-  (2.33e-122, 2.33e-122j)
| (-0.035175810154686648468 + 4.8401940506472109755e-466j)  +/-  (1.78e-127, 1.78e-127j)
| (-6.2474016878308504767 + 5.9502141049492556117e-458j)  +/-  (9.66e-119, 9.66e-119j)
| (-0.74196378430272585765 + 2.0707341400895775383e-478j)  +/-  (1.46e-125, 1.46e-125j)
| (8.9363640954970245108 - 1.2702079092866067163e-470j)  +/-  (2.85e-119, 2.85e-119j)
-------------------------------------------------
The weights are:
| (1.4596407251000200682e-11 - 1.4184286063526661319e-364j)  +/-  (1.47e-31, 1.19e-90j)
| (7.3114595547349715258e-22 - 1.0871017979112059387e-371j)  +/-  (1.22e-37, 9.96e-97j)
| (1.4653771844874971615e-13 - 5.4787660235678196496e-366j)  +/-  (2.78e-33, 2.26e-92j)
| (8.1053139231479561098e-10 + 2.4953794672215364767e-365j)  +/-  (1.51e-31, 1.23e-90j)
| (3.7106822712034893572e-26 + 6.4373048283665629203e-374j)  +/-  (2.75e-39, 2.23e-98j)
| (8.7334912124985701376e-06 - 4.2963881770626894117e-363j)  +/-  (2.45e-27, 1.99e-86j)
| (2.7338098441128023192e-08 - 1.7521357757295872492e-363j)  +/-  (1.2e-30, 9.79e-90j)
| (0.00065488678516407056701 - 1.6466159182301098868e-361j)  +/-  (6.61e-25, 5.38e-84j)
| (7.3114595547349715258e-22 + 6.2462803475195370146e-371j)  +/-  (3.62e-39, 2.95e-98j)
| (1.4653771844874971615e-13 + 2.4649437416687686297e-367j)  +/-  (1.18e-35, 9.57e-95j)
| (3.7106822712034893572e-26 - 2.9204984408713082835e-373j)  +/-  (5.02e-41, 4.08e-100j)
| (8.940564208373111493e-05 + 1.6637745095098740593e-362j)  +/-  (1.75e-28, 1.43e-87j)
| (5.9496542922619425684e-07 + 9.3884321524891284743e-364j)  +/-  (5.34e-31, 4.34e-90j)
| (0.0035015365197902350635 + 3.9415984381397314415e-361j)  +/-  (9.55e-27, 7.77e-86j)
| (1.4073293626892279648e-18 - 4.2868480961834442676e-369j)  +/-  (1.56e-38, 1.27e-97j)
| (0.093533445410553869952 - 2.2794945361411424742e-360j)  +/-  (1.4e-20, 1.14e-79j)
| (2.7338098441128023192e-08 - 1.7016127584328716464e-364j)  +/-  (1.53e-32, 1.25e-91j)
| (7.2095479769799078118e-16 - 1.4845673254394695423e-368j)  +/-  (1.1e-37, 8.92e-97j)
| (0.041331714832852290521 + 1.7179323790853511018e-360j)  +/-  (2.16e-25, 1.76e-84j)
| (8.940564208373111493e-05 + 6.1734858860744596714e-362j)  +/-  (3.06e-31, 2.49e-90j)
| (-13.375843454305893441 + 2.0516712485181242839e-357j)  +/-  (9.5e-24, 7.73e-83j)
| (0.041331714832852290521 + 1.0026890264827759552e-360j)  +/-  (1.5e-26, 1.22e-85j)
| (0.00065488678516407056701 - 5.5476080153527676173e-362j)  +/-  (1.87e-30, 1.52e-89j)
| (8.7334912124985701376e-06 - 2.0694800345204638794e-362j)  +/-  (7.82e-33, 6.36e-92j)
| (0.093533445410553869952 - 3.3207109234479902227e-360j)  +/-  (2.77e-26, 2.25e-85j)
| (6.8700196382363714361 - 1.0249418639051218359e-357j)  +/-  (3.17e-24, 2.58e-83j)
| (0.1648995652024257205 + 5.5880275425172569283e-360j)  +/-  (1.35e-25, 1.1e-84j)
| (5.9496542922619425684e-07 + 6.2430233193184529958e-363j)  +/-  (5.2e-34, 4.24e-93j)
| (7.2095479769799078118e-16 + 1.679318271371033327e-367j)  +/-  (2.96e-39, 2.43e-98j)
| (0.013882177903690141146 - 8.5569500321184659041e-361j)  +/-  (3.01e-30, 2.47e-89j)
| (1.4596407251000200682e-11 - 2.8662145742305739345e-366j)  +/-  (1.27e-37, 1.03e-96j)
| (0.0035015365197902350635 + 1.6193610536723677665e-361j)  +/-  (2.13e-32, 1.66e-91j)
| (0.013882177903690141146 - 4.2147045668985601428e-361j)  +/-  (8.52e-32, 6.54e-91j)
| (6.8700196382363714361 - 1.0354977155575730872e-357j)  +/-  (3.82e-28, 2.73e-87j)
| (8.1053139231479561098e-10 + 5.2889578327462922352e-364j)  +/-  (5.37e-37, 4.08e-96j)
| (0.1648995652024257205 + 6.9420495962114782746e-360j)  +/-  (5.17e-31, 3.2e-90j)
| (1.4073293626892279648e-18 + 5.616125701982036426e-370j)  +/-  (5.42e-42, 5.14e-101j)
