Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 33
-------------------------------------------------
Trying to find an order 33 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^37 - 73074439482085130363568/14621279200179974225*t^35 + 294653687411165763670375356/424017096805219252525*t^33 - 24141654432541497639899336544/424017096805219252525*t^31 + 260123066842126161408383207988/84803419361043850505*t^29 - 335803614178362862375835951652/2924255840035994845*t^27 + 1800626417973463762314711489411/584851168007198969*t^25 - 35120008768438635303918685503474/584851168007198969*t^23 + 4010157841081322371363819503349743/4678809344057591752*t^21 - 41806496083995016672836453403232745/4678809344057591752*t^19 + 1261817325017333291122867946421632205/18715237376230367008*t^17 - 1694063067475863582860519175709635945/4678809344057591752*t^15 + 50456300599263373438648123080399923505/37430474752460734016*t^13 - 125235377789013325497162229589847033045/37430474752460734016*t^11 + 781597536174991577988635028178563699975/149721899009842936064*t^9 - 349285759145664089837700687230662682175/74860949504921468032*t^7 + 4858918359874475236023799959776897389425/2395550384157486977024*t^5 - 711729767426906450280311158484954650275/2395550384157486977024*t^3 + 1753871587251565821518467554878587275/9582201536629947908096*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
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (-7.6005065190888063307 - 3.3147146438736747133e-932j)  +/-  (1.17e-248, 1.17e-248j)
| (-2.4080547711611803358 - 2.1997419570765760688e-932j)  +/-  (1.22e-248, 1.22e-248j)
| (-6.318963651077934196 + 6.1599217801588022229e-941j)  +/-  (4.59e-247, 4.59e-247j)
| (6.9011183445965259456 + 4.6385079645848421818e-954j)  +/-  (1.13e-247, 1.13e-247j)
| (-4.8550724652928432164 + 2.7473607045879159788e-962j)  +/-  (1.74e-246, 1.74e-246j)
| (-6.9011183445965259456 + 1.9032338349449372819e-974j)  +/-  (1.09e-247, 1.09e-247j)
| (7.6005065190888063307 + 1.7645898426342546615e-980j)  +/-  (1.1e-248, 1.1e-248j)
| (5.7967228708725628323 - 1.8509674008952488643e-977j)  +/-  (1.1e-246, 1.1e-246j)
| (-4.4175800982614768718 - 1.2495080436077590026e-987j)  +/-  (1.41e-246, 1.41e-246j)
| (6.318963651077934196 + 5.4478301769605245814e-997j)  +/-  (4.36e-247, 4.36e-247j)
| (1.2763842481344272397 + 5.8752943916523755829e-1003j)  +/-  (4.34e-251, 4.34e-251j)
| (3.5857222701470677907 + 2.7957453296137267133e-998j)  +/-  (4e-247, 4e-247j)
| (-1.2763842481344272397 - 2.9217117221778260245e-1003j)  +/-  (4.03e-251, 4.03e-251j)
| (5.3125212099520468705 + 8.6022118842024166228e-997j)  +/-  (1.6e-246, 1.6e-246j)
| (2.0274614119742859684 + 6.176997421758404123e-1006j)  +/-  (2.21e-249, 2.21e-249j)
| (2.7937027003865612244 - 3.126806628589126735e-1003j)  +/-  (5.36e-248, 5.36e-248j)
| (3.1857420194774298947 - 1.2959328193176894475e-1007j)  +/-  (1.62e-247, 1.62e-247j)
| (-5.7967228708725628323 + 2.3429181072011624622e-1019j)  +/-  (1.13e-246, 1.13e-246j)
| (-2.0274614119742859684 - 2.0939221737784485445e-1036j)  +/-  (2.34e-249, 2.34e-249j)
| (-5.3125212099520468705 - 5.4045602351950440736e-1037j)  +/-  (1.67e-246, 1.67e-246j)
| (4.8550724652928432164 + 1.0256078447646625463e-1041j)  +/-  (1.8e-246, 1.8e-246j)
| (2.4080547711611803358 + 1.8244560517650597933e-1044j)  +/-  (1.23e-248, 1.23e-248j)
| (-0.024873053894109548365 + 2.0479567811416556168e-1051j)  +/-  (2.4e-255, 2.4e-255j)
| (4.4175800982614768718 + 3.1353825709814701117e-1042j)  +/-  (1.36e-246, 1.36e-246j)
| (-3.995532755413072003 - 7.7801477992625962014e-1044j)  +/-  (9.15e-247, 9.15e-247j)
| (7.4693764843701046569e-1068 - 1.2034131558389144938e-1068j)  +/-  (2.8e-1066, 2.8e-1066j)
| (0.90267777653929958328 - 1.9202213086349395236e-1052j)  +/-  (3.64e-252, 3.64e-252j)
| (-3.5857222701470677907 - 3.2934512166631249992e-1046j)  +/-  (4.3e-247, 4.3e-247j)
| (-3.1857420194774298947 + 2.2086838091479578107e-1052j)  +/-  (1.71e-247, 1.71e-247j)
| (-0.52464762327529031788 - 1.263007154466995455e-1061j)  +/-  (2.01e-253, 2.01e-253j)
| (-1.6506801238857845559 + 4.5006902003677558183e-1057j)  +/-  (3.91e-250, 3.91e-250j)
| (1.6506801238857845559 + 1.1685225565463000486e-1057j)  +/-  (3.73e-250, 3.73e-250j)
| (0.52464762327529031788 + 6.6743704884830224654e-1061j)  +/-  (2.08e-253, 2.08e-253j)
| (0.024873053894109548365 - 2.28981166735551565e-1062j)  +/-  (2.4e-255, 2.4e-255j)
| (-2.7937027003865612244 - 4.9606994893963366132e-1059j)  +/-  (5.51e-248, 5.51e-248j)
| (-0.90267777653929958328 - 2.1466455051304304726e-1063j)  +/-  (3.91e-252, 3.91e-252j)
| (3.995532755413072003 - 5.5252334012890120861e-1060j)  +/-  (8.8e-247, 8.8e-247j)
-------------------------------------------------
The weights are:
| (3.7106822712034893572e-26 - 5.5208261631494837298e-948j)  +/-  (3.92e-92, 7.33e-216j)
| (0.00065488678516407056701 - 4.0963793699531104568e-935j)  +/-  (2.69e-75, 5.03e-199j)
| (1.4073293626892279648e-18 - 5.736906070396838859e-944j)  +/-  (1.25e-89, 2.34e-213j)
| (7.3114595547349715258e-22 - 4.9083359456900783264e-946j)  +/-  (3.26e-93, 6.1e-217j)
| (1.4596407251000200682e-11 + 4.0663602244109217603e-940j)  +/-  (1.2e-86, 2.25e-210j)
| (7.3114595547349715258e-22 + 1.0169575456873126723e-945j)  +/-  (6.04e-91, 1.13e-214j)
| (3.7106822712034893572e-26 + 2.8642102075450741309e-948j)  +/-  (4.49e-95, 8.39e-219j)
| (7.2095479769799078118e-16 - 6.8907174377421330825e-943j)  +/-  (9.16e-92, 1.71e-215j)
| (8.1053139231479561098e-10 - 4.1167609259655783105e-939j)  +/-  (2.08e-87, 3.89e-211j)
| (1.4073293626892279648e-18 + 2.5709258082058209619e-944j)  +/-  (1.07e-92, 2.01e-216j)
| (0.041331714832852290521 + 5.9657781867092916603e-935j)  +/-  (5.97e-76, 1.12e-199j)
| (5.9496542922619425684e-07 + 4.726986626287882271e-938j)  +/-  (1e-87, 1.87e-211j)
| (0.041331714832852290521 + 1.942309663859413098e-934j)  +/-  (4.2e-77, 7.86e-201j)
| (1.4653771844874971615e-13 + 1.1606039352149114226e-941j)  +/-  (2e-91, 3.73e-215j)
| (0.0035015365197902350635 + 8.9837245164671589765e-936j)  +/-  (1.21e-82, 2.26e-206j)
| (8.940564208373111493e-05 + 8.7467116174296866499e-937j)  +/-  (7.82e-86, 1.46e-209j)
| (8.7334912124985701376e-06 - 2.2080322682368349273e-937j)  +/-  (5.72e-87, 1.07e-210j)
| (7.2095479769799078118e-16 + 1.6684078438256223185e-942j)  +/-  (2.2e-94, 4.12e-218j)
| (0.0035015365197902350635 + 1.046982416178320598e-934j)  +/-  (9.12e-86, 1.71e-209j)
| (1.4653771844874971615e-13 - 3.085086729476526931e-941j)  +/-  (2.04e-93, 3.82e-217j)
| (1.4596407251000200682e-11 - 1.3699960217240000397e-940j)  +/-  (1.11e-92, 2.08e-216j)
| (0.00065488678516407056701 - 2.9911735307747976466e-936j)  +/-  (1.46e-87, 2.73e-211j)
| (6.8700196382363714361 - 7.5035294859505889136e-932j)  +/-  (7.29e-85, 1.36e-208j)
| (8.1053139231479561098e-10 + 1.2120096524616405252e-939j)  +/-  (5.18e-92, 9.69e-216j)
| (2.7338098441128023192e-08 + 3.3918335990106505489e-938j)  +/-  (5.82e-93, 1.09e-216j)
| (-13.375843454305893441 + 1.4789233789049872514e-931j)  +/-  (5.22e-85, 9.73e-209j)
| (0.093533445410553869952 - 1.4173458147150435858e-934j)  +/-  (1.13e-86, 2.12e-210j)
| (5.9496542922619425684e-07 - 2.4058152186946705329e-937j)  +/-  (9.71e-93, 1.82e-216j)
| (8.7334912124985701376e-06 + 1.5882070643178638245e-936j)  +/-  (1.97e-92, 3.69e-216j)
| (0.1648995652024257205 + 5.7066672425180202084e-934j)  +/-  (3.02e-88, 5.55e-212j)
| (0.013882177903690141146 - 1.2943819973273327014e-934j)  +/-  (7.98e-90, 1.5e-213j)
| (0.013882177903690141146 - 2.4153637377219425974e-935j)  +/-  (8.85e-90, 1.65e-213j)
| (0.1648995652024257205 + 3.6648716540452995442e-934j)  +/-  (1.77e-88, 3.23e-212j)
| (6.8700196382363714361 - 7.3501047181627791087e-932j)  +/-  (2.14e-86, 3.86e-210j)
| (8.940564208373111493e-05 - 1.1797878080133994904e-935j)  +/-  (3.51e-92, 6.53e-216j)
| (0.093533445410553869952 - 3.1171280927778052561e-934j)  +/-  (8.82e-90, 1.5e-213j)
| (2.7338098441128023192e-08 - 8.4085071721140312309e-939j)  +/-  (1.44e-94, 3.48e-218j)
