Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 5 30
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P2 : t^9 - 21*t^7 + 108*t^5 - 135*t^3 + 45*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^39 - 506766691707880816268970589208086207397592012/845539399497391266332019985565096931719317*t^37 + 1755757989450075364289455547230919527050791894448/10992012193466086462316259812346260112351121*t^35 - 275514300962713215483345403545048150877515546057495/10992012193466086462316259812346260112351121*t^33 + 28417359252958387656608830349226950037051580644050790/10992012193466086462316259812346260112351121*t^31 - 2037275074188544674307919427033235083623814133121324370/10992012193466086462316259812346260112351121*t^29 + 104721705070709042843087347493113143656247187722812667270/10992012193466086462316259812346260112351121*t^27 - 302028365436169940597745755269953936163161976198728137970/845539399497391266332019985565096931719317*t^25 + 8326835132398548899323195658665584094385340539792123337000/845539399497391266332019985565096931719317*t^23 - 169043411393546331982836741185826809144749949139297220430250/845539399497391266332019985565096931719317*t^21 + 2516527423084774727073920413863534445623056827723517850477750/845539399497391266332019985565096931719317*t^19 - 27216422392423113812260493510666624023157189047093187518929000/845539399497391266332019985565096931719317*t^17 + 210673544122034545724743341982319018673924094570752648299093250/845539399497391266332019985565096931719317*t^15 - 1142036524988218086672079252639529924989458628521806229579588750/845539399497391266332019985565096931719317*t^13 + 4201444082399457888788016582244248267502792759307953038174596250/845539399497391266332019985565096931719317*t^11 - 10017978217672225491523404012366021328945762146439096723990848750/845539399497391266332019985565096931719317*t^9 + 14462380397535414513503124333658476281847856340206058957955751875/845539399497391266332019985565096931719317*t^7 - 11456879193245709282568598518086964939526280789650273290028321250/845539399497391266332019985565096931719317*t^5 + 4348999188232741762257787387362198593801874617635071710795081250/845539399497391266332019985565096931719317*t^3 - 598452682048084449352711595522475942733186027630331044574053125/845539399497391266332019985565096931719317*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:
| (-5.4592413530391518948 - 4.8669204000289645152e-867j)  +/-  (1.21e-246, 1.21e-246j)
| (8.7797988420646721143 - 1.1079530238883567331e-865j)  +/-  (5.34e-247, 5.34e-247j)
| (10.606869924827848124 + 1.1789095598639417382e-870j)  +/-  (1.58e-248, 1.58e-248j)
| (9.6100649513506269092 + 1.739393249347825651e-869j)  +/-  (1.39e-247, 1.39e-247j)
| (6.0635237195454878224 + 5.9653222310911882304e-871j)  +/-  (1.79e-246, 1.79e-246j)
| (7.3430251723189448592 + 3.3123258525762674189e-882j)  +/-  (1.96e-246, 1.96e-246j)
| (-4.8716660335033249925 - 2.2046119525459681138e-896j)  +/-  (5.71e-247, 5.71e-247j)
| (-2.5466499872151109563 + 1.8959433241682140028e-899j)  +/-  (2.25e-248, 2.25e-248j)
| (-8.0345008725841273954 + 3.4457138720261855703e-896j)  +/-  (1.3e-246, 1.3e-246j)
| (-9.6100649513506269092 - 2.2967214141513381487e-898j)  +/-  (1.43e-247, 1.43e-247j)
| (-10.606869924827848124 - 2.9090856248577301481e-899j)  +/-  (1.48e-248, 1.48e-248j)
| (2.2408693739212025955 + 7.158918445660829853e-898j)  +/-  (1.53e-248, 1.53e-248j)
| (8.0345008725841273954 - 9.0456927669794147302e-899j)  +/-  (1.22e-246, 1.22e-246j)
| (-8.7797988420646721143 + 2.5564255343154970291e-910j)  +/-  (5.66e-247, 5.66e-247j)
| (-6.6892766625879486698 - 3.079503750446315208e-909j)  +/-  (2.21e-246, 2.21e-246j)
| (6.6892766625879486698 - 3.8861562760010001594e-917j)  +/-  (2.16e-246, 2.16e-246j)
| (2.3344142183389772393 - 8.1665952304679960844e-932j)  +/-  (3.12e-248, 3.12e-248j)
| (-3.1683441568033864243 + 5.4951001626609640023e-940j)  +/-  (2.73e-248, 2.73e-248j)
| (5.4592413530391518948 - 4.6045849883604594288e-944j)  +/-  (1.07e-246, 1.07e-246j)
| (3.7313022243357029508 + 9.3658831569248418103e-967j)  +/-  (8.12e-248, 8.12e-248j)
| (-3.7313022243357029508 + 4.5448658423104088933e-976j)  +/-  (8.55e-248, 8.55e-248j)
| (3.2952671934789503368e-984 + 2.4234177062571788196e-985j)  +/-  (1.29e-982, 1.29e-982j)
| (-7.3430251723189448592 - 5.9600793107090373672e-976j)  +/-  (2.08e-246, 2.08e-246j)
| (-2.3344142183389772393 + 2.0703372894195859694e-980j)  +/-  (3.05e-248, 3.05e-248j)
| (-1.0379709584894152952 - 1.4748758978023048456e-982j)  +/-  (7.05e-252, 7.05e-252j)
| (1.0379709584894152952 + 4.8219253944759671604e-982j)  +/-  (6.28e-252, 6.28e-252j)
| (-6.0635237195454878224 - 3.5381779776188966228e-977j)  +/-  (1.88e-246, 1.88e-246j)
| (4.8716660335033249925 + 3.8717130961378064771e-981j)  +/-  (5.59e-247, 5.59e-247j)
| (-2.2408693739212025955 - 7.2962112142689816846e-990j)  +/-  (1.61e-248, 1.61e-248j)
| (-0.56112531112948754086 + 4.8397611369418859489e-993j)  +/-  (7.07e-253, 7.07e-253j)
| (-4.2969502164958322547 - 7.4776977095169608779e-988j)  +/-  (2.32e-247, 2.32e-247j)
| (3.1683441568033864243 + 1.3961926348962718664e-987j)  +/-  (2.71e-248, 2.71e-248j)
| (0.74196378430272585765 + 4.2339327868653767922e-998j)  +/-  (2.48e-252, 2.48e-252j)
| (0.56112531112948754086 - 3.7061765597277811157e-998j)  +/-  (7.07e-253, 7.07e-253j)
| (4.2969502164958322547 - 4.7267949362196402019e-994j)  +/-  (2.27e-247, 2.27e-247j)
| (-0.74196378430272585765 + 3.0477837338385280823e-1000j)  +/-  (2.48e-252, 2.48e-252j)
| (-1.5971926462526149049 + 1.3731031706208926663e-998j)  +/-  (9.32e-251, 9.32e-251j)
| (1.5971926462526149049 - 1.6871698756829996898e-997j)  +/-  (8.29e-251, 8.29e-251j)
| (2.5466499872151109563 - 1.0123286829961345135e-998j)  +/-  (2.25e-248, 2.25e-248j)
-------------------------------------------------
The weights are:
| (8.0147642229863236369e-08 - 1.3865542639096669057e-873j)  +/-  (1.64e-83, 2.16e-206j)
| (5.6821220426538584002e-18 + 3.2895183875187923458e-881j)  +/-  (1.16e-91, 1.53e-214j)
| (1.7005097898217682497e-25 + 2.0631735279451829319e-885j)  +/-  (3.37e-95, 4.45e-218j)
| (3.1384867207094217919e-21 - 4.428124880282956118e-883j)  +/-  (2.3e-93, 3.04e-216j)
| (2.5436169243214942947e-09 + 3.8000177046612666252e-876j)  +/-  (7.31e-88, 9.65e-211j)
| (5.2335703237283023214e-13 + 2.1653490194644989684e-878j)  +/-  (3.71e-90, 4.9e-213j)
| (1.626155254523507092e-06 + 5.0387320220273524111e-873j)  +/-  (1.18e-86, 1.55e-209j)
| (0.015162546756262970036 + 8.7385351512634509788e-870j)  +/-  (2.09e-78, 2.76e-201j)
| (2.7391003267531170491e-15 + 5.2495614755432380503e-879j)  +/-  (3.92e-95, 5.18e-218j)
| (3.1384867207094217919e-21 + 1.6512604564930712669e-882j)  +/-  (1.78e-98, 2.35e-221j)
| (1.7005097898217682497e-25 - 6.5210418187625597904e-885j)  +/-  (1.81e-100, 2.39e-223j)
| (0.055448411244771658465 + 1.4852130627029229865e-869j)  +/-  (1.16e-81, 1.53e-204j)
| (2.7391003267531170491e-15 - 1.0292244808554797044e-879j)  +/-  (5.75e-95, 7.59e-218j)
| (5.6821220426538584002e-18 - 1.2786736117534820502e-880j)  +/-  (3.62e-97, 4.77e-220j)
| (4.891952067227788694e-11 + 3.2044072472873018737e-876j)  +/-  (4.63e-94, 6.11e-217j)
| (4.891952067227788694e-11 - 3.2749731817364246262e-877j)  +/-  (1.46e-93, 1.93e-216j)
| (-0.043913954511369437534 - 1.604711707841982083e-869j)  +/-  (4.12e-84, 5.44e-207j)
| (0.0014941463608262759853 - 3.93423661926723425e-871j)  +/-  (7.32e-88, 9.66e-211j)
| (8.0147642229863236369e-08 - 3.5877516947346729927e-875j)  +/-  (1.64e-92, 2.17e-215j)
| (0.00021277785009109738498 + 1.3980754160599411073e-872j)  +/-  (6.63e-90, 8.76e-213j)
| (0.00021277785009109738498 + 7.4185436872200277337e-872j)  +/-  (6.51e-90, 8.59e-213j)
| (0.21708940387361542441 - 2.6374973970303435433e-869j)  +/-  (3.27e-84, 4.32e-207j)
| (5.2335703237283023214e-13 - 1.4516523501884342518e-877j)  +/-  (3.11e-96, 4.11e-219j)
| (-0.043913954511369437534 - 3.9970665694112132075e-869j)  +/-  (2.96e-87, 3.91e-210j)
| (0.13661685852411881259 + 3.6801580728498180653e-869j)  +/-  (2.62e-84, 3.46e-207j)
| (0.13661685852411881259 + 2.5056851334813992721e-869j)  +/-  (6.17e-85, 8.15e-208j)
| (2.5436169243214942947e-09 - 7.2111649825229126388e-875j)  +/-  (2.85e-94, 3.77e-217j)
| (1.626155254523507092e-06 + 2.8759895043368119561e-874j)  +/-  (6.79e-94, 8.98e-217j)
| (0.055448411244771658465 + 3.5489883575852577442e-869j)  +/-  (1.1e-87, 1.45e-210j)
| (0.22090004471416629781 + 7.5200691392814504723e-869j)  +/-  (9.19e-87, 1.21e-209j)
| (2.2235034755781654552e-05 - 1.7195340120294627033e-872j)  +/-  (6.74e-92, 8.89e-215j)
| (0.0014941463608262759853 - 1.0466484660569756446e-871j)  +/-  (1.02e-91, 1.35e-214j)
| (-0.056648950697857063551 - 6.9759230537688455714e-869j)  +/-  (2.76e-87, 3.66e-210j)
| (0.22090004471416629781 + 6.1200713019491817184e-869j)  +/-  (3.03e-87, 4.01e-210j)
| (2.2235034755781654552e-05 - 2.0544965045876619232e-873j)  +/-  (1.68e-93, 2.23e-216j)
| (-0.056648950697857063551 - 9.1667610406447247305e-869j)  +/-  (3.25e-88, 4.35e-211j)
| (0.062159473891466594766 - 1.0517759075224395043e-869j)  +/-  (1.7e-89, 2.27e-212j)
| (0.062159473891466594766 - 5.761451561072978088e-870j)  +/-  (1.84e-90, 2.52e-213j)
| (0.015162546756262970036 + 3.1837563025449779625e-870j)  +/-  (7.87e-91, 1.01e-213j)
