Starting with polynomial:
P : 64*t^6 - 480*t^4 + 720*t^2 - 120
Extension levels are: 6 32
-------------------------------------------------
Trying to find an order 32 Kronrod extension for:
P1 : 64*t^6 - 480*t^4 + 720*t^2 - 120
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 64*t^38 - 13648276674734528586881411936/700595787372387283311781*t^36 + 5546929808392009909442907600560/2101787362117161849935343*t^34 - 1918956527942276315832719311117880/9107745235841034683053153*t^32 + 14396247908198499158066916269702640/1301106462263004954721879*t^30 - 3680523732514124464743563741532732920/9107745235841034683053153*t^28 + 13772391545298501179996552794258949340/1301106462263004954721879*t^26 - 20235436226387824196733857697339335250/100085112481769611901683*t^24 + 567771204590218441979978666589798202125/200170224963539223803366*t^22 - 1063768561239950286824372681751460223625/36394586357007131600612*t^20 + 16003824658182293319730155073226952904875/72789172714014263201224*t^18 - 173590228476213661729322651214910204349625/145578345428028526402448*t^16 + 665803530047611859918874792800492954548125/145578345428028526402448*t^14 - 3512986489956079566904748639984388065716875/291156690856057052804896*t^12 + 82258807722551332686358643353739343575625/3908143501423584601408*t^10 - 26707786577634422137723146749711103584664375/1164626763424228211219584*t^8 + 133231971690197589573051168691884520603850625/9317014107393825689756672*t^6 - 82029198926422262900053390708781415481809375/18634028214787651379513344*t^4 + 18501201902498849290951060686243859083403125/37268056429575302759026688*t^2 - 615962444143380278091548235801288166884375/74536112859150605518053376
-------------------------------------------------
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
Positive weights:   38 out of 38
Indefinite weights: 0 out of 38
Negative weights:   0 out of 38
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (3.5069544949071114725 + 4.1392394495743699609e-441j)  +/-  (2.1e-119, 2.1e-119j)
| (-4.7735632435563741199 - 2.527093292596743524e-448j)  +/-  (8.24e-119, 8.24e-119j)
| (5.7170249579508642034 + 1.4242540479763247121e-448j)  +/-  (4.63e-119, 4.63e-119j)
| (4.7735632435563741199 + 3.1737061768675930083e-458j)  +/-  (7.76e-119, 7.76e-119j)
| (6.2408401128468206223 + 7.3855258923470820923e-467j)  +/-  (1.81e-119, 1.81e-119j)
| (-4.3360331141978372008 - 2.1656189718398587611e-469j)  +/-  (6.26e-119, 6.26e-119j)
| (-6.2408401128468206223 - 3.0132683064813130293e-472j)  +/-  (1.95e-119, 1.95e-119j)
| (-7.52695927508237471 - 4.5584674891526881565e-475j)  +/-  (4.81e-121, 4.81e-121j)
| (6.8249938899586044398 - 2.5406326386735101962e-471j)  +/-  (4.32e-120, 4.32e-120j)
| (5.2316720867284919205 + 1.3385336361702336117e-475j)  +/-  (6.76e-119, 6.76e-119j)
| (-5.2316720867284919205 - 7.2003259324825433078e-481j)  +/-  (7.13e-119, 7.13e-119j)
| (-3.1107063281062101945 - 1.3294273900120405928e-481j)  +/-  (8.38e-120, 8.38e-120j)
| (-3.9147847266537727501 + 6.5883722701652872094e-481j)  +/-  (4.33e-119, 4.33e-119j)
| (-3.5069544949071114725 - 9.8211439696672499304e-483j)  +/-  (2.14e-119, 2.14e-119j)
| (1.9895261751431100462 + 3.1283450504593212368e-482j)  +/-  (1.91e-121, 1.91e-121j)
| (-5.7170249579508642034 + 2.4659009008245883271e-484j)  +/-  (4.55e-119, 4.55e-119j)
| (2.3506049736744922228 - 5.9657977071262234088e-484j)  +/-  (9.37e-121, 9.37e-121j)
| (-1.6483203896639094201 + 5.6785707290143062649e-490j)  +/-  (4.04e-122, 4.04e-122j)
| (-1.0433594960469527705 - 9.2264806762770141377e-492j)  +/-  (1.32e-123, 1.32e-123j)
| (7.52695927508237471 + 1.2599903996118718913e-487j)  +/-  (5.15e-121, 5.15e-121j)
| (4.3360331141978372008 - 8.925887467080917909e-487j)  +/-  (6.21e-119, 6.21e-119j)
| (1.6483203896639094201 + 4.4451751051990438518e-501j)  +/-  (4.56e-122, 4.56e-122j)
| (3.9147847266537727501 - 5.4800300867661842994e-499j)  +/-  (4.28e-119, 4.28e-119j)
| (-1.3358490740136969497 - 2.8543701607587641018e-504j)  +/-  (8.71e-123, 8.71e-123j)
| (-2.3506049736744922228 + 1.2201972531137369131e-502j)  +/-  (8.46e-121, 8.46e-121j)
| (-6.8249938899586044398 - 1.1489637614571121269e-502j)  +/-  (4.64e-120, 4.64e-120j)
| (0.43607741192761650868 + 1.8191916254322448357e-507j)  +/-  (9.84e-126, 9.84e-126j)
| (1.3358490740136969497 + 2.1905140771612830936e-503j)  +/-  (8.6e-123, 8.6e-123j)
| (-2.7251484207085156695 + 1.7769446138832798827e-501j)  +/-  (2.77e-120, 2.77e-120j)
| (-0.74325830654263004983 - 4.2839011142856854153e-506j)  +/-  (1.54e-124, 1.54e-124j)
| (-0.1412668099122580726 - 8.2475429504916452766e-508j)  +/-  (5.44e-127, 5.44e-127j)
| (0.1412668099122580726 + 9.7120946923239161922e-508j)  +/-  (5.44e-127, 5.44e-127j)
| (0.74325830654263004983 + 3.5618682566421494494e-506j)  +/-  (1.41e-124, 1.41e-124j)
| (3.1107063281062101945 - 4.0988510013279033024e-501j)  +/-  (8.43e-120, 8.43e-120j)
| (-1.9895261751431100462 - 5.0536203816521617672e-505j)  +/-  (2.08e-121, 2.08e-121j)
| (-0.43607741192761650868 + 4.010394684845014569e-510j)  +/-  (1.12e-125, 1.12e-125j)
| (1.0433594960469527705 + 9.5098347674647733005e-507j)  +/-  (1.35e-123, 1.35e-123j)
| (2.7251484207085156695 + 1.4915334635338914269e-507j)  +/-  (2.86e-120, 2.86e-120j)
-------------------------------------------------
The weights are:
| (1.0331776457551530369e-06 - 1.8841327312030650044e-446j)  +/-  (5.4e-21, 2.78e-80j)
| (3.2022577069000089962e-11 - 1.1001591908370727237e-450j)  +/-  (1.08e-26, 5.57e-86j)
| (1.8097216435326343858e-15 - 1.7806763415482216986e-452j)  +/-  (3.01e-29, 1.55e-88j)
| (3.2022577069000089962e-11 - 7.1923451819269806248e-450j)  +/-  (1.03e-26, 5.31e-86j)
| (3.7665399865441514966e-18 + 5.0241819338729792813e-454j)  +/-  (6.96e-31, 3.59e-90j)
| (1.6536449674403437507e-09 + 1.1237635756637023845e-449j)  +/-  (3.6e-27, 1.86e-86j)
| (3.7665399865441514966e-18 + 1.4090919234558897408e-454j)  +/-  (2.43e-33, 1.25e-92j)
| (1.133108469602283446e-25 + 1.2210330438786129459e-458j)  +/-  (1.22e-36, 6.32e-96j)
| (2.0861605047080517191e-21 - 7.4181560434088862707e-456j)  +/-  (3.97e-34, 2.05e-93j)
| (3.4437587839510597774e-13 + 4.131325725728108171e-451j)  +/-  (1.56e-29, 8.04e-89j)
| (3.4437587839510597774e-13 + 8.1538786104339569431e-452j)  +/-  (5.91e-31, 3.05e-90j)
| (1.3834874876971774484e-05 - 3.4578961578079889419e-447j)  +/-  (3.48e-26, 1.8e-85j)
| (5.161680057184899238e-08 - 9.1198916544176998311e-449j)  +/-  (2.91e-28, 1.5e-87j)
| (1.0331776457551530369e-06 + 6.0972700058612883239e-448j)  +/-  (2.08e-27, 1.08e-86j)
| (0.0037995055989104453709 - 1.0671622934132761788e-444j)  +/-  (1.01e-24, 5.2e-84j)
| (1.8097216435326343858e-15 - 4.2665101033572525016e-453j)  +/-  (1.93e-33, 9.93e-93j)
| (0.00082833762445007336581 + 3.7866008103762470281e-445j)  +/-  (1.91e-26, 9.86e-86j)
| (0.012225258707645929936 - 1.0217343626614539329e-444j)  +/-  (6.62e-24, 3.41e-83j)
| (0.05565138275192627269 - 5.8657318373223145014e-444j)  +/-  (2.85e-21, 1.47e-80j)
| (1.133108469602283446e-25 + 3.3514321741188526219e-458j)  +/-  (8.23e-40, 4.24e-99j)
| (1.6536449674403437507e-09 + 1.0630672958442530665e-448j)  +/-  (4.56e-32, 2.35e-91j)
| (0.012225258707645929936 + 2.8339744101956136105e-444j)  +/-  (2.22e-26, 1.14e-85j)
| (5.161680057184899238e-08 - 1.6596478582790362065e-447j)  +/-  (2.3e-31, 1.18e-90j)
| (0.028232908732397179983 + 2.8345028267147887997e-444j)  +/-  (2.23e-25, 1.15e-84j)
| (0.00082833762445007336581 - 7.4751849578724948508e-446j)  +/-  (6.98e-29, 3.6e-88j)
| (2.0861605047080517191e-21 - 2.3822935394459431057e-456j)  +/-  (2.56e-39, 1.32e-98j)
| (0.14175281271776707463 + 1.92525899112227613e-443j)  +/-  (6.34e-26, 3.27e-85j)
| (0.028232908732397179983 - 6.322558204868103039e-444j)  +/-  (7.82e-27, 4.03e-86j)
| (0.00012770839154437274141 + 1.7056479082626445812e-446j)  +/-  (1.27e-29, 6.57e-89j)
| (0.099566360501894253295 + 9.8555510425217624633e-444j)  +/-  (1.8e-26, 9.29e-86j)
| (0.15780080361812736533 + 2.0214203195206102082e-443j)  +/-  (1.1e-26, 5.66e-86j)
| (0.15780080361812736533 - 2.191109028884507734e-443j)  +/-  (1.18e-26, 6.06e-86j)
| (0.099566360501894253295 - 1.5156582464472974254e-443j)  +/-  (9.74e-28, 4.99e-87j)
| (1.3834874876971774484e-05 + 5.7749627054518614302e-446j)  +/-  (1.74e-32, 8.9e-92j)
| (0.0037995055989104453709 + 2.9461438792047595419e-445j)  +/-  (5.12e-30, 2.75e-89j)
| (0.14175281271776707463 - 1.4994131054495763006e-443j)  +/-  (6.1e-28, 3.3e-87j)
| (0.05565138275192627269 + 1.0834135334763296159e-443j)  +/-  (3.55e-29, 1.98e-88j)
| (0.00012770839154437274141 - 1.3596432191043332568e-445j)  +/-  (5.93e-32, 2.95e-91j)
