Starting with polynomial:
P : t^6 - 15*t^4 + 45*t^2 - 15
Extension levels are: 6 38
-------------------------------------------------
Trying to find an order 38 Kronrod extension for:
P1 : t^6 - 15*t^4 + 45*t^2 - 15
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^44 - 8169671914544901765548784855756271/6237269475162519549492670996882*t^42 + 47424251396867212726290577804061033571/68609964226787715044419380965702*t^40 - 112919110130118498011861054921283033822309/548879713814301720355355047725616*t^38 + 21719724782242313079815979517210438689793227/548879713814301720355355047725616*t^36 - 2899101136241919599566065986725829073661126065/548879713814301720355355047725616*t^34 + 1497026984888819981502970609165505867307125745/2935185635370597435055374586768*t^32 - 26817773327604436570445694419172064303915812615/733796408842649358763843646692*t^30 + 1448023092304841997526823050146410854081242170985/733796408842649358763843646692*t^28 - 59404678947089084184562248874557264221400922944555/733796408842649358763843646692*t^26 + 1856888449049577745126270705067093149373484829706625/733796408842649358763843646692*t^24 - 88288990938356695854548792106339979372329214487990625/1467592817685298717527687293384*t^22 + 1586417664455318552426825593593651870741174231733785375/1467592817685298717527687293384*t^20 - 21313604803439128081776466656955682464438296257363125125/1467592817685298717527687293384*t^18 + 210707853844910341423611722495707760957769378454732740375/1467592817685298717527687293384*t^16 - 749474841562407784531744906046338205925851033873299546875/733796408842649358763843646692*t^14 + 3720665384520214581219915081511578539655734624931530960625/733796408842649358763843646692*t^12 - 12354238245653042049691566864397781765023219063457308640625/733796408842649358763843646692*t^10 + 25832844190032984712176786706137598740806263301939527516875/733796408842649358763843646692*t^8 - 124346529587485208295090812328417378694838066300050546524375/2935185635370597435055374586768*t^6 + 74322223122432879869658948736530461266170614855574167465625/2935185635370597435055374586768*t^4 - 16576034493817407424360705889253055399644218443533254596875/2935185635370597435055374586768*t^2 + 583926872127114303989168714956303789022526093085681115625/2935185635370597435055374586768
-------------------------------------------------
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
Positive weights:   44 out of 44
Indefinite weights: 0 out of 44
Negative weights:   0 out of 44
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-5.3857549304838168525 + 1.6385479753319840738e-551j)  +/-  (9.61e-246, 9.61e-246j)
| (-8.9605400294114729572 + 1.8722735597640027469e-572j)  +/-  (1.94e-245, 1.94e-245j)
| (-9.6802559848773503863 + 2.1115982327179199153e-599j)  +/-  (7.39e-246, 7.39e-246j)
| (7.6659306795642063599 + 4.1014137659207292592e-612j)  +/-  (4.97e-245, 4.97e-245j)
| (10.483692108180210272 - 7.9165069413431679387e-616j)  +/-  (1.65e-246, 1.65e-246j)
| (-11.450245045966977438 + 2.2462579031959968174e-632j)  +/-  (1.65e-247, 1.65e-247j)
| (-7.0661586633368116716 - 6.4937640408684546047e-664j)  +/-  (4.4e-245, 4.4e-245j)
| (-22.853967592168568165 + 9.1760258085211856928e-692j)  +/-  (3.51e-251, 3.51e-251j)
| (9.6802559848773503863 + 9.8562041704578315555e-686j)  +/-  (7.38e-246, 7.38e-246j)
| (5.9297496007396439002 + 8.7796132992821771683e-686j)  +/-  (2.03e-245, 2.03e-245j)
| (22.853967592168568165 + 1.9307914145960739369e-694j)  +/-  (3.47e-251, 3.47e-251j)
| (-10.483692108180210272 - 1.9267064752749124105e-687j)  +/-  (1.72e-246, 1.72e-246j)
| (-7.6659306795642063599 - 1.8083722482992519574e-713j)  +/-  (4.53e-245, 4.53e-245j)
| (-2.3541363499954723136 - 5.9353263681983814376e-735j)  +/-  (2.48e-249, 2.48e-249j)
| (-5.9297496007396439002 + 5.1874813993786309635e-735j)  +/-  (2.18e-245, 2.18e-245j)
| (11.450245045966977438 - 6.9555460060785223526e-752j)  +/-  (1.78e-247, 1.78e-247j)
| (2.8336096496521669988 + 6.737445575202071846e-753j)  +/-  (1.45e-248, 1.45e-248j)
| (-4.3345969869126155177 - 1.6120015372812148191e-749j)  +/-  (1.2e-246, 1.2e-246j)
| (-1.4443294268802365917 - 5.5578267512771447569e-766j)  +/-  (4.72e-251, 4.72e-251j)
| (8.9605400294114729572 + 2.5960266532801420826e-758j)  +/-  (2e-245, 2e-245j)
| (3.3242574335521189524 - 8.0782827171467647114e-764j)  +/-  (8.02e-248, 8.02e-248j)
| (1.8891758777537106755 - 4.4137293694783788871e-770j)  +/-  (3.72e-250, 3.72e-250j)
| (-8.294285914258408684 + 2.9009747057414174051e-764j)  +/-  (3.42e-245, 3.42e-245j)
| (8.294285914258408684 - 1.4617710820084232481e-778j)  +/-  (3.5e-245, 3.5e-245j)
| (-0.61670659019259415219 + 5.4163448366791993429e-786j)  +/-  (4.69e-253, 4.69e-253j)
| (-3.3242574335521189524 + 1.1130603098379294212e-778j)  +/-  (7.34e-248, 7.34e-248j)
| (2.3541363499954723136 + 7.4817542546855720705e-787j)  +/-  (2.5e-249, 2.5e-249j)
| (1.0233100330197504113 + 2.7430891566482252467e-789j)  +/-  (5.09e-252, 5.09e-252j)
| (-2.8336096496521669988 - 3.9264933122822384525e-784j)  +/-  (1.43e-248, 1.43e-248j)
| (-1.8891758777537106755 + 1.8875488522000179283e-787j)  +/-  (3.72e-250, 3.72e-250j)
| (-6.4888536175677585353 - 3.1774881860869700528e-781j)  +/-  (3.21e-245, 3.21e-245j)
| (-0.20715065405201812683 - 4.9154572800667384401e-825j)  +/-  (2.72e-254, 2.72e-254j)
| (5.3857549304838168525 - 1.5537862942812932108e-790j)  +/-  (1.1e-245, 1.1e-245j)
| (7.0661586633368116716 + 1.2195430435696085627e-790j)  +/-  (5.05e-245, 5.05e-245j)
| (0.20715065405201812683 - 7.0828445078337706394e-799j)  +/-  (2.87e-254, 2.87e-254j)
| (4.8545901289404849665 + 3.5664502264461496574e-792j)  +/-  (3.8e-246, 3.8e-246j)
| (1.4443294268802365917 + 2.787763084565747082e-797j)  +/-  (4.59e-251, 4.59e-251j)
| (3.8246633877597012236 + 1.4977146758892725094e-792j)  +/-  (3.3e-247, 3.3e-247j)
| (4.3345969869126155177 - 1.9530847456105100378e-792j)  +/-  (1.24e-246, 1.24e-246j)
| (-3.8246633877597012236 + 4.6854830863038083366e-792j)  +/-  (3.16e-247, 3.16e-247j)
| (-1.0233100330197504113 + 7.0835624530987170051e-798j)  +/-  (5.3e-252, 5.3e-252j)
| (-4.8545901289404849665 + 1.2238406421492328716e-789j)  +/-  (3.9e-246, 3.9e-246j)
| (6.4888536175677585353 - 3.0325050737347465525e-800j)  +/-  (3.15e-245, 3.15e-245j)
| (0.61670659019259415219 - 4.8363998859202778269e-807j)  +/-  (4.69e-253, 4.69e-253j)
-------------------------------------------------
The weights are:
| (1.0775588397881488946e-07 + 5.3839887416226538189e-558j)  +/-  (5.46e-74, 2.29e-196j)
| (1.0103772246071118575e-18 - 5.8072303028041339025e-565j)  +/-  (9.05e-84, 3.79e-206j)
| (1.3497887012864753281e-21 + 1.537973366278611449e-566j)  +/-  (2.55e-85, 1.07e-207j)
| (4.2391130263838078933e-14 - 4.3419771119541145896e-563j)  +/-  (1.6e-83, 6.72e-206j)
| (4.6879214535171736347e-25 - 6.7436595276448573766e-569j)  +/-  (2.66e-89, 1.11e-211j)
| (1.5071478680321217012e-29 + 8.6139455394073611184e-571j)  +/-  (1.24e-89, 5.18e-212j)
| (3.3711381981731450705e-12 + 3.503593160062064691e-561j)  +/-  (2.58e-81, 1.08e-203j)
| (1.567920062562580651e-60 - 3.1011760499901111398e-586j)  +/-  (5.66e-104, 2.37e-226j)
| (1.3497887012864753281e-21 + 4.3839263626036845739e-567j)  +/-  (1.32e-88, 5.52e-211j)
| (5.0913444571483701315e-09 + 2.8207394698732418541e-560j)  +/-  (1.46e-81, 6.12e-204j)
| (1.567920062562580651e-60 - 1.9182909003123843961e-586j)  +/-  (1.79e-105, 7.51e-228j)
| (4.6879214535171736347e-25 - 2.0992441450426123165e-568j)  +/-  (2.67e-88, 1.12e-210j)
| (4.2391130263838078933e-14 - 2.4853400100454905533e-562j)  +/-  (1.1e-83, 4.62e-206j)
| (0.011812144475183004326 + 9.2061340651264152545e-556j)  +/-  (4.42e-71, 1.85e-193j)
| (5.0913444571483701315e-09 + 5.8673534867062674632e-559j)  +/-  (7.63e-81, 3.2e-203j)
| (1.5071478680321217012e-29 + 3.1028265414656274613e-571j)  +/-  (1.76e-93, 7.39e-216j)
| (0.0034953021507671888167 + 1.3185765358691452423e-556j)  +/-  (2.6e-76, 1.09e-198j)
| (1.708626303188660191e-05 + 3.2118300592825469526e-557j)  +/-  (4.54e-79, 1.9e-201j)
| (0.060850612688005098532 + 3.4016268545994077543e-555j)  +/-  (1.3e-68, 5.43e-191j)
| (1.0103772246071118575e-18 - 1.447035656978913635e-565j)  +/-  (2.23e-89, 9.35e-212j)
| (0.00078786951523292518183 - 4.375438241771554232e-557j)  +/-  (4.71e-79, 1.97e-201j)
| (0.03053840292928089264 + 8.9405190467740216896e-556j)  +/-  (9.46e-74, 3.96e-196j)
| (2.9651154304875376294e-16 + 1.4081553967511424299e-563j)  +/-  (2.52e-86, 1.06e-208j)
| (2.9651154304875376294e-16 + 2.9938972024299361588e-564j)  +/-  (1.47e-88, 6.14e-211j)
| (0.13390631893207550461 + 6.814284697309402759e-555j)  +/-  (4.95e-72, 2.07e-194j)
| (0.00078786951523292518183 + 1.8486620158709107807e-556j)  +/-  (8.78e-79, 3.68e-201j)
| (0.011812144475183004326 - 3.605927535015149958e-556j)  +/-  (1.97e-77, 8.25e-200j)
| (0.097077929248705033423 + 3.6212675564289577428e-555j)  +/-  (2e-73, 8.36e-196j)
| (0.0034953021507671888167 - 4.2465690948399295156e-556j)  +/-  (1.53e-77, 6.4e-200j)
| (0.03053840292928089264 - 1.8601512070555544794e-555j)  +/-  (3.97e-75, 1.66e-197j)
| (1.6290160065070843076e-10 - 4.3592144189762209898e-560j)  +/-  (6.49e-84, 2.72e-206j)
| (0.16137838328547055011 - 7.2600816891766926755e-555j)  +/-  (1.11e-73, 4.67e-196j)
| (1.0775588397881488946e-07 - 1.6391683970266928899e-559j)  +/-  (6.28e-86, 2.63e-208j)
| (3.3711381981731450705e-12 + 4.7281495974146599828e-562j)  +/-  (2e-88, 8.39e-211j)
| (0.16137838328547055011 + 6.7222822760979731293e-555j)  +/-  (3.42e-76, 1.43e-198j)
| (1.5989652410563840592e-06 + 8.1092490879059217532e-559j)  +/-  (1.66e-85, 6.93e-208j)
| (0.060850612688005098532 - 1.962971192882194584e-555j)  +/-  (1.39e-79, 5.81e-202j)
| (0.00013423853346299591147 + 1.3068073000934532593e-557j)  +/-  (2.69e-84, 1.12e-206j)
| (1.708626303188660191e-05 - 3.4732700100840598621e-558j)  +/-  (3.88e-85, 1.61e-207j)
| (0.00013423853346299591147 - 7.710144835063144449e-557j)  +/-  (4.19e-85, 1.68e-207j)
| (0.097077929248705033423 - 5.3201678336092227574e-555j)  +/-  (3.54e-82, 1.25e-204j)
| (1.5989652410563840592e-06 - 1.5633850095431067364e-557j)  +/-  (1.86e-86, 7.46e-209j)
| (1.6290160065070843076e-10 - 4.0495176601666376953e-561j)  +/-  (4.08e-89, 2.03e-211j)
| (0.13390631893207550461 - 5.4140543865266058578e-555j)  +/-  (4.56e-82, 1.18e-204j)
