Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 47
-------------------------------------------------
Trying to find an order 47 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^51 - 376815643136787275887745586686231787907/317748388298858572428944674243562367*t^49 + 2945948386932010065409124300907352973930306/4554393565616972871481540330824393927*t^47 - 981860515611299147220087180412900915939810210/4554393565616972871481540330824393927*t^45 + 6790190608767327850241624561592601349173503520/138011926230817359741864858509830119*t^43 - 8736190037024113916057498768165516791290005920/1069859893262150075518332236510311*t^41 + 1093238345649654795805707100486221524376939058070/1069859893262150075518332236510311*t^39 - 105546655908671538598602175816854375201605687084710/1069859893262150075518332236510311*t^37 + 7979213950661897191165809599013906222401489040541575/1069859893262150075518332236510311*t^35 - 476769836949434110547906499296541061656270694625979675/1069859893262150075518332236510311*t^33 + 22633660795207107498576626455724725930201094251646363700/1069859893262150075518332236510311*t^31 - 855321692283887378073680754753216023566313922610998299700/1069859893262150075518332236510311*t^29 + 886381583482698842221589387923358875089365718439594493400/36891720457315519845459732293459*t^27 - 21107785295616349636113285098542965842732914602412370307000/36891720457315519845459732293459*t^25 + 395766019964847752093829828183495715463550196625922929917500/36891720457315519845459732293459*t^23 - 5788708549360591137955923190528245204028747148457244427257500/36891720457315519845459732293459*t^21 + 65222347617998821284012137170898757092865908281506615135635625/36891720457315519845459732293459*t^19 - 556749307831863080848805347709430861476545790676800025452713125/36891720457315519845459732293459*t^17 + 3523192498605688239929187322334107500646952781076726975525931250/36891720457315519845459732293459*t^15 - 16064032548030960894944954400556341788983215384989880289241231250/36891720457315519845459732293459*t^13 + 50809200490630472438918972819431726344979998151816346190284925000/36891720457315519845459732293459*t^11 - 105842237191660654380379990671143572410601517075604153524857425000/36891720457315519845459732293459*t^9 + 134826844961550731338285840207413937299981473828080042029447993750/36891720457315519845459732293459*t^7 - 93719427149152737014272572861258721410257862329733366630834843750/36891720457315519845459732293459*t^5 + 29160749845685108583966455882163671562427420289832882376140140625/36891720457315519845459732293459*t^3 - 2595094446405392360052261328293793297238694020944356318651328125/36891720457315519845459732293459*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
Positive weights:   51 out of 51
Indefinite weights: 0 out of 51
Negative weights:   0 out of 51
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (8.6326263058808418555 + 5.8700931985898224187e-736j)  +/-  (4.51e-243, 4.51e-243j)
| (-6.5200759680120481449 + 6.2127491271392346887e-739j)  +/-  (1.74e-243, 1.74e-243j)
| (-7.5457907993080999204 - 1.0644690394193414251e-750j)  +/-  (4.38e-243, 4.38e-243j)
| (11.920720846616127927 - 1.7198585957924294923e-761j)  +/-  (2.9e-245, 2.9e-245j)
| (12.855796910143767684 + 1.8337174650708384452e-761j)  +/-  (1.89e-246, 1.89e-246j)
| (-12.855796910143767684 - 8.6943075891954495389e-757j)  +/-  (1.84e-246, 1.84e-246j)
| (-10.451644611507147367 + 1.8270624419630251443e-759j)  +/-  (6.83e-244, 6.83e-244j)
| (3.6684764100623034566 + 6.4331423073891899949e-768j)  +/-  (2.24e-246, 2.24e-246j)
| (10.451644611507147367 + 2.9828356434523216671e-765j)  +/-  (6.66e-244, 6.66e-244j)
| (2.3344142183389772393 + 8.9922543525688258659e-770j)  +/-  (1.05e-248, 1.05e-248j)
| (6.0244851839753978513 + 2.9160381134656686022e-765j)  +/-  (9.34e-244, 9.34e-244j)
| (4.1260913596368291663 + 3.8914253935264020231e-767j)  +/-  (1.21e-245, 1.21e-245j)
| (11.145107916717971161 + 3.3000492775924700811e-766j)  +/-  (1.82e-244, 1.82e-244j)
| (-4.5899370091218410373 + 3.0860472793450912722e-765j)  +/-  (4.11e-245, 4.11e-245j)
| (-2.7718864340925941041 + 1.2552918199777737367e-768j)  +/-  (7.86e-248, 7.86e-248j)
| (-11.920720846616127927 + 1.6995794970194915962e-763j)  +/-  (2.67e-245, 2.67e-245j)
| (-11.145107916717971161 + 1.2948690970644339833e-769j)  +/-  (1.74e-244, 1.74e-244j)
| (-7.0265644466298689223 + 2.3514573587948415455e-777j)  +/-  (3.02e-243, 3.02e-243j)
| (9.8108475668250068764 - 2.1539355206231809076e-787j)  +/-  (1.5e-243, 1.5e-243j)
| (7.5457907993080999204 - 7.2775425756167103987e-786j)  +/-  (4.02e-243, 4.02e-243j)
| (5.0604552397345159161 + 4.1853275067273048117e-790j)  +/-  (1.42e-244, 1.42e-244j)
| (1.1080238629502907681 + 2.9917522262987141242e-799j)  +/-  (1.86e-251, 1.86e-251j)
| (-6.0244851839753978513 - 3.8447615665651239791e-790j)  +/-  (9.12e-244, 9.12e-244j)
| (-3.6684764100623034566 - 9.6688021542662613331e-801j)  +/-  (2.2e-246, 2.2e-246j)
| (1.4959265154144686186 + 1.6082493314220269239e-806j)  +/-  (1.79e-250, 1.79e-250j)
| (8.0801126033536608444 + 2.2546643522486379428e-797j)  +/-  (4.73e-243, 4.73e-243j)
| (3.2169613839998603525 - 1.6037540355591837106e-807j)  +/-  (4.55e-247, 4.55e-247j)
| (-5.0604552397345159161 + 1.0812571614844272446e-811j)  +/-  (1.4e-244, 1.4e-244j)
| (-8.6326263058808418555 - 1.7811881749401850812e-834j)  +/-  (4.33e-243, 4.33e-243j)
| (-2.3344142183389772393 + 9.0543529496056644638e-856j)  +/-  (1.04e-248, 1.04e-248j)
| (7.0265644466298689223 - 4.3650081390852765755e-849j)  +/-  (2.94e-243, 2.94e-243j)
| (-5.5383326975124923442 + 3.6704181309750409742e-867j)  +/-  (3.83e-244, 3.83e-244j)
| (-9.8108475668250068764 - 7.8380713455728001116e-895j)  +/-  (1.59e-243, 1.59e-243j)
| (4.5899370091218410373 + 7.3811457604572538845e-906j)  +/-  (4.02e-245, 4.02e-245j)
| (5.5383326975124923442 + 1.9019510574628032053e-907j)  +/-  (3.96e-244, 3.96e-244j)
| (-1.4959265154144686186 - 1.0854387664623399659e-922j)  +/-  (1.68e-250, 1.68e-250j)
| (-3.2169613839998603525 - 1.5135389877743428706e-914j)  +/-  (4.53e-247, 4.53e-247j)
| (0.74196378430272585765 - 5.0301944029516027633e-922j)  +/-  (1.64e-252, 1.64e-252j)
| (6.5200759680120481449 - 4.9886653895623438085e-912j)  +/-  (1.77e-243, 1.77e-243j)
| (-4.1260913596368291663 + 1.1540014298441850042e-919j)  +/-  (1.06e-245, 1.06e-245j)
| (-1.9072665873636074671 - 1.5400326969320121347e-928j)  +/-  (1.42e-249, 1.42e-249j)
| (-9.207540606262562473 - 8.7946586688984394332e-939j)  +/-  (3.25e-243, 3.25e-243j)
| (1.9072665873636074671 + 4.5009149898477790644e-963j)  +/-  (1.52e-249, 1.52e-249j)
| (9.207540606262562473 + 1.8331319968990614559e-954j)  +/-  (3.2e-243, 3.2e-243j)
| (-1.1080238629502907681 - 5.0657049318816648581e-972j)  +/-  (2.02e-251, 2.02e-251j)
| (-0.37658079922027619434 - 1.1883727836699986453e-973j)  +/-  (1.28e-253, 1.28e-253j)
| (-8.0801126033536608444 - 6.9731800872967880229e-968j)  +/-  (5.17e-243, 5.17e-243j)
| (-8.2614642162832014556e-998 - 1.7371561312572637922e-997j)  +/-  (9.81e-996, 9.81e-996j)
| (0.37658079922027619434 - 2.5032645093378711237e-992j)  +/-  (1.28e-253, 1.28e-253j)
| (2.7718864340925941041 - 1.3583967492315225024e-987j)  +/-  (7.5e-248, 7.5e-248j)
| (-0.74196378430272585765 - 3.3163102489259156682e-992j)  +/-  (1.72e-252, 1.72e-252j)
-------------------------------------------------
The weights are:
| (1.4758360778158692953e-17 - 3.842826246543584649e-752j)  +/-  (1.97e-74, 1.74e-194j)
| (1.1730475600976656707e-10 + 2.5712070429649905924e-748j)  +/-  (9.36e-69, 8.27e-189j)
| (9.0788204304049869292e-14 - 1.5306439852342665489e-750j)  +/-  (6.19e-72, 5.47e-192j)
| (4.6224874069092227697e-32 - 1.0077454771594452021e-760j)  +/-  (2.36e-82, 2.08e-202j)
| (5.5690438658536513791e-37 + 2.4627708689892823157e-763j)  +/-  (4e-84, 3.53e-204j)
| (5.5690438658536513791e-37 - 2.3908989432615041692e-763j)  +/-  (1.47e-85, 1.3e-205j)
| (5.0406549914652865442e-25 + 5.2997302373274259926e-757j)  +/-  (6.1e-81, 5.39e-201j)
| (0.00021687471903402849967 - 6.3196616703856192606e-747j)  +/-  (8.73e-62, 7.71e-182j)
| (5.0406549914652865442e-25 - 7.0990631236107422336e-757j)  +/-  (1.09e-80, 9.59e-201j)
| (0.011324142113317128083 - 1.0781985220868095811e-745j)  +/-  (7.85e-55, 6.94e-175j)
| (2.5730780327457904226e-09 + 5.8201913264207820153e-749j)  +/-  (1e-71, 8.84e-192j)
| (3.6936632781150751362e-05 + 3.7206371333667356923e-747j)  +/-  (8.16e-65, 7.21e-185j)
| (3.0918330597268383597e-28 + 1.1758686613720238902e-758j)  +/-  (7.8e-82, 6.89e-202j)
| (4.9608187306766727643e-06 + 1.4321460703306678938e-746j)  +/-  (1.71e-69, 1.51e-189j)
| (0.0037799354816876385794 + 4.8907585854221730882e-745j)  +/-  (1.01e-61, 8.92e-182j)
| (4.6224874069092227697e-32 + 9.247676992898289796e-761j)  +/-  (1.96e-86, 1.73e-206j)
| (3.0918330597268383597e-28 - 9.9551139277423964863e-759j)  +/-  (5.55e-85, 4.91e-205j)
| (3.885881721843316001e-12 + 2.2977119362720984023e-749j)  +/-  (9.05e-77, 7.99e-197j)
| (3.1074787396106424831e-22 + 2.9327454794989277751e-755j)  +/-  (3.38e-82, 2.98e-202j)
| (9.0788204304049869292e-14 - 7.107240901437534909e-751j)  +/-  (6.93e-79, 6.12e-199j)
| (5.1999105739924506002e-07 + 6.2940176528271322481e-748j)  +/-  (2.53e-73, 2.23e-193j)
| (0.080947564761231225677 + 2.5313656954818224877e-744j)  +/-  (2.73e-56, 2.41e-176j)
| (2.5730780327457904226e-09 - 7.9069005356840599484e-748j)  +/-  (1.6e-76, 1.41e-196j)
| (0.00021687471903402849967 + 9.4681593451709836347e-746j)  +/-  (3.25e-71, 2.87e-191j)
| (0.052227135045083344473 - 1.1031336782697449582e-744j)  +/-  (3.97e-61, 3.5e-181j)
| (1.4401677491096192118e-15 + 1.6541946360162812184e-751j)  +/-  (5.87e-80, 5.19e-200j)
| (0.0010124118828583632721 + 5.0828993447641572051e-747j)  +/-  (6.78e-69, 5.99e-189j)
| (5.1999105739924506002e-07 - 5.172730799134688053e-747j)  +/-  (4.44e-75, 3.92e-195j)
| (1.4758360778158692953e-17 - 7.4808515255151409418e-753j)  +/-  (1.93e-83, 1.71e-203j)
| (0.011324142113317128083 - 1.0173623874933191062e-744j)  +/-  (3.97e-69, 3.51e-189j)
| (3.885881721843316001e-12 + 3.3352902226839653438e-750j)  +/-  (1.29e-79, 1.14e-199j)
| (4.1998145335218049325e-08 + 1.8675298766601544325e-747j)  +/-  (1.59e-76, 1.41e-196j)
| (3.1074787396106424831e-22 - 1.7584478510080674273e-755j)  +/-  (9.91e-86, 8.75e-206j)
| (4.9608187306766727643e-06 - 1.6732111184618599297e-747j)  +/-  (2.46e-75, 2.17e-195j)
| (4.1998145335218049325e-08 - 2.0443868614944851722e-748j)  +/-  (2.33e-77, 2.06e-197j)
| (0.052227135045083344473 - 3.6676898894678103017e-744j)  +/-  (2.11e-70, 1.86e-190j)
| (0.0010124118828583632721 - 2.219135641378293002e-745j)  +/-  (3.25e-74, 2.87e-194j)
| (0.10952560042968894515 - 4.5134328738977217418e-744j)  +/-  (4.03e-70, 3.56e-190j)
| (1.1730475600976656707e-10 - 1.4682007022908046575e-749j)  +/-  (1.88e-79, 1.66e-199j)
| (3.6936632781150751362e-05 - 3.7930047567422695062e-746j)  +/-  (5.47e-76, 4.83e-196j)
| (0.027208957752314274887 + 2.0004622368699856161e-744j)  +/-  (6.48e-73, 5.72e-193j)
| (9.1356668809122989735e-20 + 4.1297939949947512817e-754j)  +/-  (9.26e-86, 8.18e-206j)
| (0.027208957752314274887 + 3.8870994295728460108e-745j)  +/-  (2.45e-74, 2.16e-194j)
| (9.1356668809122989735e-20 - 1.1069343576979184176e-753j)  +/-  (1.83e-85, 1.62e-205j)
| (0.080947564761231225677 + 5.9433826138338739666e-744j)  +/-  (1.05e-73, 9.31e-194j)
| (0.13804231709533451991 + 8.4299761087458786793e-744j)  +/-  (5.16e-74, 4.59e-194j)
| (1.4401677491096192118e-15 + 1.1241338073714846538e-751j)  +/-  (1.09e-83, 9.66e-204j)
| (0.15134519716875011177 - 7.7376517738692863236e-744j)  +/-  (3.27e-74, 2.94e-194j)
| (0.13804231709533451991 + 6.3797034689345624986e-744j)  +/-  (3.15e-74, 2.83e-194j)
| (0.0037799354816876385794 + 1.6721919608086768955e-746j)  +/-  (1.68e-76, 1.45e-196j)
| (0.10952560042968894515 - 7.8789315109026748501e-744j)  +/-  (1.2e-74, 1.04e-194j)
