Starting with polynomial:
P : 512*t^9 - 9216*t^7 + 48384*t^5 - 80640*t^3 + 30240*t
Extension levels are: 9 46
-------------------------------------------------
Trying to find an order 46 Kronrod extension for:
P1 : 512*t^9 - 9216*t^7 + 48384*t^5 - 80640*t^3 + 30240*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 512*t^55 - 140293532295767141014176054278771611745843240147200/424222306338984413743764211130890177598635909*t^53 + 209237422360563337756954662856384164411352941434183808/2121111531694922068718821055654450887993179545*t^51 - 1493964980926637834721580582195518080783651576335488447424/82723349736101960680034021170523584631734002255*t^49 + 3575879747070907822408092080704234583528559399862144628322752/1571743644985937252920646402239948108002946042845*t^47 - 329397917118237244744535435004102609822964297885750074358644064/1571743644985937252920646402239948108002946042845*t^45 + 1534509867924273493137632961090898282907836597980811903326738000/104782909665729150194709760149329873866863069523*t^43 - 2031534453768609438348146517797099277970744792609294824240428136/2555680723554369516944140491447070094313733403*t^41 + 6693430311630791120981478486688407789733150485896632590296313738/196590824888797655149549268572851545716441031*t^39 - 12030853034564456381535729173056919108493857198170199319698588979/10346885520463034481555224661729028721917949*t^37 + 659441636556025226755935615625313666381847770135903727834786641511/20693771040926068963110449323458057443835898*t^35 - 29107649598758034685756517797538230078531021613251452837880072382175/41387542081852137926220898646916114887671796*t^33 + 258904741995070069598993212990104160190640672490216956531768319108005/20693771040926068963110449323458057443835898*t^31 - 7415491353310673916932250375307742074782593298939955249372152187552065/41387542081852137926220898646916114887671796*t^29 + 170404593010334499653331628393399861304676250751871238088710279860502185/82775084163704275852441797293832229775343592*t^27 - 3124555226274321772678795449650505609288083425980602838244934073638057865/165550168327408551704883594587664459550687184*t^25 + 181461108307881126235189760849055514855632429569960814997524040745695186875/1324401346619268413639068756701315676405497472*t^23 - 2065107696196375368397229868808347021013926686681436381447136670688389682375/2648802693238536827278137513402631352810994944*t^21 + 18183543082252591704870030244486982951372684505010968593658831177039564775875/5297605386477073654556275026805262705621989888*t^19 - 121851965967107644363757590669590336845829576487440911003781649629747181072875/10595210772954147309112550053610525411243979776*t^17 + 304296515283395207602127438060143278799973164847478644731387580472678891321375/10595210772954147309112550053610525411243979776*t^15 - 1102827737169257912158081229578971211399088223882982541933352132146000331871875/21190421545908294618225100107221050822487959552*t^13 + 2800745701728447084960542423893442487673189854787038555318310186815169981981875/42380843091816589236450200214442101644975919104*t^11 - 4756159846198702694006459868430830144183580116748068703376432124000268568851875/84761686183633178472900400428884203289951838208*t^9 + 10116011610869745103850621991344275184756764863832288584166625597568306853430625/339046744734532713891601601715536813159807352832*t^7 - 6103426311970099575963446885908647339031125602766122565194216918218156309963125/678093489469065427783203203431073626319614705664*t^5 + 1758588766897228875833203668080943799103125286648268616785672533262182602640625/1356186978938130855566406406862147252639229411328*t^3 - 160333823114756615977209943896885593936798847647557626187042036534221960665625/2712373957876261711132812813724294505278458822656*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:   55 out of 55
Indefinite weights: 0 out of 55
Negative weights:   0 out of 55
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (7.6100908078064176016 + 1.0296561807744590736e-880j)  +/-  (1.37e-243, 1.37e-243j)
| (8.6404997747479196126 + 9.7680780571091142727e-885j)  +/-  (4.94e-245, 4.94e-245j)
| (-8.6404997747479196126 - 2.7148275490457769551e-887j)  +/-  (5.24e-245, 5.24e-245j)
| (-9.2967680079378977885 - 1.19427233345145324e-888j)  +/-  (3.3e-246, 3.3e-246j)
| (8.096381079117947178 - 9.1511313868039453013e-886j)  +/-  (3.18e-244, 3.18e-244j)
| (-7.6100908078064176016 - 2.2372268808764110096e-885j)  +/-  (1.34e-243, 1.34e-243j)
| (-5.5749230359879728831 - 6.4563577377184294986e-884j)  +/-  (1.16e-242, 1.16e-242j)
| (-6.335548593788833321 + 2.4453689631059736524e-894j)  +/-  (1.02e-242, 1.02e-242j)
| (-8.096381079117947178 + 4.1368928495934864916e-905j)  +/-  (3.44e-244, 3.44e-244j)
| (6.335548593788833321 - 1.2202200265783376524e-912j)  +/-  (9.62e-243, 9.62e-243j)
| (1.2082378575804816493 - 1.1792570720025340948e-936j)  +/-  (1.32e-249, 1.32e-249j)
| (1.4685532892166679317 - 8.0057930467230243397e-936j)  +/-  (1.09e-248, 1.09e-248j)
| (6.7381964148703138996 - 2.4158053866454488649e-929j)  +/-  (6.87e-243, 6.87e-243j)
| (-1.7196813698538797583 + 4.7895271072697294473e-945j)  +/-  (5.88e-248, 5.88e-248j)
| (-7.1609154703235764075 - 2.8789850582922453701e-939j)  +/-  (3.29e-243, 3.29e-243j)
| (3.8398354228241029498 + 9.9235222157689083451e-941j)  +/-  (8e-244, 8e-244j)
| (-6.7381964148703138996 + 5.1291099619832043495e-940j)  +/-  (6.95e-243, 6.95e-243j)
| (-3.8398354228241029498 + 4.7242557053545924097e-943j)  +/-  (7.25e-244, 7.25e-244j)
| (9.2967680079378977885 + 9.7103625222819186959e-945j)  +/-  (3.28e-246, 3.28e-246j)
| (7.1609154703235764075 - 1.1095930075724191253e-941j)  +/-  (3.49e-243, 3.49e-243j)
| (3.5126475473428749741 + 1.9718668750927137223e-948j)  +/-  (2.67e-244, 2.67e-244j)
| (1.7196813698538797583 - 2.153313194930120507e-951j)  +/-  (5.95e-248, 5.95e-248j)
| (-4.5118670684325743927 - 1.4076380905833297836e-945j)  +/-  (3.7e-243, 3.7e-243j)
| (-3.5126475473428749741 - 1.0537057210566673547e-948j)  +/-  (2.67e-244, 2.67e-244j)
| (-4.8579114546854733697 + 1.2164723487888322408e-946j)  +/-  (6.55e-243, 6.55e-243j)
| (4.8579114546854733697 + 8.3685190364698691197e-948j)  +/-  (6.87e-243, 6.87e-243j)
| (2.8751182404649704127 - 1.2129897988818280674e-959j)  +/-  (2e-245, 2e-245j)
| (3.1909932017815276072 + 1.2092334184247307462e-957j)  +/-  (7.91e-245, 7.91e-245j)
| (-0.94471159736458183871 - 2.7376489747144553158e-963j)  +/-  (1.54e-250, 1.54e-250j)
| (-1.4685532892166679317 + 8.2560445685418893668e-962j)  +/-  (1.06e-248, 1.06e-248j)
| (5.9487718661880118684 + 1.8241910788217951949e-954j)  +/-  (1.26e-242, 1.26e-242j)
| (-2.8751182404649704127 - 6.7985614755802691077e-967j)  +/-  (2.16e-245, 2.16e-245j)
| (-5.2118458795080798089 + 2.9443475380902408243e-964j)  +/-  (9.99e-243, 9.99e-243j)
| (-5.9487718661880118684 - 4.4760647509957079159e-964j)  +/-  (1.24e-242, 1.24e-242j)
| (-0.72355101875283757332 + 1.3440306546313120662e-972j)  +/-  (2.22e-251, 2.22e-251j)
| (-3.1909932017815276072 - 6.5585093773630362128e-966j)  +/-  (8.15e-245, 8.15e-245j)
| (-4.1727484442038494998 + 8.3134666221482014925e-965j)  +/-  (1.78e-243, 1.78e-243j)
| (0.94471159736458183871 + 4.6681214801912394971e-972j)  +/-  (1.6e-250, 1.6e-250j)
| (4.5118670684325743927 - 4.7844500850786199898e-963j)  +/-  (3.87e-243, 3.87e-243j)
| (-2.566075231989804616 - 8.1699112384534267618e-971j)  +/-  (5.69e-246, 5.69e-246j)
| (-2.2665805845318431118 + 8.4406041477625325162e-973j)  +/-  (1.38e-246, 1.38e-246j)
| (4.1727484442038494998 + 2.1375398079517189927e-967j)  +/-  (1.87e-243, 1.87e-243j)
| (2.566075231989804616 + 2.3346457597835742572e-980j)  +/-  (5.38e-246, 5.38e-246j)
| (1.9823892518994977089 - 9.0823077661723516206e-982j)  +/-  (2.93e-247, 2.93e-247j)
| (5.2118458795080798089 + 2.3229809616299009797e-979j)  +/-  (9.7e-243, 9.7e-243j)
| (-0.53576195638226729978 - 2.1463581830152268777e-1008j)  +/-  (3.2e-252, 3.2e-252j)
| (-1.2082378575804816493 + 7.6274126305555900976e-1009j)  +/-  (1.38e-249, 1.38e-249j)
| (5.5749230359879728831 + 1.2314852157273785729e-1006j)  +/-  (1.28e-242, 1.28e-242j)
| (0.53576195638226729978 - 9.0871087008918686363e-1017j)  +/-  (3.22e-252, 3.22e-252j)
| (2.2665805845318431118 - 1.6799997468771247728e-1013j)  +/-  (1.3e-246, 1.3e-246j)
| (-1.9823892518994977089 - 7.7516541017560998884e-1015j)  +/-  (2.82e-247, 2.82e-247j)
| (-0.28176056646754086541 + 9.0506355770086077503e-1022j)  +/-  (1.36e-253, 1.36e-253j)
| (-4.0081141331742400777e-1040 + 2.5830082788441848117e-1040j)  +/-  (2.62e-1038, 2.62e-1038j)
| (0.72355101875283757332 - 6.0932936312248839366e-1018j)  +/-  (2.22e-251, 2.22e-251j)
| (0.28176056646754086541 - 1.0757272727258940607e-1021j)  +/-  (1.21e-253, 1.21e-253j)
-------------------------------------------------
The weights are:
| (1.8525307158668666439e-26 - 6.1233147007753516133e-907j)  +/-  (2.36e-65, 1.73e-188j)
| (1.2452834535175864342e-33 + 2.4221323404875723853e-909j)  +/-  (2.2e-68, 1.62e-191j)
| (1.2452834535175864342e-33 - 9.9255012674007298376e-909j)  +/-  (6.76e-70, 4.96e-193j)
| (1.244089591693862392e-38 + 1.9185557342326102299e-911j)  +/-  (8.86e-72, 6.51e-195j)
| (9.7878553590825634225e-30 - 3.2682685481693100966e-907j)  +/-  (4.63e-68, 3.4e-191j)
| (1.8525307158668666439e-26 - 9.6859924832313818083e-905j)  +/-  (9.49e-68, 6.97e-191j)
| (6.602118117311265317e-15 - 2.696374834778531098e-897j)  +/-  (2.37e-62, 1.74e-185j)
| (8.2195945982581373983e-19 + 3.6717404992883807722e-900j)  +/-  (8.33e-65, 6.12e-188j)
| (9.7878553590825634225e-30 + 1.3948589824100580489e-906j)  +/-  (3.75e-69, 2.75e-192j)
| (8.2195945982581373983e-19 - 2.1314090831705872681e-901j)  +/-  (3.35e-67, 2.46e-190j)
| (0.034834848838135075782 - 6.4978479311140623069e-890j)  +/-  (1.33e-36, 9.75e-160j)
| (0.016562503353142236575 + 3.0374344785477082792e-890j)  +/-  (1.73e-40, 1.27e-163j)
| (4.4438452444460684385e-21 + 1.1150538094771556523e-902j)  +/-  (3.36e-68, 2.47e-191j)
| (0.0074182727092749999464 - 2.4603694803462224701e-890j)  +/-  (8.98e-45, 6.59e-168j)
| (1.3166844869271794278e-23 + 4.2529540123695758902e-903j)  +/-  (4.5e-68, 3.3e-191j)
| (7.3543485464038315506e-08 + 7.2912119610239756341e-895j)  +/-  (9.57e-61, 7.03e-184j)
| (4.4438452444460684385e-21 - 1.3684439996106365146e-901j)  +/-  (4.13e-67, 3.03e-190j)
| (7.3543485464038315506e-08 + 4.0484252920147843057e-894j)  +/-  (2.64e-60, 1.94e-183j)
| (1.244089591693862392e-38 - 5.2005418710546375858e-912j)  +/-  (4.09e-77, 3e-200j)
| (1.3166844869271794278e-23 - 3.8372359915489839491e-904j)  +/-  (2.63e-70, 1.93e-193j)
| (8.0150119244099100366e-07 - 3.7181278683941649767e-894j)  +/-  (2.34e-60, 1.72e-183j)
| (0.0074182727092749999464 - 1.2898819510374253838e-890j)  +/-  (1.07e-49, 7.86e-173j)
| (2.7867846798681273172e-10 + 2.0177791440961050286e-895j)  +/-  (5.96e-64, 4.38e-187j)
| (8.0150119244099100366e-07 - 1.6713937778634609239e-893j)  +/-  (3.71e-61, 2.72e-184j)
| (1.1122589666965603674e-11 - 4.3596105931923873366e-896j)  +/-  (5.75e-65, 4.22e-188j)
| (1.1122589666965603674e-11 - 2.8877678443251585516e-897j)  +/-  (1.93e-67, 1.42e-190j)
| (4.5351105563937586937e-05 - 7.6133105573979135561e-893j)  +/-  (2.27e-60, 1.67e-183j)
| (6.8052140748002879359e-06 + 1.742853269236272526e-893j)  +/-  (1.92e-61, 1.41e-184j)
| (0.058672566252651955626 + 2.1014415609540892936e-889j)  +/-  (2.33e-52, 1.71e-175j)
| (0.016562503353142236575 + 5.245432803199988586e-890j)  +/-  (7.06e-54, 5.18e-177j)
| (9.1691534830587613627e-17 + 3.1004852665870379771e-900j)  +/-  (3.15e-70, 2.31e-193j)
| (4.5351105563937586937e-05 - 2.4187459238525415521e-892j)  +/-  (7.35e-62, 5.4e-185j)
| (3.2266156853125232778e-13 + 1.0889990169658679104e-896j)  +/-  (1.15e-67, 8.41e-191j)
| (9.1691534830587613627e-17 - 1.0248406213708235088e-898j)  +/-  (1.28e-69, 9.37e-193j)
| (0.06111386937890979441 - 3.690248720470661547e-889j)  +/-  (2.34e-55, 1.72e-178j)
| (6.8052140748002879359e-06 + 6.5202332769551198936e-893j)  +/-  (1.56e-63, 1.15e-186j)
| (5.1974846399607506597e-09 - 9.2563282736287092112e-895j)  +/-  (1.42e-65, 1.04e-188j)
| (0.058672566252651955626 + 1.4860822814478362652e-889j)  +/-  (1.24e-58, 9.14e-182j)
| (2.7867846798681273172e-10 + 2.0612267637901352805e-896j)  +/-  (2.97e-70, 2.18e-193j)
| (0.00023763225898265469879 + 8.5997550213861275389e-892j)  +/-  (6.43e-63, 4.72e-186j)
| (0.00097119961794876849734 - 2.9323622599512970467e-891j)  +/-  (1.66e-62, 1.22e-185j)
| (5.1974846399607506597e-09 - 1.2964065727132963751e-895j)  +/-  (1.91e-69, 1.41e-192j)
| (0.00023763225898265469879 + 3.1376857922070059199e-892j)  +/-  (4.56e-66, 3.35e-189j)
| (0.0030360521498232658401 + 4.3639072202572287049e-891j)  +/-  (1.23e-64, 9.05e-188j)
| (3.2266156853125232778e-13 + 3.5067382078613922338e-898j)  +/-  (3.83e-73, 2.82e-196j)
| (0.093381636835913635277 + 3.8396683224985203038e-889j)  +/-  (3.33e-64, 2.45e-187j)
| (0.034834848838135075782 - 1.0149453247119167561e-889j)  +/-  (1.1e-64, 8.1e-188j)
| (6.602118117311265317e-15 - 3.6200483715820800807e-899j)  +/-  (3.74e-74, 2.75e-197j)
| (0.093381636835913635277 + 3.1588060670965358198e-889j)  +/-  (3.34e-65, 2.46e-188j)
| (0.00097119961794876849734 - 1.2235485713800413362e-891j)  +/-  (1.2e-66, 8.79e-190j)
| (0.0030360521498232658401 + 9.2672521469795528408e-891j)  +/-  (2.43e-66, 1.78e-189j)
| (0.14341150368834116472 - 2.7944867390488595908e-889j)  +/-  (2.47e-65, 1.81e-188j)
| (0.16061375612988950381 + 2.3618659434237175506e-889j)  +/-  (4.63e-66, 3.42e-189j)
| (0.06111386937890979441 - 2.8331899205422008344e-889j)  +/-  (2.13e-66, 1.72e-189j)
| (0.14341150368834116472 - 2.5224411656767985375e-889j)  +/-  (1.91e-66, 1.33e-189j)
