Starting with polynomial:
P : 64*t^6 - 480*t^4 + 720*t^2 - 120
Extension levels are: 6 51
-------------------------------------------------
Trying to find an order 51 Kronrod extension for:
P1 : 64*t^6 - 480*t^4 + 720*t^2 - 120
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 64*t^57 - 6514780041361137300936536605460467707159453302565302110880/141049776424247813923944329821556430467928027552521411*t^55 + 50155007653442479234768118343995653498126636204300988575802960/3244144857757699720250719585895797900762344633707992453*t^53 - 10352367281442442596197291915017868798635727894607506320704227960/3244144857757699720250719585895797900762344633707992453*t^51 + 1477821916851657182282223530699112490828191964819884861747152967000/3244144857757699720250719585895797900762344633707992453*t^49 - 155113814020583849083762105776340349622253739861027216645280899234100/3244144857757699720250719585895797900762344633707992453*t^47 + 11493956411216032368282012764831124869267160441834469449483229806750/3001059072856336466466900634501200648253787820266413*t^45 - 719902127584264923736197865153077890840881582774994324994260026615125/3001059072856336466466900634501200648253787820266413*t^43 + 143353643781945117787937000243803224216658202573045199773572420983807375/12004236291425345865867602538004802593015151281065652*t^41 - 11471242786205005579627598437124392525793802518321441780352279351646025625/24008472582850691731735205076009605186030302562131304*t^39 + 743177651017558247715804334446564957498101614528989868374099845031600582375/48016945165701383463470410152019210372060605124262608*t^37 - 39154530207761771578621716735483812974780216441291272301623922394790058393125/96033890331402766926940820304038420744121210248525216*t^35 + 420262348396801205945975982360198433369103556536254534898422050651615991558125/48016945165701383463470410152019210372060605124262608*t^33 - 14704203434957061467830891240408928180451687594543958374728420650734471739944375/96033890331402766926940820304038420744121210248525216*t^31 + 418484803102950561996115795067095734865909767943191679281690936465077265694978125/192067780662805533853881640608076841488242420497050432*t^29 - 9652218582470912320755855756794892260076881718337650919641887491212049791444039375/384135561325611067707763281216153682976484840994100864*t^27 + 717630183337755386221706418854208834761992229985824814232015464663210122223781546875/3073084490604888541662106249729229463811878727952806912*t^25 - 10666350011559551998563946657320205835898396395529465834486883506050530110732048328125/6146168981209777083324212499458458927623757455905613824*t^23 + 125485611181715296298573002452157708819520445830743644735223860216845644148424615796875/12292337962419554166648424998916917855247514911811227648*t^21 - 1153126681564151131472715832986689437943163563286093954334336732337994583566983165390625/24584675924839108333296849997833835710495029823622455296*t^19 + 4067934075570645451585046336617662640623291921441540418610236188807416576984915466046875/24584675924839108333296849997833835710495029823622455296*t^17 - 21546465312513618982336644015413546541472071899514552288646310832723086648781282227578125/49169351849678216666593699995667671420990059647244910592*t^15 + 83138580403951064400272298647955616986688779439251556770845990648563055891712762532734375/98338703699356433333187399991335342841980119294489821184*t^13 - 224221228005778647831654896269859882386306754270842177181544186953349641990602161696328125/196677407398712866666374799982670685683960238588979642368*t^11 + 796448568064265826588256552731814562453830339243550428222656975558309740024448022578515625/786709629594851466665499199930682742735840954355918569472*t^9 - 850091796715687575425240504927023261001213283360958977535183864016280053459031970975359375/1573419259189702933330998399861365485471681908711837138944*t^7 + 466550268245167084752698356648390805270226131180317092495794897012752493826861516680390625/3146838518379405866661996799722730970943363817423674277888*t^5 - 95028747902755215175904123448225393698345379376542457130770169160596273441813997034921875/6293677036758811733323993599445461941886727634847348555776*t^3 + 116885759186313047510708417885054800427177999885459086584111454783871575252818903046875/786709629594851466665499199930682742735840954355918569472*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:
| (-7.4728848335562004889 + 7.2401099826798384575e-846j)  +/-  (1.22e-242, 1.22e-242j)
| (-8.937753300838428221 + 3.0243695582629023808e-849j)  +/-  (1.32e-244, 1.32e-244j)
| (9.5879209791173017044 + 1.1814157485749707278e-849j)  +/-  (7.59e-246, 7.59e-246j)
| (4.187763354373902929 + 3.7172871033479536758e-845j)  +/-  (5.88e-243, 5.88e-243j)
| (-2.127657752600529165 - 1.80169329130876637e-850j)  +/-  (1.99e-246, 1.99e-246j)
| (7.9174521412097933564 - 2.6094271867881258867e-844j)  +/-  (4.1e-243, 4.1e-243j)
| (8.3988911145208809566 + 9.3126553444511196722e-848j)  +/-  (9.95e-244, 9.95e-244j)
| (-9.5879209791173017044 + 6.994192388655890739e-855j)  +/-  (7.39e-246, 7.39e-246j)
| (8.937753300838428221 - 2.6948834275646331199e-850j)  +/-  (1.31e-244, 1.31e-244j)
| (7.0546095430641243698 - 3.2709428931253720314e-850j)  +/-  (2.79e-242, 2.79e-242j)
| (-5.9040169740315446499 - 3.8947150964630408859e-856j)  +/-  (5.71e-242, 5.71e-242j)
| (5.1949898229090043267 - 5.15521217308835151e-864j)  +/-  (4.08e-242, 4.08e-242j)
| (-2.9226205127833468226 + 4.2096763925612236701e-883j)  +/-  (8.27e-245, 8.27e-245j)
| (-1.3358490740136969497 + 4.4807116062852418776e-888j)  +/-  (2.18e-249, 2.18e-249j)
| (-5.544983782674568093 + 1.3310439317994725893e-879j)  +/-  (6.02e-242, 6.02e-242j)
| (5.544983782674568093 + 8.5732578273218284795e-883j)  +/-  (5.37e-242, 5.37e-242j)
| (-6.6562840490479829249 + 1.1832702657986750203e-889j)  +/-  (4.54e-242, 4.54e-242j)
| (-7.0546095430641243698 - 5.0361706699304673051e-892j)  +/-  (2.77e-242, 2.77e-242j)
| (-2.3506049736744922228 + 2.5785064123232133044e-900j)  +/-  (7.07e-246, 7.07e-246j)
| (2.6244952111538699732 + 5.5788672759458214849e-898j)  +/-  (2.51e-245, 2.51e-245j)
| (6.6562840490479829249 - 6.3155703342972619898e-894j)  +/-  (4.28e-242, 4.28e-242j)
| (2.3506049736744922228 - 1.4913129980088635481e-910j)  +/-  (7.27e-246, 7.27e-246j)
| (1.9010673934948053018 - 1.9785843800479634343e-912j)  +/-  (3.69e-247, 3.69e-247j)
| (-4.5172768011296701668 + 1.7213618111227422497e-906j)  +/-  (1.22e-242, 1.22e-242j)
| (4.8527565744015009473 - 1.2426874318717331382e-905j)  +/-  (2.33e-242, 2.33e-242j)
| (-8.3988911145208809566 - 3.0482000094521545655e-917j)  +/-  (9.79e-244, 9.79e-244j)
| (7.4728848335562004889 - 2.011042291853769683e-924j)  +/-  (1.2e-242, 1.2e-242j)
| (-4.8527565744015009473 - 1.220271596327823676e-928j)  +/-  (2.24e-242, 2.24e-242j)
| (3.2305604758736256486 - 2.2548747178637566951e-937j)  +/-  (2.55e-244, 2.55e-244j)
| (-1.9010673934948053018 - 1.3967274472108523118e-943j)  +/-  (3.79e-247, 3.79e-247j)
| (-2.6244952111538699732 - 1.450021056434587573e-941j)  +/-  (2.38e-245, 2.38e-245j)
| (-6.2737311065510194303 + 1.0110855703370262081e-937j)  +/-  (5.63e-242, 5.63e-242j)
| (5.9040169740315446499 - 1.147110551398734788e-945j)  +/-  (6.47e-242, 6.47e-242j)
| (1.627566154332680436 - 3.0089681589962721077e-960j)  +/-  (3.35e-248, 3.35e-248j)
| (-3.5445490837834343759 + 1.0639703137212371861e-955j)  +/-  (8.6e-244, 8.6e-244j)
| (-7.9174521412097933564 - 1.3447158975778471688e-956j)  +/-  (4.16e-243, 4.16e-243j)
| (4.5172768011296701668 + 1.1380442848934802582e-953j)  +/-  (1.27e-242, 1.27e-242j)
| (1.3358490740136969497 - 7.4665011361766544906e-966j)  +/-  (2.03e-249, 2.03e-249j)
| (2.9226205127833468226 - 9.6149755389849400239e-962j)  +/-  (7.9e-245, 7.9e-245j)
| (-3.8636342433235053686 - 2.7113904637079876738e-958j)  +/-  (2.45e-243, 2.45e-243j)
| (-1.0386441910834042007 + 1.1425674228483873871e-966j)  +/-  (1.14e-250, 1.14e-250j)
| (-0.10477009758297915618 + 2.0543057252476655654e-969j)  +/-  (1.54e-254, 1.54e-254j)
| (1.0386441910834042007 - 4.3877163885606745867e-966j)  +/-  (1.15e-250, 1.15e-250j)
| (2.127657752600529165 + 1.1691824153312659003e-962j)  +/-  (2.36e-246, 2.36e-246j)
| (3.5445490837834343759 - 4.3909504545062223939e-959j)  +/-  (7.73e-244, 7.73e-244j)
| (-3.2305604758736256486 - 3.7070921119750344935e-959j)  +/-  (2.59e-244, 2.59e-244j)
| (-4.187763354373902929 + 9.8542362135621507694e-957j)  +/-  (5.51e-243, 5.51e-243j)
| (0.10477009758297915618 - 5.0325081356039866888e-970j)  +/-  (1.54e-254, 1.54e-254j)
| (0.43607741192761650868 + 2.0850521594352432729e-968j)  +/-  (3.88e-253, 3.88e-253j)
| (-1.627566154332680436 + 3.3654037830471894095e-964j)  +/-  (3.24e-248, 3.24e-248j)
| (-5.1949898229090043267 + 2.5578676027563017926e-961j)  +/-  (3.81e-242, 3.81e-242j)
| (-0.73897310250561042695 - 8.8619632237833549378e-972j)  +/-  (6.78e-252, 6.78e-252j)
| (6.2737311065510194303 + 2.1131155838810211103e-968j)  +/-  (5.73e-242, 5.73e-242j)
| (3.8636342433235053686 - 4.9584187947528943256e-976j)  +/-  (2.32e-243, 2.32e-243j)
| (0.73897310250561042695 - 8.6106763399362879375e-984j)  +/-  (6.38e-252, 6.38e-252j)
| (-2.1697892526156134955e-1010 + 2.0246504148517535045e-1011j)  +/-  (1.24e-1008, 1.24e-1008j)
| (-0.43607741192761650868 - 4.0740037461191631508e-985j)  +/-  (3.2e-253, 3.2e-253j)
-------------------------------------------------
The weights are:
| (1.3560058741581757726e-25 + 1.118410000654889169e-863j)  +/-  (3.47e-75, 4.72e-195j)
| (6.6351492995817011393e-36 - 3.9580805211817734593e-869j)  +/-  (1.41e-79, 1.92e-199j)
| (5.0464504776178678873e-41 - 2.1321938060419374069e-871j)  +/-  (1.35e-82, 1.83e-202j)
| (4.4591342885305721045e-09 - 8.3962817495207547189e-853j)  +/-  (8.98e-64, 1.22e-183j)
| (0.0012591892162710440991 + 3.4399057607458747212e-850j)  +/-  (9.45e-49, 1.28e-168j)
| (1.5511252965847902688e-28 + 9.8479365461219216289e-865j)  +/-  (1.65e-78, 2.24e-198j)
| (6.5959196091071606708e-32 - 1.4938523809509265146e-866j)  +/-  (6.2e-80, 8.42e-200j)
| (5.0464504776178678873e-41 + 8.3595451259805214752e-872j)  +/-  (6.08e-85, 8.27e-205j)
| (6.6351492995817011393e-36 + 1.0935547619053471611e-868j)  +/-  (1.44e-81, 1.95e-201j)
| (5.5944693218295827986e-23 + 1.1099087907813735218e-861j)  +/-  (3.59e-77, 4.88e-197j)
| (1.4935457922353117226e-16 + 9.1793972780984068793e-859j)  +/-  (1.18e-75, 1.6e-195j)
| (3.7128135038430283695e-13 - 7.0307286462851396169e-856j)  +/-  (2.33e-72, 3.17e-192j)
| (3.3483405953943038115e-05 - 9.0924898400526079001e-852j)  +/-  (1.53e-62, 2.08e-182j)
| (0.027978074566484753839 - 1.0557412355096183014e-849j)  +/-  (2.06e-48, 2.8e-168j)
| (8.8629699145193867083e-15 - 9.0282960549084178505e-858j)  +/-  (1.11e-74, 1.51e-194j)
| (8.8629699145193867083e-15 + 6.4724681164045677208e-857j)  +/-  (2.11e-74, 2.87e-194j)
| (1.260200057561320067e-20 + 5.3087502705212962021e-861j)  +/-  (1.48e-78, 2.01e-198j)
| (5.5944693218295827986e-23 - 2.8308895490964432467e-862j)  +/-  (1.13e-79, 1.53e-199j)
| (0.00056423608837037460464 - 1.4478122806073555075e-850j)  +/-  (2.2e-61, 2.99e-181j)
| (0.0001669500899118988131 + 1.6478120572127627986e-850j)  +/-  (1.09e-64, 1.49e-184j)
| (1.260200057561320067e-20 - 2.3315848598069684761e-860j)  +/-  (6.1e-79, 8.29e-199j)
| (0.00056423608837037460464 - 5.1367775141057828945e-850j)  +/-  (3.15e-63, 4.28e-183j)
| (0.0038669811527629206209 - 1.4157324399071069733e-849j)  +/-  (1.35e-60, 1.83e-180j)
| (2.575972159711384965e-10 + 3.4821745680124599602e-855j)  +/-  (2.68e-74, 3.64e-194j)
| (1.1322514810654023018e-11 + 7.4292870203306909216e-855j)  +/-  (3.07e-74, 4.17e-194j)
| (6.5959196091071606708e-32 + 4.9988318814013803408e-867j)  +/-  (1.63e-85, 2.21e-205j)
| (1.3560058741581757726e-25 - 3.969070161016073336e-863j)  +/-  (1.34e-81, 1.83e-201j)
| (1.1322514810654023018e-11 - 5.466593863783657028e-856j)  +/-  (1.16e-75, 1.58e-195j)
| (5.1524009288004387113e-06 + 1.6571815380499324843e-851j)  +/-  (1.78e-70, 2.42e-190j)
| (0.0038669811527629206209 - 5.3022857718449722603e-850j)  +/-  (6.8e-64, 9.25e-184j)
| (0.0001669500899118988131 + 3.7869122221296820191e-851j)  +/-  (1.65e-67, 2.24e-187j)
| (1.7083953521835939748e-18 - 7.7619812895342988739e-860j)  +/-  (3.42e-79, 4.64e-199j)
| (1.4935457922353117226e-16 - 5.396214179753332798e-858j)  +/-  (8.1e-79, 1.1e-198j)
| (0.011422954464215061371 + 1.6352253472402160175e-849j)  +/-  (1.28e-65, 1.73e-185j)
| (6.2449000124420856229e-07 - 4.8261716585796837729e-853j)  +/-  (3.37e-73, 4.58e-193j)
| (1.5511252965847902688e-28 - 3.0347499183138219326e-865j)  +/-  (2.13e-84, 2.9e-204j)
| (2.575972159711384965e-10 - 9.1957154027780215319e-854j)  +/-  (1.49e-75, 2.03e-195j)
| (0.027978074566484753839 - 2.0460812396321168373e-849j)  +/-  (2.78e-66, 3.78e-186j)
| (3.3483405953943038115e-05 - 5.1052876209709084895e-851j)  +/-  (1.5e-71, 2.04e-191j)
| (5.9662695529006535617e-08 + 1.0193775739844441504e-853j)  +/-  (3.91e-75, 5.31e-195j)
| (0.05728008241057939982 + 1.6717397979863447759e-849j)  +/-  (8.53e-67, 1.16e-186j)
| (0.2621303381792102909 - 3.7508640544152772863e-848j)  +/-  (2.86e-67, 3.89e-187j)
| (0.05728008241057939982 + 2.7755890112203454407e-849j)  +/-  (4.02e-67, 5.46e-187j)
| (0.0012591892162710440991 + 1.0563332380146309929e-849j)  +/-  (2.62e-69, 3.56e-189j)
| (6.2449000124420856229e-07 - 5.7983490075631590345e-852j)  +/-  (4.83e-74, 6.56e-194j)
| (5.1524009288004387113e-06 + 2.1398375126104487764e-852j)  +/-  (1.13e-73, 1.53e-193j)
| (4.4591342885305721045e-09 - 1.9799241711200909742e-854j)  +/-  (2.68e-76, 3.64e-196j)
| (0.2621303381792102909 - 3.9434797859538319258e-848j)  +/-  (1.06e-69, 1.45e-189j)
| (0.14288198180681904288 + 7.1059517232877201306e-849j)  +/-  (4.5e-70, 6.12e-190j)
| (0.011422954464215061371 + 7.1908592166467253519e-850j)  +/-  (3.45e-71, 4.69e-191j)
| (3.7128135038430283695e-13 + 7.549695262209814636e-857j)  +/-  (6.95e-79, 9.45e-199j)
| (0.09830288105503219667 - 2.860080775574035733e-849j)  +/-  (1.41e-71, 1.9e-191j)
| (1.7083953521835939748e-18 + 3.8918467599530886849e-859j)  +/-  (7.92e-83, 1.08e-202j)
| (5.9662695529006535617e-08 + 2.530905507769014103e-852j)  +/-  (9.52e-77, 1.3e-196j)
| (0.09830288105503219667 - 4.0867401631248067178e-849j)  +/-  (6.32e-72, 8.63e-192j)
| (-0.21178598743534163003 + 6.8367104863679870698e-848j)  +/-  (4.69e-71, 6.57e-191j)
| (0.14288198180681904288 + 5.7648544388804658678e-849j)  +/-  (3.57e-72, 4.57e-192j)
