Starting with polynomial:
P : t^6 - 15*t^4 + 45*t^2 - 15
Extension levels are: 6 51
-------------------------------------------------
Trying to find an order 51 Kronrod extension for:
P1 : t^6 - 15*t^4 + 45*t^2 - 15
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^57 - 203586876292535540654266768920639615848732915705165690965/141049776424247813923944329821556430467928027552521411*t^55 + 3134687978340154952173007396499728343632914762768811785987685/3244144857757699720250719585895797900762344633707992453*t^53 - 1294045910180305324524661489377233599829465986825938290088028495/3244144857757699720250719585895797900762344633707992453*t^51 + 369455479212914295570555882674778122707047991204971215436788241750/3244144857757699720250719585895797900762344633707992453*t^49 - 77556907010291924541881052888170174811126869930513608322640449617050/3244144857757699720250719585895797900762344633707992453*t^47 + 11493956411216032368282012764831124869267160441834469449483229806750/3001059072856336466466900634501200648253787820266413*t^45 - 1439804255168529847472395730306155781681763165549988649988520053230250/3001059072856336466466900634501200648253787820266413*t^43 + 143353643781945117787937000243803224216658202573045199773572420983807375/3001059072856336466466900634501200648253787820266413*t^41 - 11471242786205005579627598437124392525793802518321441780352279351646025625/3001059072856336466466900634501200648253787820266413*t^39 + 743177651017558247715804334446564957498101614528989868374099845031600582375/3001059072856336466466900634501200648253787820266413*t^37 - 39154530207761771578621716735483812974780216441291272301623922394790058393125/3001059072856336466466900634501200648253787820266413*t^35 + 1681049393587204823783903929440793733476414226145018139593688202606463966232500/3001059072856336466466900634501200648253787820266413*t^33 - 58816813739828245871323564961635712721806750378175833498913682602937886959777500/3001059072856336466466900634501200648253787820266413*t^31 + 1673939212411802247984463180268382939463639071772766717126763745860309062779912500/3001059072856336466466900634501200648253787820266413*t^29 - 38608874329883649283023423027179569040307526873350603678567549964848199165776157500/3001059072856336466466900634501200648253787820266413*t^27 + 717630183337755386221706418854208834761992229985824814232015464663210122223781546875/3001059072856336466466900634501200648253787820266413*t^25 - 10666350011559551998563946657320205835898396395529465834486883506050530110732048328125/3001059072856336466466900634501200648253787820266413*t^23 + 125485611181715296298573002452157708819520445830743644735223860216845644148424615796875/3001059072856336466466900634501200648253787820266413*t^21 - 1153126681564151131472715832986689437943163563286093954334336732337994583566983165390625/3001059072856336466466900634501200648253787820266413*t^19 + 8135868151141290903170092673235325281246583842883080837220472377614833153969830932093750/3001059072856336466466900634501200648253787820266413*t^17 - 43092930625027237964673288030827093082944143799029104577292621665446173297562564455156250/3001059072856336466466900634501200648253787820266413*t^15 + 166277160807902128800544597295911233973377558878503113541691981297126111783425525065468750/3001059072856336466466900634501200648253787820266413*t^13 - 448442456011557295663309792539719764772613508541684354363088373906699283981204323392656250/3001059072856336466466900634501200648253787820266413*t^11 + 796448568064265826588256552731814562453830339243550428222656975558309740024448022578515625/3001059072856336466466900634501200648253787820266413*t^9 - 850091796715687575425240504927023261001213283360958977535183864016280053459031970975359375/3001059072856336466466900634501200648253787820266413*t^7 + 466550268245167084752698356648390805270226131180317092495794897012752493826861516680390625/3001059072856336466466900634501200648253787820266413*t^5 - 95028747902755215175904123448225393698345379376542457130770169160596273441813997034921875/3001059072856336466466900634501200648253787820266413*t^3 + 1870172146981008760171334686160876806834847998167345385345783276541945204045102448750000/3001059072856336466466900634501200648253787820266413*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: 0
  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:
| (-11.196968197538791045 - 2.6085530199601738844e-856j)  +/-  (6.23e-243, 6.23e-243j)
| (-8.8723956175664167367 + 2.4572972303026250776e-854j)  +/-  (8.11e-242, 8.11e-242j)
| (12.639891935190602665 - 3.0106718454675156318e-857j)  +/-  (2.05e-244, 2.05e-244j)
| (5.4640039469572120523 - 1.0048133657713790324e-855j)  +/-  (3.16e-243, 3.16e-243j)
| (9.4134071771713572633 - 9.6708548722579456163e-854j)  +/-  (6.18e-242, 6.18e-242j)
| (9.9767244930479476112 - 1.4293533958456984587e-861j)  +/-  (3.7e-242, 3.7e-242j)
| (-9.9767244930479476112 - 4.0126606654420298458e-867j)  +/-  (3.77e-242, 3.77e-242j)
| (13.559367883629212705 - 4.5052182568858697575e-870j)  +/-  (1.1e-245, 1.1e-245j)
| (11.877825723050309671 - 4.0658472879079885593e-867j)  +/-  (1.44e-243, 1.44e-243j)
| (-13.559367883629212705 + 6.0946970017326859875e-872j)  +/-  (1.09e-245, 1.09e-245j)
| (-9.4134071771713572633 + 8.3799025027107138129e-868j)  +/-  (6.49e-242, 6.49e-242j)
| (-5.9223917317646193142 - 2.4602250236438528066e-869j)  +/-  (8.57e-243, 8.57e-243j)
| (-7.8417912685972408247 + 2.2719206404139983616e-868j)  +/-  (7.2e-242, 7.2e-242j)
| (-1.4688647015101826989 - 5.2921106671406808726e-878j)  +/-  (1.84e-250, 1.84e-250j)
| (-2.6885152908656230663 - 8.2039375089600269634e-875j)  +/-  (5.27e-247, 5.27e-247j)
| (3.3242574335521189524 - 6.0361021831658742254e-874j)  +/-  (9.9e-246, 9.9e-246j)
| (7.3468250639481171922 - 1.4423789769463472159e-868j)  +/-  (5.42e-242, 5.42e-242j)
| (-8.3495408771563717608 + 1.9278913947041004285e-874j)  +/-  (8.54e-242, 8.54e-242j)
| (-1.8891758777537106755 - 9.2445177743341544295e-885j)  +/-  (3.12e-249, 3.12e-249j)
| (-10.568255081667387752 - 3.9786939827957070701e-877j)  +/-  (1.74e-242, 1.74e-242j)
| (6.8628341624138041238 - 7.056181306365654445e-876j)  +/-  (3.15e-242, 3.15e-242j)
| (5.0127493867836608787 - 9.473132280258388358e-885j)  +/-  (1.24e-243, 1.24e-243j)
| (3.0089624498159276866 - 9.2505517196299652041e-890j)  +/-  (2.91e-246, 2.91e-246j)
| (11.196968197538791045 - 1.1239772732033244857e-885j)  +/-  (6.29e-243, 6.29e-243j)
| (-3.3242574335521189524 + 3.7705891402158219913e-901j)  +/-  (1.03e-245, 1.03e-245j)
| (1.8891758777537106755 + 6.9990224686375024311e-908j)  +/-  (3.07e-249, 3.07e-249j)
| (10.568255081667387752 + 1.4349875108177890627e-900j)  +/-  (1.86e-242, 1.86e-242j)
| (-6.3883941171509300791 + 5.1332564193781665221e-910j)  +/-  (1.74e-242, 1.74e-242j)
| (3.7115967219970427538 - 1.7866348927652052338e-919j)  +/-  (3.48e-245, 3.48e-245j)
| (-11.877825723050309671 - 1.4617225344464558586e-916j)  +/-  (1.5e-243, 1.5e-243j)
| (-5.0127493867836608787 - 5.6599350504569155198e-919j)  +/-  (1.16e-243, 1.16e-243j)
| (-12.639891935190602665 - 4.4403260570558098228e-924j)  +/-  (1.93e-244, 1.93e-244j)
| (2.6885152908656230663 - 4.3837044306095172543e-933j)  +/-  (4.94e-247, 4.94e-247j)
| (1.4688647015101826989 - 7.642883545862453782e-944j)  +/-  (1.71e-250, 1.71e-250j)
| (8.8723956175664167367 - 3.3607134392786296101e-934j)  +/-  (8.29e-242, 8.29e-242j)
| (8.3495408771563717608 - 4.5088182892027518032e-952j)  +/-  (8.64e-242, 8.64e-242j)
| (4.5687024390469613087 - 8.5834308955022486292e-969j)  +/-  (3.66e-244, 3.66e-244j)
| (7.8417912685972408247 - 6.1230405443800855671e-966j)  +/-  (7.55e-242, 7.55e-242j)
| (2.3017261291166986062 + 1.4646642247823780551e-978j)  +/-  (4.32e-248, 4.32e-248j)
| (-5.4640039469572120523 + 9.3941835656475447948e-973j)  +/-  (3.18e-243, 3.18e-243j)
| (-3.0089624498159276866 - 2.4662530444986944985e-976j)  +/-  (2.95e-246, 2.95e-246j)
| (-4.1332095668480186871 - 1.1271968793584792557e-974j)  +/-  (1.06e-244, 1.06e-244j)
| (5.9223917317646193142 - 4.9657454606822779066e-972j)  +/-  (8.11e-243, 8.11e-243j)
| (1.0450657837923576526 + 3.2844704742239501233e-982j)  +/-  (9.52e-252, 9.52e-252j)
| (-1.0450657837923576526 - 5.7733235267376730918e-982j)  +/-  (1.01e-251, 1.01e-251j)
| (-0.61670659019259415219 + 5.46917664771984601e-983j)  +/-  (5.29e-253, 5.29e-253j)
| (-7.3468250639481171922 + 8.3353969101512223948e-972j)  +/-  (5.16e-242, 5.16e-242j)
| (-2.2232050019692952032e-1009 + 9.6347437798790051325e-1010j)  +/-  (1.38e-1007, 1.38e-1007j)
| (0.1481672929330017477 + 1.3059124259588942249e-986j)  +/-  (1.79e-254, 1.79e-254j)
| (6.3883941171509300791 - 4.8745759816569611821e-977j)  +/-  (1.76e-242, 1.76e-242j)
| (-4.5687024390469613087 - 1.4174814022665315807e-976j)  +/-  (3.71e-244, 3.71e-244j)
| (-2.3017261291166986062 + 9.3803972794467031601e-981j)  +/-  (4.16e-248, 4.16e-248j)
| (-6.8628341624138041238 + 1.0651345127801201376e-979j)  +/-  (3.29e-242, 3.29e-242j)
| (4.1332095668480186871 - 2.0315124583107831966e-985j)  +/-  (1.09e-244, 1.09e-244j)
| (0.61670659019259415219 - 3.7543306704018882767e-991j)  +/-  (5.29e-253, 5.29e-253j)
| (-3.7115967219970427538 + 3.4634723346542256555e-987j)  +/-  (3.43e-245, 3.43e-245j)
| (-0.1481672929330017477 + 1.3616454065869054716e-995j)  +/-  (1.79e-254, 1.79e-254j)
-------------------------------------------------
The weights are:
| (1.5511252965847902688e-28 - 1.6195362699971022553e-875j)  +/-  (4.04e-64, 6.54e-184j)
| (1.7083953521835939748e-18 - 3.9374243172913318593e-870j)  +/-  (1.63e-58, 2.64e-178j)
| (6.6351492995817011393e-36 + 5.2943450385554596176e-879j)  +/-  (2.99e-68, 4.84e-188j)
| (5.9662695529006535617e-08 + 2.0588766123287626012e-862j)  +/-  (4.71e-49, 7.63e-169j)
| (1.260200057561320067e-20 - 1.058974818723823587e-870j)  +/-  (1.06e-61, 1.71e-181j)
| (5.5944693218295827986e-23 + 5.1654871709636913363e-872j)  +/-  (4.28e-63, 6.92e-183j)
| (5.5944693218295827986e-23 - 1.5211659983908879213e-872j)  +/-  (1.53e-64, 2.47e-184j)
| (5.0464504776178678873e-41 - 1.0402176457608479807e-881j)  +/-  (3.7e-71, 5.98e-191j)
| (6.5959196091071606708e-32 - 7.1743951825780357719e-877j)  +/-  (1.38e-67, 2.23e-187j)
| (5.0464504776178678873e-41 + 4.4367612523911541109e-882j)  +/-  (1.84e-73, 2.98e-193j)
| (1.260200057561320067e-20 + 2.8827508110533531852e-871j)  +/-  (7.43e-64, 1.2e-183j)
| (4.4591342885305721045e-09 - 1.0611777069943698232e-864j)  +/-  (4.7e-57, 7.6e-177j)
| (8.8629699145193867083e-15 - 4.7816230450419140026e-868j)  +/-  (1.28e-61, 2.08e-181j)
| (0.05728008241057939982 + 9.2100186483663086433e-860j)  +/-  (1.28e-32, 2.08e-152j)
| (0.0038669811527629206209 - 2.8999788729180112149e-860j)  +/-  (7.56e-44, 1.22e-163j)
| (0.00056423608837037460464 - 3.2231147103555987228e-860j)  +/-  (1.06e-48, 1.71e-168j)
| (3.7128135038430283695e-13 - 2.7480526510528960435e-866j)  +/-  (1.05e-62, 1.71e-182j)
| (1.4935457922353117226e-16 + 4.8089625283195603505e-869j)  +/-  (1.32e-62, 2.13e-182j)
| (0.027978074566484753839 - 5.7965754721751614903e-860j)  +/-  (8.97e-40, 1.45e-159j)
| (1.3560058741581757726e-25 + 5.9843602955146361241e-874j)  +/-  (1.44e-67, 2.33e-187j)
| (1.1322514810654023018e-11 + 2.5807455862387573513e-865j)  +/-  (5.17e-62, 8.36e-182j)
| (6.2449000124420856229e-07 - 6.0400192976586121923e-862j)  +/-  (3.32e-57, 5.37e-177j)
| (0.0012591892162710440991 + 6.4778383144672645115e-860j)  +/-  (6.53e-50, 1.06e-169j)
| (1.5511252965847902688e-28 + 4.6871138681201349586e-875j)  +/-  (2.41e-71, 3.9e-191j)
| (0.00056423608837037460464 - 7.840516384409074654e-861j)  +/-  (1.58e-53, 2.56e-173j)
| (0.027978074566484753839 - 1.1928642387617401698e-859j)  +/-  (1.03e-46, 1.66e-166j)
| (1.3560058741581757726e-25 - 1.8694804307522730526e-873j)  +/-  (4.36e-70, 7.05e-190j)
| (2.575972159711384965e-10 + 1.8623782950153893225e-865j)  +/-  (6.54e-63, 1.06e-182j)
| (0.0001669500899118988131 + 1.074258376800048758e-860j)  +/-  (2.9e-55, 4.7e-175j)
| (6.5959196091071606708e-32 + 2.6622981991460914618e-877j)  +/-  (3.6e-74, 5.82e-194j)
| (6.2449000124420856229e-07 - 2.5970891451710555366e-863j)  +/-  (1.39e-61, 2.24e-181j)
| (6.6351492995817011393e-36 - 2.1043152860338930163e-879j)  +/-  (3.3e-76, 5.33e-196j)
| (0.0038669811527629206209 - 8.524047535028511577e-860j)  +/-  (5.25e-54, 8.5e-174j)
| (0.05728008241057939982 + 1.598798651403838823e-859j)  +/-  (4.31e-49, 6.97e-169j)
| (1.7083953521835939748e-18 + 1.7376409485261413193e-869j)  +/-  (8.76e-70, 1.42e-189j)
| (1.4935457922353117226e-16 - 2.3438847868370739255e-868j)  +/-  (2.88e-69, 4.67e-189j)
| (5.1524009288004387113e-06 + 1.2948143247204177209e-861j)  +/-  (1.5e-62, 2.43e-182j)
| (8.8629699145193867083e-15 + 2.698885424726357406e-867j)  +/-  (1.73e-68, 2.8e-188j)
| (0.011422954464215061371 + 9.6748160202769683137e-860j)  +/-  (1.3e-56, 2.11e-176j)
| (5.9662695529006535617e-08 + 5.4746135521658392066e-864j)  +/-  (6.63e-67, 1.07e-186j)
| (0.0012591892162710440991 + 1.8754708359087227968e-860j)  +/-  (6.92e-62, 1.12e-181j)
| (3.3483405953943038115e-05 - 4.9122934530394126295e-862j)  +/-  (2.79e-65, 4.51e-185j)
| (4.4591342885305721045e-09 + 2.6425820084608464316e-863j)  +/-  (4.43e-67, 7.18e-187j)
| (0.09830288105503219667 - 2.3307823716500499054e-859j)  +/-  (7.72e-58, 1.26e-177j)
| (0.09830288105503219667 - 1.5819543095285776697e-859j)  +/-  (2.75e-58, 4.48e-178j)
| (0.14288198180681904288 + 3.2033354688670538129e-859j)  +/-  (5.26e-58, 8.57e-178j)
| (3.7128135038430283695e-13 + 4.0164674227547752958e-867j)  +/-  (4.66e-71, 7.6e-191j)
| (-0.21178598743534163003 + 3.8289796787766685379e-858j)  +/-  (7.16e-59, 1.15e-178j)
| (0.2621303381792102909 - 2.2133617721121544459e-858j)  +/-  (5.93e-59, 9.48e-179j)
| (2.575972159711384965e-10 - 2.3953728069530805451e-864j)  +/-  (3.51e-68, 5.63e-188j)
| (5.1524009288004387113e-06 + 1.1537968660212992044e-862j)  +/-  (1.06e-66, 1.69e-186j)
| (0.011422954464215061371 + 3.9374184978346541443e-860j)  +/-  (1.71e-63, 2.74e-183j)
| (1.1322514810654023018e-11 - 2.9168003315188295439e-866j)  +/-  (1.93e-70, 3.19e-190j)
| (3.3483405953943038115e-05 - 3.5469272964804460843e-861j)  +/-  (4.45e-66, 7.73e-186j)
| (0.14288198180681904288 + 4.0190140760193366913e-859j)  +/-  (5.2e-63, 1.03e-182j)
| (0.0001669500899118988131 + 2.0495321731483766087e-861j)  +/-  (1.45e-65, 2.26e-185j)
| (0.2621303381792102909 - 2.0964194809401361625e-858j)  +/-  (1.56e-62, 3.5e-182j)
