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
Positive weights:   56 out of 57
Indefinite weights: 0 out of 57
Negative weights:   1 out of 57
Extension rule has valid weights: 0
**************************************
*** EXTENSION WITH INVALID WEIGHTS ***
**************************************
