Starting with polynomial:
P : 64*t^6 - 480*t^4 + 720*t^2 - 120
Extension levels are: 6 41
-------------------------------------------------
Trying to find an order 41 Kronrod extension for:
P1 : 64*t^6 - 480*t^4 + 720*t^2 - 120
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 64*t^47 - 527071428867678891335024735464482908526880/16188442151594219121643968296810508779*t^45 + 3303060409196417247527898901971904568259280/437525463556600516801188332346229967*t^43 - 120023300106815050037211253700575220449277914440/113319095061159533851507778077673561453*t^41 + 11406994093435743440793267440002167516112171512300/113319095061159533851507778077673561453*t^39 - 779185289814859325256469588150216864199911933238370/113319095061159533851507778077673561453*t^37 + 1070577821541427234295366137199953464168653247574725/3062678244896203617608318326423609769*t^35 - 11824505386910208941266386109693601651191263387707925/875050927113201033602376664692459934*t^33 + 352183218545770880649230041970366452752185956083614475/875050927113201033602376664692459934*t^31 - 16281101861549444934328550268016058383618939643725193625/1750101854226402067204753329384919868*t^29 + 1529226247328797244003642299886625514238722297060505775/9138913076900271891408633573811592*t^27 - 16376461923645147790354961782145200412372750954588465895375/7000407416905608268819013317539679472*t^25 + 354203546400365121604641945172753717768282117849463386625625/14000814833811216537638026635079358944*t^23 - 5876065341774861939076594689656341280695394214366516433486875/28001629667622433075276053270158717888*t^21 + 73836091780555719678242928611866621150889659073352705470221875/56003259335244866150552106540317435776*t^19 - 690641229656138952648624478229994942119763139372246584188233125/112006518670489732301104213080634871552*t^17 + 9394927236451280538775336638150443127911117408636503629154696875/448026074681958929204416852322539486208*t^15 - 45028446568573706963240603727893085176750713286060222262812315625/896052149363917858408833704645078972416*t^13 + 145757518145355264926601197884629965623903839654680295194604590625/1792104298727835716817667409290157944832*t^11 - 300643198216446261764642514833742816220412196165499414919380359375/3584208597455671433635334818580315889664*t^9 + 364370741402025414221528140380709816134443203958022651197775103125/7168417194911342867270669637160631779328*t^7 - 231735035799038062654492104636697525475208702693831741888999609375/14336834389822685734541339274321263558656*t^5 + 66306062691762510099444243724060850693187666582382796261315484375/28673668779645371469082678548642527117312*t^3 - 6486660812951389248492850895671098532993880187519949428960140625/57347337559290742938165357097285054234624*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:
| (7.0151938339434198513 + 7.3579081439871788926e-871j)  +/-  (5.96e-245, 5.96e-245j)
| (8.1140888780193462516 + 3.0612988679653951225e-883j)  +/-  (3.25e-246, 3.25e-246j)
| (-8.8390082633083679455 - 2.857179578433715275e-891j)  +/-  (2.34e-247, 2.34e-247j)
| (-4.1195574730497532381 + 4.1513731322599078522e-886j)  +/-  (6.36e-245, 6.36e-245j)
| (-8.1140888780193462516 + 1.7749942316912322328e-890j)  +/-  (3.21e-246, 3.21e-246j)
| (-7.5309047619671544898 + 1.2219716070270003808e-888j)  +/-  (1.9e-245, 1.9e-245j)
| (-7.0151938339434198513 - 3.6169468918961637281e-888j)  +/-  (7.12e-245, 7.12e-245j)
| (-5.266855900234435994 + 6.1871602278607937235e-892j)  +/-  (2.87e-244, 2.87e-244j)
| (-2.6949188449413679115 + 3.2869758143136594713e-907j)  +/-  (5.81e-247, 5.81e-247j)
| (6.0963953019723864976 - 4.8331812785867681371e-907j)  +/-  (2.3e-244, 2.3e-244j)
| (8.8390082633083679455 + 1.1720158000919913967e-923j)  +/-  (2.32e-247, 2.32e-247j)
| (5.6732013226594396628 - 4.0956400238687107649e-932j)  +/-  (3.15e-244, 3.15e-244j)
| (-3.7546047839370382694 - 2.6734951130071212022e-950j)  +/-  (2.68e-245, 2.68e-245j)
| (-1.6715203964488062534 + 2.0741018068342139579e-955j)  +/-  (2.72e-249, 2.72e-249j)
| (6.5412523712333969958 + 9.1249656656782614345e-950j)  +/-  (1.37e-244, 1.37e-244j)
| (1.3358490740136969497 - 1.1525674884728131739e-966j)  +/-  (2.92e-250, 2.92e-250j)
| (5.266855900234435994 + 3.1834617947114839771e-958j)  +/-  (2.89e-244, 2.89e-244j)
| (-6.5412523712333969958 + 1.5842784206332472387e-964j)  +/-  (1.34e-244, 1.34e-244j)
| (-1.0025645314884142815 - 4.8026860464361112772e-972j)  +/-  (3.39e-251, 3.39e-251j)
| (7.5309047619671544898 + 6.7859768712945063719e-966j)  +/-  (1.76e-245, 1.76e-245j)
| (2.3506049736744922228 + 2.5314659797851452765e-969j)  +/-  (1.07e-247, 1.07e-247j)
| (1.6715203964488062534 - 1.4383679279458255975e-971j)  +/-  (2.55e-249, 2.55e-249j)
| (-5.6732013226594396628 + 1.5679752676008125022e-965j)  +/-  (2.98e-244, 2.98e-244j)
| (3.0431957870625358263 - 6.9179912572608670053e-968j)  +/-  (2.35e-246, 2.35e-246j)
| (-1.3358490740136969497 - 2.8704846900757171491e-972j)  +/-  (3.04e-250, 3.04e-250j)
| (3.3961469243401314713 + 8.4971298560916605868e-967j)  +/-  (8.19e-246, 8.19e-246j)
| (2.0096436639414367988 - 4.7476552558630368333e-973j)  +/-  (1.79e-248, 1.79e-248j)
| (-2.0096436639414367988 + 1.1901181739808801903e-973j)  +/-  (1.79e-248, 1.79e-248j)
| (-4.8740075655985038561 - 1.6784930266797726746e-967j)  +/-  (2.07e-244, 2.07e-244j)
| (-0.67363928554479924218 - 1.4471227261112603366e-976j)  +/-  (3.63e-252, 3.63e-252j)
| (4.4921995334618140618 + 1.8606028844182845901e-968j)  +/-  (1.32e-244, 1.32e-244j)
| (2.6949188449413679115 + 1.2804398634419722175e-977j)  +/-  (5.73e-247, 5.73e-247j)
| (0.43607741192761650868 + 9.9445758372716161645e-984j)  +/-  (8.78e-253, 8.78e-253j)
| (1.0025645314884142815 + 2.5133819395426792911e-982j)  +/-  (3.61e-251, 3.61e-251j)
| (-2.3506049736744922228 + 1.9990356304818179471e-978j)  +/-  (1.09e-247, 1.09e-247j)
| (4.8740075655985038561 + 2.3652173326166227079e-974j)  +/-  (2.08e-244, 2.08e-244j)
| (3.7546047839370382694 - 1.3065342112552918712e-979j)  +/-  (2.66e-245, 2.66e-245j)
| (0.67363928554479924218 - 2.0941365266168569325e-991j)  +/-  (3.54e-252, 3.54e-252j)
| (-6.0963953019723864976 - 1.0502589562724048167e-982j)  +/-  (2.61e-244, 2.61e-244j)
| (-3.3961469243401314713 + 1.1671921836604969288e-983j)  +/-  (9.97e-246, 9.97e-246j)
| (-0.31778030971023022054 + 7.3850298194736701848e-992j)  +/-  (2.3e-253, 2.3e-253j)
| (-3.0431957870625358263 - 1.3816889489530074559e-984j)  +/-  (2.62e-246, 2.62e-246j)
| (0.31778030971023022054 - 7.240748803991708982e-992j)  +/-  (2.3e-253, 2.3e-253j)
| (1.0781499335293885521e-1002 + 5.9917174359191687982e-1003j)  +/-  (5.8e-1001, 5.8e-1001j)
| (-4.4921995334618140618 - 1.1373421306449099535e-989j)  +/-  (1.27e-244, 1.27e-244j)
| (-0.43607741192761650868 + 1.0186968201475248506e-998j)  +/-  (8.51e-253, 8.51e-253j)
| (4.1195574730497532381 + 6.8764563509871717969e-1000j)  +/-  (6.59e-245, 6.59e-245j)
-------------------------------------------------
The weights are:
| (1.1762941366610946005e-22 - 6.1863684177337681296e-892j)  +/-  (1.85e-81, 1.5e-203j)
| (9.1111302057580507757e-30 + 2.0528292198756243652e-896j)  +/-  (2.13e-84, 1.73e-206j)
| (5.7280419654552226944e-35 + 3.9571297796540193092e-900j)  +/-  (1.64e-87, 1.33e-209j)
| (8.8644041484651151005e-09 + 1.5084518111323551952e-886j)  +/-  (1.24e-73, 1.01e-195j)
| (9.1111302057580507757e-30 - 1.4910448041244360893e-897j)  +/-  (4.63e-86, 3.76e-208j)
| (7.1722662270143139262e-26 + 1.393935599767562801e-895j)  +/-  (5.13e-85, 4.17e-207j)
| (1.1762941366610946005e-22 - 6.1687989817929855042e-894j)  +/-  (3.93e-84, 3.19e-206j)
| (2.0197881889708258572e-13 - 4.284422133672723991e-889j)  +/-  (4.64e-80, 3.77e-202j)
| (0.00013697223196759176706 + 4.805876160160544171e-884j)  +/-  (3.68e-70, 2.99e-192j)
| (1.7659062081773396715e-17 - 4.3040235958365572803e-890j)  +/-  (4.05e-85, 3.29e-207j)
| (5.7280419654552226944e-35 - 3.4398859162408341047e-899j)  +/-  (3.14e-92, 2.55e-214j)
| (2.4585828066700962647e-15 + 3.8551330250360657333e-889j)  +/-  (1.58e-84, 1.28e-206j)
| (1.5391813687027023809e-07 - 7.6996187395635037997e-886j)  +/-  (1.08e-77, 8.79e-200j)
| (0.011626489065011771439 - 1.3072787002244475968e-882j)  +/-  (1.03e-67, 8.4e-190j)
| (6.7540961549774192709e-20 + 4.7149557619651274591e-891j)  +/-  (1.73e-86, 1.41e-208j)
| (0.031684676416015896083 + 5.3446278961996841184e-882j)  +/-  (3.35e-67, 2.72e-189j)
| (2.0197881889708258572e-13 - 3.0098006780660642669e-888j)  +/-  (2.62e-84, 2.13e-206j)
| (6.7540961549774192709e-20 + 1.6483766976931066827e-892j)  +/-  (2.6e-87, 2.12e-209j)
| (0.068530228511217943377 - 1.0759134553187267125e-881j)  +/-  (2.34e-66, 1.9e-188j)
| (7.1722662270143139262e-26 - 3.9317229393857107157e-894j)  +/-  (2.78e-89, 2.26e-211j)
| (0.00077004246134112339968 - 3.1119245957762138292e-883j)  +/-  (2e-76, 1.62e-198j)
| (0.011626489065011771439 - 2.1251217080968985807e-882j)  +/-  (1.11e-72, 9.02e-195j)
| (2.4585828066700962647e-15 + 4.077394730873879446e-890j)  +/-  (5.5e-86, 4.47e-208j)
| (1.879651324256194465e-05 - 3.4340682587108441044e-884j)  +/-  (7.08e-80, 5.75e-202j)
| (0.031684676416015896083 + 3.6347537548165460815e-882j)  +/-  (8.19e-73, 6.65e-195j)
| (1.9645318681801157975e-06 + 9.8780946443726892417e-885j)  +/-  (2.7e-81, 2.19e-203j)
| (0.0033748084556455907316 + 8.3393917638304362526e-883j)  +/-  (1.14e-75, 9.23e-198j)
| (0.0033748084556455907316 + 4.6253734970230762455e-883j)  +/-  (4.54e-77, 3.69e-199j)
| (1.0520346586903371141e-11 + 3.6278979488566738378e-888j)  +/-  (1.58e-85, 1.29e-207j)
| (0.11579723291745267366 + 4.3216783111193037284e-881j)  +/-  (7.35e-73, 5.97e-195j)
| (3.6619215531675927828e-10 - 1.1601457584852628796e-886j)  +/-  (3.66e-85, 2.97e-207j)
| (0.00013697223196759176706 + 1.0801534282581261075e-883j)  +/-  (8.14e-80, 6.61e-202j)
| (0.029960889889101616277 - 1.7555838104666223689e-880j)  +/-  (5.64e-75, 4.58e-197j)
| (0.068530228511217943377 - 1.4347157701723232434e-881j)  +/-  (2.52e-75, 2.05e-197j)
| (0.00077004246134112339968 - 1.5498783656449510461e-883j)  +/-  (2.04e-80, 1.66e-202j)
| (1.0520346586903371141e-11 + 2.0144352464955375822e-887j)  +/-  (6.4e-86, 5.2e-208j)
| (1.5391813687027023809e-07 - 2.5432011425432141644e-885j)  +/-  (1.36e-83, 1.1e-205j)
| (0.11579723291745267366 + 5.2398292895826876883e-881j)  +/-  (3.9e-77, 3.17e-199j)
| (1.7659062081773396715e-17 - 3.0160573689317225084e-891j)  +/-  (2.43e-90, 1.97e-212j)
| (1.9645318681801157975e-06 + 3.4336873429652000213e-885j)  +/-  (5.85e-85, 4.75e-207j)
| (0.14625212200759523977 + 1.6453422981008087454e-880j)  +/-  (1.35e-79, 1.09e-201j)
| (1.879651324256194465e-05 - 1.3560930917472822722e-884j)  +/-  (2.74e-84, 2.22e-206j)
| (0.14625212200759523977 + 1.80147940315888649e-880j)  +/-  (2.13e-79, 1.72e-201j)
| (0.18369122768016367134 - 9.1118970662077083415e-881j)  +/-  (5.68e-80, 4.61e-202j)
| (3.6619215531675927828e-10 - 2.5436176925720274606e-887j)  +/-  (2.44e-87, 1.99e-209j)
| (0.029960889889101616277 - 1.5500966091807748619e-880j)  +/-  (4.01e-80, 3.22e-202j)
| (8.8644041484651151005e-09 + 5.800532880421394601e-886j)  +/-  (8.13e-87, 6.48e-209j)
