Starting with polynomial:
P : t^6 - 15*t^4 + 45*t^2 - 15
Extension levels are: 6 41
-------------------------------------------------
Trying to find an order 41 Kronrod extension for:
P1 : t^6 - 15*t^4 + 45*t^2 - 15
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^47 - 16470982152114965354219522983265090891465/16188442151594219121643968296810508779*t^45 + 206441275574776077970493681373244035516205/437525463556600516801188332346229967*t^43 - 15002912513351881254651406712571902556159739305/113319095061159533851507778077673561453*t^41 + 2851748523358935860198316860000541879028042878075/113319095061159533851507778077673561453*t^39 - 389592644907429662628234794075108432099955966619185/113319095061159533851507778077673561453*t^37 + 1070577821541427234295366137199953464168653247574725/3062678244896203617608318326423609769*t^35 - 11824505386910208941266386109693601651191263387707925/437525463556600516801188332346229967*t^33 + 704366437091541761298460083940732905504371912167228950/437525463556600516801188332346229967*t^31 - 32562203723098889868657100536032116767237879287450387250/437525463556600516801188332346229967*t^29 + 3058452494657594488007284599773251028477444594121011550/1142364134612533986426079196726449*t^27 - 32752923847290295580709923564290400824745501909176931790750/437525463556600516801188332346229967*t^25 + 708407092800730243209283890345507435536564235698926773251250/437525463556600516801188332346229967*t^23 - 11752130683549723878153189379312682561390788428733032866973750/437525463556600516801188332346229967*t^21 + 147672183561111439356485857223733242301779318146705410940443750/437525463556600516801188332346229967*t^19 - 1381282459312277905297248956459989884239526278744493168376466250/437525463556600516801188332346229967*t^17 + 9394927236451280538775336638150443127911117408636503629154696875/437525463556600516801188332346229967*t^15 - 45028446568573706963240603727893085176750713286060222262812315625/437525463556600516801188332346229967*t^13 + 145757518145355264926601197884629965623903839654680295194604590625/437525463556600516801188332346229967*t^11 - 300643198216446261764642514833742816220412196165499414919380359375/437525463556600516801188332346229967*t^9 + 364370741402025414221528140380709816134443203958022651197775103125/437525463556600516801188332346229967*t^7 - 231735035799038062654492104636697525475208702693831741888999609375/437525463556600516801188332346229967*t^5 + 66306062691762510099444243724060850693187666582382796261315484375/437525463556600516801188332346229967*t^3 - 6486660812951389248492850895671098532993880187519949428960140625/437525463556600516801188332346229967*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:   47 out of 47
Indefinite weights: 0 out of 47
Negative weights:   0 out of 47
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (8.6216049176369692372 + 8.6311734437729299621e-748j)  +/-  (3.27e-244, 3.27e-244j)
| (-7.4484590451762962213 - 1.0012708145627516307e-767j)  +/-  (3.74e-244, 3.74e-244j)
| (11.475054537595649553 + 1.6684659526578663852e-784j)  +/-  (4.88e-246, 4.88e-246j)
| (-10.650307651314074958 - 2.407438428192526172e-782j)  +/-  (2.59e-245, 2.59e-245j)
| (-12.500245363898551156 + 4.9761529286025917171e-788j)  +/-  (3.46e-247, 3.46e-247j)
| (-11.475054537595649553 + 3.7877863993830382247e-790j)  +/-  (4.66e-246, 4.66e-246j)
| (-6.8928876023784768907 + 2.0672878050856570133e-802j)  +/-  (2.96e-244, 2.96e-244j)
| (10.650307651314074958 + 4.0554498021115455752e-816j)  +/-  (2.88e-245, 2.88e-245j)
| (6.3529295051077876595 - 1.6220840910497910365e-814j)  +/-  (1.76e-244, 1.76e-244j)
| (-3.3242574335521189524 + 9.0598236537257796783e-819j)  +/-  (1.58e-247, 1.58e-247j)
| (4.80287704021348743 + 6.6970615713520141025e-820j)  +/-  (1.27e-245, 1.27e-245j)
| (-8.0231182525779608027 - 3.0695140169814115478e-817j)  +/-  (4.52e-244, 4.52e-244j)
| (-9.9209822626388943802 + 4.8088254039033857328e-827j)  +/-  (8.97e-245, 8.97e-245j)
| (9.9209822626388943802 - 2.5311901113141788893e-830j)  +/-  (8.66e-245, 8.66e-245j)
| (3.3242574335521189524 + 7.2277831963292935679e-836j)  +/-  (1.6e-247, 1.6e-247j)
| (2.8420653250831383955 - 5.6808247979361646922e-835j)  +/-  (2.44e-248, 2.44e-248j)
| (7.4484590451762962213 - 4.5767084929574197923e-830j)  +/-  (3.84e-244, 3.84e-244j)
| (-5.8259340493623970266 - 4.3468388354980010086e-842j)  +/-  (8.87e-245, 8.87e-245j)
| (12.500245363898551156 - 9.6718512212364203819e-850j)  +/-  (3.34e-247, 3.34e-247j)
| (5.3098130067946637298 - 4.041150419681807259e-848j)  +/-  (3.9e-245, 3.9e-245j)
| (9.2507278183034375714 - 1.3246883194807743245e-847j)  +/-  (2.07e-244, 2.07e-244j)
| (-9.2507278183034375714 + 1.5117492140171296242e-845j)  +/-  (1.94e-244, 1.94e-244j)
| (2.3638868144411544262 - 3.191068083077689682e-857j)  +/-  (3.82e-249, 3.82e-249j)
| (-3.8111907800109184732 + 1.8601679094921104448e-851j)  +/-  (8.24e-247, 8.24e-247j)
| (8.0231182525779608027 - 1.7167449702952276701e-851j)  +/-  (4.17e-244, 4.17e-244j)
| (5.8259340493623970266 + 1.6586629049518799691e-851j)  +/-  (9.24e-245, 9.24e-245j)
| (1.8891758777537106755 - 3.1024401655100497826e-863j)  +/-  (4.29e-250, 4.29e-250j)
| (6.8928876023784768907 + 6.756284650428166071e-856j)  +/-  (3.05e-244, 3.05e-244j)
| (-5.3098130067946637298 + 3.1314346601286951129e-878j)  +/-  (3.7e-245, 3.7e-245j)
| (-0.61670659019259415219 + 8.3770671299400551407e-901j)  +/-  (1.34e-252, 1.34e-252j)
| (-1.8891758777537106755 - 2.0355202837291054445e-897j)  +/-  (4.48e-250, 4.48e-250j)
| (-1.4178403575851433855 - 5.8598455613665176098e-902j)  +/-  (5.51e-251, 5.51e-251j)
| (1.4178403575851433855 + 9.907874313790491007e-904j)  +/-  (4.43e-251, 4.43e-251j)
| (-6.3529295051077876595 - 4.1082536185120620128e-912j)  +/-  (1.75e-244, 1.75e-244j)
| (-8.6216049176369692372 - 9.877716261928914923e-937j)  +/-  (3.38e-244, 3.38e-244j)
| (-4.80287704021348743 - 5.2533829791204796891e-954j)  +/-  (1.26e-245, 1.26e-245j)
| (0.95266981376477712897 + 1.1550034239774372563e-973j)  +/-  (5.64e-252, 5.64e-252j)
| (0.61670659019259415219 + 4.2480060301683167411e-974j)  +/-  (1.42e-252, 1.42e-252j)
| (3.8111907800109184732 - 5.3217608527335189819e-967j)  +/-  (8.07e-247, 8.07e-247j)
| (-0.95266981376477712897 + 3.9505331805700566718e-972j)  +/-  (5.57e-252, 5.57e-252j)
| (-0.44940922384733012818 - 6.3921696481197746244e-978j)  +/-  (3.31e-253, 3.31e-253j)
| (-2.8420653250831383955 + 6.1192987794068959079e-966j)  +/-  (2.66e-248, 2.66e-248j)
| (-1.022141862407910415e-982 - 3.8037157319206169072e-982j)  +/-  (1.85e-980, 1.85e-980j)
| (0.44940922384733012818 + 3.8412848409040364889e-981j)  +/-  (2.79e-253, 2.79e-253j)
| (-4.3037287550205035883 + 7.3185238289932353155e-975j)  +/-  (3.64e-246, 3.64e-246j)
| (-2.3638868144411544262 + 2.6867372133457345013e-982j)  +/-  (3.72e-249, 3.72e-249j)
| (4.3037287550205035883 + 5.0117325169732467244e-984j)  +/-  (3.59e-246, 3.59e-246j)
-------------------------------------------------
The weights are:
| (1.7659062081773396715e-17 - 6.811872760194883189e-764j)  +/-  (2.17e-80, 2.17e-201j)
| (2.0197881889708258572e-13 - 1.2620833920268118164e-763j)  +/-  (5.27e-78, 5.26e-199j)
| (9.1111302057580507757e-30 + 3.0470625368486262095e-771j)  +/-  (1.76e-86, 1.76e-207j)
| (7.1722662270143139262e-26 + 4.0551503892778017398e-770j)  +/-  (2e-85, 1.99e-206j)
| (5.7280419654552226944e-35 + 1.1448148866693298596e-774j)  +/-  (3.73e-89, 3.72e-210j)
| (9.1111302057580507757e-30 - 4.3264102957654483076e-772j)  +/-  (3.7e-87, 3.69e-208j)
| (1.0520346586903371141e-11 + 1.0715507083605063644e-762j)  +/-  (1.29e-78, 1.29e-199j)
| (7.1722662270143139262e-26 - 3.8522402744762235317e-769j)  +/-  (7.84e-88, 7.82e-209j)
| (3.6619215531675927828e-10 - 4.9727772114135188425e-761j)  +/-  (1.13e-79, 1.13e-200j)
| (0.00077004246134112339968 - 4.6834670611560753958e-758j)  +/-  (2.8e-69, 2.8e-190j)
| (1.9645318681801157975e-06 + 3.608205168954389453e-759j)  +/-  (1.3e-75, 1.3e-196j)
| (2.4585828066700962647e-15 + 1.197996157828665342e-764j)  +/-  (5.88e-82, 5.87e-203j)
| (1.1762941366610946005e-22 - 1.7990469840845931988e-768j)  +/-  (1.56e-85, 1.55e-206j)
| (1.1762941366610946005e-22 + 2.5673054615056036272e-767j)  +/-  (2.63e-87, 2.63e-208j)
| (0.00077004246134112339968 - 1.0561522159342344478e-757j)  +/-  (2.5e-72, 2.49e-193j)
| (0.0033748084556455907316 + 2.7837837291857250741e-757j)  +/-  (2.03e-70, 2.03e-191j)
| (2.0197881889708258572e-13 - 1.7288353743882002254e-762j)  +/-  (1.42e-83, 1.42e-204j)
| (8.8644041484651151005e-09 + 4.4808518044631309373e-761j)  +/-  (3.8e-81, 3.79e-202j)
| (5.7280419654552226944e-35 - 6.2343001294716709796e-774j)  +/-  (2e-93, 2e-214j)
| (1.5391813687027023809e-07 - 9.650643557166744117e-760j)  +/-  (9.7e-80, 9.68e-201j)
| (6.7540961549774192709e-20 - 1.3690186790619231921e-765j)  +/-  (6.71e-87, 6.69e-208j)
| (6.7540961549774192709e-20 + 4.8190743489573639311e-767j)  +/-  (1.46e-88, 1.45e-209j)
| (0.011626489065011771439 - 6.994396729582303963e-757j)  +/-  (2.48e-73, 2.48e-194j)
| (0.00013697223196759176706 + 1.4466736879628825551e-758j)  +/-  (1.48e-79, 1.48e-200j)
| (2.4585828066700962647e-15 + 3.3317892561688424866e-763j)  +/-  (4.73e-85, 4.72e-206j)
| (8.8644041484651151005e-09 + 2.3156259839086481134e-760j)  +/-  (7.1e-82, 7.08e-203j)
| (0.031684676416015896083 + 1.7377466605466215688e-756j)  +/-  (1.02e-74, 1.02e-195j)
| (1.0520346586903371141e-11 + 9.6167055787200717156e-762j)  +/-  (1.77e-83, 1.77e-204j)
| (1.5391813687027023809e-07 - 2.2941615448200088287e-760j)  +/-  (6.92e-85, 6.91e-206j)
| (0.029960889889101616277 - 4.8188019385550836728e-755j)  +/-  (2.19e-75, 2.19e-196j)
| (0.031684676416015896083 + 1.1130720266333339902e-756j)  +/-  (7.01e-78, 7e-199j)
| (0.068530228511217943377 - 3.3117925459841235729e-756j)  +/-  (5.88e-76, 5.87e-197j)
| (0.068530228511217943377 - 4.6154423497784221447e-756j)  +/-  (1.39e-75, 1.39e-196j)
| (3.6619215531675927828e-10 - 7.5338685484496114562e-762j)  +/-  (2.44e-86, 2.43e-207j)
| (1.7659062081773396715e-17 - 8.8393303299216401006e-766j)  +/-  (4.6e-90, 4.6e-211j)
| (1.9645318681801157975e-06 + 1.0263899723960671164e-759j)  +/-  (6.82e-85, 6.81e-206j)
| (0.11579723291745267366 + 1.6700149070399937354e-755j)  +/-  (6.32e-78, 6.31e-199j)
| (0.029960889889101616277 - 5.5612940454569670621e-755j)  +/-  (5.24e-78, 5.23e-199j)
| (0.00013697223196759176706 + 3.7390124610937458187e-758j)  +/-  (4.9e-83, 4.89e-204j)
| (0.11579723291745267366 + 1.3376716570064192453e-755j)  +/-  (7.47e-79, 7.46e-200j)
| (0.14625212200759523977 + 5.1265253768653703004e-755j)  +/-  (2.58e-78, 2.57e-199j)
| (0.0033748084556455907316 + 1.4034761938614908201e-757j)  +/-  (6.69e-83, 6.68e-204j)
| (0.18369122768016367134 - 2.8576096400432652526e-755j)  +/-  (4.98e-79, 4.98e-200j)
| (0.14625212200759523977 + 5.6903659594890914608e-755j)  +/-  (4.59e-79, 4.59e-200j)
| (1.879651324256194465e-05 - 4.0674172560398650276e-759j)  +/-  (9.77e-85, 9.76e-206j)
| (0.011626489065011771439 - 3.9842516023050174508e-757j)  +/-  (1.47e-82, 1.47e-203j)
| (1.879651324256194465e-05 - 1.2175598196957805872e-758j)  +/-  (6.42e-85, 6.33e-206j)
