Starting with polynomial:
P : t^7 - 21*t^5 + 105*t^3 - 105*t
Extension levels are: 7 50
-------------------------------------------------
Trying to find an order 50 Kronrod extension for:
P1 : t^7 - 21*t^5 + 105*t^3 - 105*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^57 - 9486404713707924363988176269132286335371473938329/6536537506862970963870041612472645306620540974*t^55 + 19164546566724001585274782691598315282298498199076535/19609612520588912891610124837417935919861622922*t^53 - 29193611267589114648740094774150568181880571547559779295/71901912575492680602570457737199098372825950714*t^51 + 8392485544137589723242753689303636583766799144716553352625/71901912575492680602570457737199098372825950714*t^49 - 38586693140491090221676977875332259421111340783207621031275/1563085055988971317447183863852154312452738059*t^47 + 6232289163141975104853664083976313680653778417881825688418775/1563085055988971317447183863852154312452738059*t^45 - 71606301945491080220021565020310287064749256622190228384318625/142098641453542847040653078532014028404794369*t^43 + 7199313140612621264755613409651732397623807239015457436119516750/142098641453542847040653078532014028404794369*t^41 - 1164615220822154136272980955265146437853463023273457814909947283125/284197282907085694081306157064028056809588738*t^39 + 76350574765417696626481465593316954144812062190239006964438656243625/284197282907085694081306157064028056809588738*t^37 - 4075795438051680668407164136075323112750092012976863036776450275208625/284197282907085694081306157064028056809588738*t^35 + 177572033272013828746858248207215732055908875045185019593674784824251875/284197282907085694081306157064028056809588738*t^33 - 3157848017548020515038585142076379194631302216357946960361088754770333750/142098641453542847040653078532014028404794369*t^31 + 91548180120684036047253636691555502850654331278952549844575456828709868750/142098641453542847040653078532014028404794369*t^29 - 2156134129887723551005715158994639449798968863007438180166449380146698603750/142098641453542847040653078532014028404794369*t^27 + 41042193613416579476634872922767410951468304119791546274719557848181014625625/142098641453542847040653078532014028404794369*t^25 - 1253831142573620794499997880842264349103064464633169632934147336259223339015625/284197282907085694081306157064028056809588738*t^23 + 15224374409652672275660689882277440055572248428813870234892569684654184013078125/284197282907085694081306157064028056809588738*t^21 - 145162176967367365062133128144079667183732984849799779612438010781117651206328125/284197282907085694081306157064028056809588738*t^19 + 1069897128374408161656526914555902583678039725188314016773491188760092606272796875/284197282907085694081306157064028056809588738*t^17 - 2986110380104523241970389556185864412846849952632336545894968388094105195570265625/142098641453542847040653078532014028404794369*t^15 + 12289220988841566935170670729354818350881215751686497352013437423810562783181328125/142098641453542847040653078532014028404794369*t^13 - 35959472704321700716862604579546944218336349629341403221880561259262241830873515625/142098641453542847040653078532014028404794369*t^11 + 71120732156563523760106675390363165774279733725833699743850010603435024178353125000/142098641453542847040653078532014028404794369*t^9 - 176580526496200316084417499422523508489665223819475281897557244700590807145551921875/284197282907085694081306157064028056809588738*t^7 + 122463203540870776731868272354616512674335354101420905795428808846992256027234109375/284197282907085694081306157064028056809588738*t^5 - 38583638692680639631987824976547091793239227202576336739486211715983009372662734375/284197282907085694081306157064028056809588738*t^3 + 3451477926405291624802425198377682914298993076555670896287536604504143207440078125/284197282907085694081306157064028056809588738*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
Positive weights:   57 out of 57
Indefinite weights: 0 out of 57
Negative weights:   0 out of 57
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (8.8886434700659730472 - 1.1551241978347621227e-938j)  +/-  (9.07e-242, 9.07e-242j)
| (-4.5996752801635594045 + 1.1312222153751574637e-945j)  +/-  (5.74e-244, 5.74e-244j)
| (11.209882830202730607 + 4.8588236930723061891e-944j)  +/-  (6.35e-243, 6.35e-243j)
| (5.9464932653164713902 + 1.3446089888627787243e-944j)  +/-  (1.17e-242, 1.17e-242j)
| (-7.8601321502070412065 - 1.175019461994480372e-942j)  +/-  (9.43e-242, 9.43e-242j)
| (12.651345242749305745 + 3.2895328843667755091e-948j)  +/-  (2.06e-244, 2.06e-244j)
| (-8.8886434700659730472 - 1.9247722570643924684e-944j)  +/-  (8.99e-242, 8.99e-242j)
| (13.570050315181742262 + 6.3940893052078703728e-949j)  +/-  (1.17e-245, 1.17e-245j)
| (-11.209882830202730607 + 6.8459129271483911107e-948j)  +/-  (6.45e-243, 6.45e-243j)
| (-1.9627863235036798593 - 3.5323555430876759111e-953j)  +/-  (6.73e-249, 6.73e-249j)
| (-5.0410569605026490211 + 6.6415002378489225237e-946j)  +/-  (1.68e-243, 1.68e-243j)
| (-6.8837251656145069691 - 3.0846008974403611391e-944j)  +/-  (4.39e-242, 4.39e-242j)
| (-11.890007195324845159 + 3.6774049897851739788e-949j)  +/-  (1.53e-243, 1.53e-243j)
| (-3.0714585469891952922 - 1.6045305419674213151e-950j)  +/-  (4.74e-246, 4.74e-246j)
| (-8.3667877758324345912 - 3.4613143733284601226e-945j)  +/-  (9.29e-242, 9.29e-242j)
| (3.7504397177257422563 + 1.0932050529561895023e-948j)  +/-  (4.64e-245, 4.64e-245j)
| (7.8601321502070412065 - 1.1449604696000643533e-944j)  +/-  (9.84e-242, 9.84e-242j)
| (-9.428735414419603812 - 2.283908560386594921e-951j)  +/-  (7.3e-242, 7.3e-242j)
| (-6.4107912009505645646 + 6.9093610423442148388e-952j)  +/-  (2.53e-242, 2.53e-242j)
| (6.8837251656145069691 + 1.8984648320037711024e-950j)  +/-  (4.38e-242, 4.38e-242j)
| (-13.570050315181742262 + 8.0508438050036874294e-958j)  +/-  (1.18e-245, 1.18e-245j)
| (-12.651345242749305745 - 1.0581869360557302337e-956j)  +/-  (2.27e-244, 2.27e-244j)
| (-5.4900543644183483326 + 5.7742688266369454232e-955j)  +/-  (5e-243, 5e-243j)
| (-2.7514064174973684361 + 6.3579363665922382777e-959j)  +/-  (8.04e-247, 8.04e-247j)
| (-5.9464932653164713902 - 8.6147852738116319997e-955j)  +/-  (1.11e-242, 1.11e-242j)
| (10.581929218902525851 + 2.3207379622941002066e-952j)  +/-  (1.94e-242, 1.94e-242j)
| (-7.3663732190624306392 - 1.1083835788169667093e-964j)  +/-  (6.94e-242, 6.94e-242j)
| (9.9911989883565408453 - 2.9645541598271644491e-966j)  +/-  (4.41e-242, 4.41e-242j)
| (-3.3723674974686665579 + 4.1630374722172270873e-981j)  +/-  (1.61e-245, 1.61e-245j)
| (4.5996752801635594045 - 1.1126035669020259387e-977j)  +/-  (5.46e-244, 5.46e-244j)
| (-4.1674616716092469176 + 7.1651445162886717772e-980j)  +/-  (1.53e-244, 1.53e-244j)
| (-10.581929218902525851 - 3.9372806157760856451e-978j)  +/-  (1.87e-242, 1.87e-242j)
| (8.3667877758324345912 + 7.3811316331115133859e-987j)  +/-  (9.53e-242, 9.53e-242j)
| (5.4900543644183483326 - 8.5500117016857170891e-993j)  +/-  (4.64e-243, 4.64e-243j)
| (6.4107912009505645646 - 2.885611979371257226e-995j)  +/-  (2.49e-242, 2.49e-242j)
| (-9.9911989883565408453 - 1.052495567611028082e-999j)  +/-  (4e-242, 4e-242j)
| (3.3723674974686665579 + 5.9628668915091476223e-1002j)  +/-  (1.61e-245, 1.61e-245j)
| (0.75997552670551499416 - 1.4335356174047400093e-1008j)  +/-  (2.07e-252, 2.07e-252j)
| (-1.1544053947399681272 - 3.5726914094879518632e-1009j)  +/-  (3.04e-251, 3.04e-251j)
| (11.890007195324845159 - 3.4865882285691538734e-998j)  +/-  (1.51e-243, 1.51e-243j)
| (4.1674616716092469176 - 1.2222072622545941993e-1005j)  +/-  (1.51e-244, 1.51e-244j)
| (5.0410569605026490211 + 9.8271764899788256669e-1005j)  +/-  (1.74e-243, 1.74e-243j)
| (2.7514064174973684361 - 1.8255100387932852389e-1015j)  +/-  (8.31e-247, 8.31e-247j)
| (1.5566390802224470764 + 1.0658151996299087288e-1022j)  +/-  (4.49e-250, 4.49e-250j)
| (2.3667594107345412886 + 3.4957864442746778197e-1017j)  +/-  (7.83e-248, 7.83e-248j)
| (-2.3667594107345412886 - 2.2914615907250684439e-1021j)  +/-  (7.67e-248, 7.67e-248j)
| (-1.5566390802224470764 - 2.9040231205204025992e-1023j)  +/-  (4.09e-250, 4.09e-250j)
| (-7.2311548397302008053e-1037 + 4.693991899644741444e-1037j)  +/-  (4.91e-1035, 4.91e-1035j)
| (0.37583297813142546528 + 2.048982229002279061e-1026j)  +/-  (1.23e-253, 1.23e-253j)
| (1.9627863235036798593 + 1.8737744834318532691e-1022j)  +/-  (5.98e-249, 5.98e-249j)
| (9.428735414419603812 + 6.6497012997757723795e-1019j)  +/-  (7.66e-242, 7.66e-242j)
| (-0.37583297813142546528 - 2.3228550989113157748e-1053j)  +/-  (1.23e-253, 1.23e-253j)
| (7.3663732190624306392 - 1.0524579908105610479e-1047j)  +/-  (6.81e-242, 6.81e-242j)
| (1.1544053947399681272 + 2.4085153390306892557e-1068j)  +/-  (2.9e-251, 2.9e-251j)
| (3.0714585469891952922 - 1.0351411419344132458e-1065j)  +/-  (4.82e-246, 4.82e-246j)
| (-3.7504397177257422563 + 6.2661275731530960274e-1071j)  +/-  (4.54e-245, 4.54e-245j)
| (-0.75997552670551499416 - 7.2390027530873647987e-1078j)  +/-  (2.13e-252, 2.13e-252j)
-------------------------------------------------
The weights are:
| (1.47618725626685955e-18 + 8.2099841662000388412e-956j)  +/-  (1.47e-57, 2.08e-177j)
| (4.4407315351346448893e-06 - 1.0156391651578422998e-950j)  +/-  (1.34e-42, 1.9e-162j)
| (1.3406446787906799345e-28 - 3.3168713886122464449e-962j)  +/-  (1.94e-63, 2.76e-183j)
| (3.8496557513102393181e-09 + 9.8594814638346247315e-952j)  +/-  (4.61e-49, 6.55e-169j)
| (7.6568129359767082034e-15 + 7.9918487701632531551e-956j)  +/-  (1e-56, 1.43e-176j)
| (5.7353453792023495549e-36 - 2.8944480326915467446e-966j)  +/-  (7.45e-67, 1.06e-186j)
| (1.47618725626685955e-18 + 1.0875646158450907447e-957j)  +/-  (4.66e-60, 6.63e-180j)
| (4.3622962228443769364e-41 + 5.158393091729796619e-969j)  +/-  (5.4e-69, 7.67e-189j)
| (1.3406446787906799345e-28 + 4.0637194785904370733e-963j)  +/-  (2.5e-66, 3.55e-186j)
| (0.023625017752111842632 + 8.28722781773834319e-948j)  +/-  (4.14e-30, 5.88e-150j)
| (5.3870695763144512896e-07 + 9.0933826662704585102e-951j)  +/-  (1.33e-48, 1.9e-168j)
| (9.7789884665329470253e-12 + 5.160458921298768784e-954j)  +/-  (2.7e-55, 3.83e-175j)
| (5.7011683379299562726e-32 - 6.6882255124617330367e-965j)  +/-  (2.44e-68, 3.46e-188j)
| (0.0010121498170993995733 - 3.0755782054922286023e-948j)  +/-  (1.44e-41, 2.04e-161j)
| (1.2904246636700197453e-16 - 1.383516071243739465e-956j)  +/-  (2.82e-59, 4.01e-179j)
| (0.00014234796152392442166 - 1.010019342455936287e-948j)  +/-  (1.02e-48, 1.45e-168j)
| (7.6568129359767082034e-15 + 1.8037678073650183405e-954j)  +/-  (5.05e-62, 7.17e-182j)
| (1.0889963382729770044e-20 - 7.255058555000391309e-959j)  +/-  (1.21e-62, 1.72e-182j)
| (2.2244018473065671533e-10 - 3.7809002177396670512e-953j)  +/-  (2.05e-55, 2.92e-175j)
| (9.7789884665329470253e-12 + 5.3100745421346052763e-953j)  +/-  (1.8e-60, 2.56e-180j)
| (4.3622962228443769364e-41 - 1.1210378719820294779e-969j)  +/-  (1.35e-73, 1.92e-193j)
| (5.7353453792023495549e-36 + 5.298588735928398784e-967j)  +/-  (3.73e-71, 5.31e-191j)
| (5.1491722329091991829e-08 - 1.2144036062212718816e-951j)  +/-  (1.11e-54, 1.57e-174j)
| (0.0032737332899493496369 + 4.5214790821383396821e-948j)  +/-  (4.64e-47, 6.59e-167j)
| (3.8496557513102393181e-09 + 2.3100597595071328973e-952j)  +/-  (8.89e-56, 1.26e-175j)
| (1.1719379982589031984e-25 + 1.6142741744305193145e-960j)  +/-  (2.67e-72, 3.79e-192j)
| (3.2071434899922759974e-13 - 8.9143156062980725767e-955j)  +/-  (9.58e-60, 1.36e-179j)
| (4.8347670785095203873e-23 - 6.0517752631424945993e-959j)  +/-  (2.38e-71, 3.38e-191j)
| (0.00046131823206685715281 + 1.3486700862921876611e-948j)  +/-  (9.94e-52, 1.41e-171j)
| (4.4407315351346448893e-06 - 7.2946279502053956531e-950j)  +/-  (4.3e-61, 6.11e-181j)
| (2.8794555913610749434e-05 + 5.8026742297567099227e-950j)  +/-  (4.69e-54, 6.66e-174j)
| (1.1719379982589031984e-25 - 1.5017487077796983058e-961j)  +/-  (1.3e-68, 1.84e-188j)
| (1.2904246636700197453e-16 - 3.7344188140945720531e-955j)  +/-  (1.67e-68, 2.37e-188j)
| (5.1491722329091991829e-08 - 4.4511804841596309442e-951j)  +/-  (1.06e-63, 1.51e-183j)
| (2.2244018473065671533e-10 - 2.7527235725350207665e-952j)  +/-  (2.84e-65, 4.04e-185j)
| (4.8347670785095203873e-23 + 3.8236212366565236694e-960j)  +/-  (1.65e-68, 2.35e-188j)
| (0.00046131823206685715281 + 3.4186381246082618837e-948j)  +/-  (1.35e-60, 1.92e-180j)
| (0.11640568125978333565 - 2.8121262347400637558e-947j)  +/-  (2.87e-52, 4.08e-172j)
| (0.081734330661398683675 + 1.707153356954311249e-947j)  +/-  (2.87e-52, 4.07e-172j)
| (5.7011683379299562726e-32 + 4.3938414974353384479e-964j)  +/-  (7.2e-77, 1.02e-196j)
| (2.8794555913610749434e-05 + 2.7249462860921324004e-949j)  +/-  (4.46e-62, 6.33e-182j)
| (5.3870695763144512896e-07 + 1.8810853479846136757e-950j)  +/-  (1.81e-63, 2.57e-183j)
| (0.0032737332899493496369 + 9.243074350135593631e-948j)  +/-  (5.74e-61, 8.15e-181j)
| (0.048095224141129063854 - 1.7552596960497221627e-947j)  +/-  (6.29e-59, 8.93e-179j)
| (0.0096748149739090408548 - 1.081174124415319224e-947j)  +/-  (9.59e-61, 1.36e-180j)
| (0.0096748149739090408548 - 5.9237299877287724247e-948j)  +/-  (3.11e-60, 4.43e-180j)
| (0.048095224141129063854 - 1.1951247259935015984e-947j)  +/-  (2.41e-59, 3.41e-179j)
| (0.14924889034877221981 - 3.3086335206649911621e-947j)  +/-  (6.06e-59, 8.58e-179j)
| (0.14091710716831026051 + 3.2343414261431860704e-947j)  +/-  (5.53e-59, 7.84e-179j)
| (0.023625017752111842632 + 1.3536278159711040011e-947j)  +/-  (2.22e-60, 3.15e-180j)
| (1.0889963382729770044e-20 + 2.235974875542856123e-957j)  +/-  (2.64e-73, 3.76e-193j)
| (0.14091710716831026051 + 2.9524979488659152804e-947j)  +/-  (1.34e-60, 1.77e-180j)
| (3.2071434899922759974e-13 - 9.8863368495274853141e-954j)  +/-  (3.39e-69, 4.82e-189j)
| (0.081734330661398683675 + 2.2646023011629690556e-947j)  +/-  (2.81e-61, 3.78e-181j)
| (0.0010121498170993995733 - 6.9744720393883377698e-948j)  +/-  (2.05e-62, 2.9e-182j)
| (0.00014234796152392442166 - 3.322753150684996849e-949j)  +/-  (7.38e-64, 1.25e-183j)
| (0.11640568125978333565 - 2.3372670332830372975e-947j)  +/-  (2.71e-61, 3.07e-181j)
