Starting with polynomial:
P : t
Extension levels are: 1 8 48
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 48 Kronrod extension for:
P2 : t^9 - 36/17*t^7 + 126/85*t^5 - 84/221*t^3 + 63/2431*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^57 - 7799784237853161230267262437743721973810611051091947936741064876/548690853501721501530898924189894305034643899744150845899494709*t^55 + 905603959903232242912524960502355335870901399913155800037597526435055754/9461152719510685708035591360156683331125976935807386854477372696992105*t^53 - 10548543004836655265009119559454504695867805425113901897931873109238782759498372/25975433951820355929754679474257051421989740535651271883391100624255975411715*t^51 + 2013298059640784366461849138198394695299491820081506699107242674894466217332915439/1652750650463863823373606566548316311065817804670360338462825912268836082568925*t^49 - 26973122028209090671108468393121880973020660971259147035106379629587073566910467608/9815315087448660665341214507460409112656183288960711397809843683065944898521575*t^47 + 13544659164025949448840329995361706989628946523595693479055608798538156042381454303372/2797364799922868289622246134626216597107012237353802748375805449673794296078648875*t^45 - 897727967108312472557454550000834727545499150922056517100558648805183144334550552/131424233024330199183568058944149241113789628252469003917115595474455921826575*t^43 + 10137858187303379527993144254418646773526913787472255373197915498437075287850738557/1291804046556221226121412872060784004118468785018170940941404511614774060880725*t^41 - 17937403159378371833258417105211886663824716960787630491414886507787428212437371790708/2414381763013577471620920657881605303697418159198961488619485032208012719786075025*t^39 + 551987168906918889080586586413903855003550216554118987950513059912397343365491165206/94489974530895744503382859755150544949021763315478924655823300855644222501749225*t^37 - 30798967984923481815874415095952014188685535216564887648189409887381361394641204827028/8031647835126138282787543079187796320666849881815708595744980572729758912648684125*t^35 + 544826407348922789762475615210795497260231866800198607296253380587790526165310576321/258549490749374070124641011857499842772598011709387387245054966077531993438852275*t^33 - 105179856729828161231708027253715745391153134772946372576700235725725994516175564656/108423979991672997149043004972499934065928198458775355941474663193803739184034825*t^31 + 28807695860492293881052469693513917055317655545033804902122178327353448304078352396936/77089449774079500972969576535447453120874949104189278074388485530794458559848760575*t^29 - 10535488980936424324320356701790333775705339079080214597277557917510509698946223455056/87722477329124949383034345712750550103064597256491247463959311121248866637069279275*t^27 + 18220976982175766739595145886723634405558046886834800968974248994736009909877804355461/568571612318402449704852240730790602519863130366146974303439979489575987462486069375*t^25 - 3901928975084642579607246899448182839722664329344945817951795956301351604057985182388/553409702656578384379389514311302853119333446889716388322014913369853961130153107525*t^23 + 692544327334202256196915638651855762638002721545645351357166835898539882909312142199398/546517236359855544501209844905789353948665384869362647849277091266974870886986655185825*t^21 - 281373080743216778031903079686156446024014777729106706181191334054301854079170229284/1530860606050015530815713851276720879408026288149475204059599695425699918450943011725*t^19 + 5351460032785678524896305108341452967978892966866795921142822349799364507618744243/252666313619905475959875101667031601455693659209136684165176648759581539938505157275*t^17 - 7769526131260508452479904428381887921274416825949502743534253831379584699404831256/4089285180544562034370742479437816047733768851906132394405780008328924439697724483375*t^15 + 2571103772973124735070842570436360783468322414158114584510733330843124433893248324/19901187878650201900604280066597371432304341745943177652774796040534098939862259152425*t^13 - 12600729742176535489376534660823102163933621266557931750973009934566822035818348296/1961032436350069894974929443485479446521681675119477736400347209840321595535657998019725*t^11 + 5174258587977804953241524062963143448978080648952046909358895580593011429870894295789/23255883662675478884507688270294300756300622985241886475971717561496373801457368198515918775*t^9 - 18852769449283865400046001988458099130518387660319557162263183129458575315008270124/3776596492229351271843128864406766789484716553158938829431304561268641899381965775827371425*t^7 + 8338089261299228168908043389255129653104770200529143249000488254603268418603629446/128584118663999340922277958954801821641979635024221012525875369586051378955147882367455741375*t^5 - 92371733017303174737487190999859586651643478434464613433687487255386857042274772/231451413595198813660100326118643278955563343043597822546575665254892482119266188261420334475*t^3 + 963982297833992155603337101854639201653534852589353754642752497590116319720361/1311558010372793277407235181338978580748192277247054327763928769777724065342508400148048562025*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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:
| (-0.98023348494587174451 - 5.9055462791469212735e-822j)  +/-  (4.24e-235, 4.24e-235j)
| (-0.80465082124262632318 + 2.1791264980729650756e-839j)  +/-  (8.31e-238, 8.31e-238j)
| (-0.95317930179769372783 + 6.5293276309769066042e-836j)  +/-  (2.15e-235, 2.15e-235j)
| (-0.99918766765738604356 + 6.4325466126387054753e-839j)  +/-  (8.67e-236, 8.67e-236j)
| (0.89109159817597078591 + 1.0657846161171196784e-848j)  +/-  (2.64e-236, 2.64e-236j)
| (0.91459429691006664118 - 4.030943136505570511e-848j)  +/-  (6.21e-236, 6.21e-236j)
| (-0.99570769785259057906 + 1.5400561788905253613e-845j)  +/-  (2.65e-235, 2.65e-235j)
| (-0.91459429691006664118 - 1.7565217217049524855e-859j)  +/-  (6.31e-236, 6.31e-236j)
| (-0.96816023950762608984 - 2.5433496802936842961e-876j)  +/-  (3.03e-235, 3.03e-235j)
| (0.96816023950762608984 + 5.4543041457028947385e-891j)  +/-  (3.48e-235, 3.48e-235j)
| (0.86487568065172464031 + 2.6215409386385669279e-893j)  +/-  (9.94e-237, 9.94e-237j)
| (0.98023348494587174451 + 1.5767135673484510566e-891j)  +/-  (3.9e-235, 3.9e-235j)
| (-0.56904088231296883305 + 7.5819476684337264681e-901j)  +/-  (1.95e-242, 1.95e-242j)
| (-0.8360311073266357943 + 1.3534898901237059948e-895j)  +/-  (3.33e-237, 3.33e-237j)
| (0.99918766765738604356 - 2.321745642185678411e-891j)  +/-  (9.43e-236, 9.43e-236j)
| (0.80465082124262632318 + 5.1285003408143773243e-896j)  +/-  (8.22e-238, 8.22e-238j)
| (0.8360311073266357943 - 3.5903307150975499128e-895j)  +/-  (3.26e-237, 3.26e-237j)
| (0.99570769785259057906 - 3.1415215000125288694e-891j)  +/-  (2.94e-235, 2.94e-235j)
| (-0.73468626142647651426 - 4.0871381760504165725e-899j)  +/-  (4.2e-239, 4.2e-239j)
| (0.98940545390497275235 + 4.2568214759215512087e-895j)  +/-  (3.86e-235, 3.86e-235j)
| (0.93531008269721163377 - 1.5482155762598835639e-894j)  +/-  (1.23e-235, 1.23e-235j)
| (0.77083428745260740464 + 9.752104686641722723e-900j)  +/-  (2.14e-238, 2.14e-238j)
| (-0.98940545390497275235 - 5.7089042794950698116e-894j)  +/-  (3.87e-235, 3.87e-235j)
| (-0.86487568065172464031 - 2.4053995734466797039e-908j)  +/-  (9.45e-237, 9.45e-237j)
| (-0.77083428745260740464 - 4.3113334158432845661e-917j)  +/-  (2.06e-238, 2.06e-238j)
| (0.32425342340380892904 + 2.0110853664247437529e-927j)  +/-  (6.65e-248, 6.65e-248j)
| (0.10983751120552356717 + 1.0698668551724139513e-932j)  +/-  (4.65e-253, 4.65e-253j)
| (0.95317930179769372783 + 1.0687813080574385202e-913j)  +/-  (2.2e-235, 2.2e-235j)
| (-0.93531008269721163377 - 1.6079907404378384895e-918j)  +/-  (1.22e-235, 1.22e-235j)
| (-0.65583817745987927119 + 1.60381667238710293e-936j)  +/-  (1.18e-240, 1.18e-240j)
| (-0.89109159817597078591 + 4.4912902180749307259e-939j)  +/-  (2.62e-236, 2.62e-236j)
| (0.73468626142647651426 - 1.6317327020673806035e-947j)  +/-  (4e-239, 4e-239j)
| (0.69631618737079254856 - 4.9131463606659778344e-949j)  +/-  (8.07e-240, 8.07e-240j)
| (0.27171792561274896157 - 3.8521814510870725972e-961j)  +/-  (3.76e-249, 3.76e-249j)
| (-0.69631618737079254856 - 3.1390327664865164808e-952j)  +/-  (8.2e-240, 8.2e-240j)
| (-0.61337143270059039731 + 1.6168802251822825653e-953j)  +/-  (1.54e-241, 1.54e-241j)
| (0.055000833185217049199 + 6.2187475615931423874e-967j)  +/-  (1.75e-254, 1.75e-254j)
| (0.56904088231296883305 + 4.0395109982930549893e-953j)  +/-  (1.98e-242, 1.98e-242j)
| (0.61337143270059039731 - 3.606799373036599101e-951j)  +/-  (1.65e-241, 1.65e-241j)
| (-0.32425342340380892904 - 2.7238720556473406691e-961j)  +/-  (6.26e-248, 6.26e-248j)
| (-0.5229777831208807195 - 9.3417448545058580995e-957j)  +/-  (1.94e-243, 1.94e-243j)
| (-0.16434566588174250528 - 2.4313418195044506768e-965j)  +/-  (9.03e-252, 9.03e-252j)
| (0.65583817745987927119 + 9.4388147720671585649e-957j)  +/-  (1.22e-240, 1.22e-240j)
| (0.5229777831208807195 - 4.2735497550868188948e-961j)  +/-  (2.06e-243, 2.06e-243j)
| (-0.10983751120552356717 + 3.8761474396648231824e-972j)  +/-  (4.49e-253, 4.49e-253j)
| (-0.47532005152781799849 + 9.1308697467503171224e-964j)  +/-  (1.66e-244, 1.66e-244j)
| (-0.27171792561274896157 + 1.0929720310642681718e-969j)  +/-  (4.15e-249, 4.15e-249j)
| (0.16434566588174250528 + 1.3189585336358740823e-970j)  +/-  (9.74e-252, 9.74e-252j)
| (0.47532005152781799849 + 2.1311621732349708483e-963j)  +/-  (1.66e-244, 1.66e-244j)
| (0.2183606755902425839 + 1.5595969353125131178e-970j)  +/-  (2e-250, 2e-250j)
| (-0.2183606755902425839 + 1.2809980692396126592e-971j)  +/-  (2.12e-250, 2.12e-250j)
| (-0.42621218551791790883 - 2.980002647827703782e-965j)  +/-  (1.42e-245, 1.42e-245j)
| (-0.055000833185217049199 + 3.6462867039717951694e-974j)  +/-  (1.75e-254, 1.75e-254j)
| (0.37580474094323351804 + 7.741813299193141612e-966j)  +/-  (1.02e-246, 1.02e-246j)
| (0.42621218551791790883 - 1.3475378322729410689e-964j)  +/-  (1.34e-245, 1.34e-245j)
| (6.467866821994122742e-987 - 4.9494090646949159119e-986j)  +/-  (2.85e-984, 2.85e-984j)
| (-0.37580474094323351804 + 9.6295506101479667613e-967j)  +/-  (1.03e-246, 1.03e-246j)
-------------------------------------------------
The weights are:
| (0.010619303158146392321 - 1.1440288539457992441e-822j)  +/-  (1.12e-42, 3.07e-155j)
| (0.032615458795387404539 - 1.1975510157425988339e-822j)  +/-  (2.48e-43, 6.78e-156j)
| (0.016430318871375281022 - 3.8121342662260491897e-822j)  +/-  (5.56e-43, 1.52e-155j)
| (0.0020861826566367242629 - 3.5085465247724544795e-823j)  +/-  (8.83e-44, 2.41e-156j)
| (0.024872590010187903368 + 8.4897368987562859711e-824j)  +/-  (1.75e-45, 4.77e-158j)
| (0.022120472443915062286 - 7.4335734247217504152e-824j)  +/-  (1.41e-45, 3.84e-158j)
| (0.0048826253118368264694 + 1.457428168523113089e-822j)  +/-  (1.23e-43, 3.36e-156j)
| (0.022120472443915062286 - 2.1458738087901608086e-822j)  +/-  (4.11e-45, 1.12e-157j)
| (0.013528254786832187764 + 6.8944074065038482288e-822j)  +/-  (9.97e-44, 2.72e-156j)
| (0.013528254786832187764 + 4.2721279444340920964e-824j)  +/-  (4.33e-48, 1.18e-160j)
| (0.027545109863220225569 - 9.5627034786943783855e-824j)  +/-  (1.21e-47, 3.3e-160j)
| (0.010619303158146392321 - 3.1988698211113907047e-824j)  +/-  (1.48e-48, 4.04e-161j)
| (0.045219251016101839111 - 7.1714300176563678335e-823j)  +/-  (7.18e-50, 1.96e-162j)
| (0.030128515302126649894 + 1.3424778988032830493e-822j)  +/-  (1.23e-47, 3.36e-160j)
| (0.0020861826566367242629 + 3.3596504611929032844e-825j)  +/-  (8.41e-50, 2.3e-162j)
| (0.032615458795387404539 - 1.1780550511625538872e-823j)  +/-  (2.79e-50, 7.63e-163j)
| (0.030128515302126649894 + 1.0658606996599115119e-823j)  +/-  (1.09e-49, 2.97e-162j)
| (0.0048826253118368264694 - 1.1413575450679831611e-824j)  +/-  (7.35e-50, 2.01e-162j)
| (0.037277671727715246019 - 9.8496429333201817405e-823j)  +/-  (2.61e-53, 7.12e-166j)
| (0.0077300493940686525758 + 2.1355546889304114885e-824j)  +/-  (7.96e-50, 2.17e-162j)
| (0.019301091529071265455 + 6.3852519521023168524e-824j)  +/-  (1.61e-50, 4.39e-163j)
| (0.035000139611642184206 + 1.2929066882019757076e-823j)  +/-  (5.99e-53, 1.64e-165j)
| (0.0077300493940686525758 - 4.586007312191288304e-822j)  +/-  (1.48e-51, 4.04e-164j)
| (0.027545109863220225569 - 1.529522163185467014e-822j)  +/-  (2.04e-53, 5.56e-166j)
| (0.035000139611642184206 + 1.0811728323370244082e-822j)  +/-  (3.45e-54, 9.43e-167j)
| (0.052070292612813151832 + 2.5996729470708208776e-823j)  +/-  (3.17e-59, 8.66e-172j)
| (0.054699835148828863981 + 3.2766809233648711614e-823j)  +/-  (1.15e-59, 3.14e-172j)
| (0.016430318871375281022 - 5.3343072587014418148e-824j)  +/-  (2.76e-52, 7.53e-165j)
| (0.019301091529071265455 + 2.7226852135836736238e-822j)  +/-  (2.66e-53, 7.26e-166j)
| (0.041492699033298887702 - 8.332267464956379948e-823j)  +/-  (1.46e-57, 3.99e-170j)
| (0.024872590010187903368 + 1.7822213757665186017e-822j)  +/-  (8.69e-54, 2.37e-166j)
| (0.037277671727715246019 - 1.4103006744486351546e-823j)  +/-  (6.62e-58, 1.81e-170j)
| (0.03944346525478119629 + 1.5300668874163297852e-823j)  +/-  (6.31e-59, 1.72e-171j)
| (0.052973611758175879194 - 2.7569322293184003859e-823j)  +/-  (9.57e-62, 2.61e-174j)
| (0.03944346525478119629 + 9.0351421369177853019e-823j)  +/-  (7.25e-58, 1.98e-170j)
| (0.04341997950277644434 + 7.7166447221218724288e-823j)  +/-  (3.01e-59, 8.22e-172j)
| (0.054946127186631762207 - 3.4675472504477300308e-823j)  +/-  (2.59e-63, 7.09e-176j)
| (0.045219251016101839111 - 1.9033678190760252644e-823j)  +/-  (2.02e-62, 5.51e-175j)
| (0.04341997950277644434 + 1.7764403760665287417e-823j)  +/-  (6.59e-62, 1.8e-174j)
| (0.052070292612813151832 + 5.1697292711499037365e-823j)  +/-  (3.14e-65, 8.58e-178j)
| (0.046883960080915791258 + 6.6846615869727808957e-823j)  +/-  (4.39e-63, 1.2e-175j)
| (0.054289033058943580085 - 4.3417997571352033336e-823j)  +/-  (6.32e-66, 1.73e-178j)
| (0.041492699033298887702 - 1.6520966217185895514e-823j)  +/-  (1.13e-62, 3.1e-175j)
| (0.046883960080915791258 + 2.0333799315812908832e-823j)  +/-  (1.66e-64, 4.54e-177j)
| (0.054699835148828863981 + 4.103666544841053181e-823j)  +/-  (1.2e-66, 3.26e-179j)
| (0.04840741122091875384 - 6.2474852747993896002e-823j)  +/-  (1.96e-65, 5.35e-178j)
| (0.052973611758175879194 - 4.8715164372090809411e-823j)  +/-  (1.31e-66, 3.57e-179j)
| (0.054289033058943580085 - 3.0949554970495296483e-823j)  +/-  (4.2e-67, 1.15e-179j)
| (0.04840741122091875384 - 2.1671750033803809764e-823j)  +/-  (4.85e-67, 1.32e-179j)
| (0.053713540245834115603 + 2.9218583866155035672e-823j)  +/-  (2.89e-67, 7.9e-180j)
| (0.053713540245834115603 + 4.5967284264584952707e-823j)  +/-  (7.96e-68, 2.17e-180j)
| (0.049783212698615954631 + 5.8529763697851054385e-823j)  +/-  (6.6e-68, 1.8e-180j)
| (0.054946127186631762207 - 3.8798067778667208033e-823j)  +/-  (1.69e-68, 4.62e-181j)
| (0.051005705734399378287 - 2.4494680473471775834e-823j)  +/-  (7.91e-69, 2.16e-181j)
| (0.049783212698615954631 + 2.3055804017229822274e-823j)  +/-  (8.11e-69, 2.21e-181j)
| (0.055028183969604791777 + 3.6682508691145251534e-823j)  +/-  (3.48e-69, 9.59e-182j)
| (0.051005705734399378287 - 5.4953910419624559987e-823j)  +/-  (2.46e-69, 6.49e-182j)
