Starting with polynomial:
P : 231/16*t^6 - 315/16*t^4 + 105/16*t^2 - 5/16
Extension levels are: 6 14 20
-------------------------------------------------
Trying to find an order 14 Kronrod extension for:
P1 : 231/16*t^6 - 315/16*t^4 + 105/16*t^2 - 5/16
Solvable: 1
-------------------------------------------------
Trying to find an order 20 Kronrod extension for:
P2 : 231/16*t^20 - 264345610739/3590901680*t^18 + 4890539045511/30612436822*t^16 - 22022509047849/114549763592*t^14 + 186516235143784/1331641001757*t^12 - 10215124913175/161411030516*t^10 + 3238994808498267/185622685093400*t^8 - 102871692107457/37124537018680*t^6 + 16645537944399/74249074037360*t^4 - 524382152749/74249074037360*t^2 + 821560883/22274722211208
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 231/16*t^40 - 122174744040742640594954381719917626744768670507886774190899452959229361506279809944095626670982970023523286349387719701704042407418610072815809268630468171/872826019431762518985620711979361031668322243922340238454555563708042533117787370740867408279924444681048573367125915209440888494381492452168463793013520*t^38 + 111854916046105382418821471511637369498044747172900745105780720183194692528097308290076672457019098210615317291946502140075239038395625237563729229997500258587/178580203575738611384457997670977267079338731106510812787802068334665502275899296053581471734072541381742538110913962251851605785950453355713667692050566192*t^36 - 2961751127124604231817700131728414788986399205106524462142172986041114283858877291237389031445279901852822472311760634992180602459834814582746890183796557119003/1726275301232139910049760644152780248433607734029604523615419993901766522000359861851287560096034566690177868405501635101232189264187715771898787689822139856*t^34 + 217348253144426598918843507122295850032028642912781276189825021670945023312663266771037584395031295469306237178125803398504703747113074476337702225168836041298759/67560137925494202843311087027979263359151648136340431583312573397700953429195901866089026783758443723647415668051677628280041588930255603618402554588039200728*t^32 - 615002383091346875353897199760032946948310970215978274469057560393299923726423503209315470194099271826647138253720536479296843968856691925031753753356481282900985/140568674070786325270760164945311693118234880799805091520118096262958435360746311947185233146852245812105106793204297000776215564064564078496353702288017046676*t^30 + 591975576578587833138059273000797043073189511840700210304529002222938052055543445908114159064904183840826143591714222521696091809769872045585382560650208592341309/132720833482269518933804753437691664274195495008026153734101650822990312532724350360642872018784961152644394755488457759353569703345031765411171393785894584300*t^28 - 2903097714233758429675772826828810315249347991685633205620448637293824951963097738301330113288796795155610928141955651016193281045468859277498527647133881594608249367/835459950659755652419109748923144001050824081676190234269005345043947618685162088940198793641982159127742779066499109800762807473263195625694602434363034955557260*t^26 + 2095178174812051919789738247120131491651305937946109809316567864828316771439443791002840615642239186831567071936183068655767878818525893176635308209994024181852279389/1002551940791706782902931698707772801260988898011428281122806414052737142422194506728238552370378590953291334879798931760915368967915834750833522921235641946668712*t^24 - 32238684206584946899726344531250178135658777092911375716608532508375832692292751839902606232651532203157585021728859187414258927253541817911310200150060137565406241039/33113273522671010988924367266014698754692662298087609459114142284437506486669293925125444360175258098297839886826982108451103273592466484016660851268058376760260792*t^22 + 3331043677183706358505511910868907140998838532827964525632416677423118075037434038062219878966302655190427095546647210805537321503900513582749174938418595018568218246459/9503509501006580153821293405346218542596794079551143914765758835633564361674087356511002531370299074211480047519343865125466639521037880912781664313932754130194847304*t^20 - 4597170649714789485230515966140367038158999456136109806242704298194995071604724911997523365005043654670491976109189697292968597361690792285895646892814627007439396008769/47517547505032900769106467026731092712983970397755719573828794178167821808370436782555012656851495371057400237596719325627333197605189404563908321569663770650974236520*t^18 + 47967180036339910845908256166303396935308614052640630783935035554096069415826558358172017470241449456895271539876089501034145206700192616403444564104140425965718882867/2375877375251645038455323351336554635649198519887785978691439708908391090418521839127750632842574768552870011879835966281366659880259470228195416078483188532548711826*t^16 - 1140833711604711362740384722700428918897647023603121372935291311035194002973418912855177216611234033102299896155044821148728201821024510317919149238492665902618169014177/365885115788753335922119796105829413889976572062719040718481715171892227924452363225673597457756514357141981829494738807330465621559958415142094076086411034012501621204*t^14 + 54169864422029196795998050134493420531950418792257232527297964412208056498888531186764072362978757770217846032448536710376369670444747535523551134674611383449264376903/156807906766608572538051341188212605952847102312593874593635020787953811967622441382431541767609934724489420784069173774570199552097125035060897461179890443148214980516*t^12 - 3865362561374896173181440126147064943223049063920052519231999193340474296853912803434887276493642092683550475794450142647978363554432252544074565152853229470504763643/147304397265601992384230047782866387410250308233042730678869261952320247605948354025920539236239635650277940736549829909444732912576087154148115796865957689018020133212*t^10 + 109110932002291807625418898719721739610544199446973269794074879087270914614196813642233602398879505385251643019998064936964466811656035030260847468180003508830045793609/85436550414049155582853427714062504697945178775164783793744171932345743611450045335033912757018988677161205627198901347477945089294130549405907162182255459630451677262960*t^8 - 239459134549157293716065629601934536881197825282067144179466779323265064125508511401573099461865875285952569601433401315677324623230235766224194858881853625750943767/6686338728056020871701572603709239498100057469360722209945196064270536456548264417524393172288442592125659570824261844585230485249105869083940560518611296840644044307536*t^6 + 24872018099550212176901854037630602908193733509733074435813689358867586137182659321658503542495809446917242754868409825913268902448012929377590477733813503468831017/51261930248429493349712056628437502818767107265098870276246503159407446166870027201020347654211393206296723376319340808486767053576478329643544297309353275778271006357776*t^4 - 936186113851815822823192622950862532433657063077266527118507204821690762762261015858500955159241840399207146290819258107998596370230813461370459104136264141640427/393008131904626115681125767484687521610547822365758005451223190888790420612670208541155998682287347914941545885114946198398547410753000527267172946038375114300077715409616*t^2 + 11783843517324105516665049500024916464890637552214783536002144611266233209368050823339830026719933071764339398148838961952653101072085098958302429697613441526315/4126585384998574214651820558589218976910752134840459057237843504332299416433037189682137986164017153106886231793706935083184747812906505536305315933402938700150816011800968
-------------------------------------------------
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:
| (0.96092376956646356979 + 2.3031350868434012225e-918j)  +/-  (8.32e-242, 8.32e-242j)
| (0.98703370674875756432 + 2.9677635615848649294e-940j)  +/-  (8.63e-242, 8.63e-242j)
| (-0.86360683867471434432 - 1.7195098842721396025e-961j)  +/-  (9.66e-243, 9.66e-243j)
| (0.97723820629620631225 + 6.9154125989463586802e-959j)  +/-  (1.32e-241, 1.32e-241j)
| (0.93246951420315202781 - 2.6620029553759627409e-969j)  +/-  (3.93e-242, 3.93e-242j)
| (0.89842846298993724946 - 1.2934798069496919257e-979j)  +/-  (2.02e-242, 2.02e-242j)
| (0.99733385180278742135 + 6.2769365874396294598e-987j)  +/-  (1.78e-242, 1.78e-242j)
| (-0.89842846298993724946 + 1.0518328197226377963e-993j)  +/-  (2.04e-242, 2.04e-242j)
| (-0.93246951420315202781 - 3.565602942839845467e-992j)  +/-  (4.03e-242, 4.03e-242j)
| (-0.080232662089308817649 + 8.0803712961456473415e-1004j)  +/-  (4.04e-254, 4.04e-254j)
| (0.82313480541220900087 + 3.0360928760213135334e-996j)  +/-  (2.98e-243, 2.98e-243j)
| (-0.97723820629620631225 + 5.3069756627405760072e-997j)  +/-  (1.27e-241, 1.27e-241j)
| (-0.98703370674875756432 - 2.4580210218245401146e-997j)  +/-  (9.13e-242, 9.13e-242j)
| (-0.77239979137307865819 + 1.0400580906608458593e-1003j)  +/-  (6.31e-244, 6.31e-244j)
| (-0.99733385180278742135 + 1.1466894730827223957e-1000j)  +/-  (1.76e-242, 1.76e-242j)
| (0.86360683867471434432 - 4.0240124076059009058e-1005j)  +/-  (1.04e-242, 1.04e-242j)
| (0.66120938646626451366 + 1.67063925875884731e-1012j)  +/-  (2.35e-245, 2.35e-245j)
| (-0.96092376956646356979 + 5.0794598498423274983e-1010j)  +/-  (8.83e-242, 8.83e-242j)
| (-0.82313480541220900087 + 2.5425292115651415457e-1016j)  +/-  (2.87e-243, 2.87e-243j)
| (-0.45979372438536253626 - 1.8557229194324894918e-1023j)  +/-  (2.7e-248, 2.7e-248j)
| (0.45979372438536253626 - 1.8452545420046729998e-1019j)  +/-  (2.89e-248, 2.89e-248j)
| (0.77239979137307865819 + 1.6831867928554837439e-1018j)  +/-  (6.33e-244, 6.33e-244j)
| (-0.041741554595635360839 + 2.1414878108363971047e-1027j)  +/-  (8.12e-255, 8.12e-255j)
| (-0.71656592391278938809 - 8.6898312134276629917e-1025j)  +/-  (1.23e-244, 1.23e-244j)
| (-0.66120938646626451366 - 1.3237881600711833842e-1027j)  +/-  (2.55e-245, 2.55e-245j)
| (0.080232662089308817649 - 8.6479429620471647258e-1028j)  +/-  (3.96e-254, 3.96e-254j)
| (0.71656592391278938809 - 3.9946471913013825412e-1029j)  +/-  (1.23e-244, 1.23e-244j)
| (0.39082501957322900088 + 8.6119994762072916454e-1034j)  +/-  (2.59e-249, 2.59e-249j)
| (-0.14942371068102733487 + 1.1693616957943488849e-1038j)  +/-  (3.99e-253, 3.99e-253j)
| (-0.60188046880803263782 - 1.6004369420495375881e-1033j)  +/-  (3.29e-246, 3.29e-246j)
| (-0.23861918608319690863 - 1.001160529424901471e-1039j)  +/-  (7.78e-252, 7.78e-252j)
| (0.32073131932970265931 - 4.0005526373397263712e-1034j)  +/-  (1.94e-250, 1.94e-250j)
| (0.53291253805075079124 - 5.2440564704211948825e-1035j)  +/-  (3.08e-247, 3.08e-247j)
| (0.041741554595635360839 + 2.6413700298397080837e-1037j)  +/-  (8.12e-255, 8.12e-255j)
| (-0.53291253805075079124 + 3.3591523343191388049e-1037j)  +/-  (3.36e-247, 3.36e-247j)
| (-0.39082501957322900088 - 1.0372407939615833147e-1039j)  +/-  (2.52e-249, 2.52e-249j)
| (0.14942371068102733487 - 4.4042360937540170051e-1039j)  +/-  (3.71e-253, 3.71e-253j)
| (0.60188046880803263782 - 1.7895766065609352596e-1043j)  +/-  (3.19e-246, 3.19e-246j)
| (0.23861918608319690863 + 8.2298154063961741834e-1050j)  +/-  (7.37e-252, 7.37e-252j)
| (-0.32073131932970265931 - 4.6431797201429043398e-1061j)  +/-  (1.91e-250, 1.91e-250j)
-------------------------------------------------
The weights are:
| (0.023798383216703232534 + 9.386469803243616236e-919j)  +/-  (7.58e-76, 2.2e-192j)
| (0.012331125621782244188 + 1.0576502871758807346e-918j)  +/-  (2.79e-76, 8.09e-193j)
| (0.035878991545512340444 - 6.27452242031414281e-920j)  +/-  (1.65e-78, 4.8e-195j)
| (0.009026330827792137059 - 3.2333238613344641438e-918j)  +/-  (3.91e-76, 1.14e-192j)
| (0.032178569946982976544 + 2.0770258194933313328e-918j)  +/-  (4.33e-77, 1.26e-193j)
| (0.034840307961397002101 - 1.3768220420246338008e-918j)  +/-  (7.75e-78, 2.25e-194j)
| (0.0067681923542198185503 - 1.1657985833007868964e-919j)  +/-  (3.44e-77, 9.98e-194j)
| (0.034840307961397002101 + 4.6276823783596066853e-920j)  +/-  (8.26e-80, 2.4e-196j)
| (0.032178569946982976544 - 3.1213918191570956077e-920j)  +/-  (2.55e-80, 7.4e-197j)
| (0.030886357960009691663 - 3.4647542107734620246e-918j)  +/-  (1.33e-81, 3.85e-198j)
| (0.04598626448261448568 - 9.019029541038539071e-919j)  +/-  (1.13e-79, 3.27e-196j)
| (0.009026330827792137059 - 2.7216434033605376946e-920j)  +/-  (1.62e-81, 4.69e-198j)
| (0.012331125621782244188 + 1.4176481209042944775e-920j)  +/-  (5.95e-82, 1.73e-198j)
| (0.054452187237736963646 - 7.8505642158518127148e-920j)  +/-  (2.17e-83, 6.29e-200j)
| (0.0067681923542198185503 - 2.1675811101550503384e-921j)  +/-  (1.15e-82, 3.34e-199j)
| (0.035878991545512340444 + 1.1763686033926565158e-918j)  +/-  (2.58e-82, 7.49e-199j)
| (0.055581362811588901973 + 7.2866142038852979837e-919j)  +/-  (3.8e-85, 1.1e-201j)
| (0.023798383216703232534 + 2.8519895715173727648e-920j)  +/-  (4.43e-82, 1.28e-198j)
| (0.04598626448261448568 + 6.9657059222462937168e-920j)  +/-  (3.25e-83, 9.43e-200j)
| (0.072055480805122657008 + 2.4680106728187894222e-919j)  +/-  (1.96e-86, 5.68e-203j)
| (0.072055480805122657008 - 6.996878299057740288e-919j)  +/-  (9.45e-87, 2.74e-203j)
| (0.054452187237736963646 + 7.2179507627652442915e-919j)  +/-  (1.59e-84, 4.61e-201j)
| (0.074440834291466460156 + 3.9834766153496672865e-918j)  +/-  (6.33e-87, 1.84e-203j)
| (0.056050407795503783644 + 1.0399690434669306659e-919j)  +/-  (1.12e-85, 3.24e-202j)
| (0.055581362811588901973 - 1.3463155431381662888e-919j)  +/-  (2.19e-86, 6.36e-203j)
| (0.030886357960009691663 + 4.0960458213174189382e-918j)  +/-  (1.85e-88, 5.37e-205j)
| (0.056050407795503783644 - 7.1392729269096927505e-919j)  +/-  (1.15e-86, 3.34e-203j)
| (0.066767611070136506653 + 8.1387039507615024421e-919j)  +/-  (1.48e-88, 4.28e-205j)
| (0.089114556592861484576 + 1.202884405391351646e-918j)  +/-  (1.15e-88, 3.33e-205j)
| (0.064313056266564695324 + 1.5277569090434584017e-919j)  +/-  (1.82e-88, 5.27e-205j)
| (0.087139820232159242358 - 5.384713410235238505e-919j)  +/-  (1.67e-89, 4.85e-206j)
| (0.075879565044882396626 - 8.2736904645594967918e-919j)  +/-  (1.24e-89, 3.6e-206j)
| (0.072510593934962979275 + 6.2024722620624346206e-919j)  +/-  (1.65e-89, 4.78e-206j)
| (0.074440834291466460156 - 4.3452688778888896348e-918j)  +/-  (4.93e-89, 1.43e-205j)
| (0.072510593934962979275 - 1.7771209454413982697e-919j)  +/-  (6.6e-90, 1.91e-206j)
| (0.066767611070136506653 - 3.4324905531057507908e-919j)  +/-  (2.28e-90, 6.64e-207j)
| (0.089114556592861484576 - 1.6458651529732608095e-918j)  +/-  (1.38e-90, 4.07e-207j)
| (0.064313056266564695324 - 6.6498524484806782218e-919j)  +/-  (2.98e-91, 8.67e-208j)
| (0.087139820232159242358 + 8.9424810352038674235e-919j)  +/-  (4.57e-91, 1.36e-207j)
| (0.075879565044882396626 + 4.132745398427538603e-919j)  +/-  (2.91e-91, 7.73e-208j)
