Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 15 28
-------------------------------------------------
Trying to find an order 15 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P2 : t^19 - 93567/667*t^17 + 56576166/7337*t^15 - 1577757510/7337*t^13 + 24226003620/7337*t^11 - 18992429820/667*t^9 + 3930143490/29*t^7 - 224016557310/667*t^5 + 250467132825/667*t^3 - 83438061525/667*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^47 - 11866605408947232567102103992235546865594811225990621964836808255228635308735045467183276702429417389/14754889366344037615700338574737211355293216469316160972180519915290685398042078456273183160004613*t^45 + 909140072970083446147499891043471062552509252818023780012862860623110904869382509166140651927292534665684/3083771877565903861681370762120077173256282242087077643185728662295753248190794397361095280440964117*t^43 - 201759868413239463275195723783129020044348630865376328128614531980523957869209641474117956461216688434639076/3083771877565903861681370762120077173256282242087077643185728662295753248190794397361095280440964117*t^41 + 2581293196915339056044739773280580240902681928897981018703829281073465235498138580127778376358686244927032559747/262120609593101828242916514780206559726783990577401599670786936295139026096217523775693098837481949945*t^39 - 12164494761016507090641731502623072010122583985859303602746780191233368092868730872783074220547964199768499484289/11396548243178340358387674555661154770729738720756591290034214621527783743313805381551873862499215215*t^37 + 22630987169745138924029359800486729056095579881945389638617219329135709549545244848407130057015253686759500281113526/262120609593101828242916514780206559726783990577401599670786936295139026096217523775693098837481949945*t^35 - 279411108917967053718982415936952670621591326915410442872785557204912258948594484700109236734578029218634202617788698/52424121918620365648583302956041311945356798115480319934157387259027805219243504755138619767496389989*t^33 + 1213715011775440016622252152621079529076836093196464962864371872185680342595581167743914903152213949047851853903036626/4765829265329124149871209359640119267759708919589119994014307932638891383567591341376238160681489999*t^31 - 45264461597555855011290480478234577639116645795422261496920463120948069493046909162923033876945410295236287749450813154/4765829265329124149871209359640119267759708919589119994014307932638891383567591341376238160681489999*t^29 + 45611480060575858462272400430631025591139292982991390004486829735141702454355261163930118854043502253476663053492232516/164338940183762901719696874470348940267576169641004137724631308022030737364399701426766833126947931*t^27 - 1044602422018474047732088770922448437332572336506788876020088438206734355095905030093875394549080496267122792222258849268/164338940183762901719696874470348940267576169641004137724631308022030737364399701426766833126947931*t^25 + 812589887209776836606318401014891123136262917765122607113004961818135528168606508773149405474143094158112933711364514850/7145171312337517466073777150884736533372876940913223379331796000957858146278247888120297092475997*t^23 - 11282936812799089192296288918379693466110268285714576037002292794043110433534929382333423618717954822079512773427640941450/7145171312337517466073777150884736533372876940913223379331796000957858146278247888120297092475997*t^21 + 6333622501074126133369934455390897944188914554823476340311328352299604951756241989344850687120155696949081964250767774000/376061648017764077161777744783407185966993523205959125227989263208308323488328836216857741709263*t^19 - 3008053959060849750284296304292270102054699340102559848135538422468923032731667089059220014427246430025940863656933361000/22121273412809651597751632046082775645117266070938772072234662541665195499313460953932808335839*t^17 + 18022516655210669951330109398412552871866798892271721356473260593834872351320131498477830521365131057843379164533452391375/22121273412809651597751632046082775645117266070938772072234662541665195499313460953932808335839*t^15 - 77999337704345324190501741330068380552148430734547654087801644279610505749458475984447090640144257640714923887710807854375/22121273412809651597751632046082775645117266070938772072234662541665195499313460953932808335839*t^13 + 235061646622199561135763334269292177701846842316307100188412382204350346797194524540027893244066152869775303674418812110000/22121273412809651597751632046082775645117266070938772072234662541665195499313460953932808335839*t^11 - 468823022838985807773375310696194429642786382377733449667099712177100208854696822887348467312002208324579759059219550302000/22121273412809651597751632046082775645117266070938772072234662541665195499313460953932808335839*t^9 + 575572768197928025319726407988411201588964327447776593133407586587772657705336521022110586434553759762784689447551974585125/22121273412809651597751632046082775645117266070938772072234662541665195499313460953932808335839*t^7 - 390485071174229944782350442403708885168390392726693491194042322275163018241707301540380945269098783390893073768818366426625/22121273412809651597751632046082775645117266070938772072234662541665195499313460953932808335839*t^5 + 122754119948671299077573432849544052544535101196601046033471691446110910204112669993971066556198353469203895765450258513750/22121273412809651597751632046082775645117266070938772072234662541665195499313460953932808335839*t^3 - 12171008483162398812255273054893434483398779187130219408254640541187241674219929925953700259948842351122346700636692446250/22121273412809651597751632046082775645117266070938772072234662541665195499313460953932808335839*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:
| (8.1074915840747069072 - 1.4628206794615163821e-919j)  +/-  (1.29e-244, 1.29e-244j)
| (-9.4880086483176372037 + 5.2328973757632204175e-930j)  +/-  (1.45e-245, 1.45e-245j)
| (11.259494195343326536 + 1.4395737704209372364e-930j)  +/-  (2.05e-247, 2.05e-247j)
| (-8.1074915840747069072 - 3.4271757573647271918e-933j)  +/-  (1.31e-244, 1.31e-244j)
| (6.3366586050468119201 + 5.4576914693023636397e-941j)  +/-  (8.91e-244, 8.91e-244j)
| (-10.291302765160083694 - 8.1872249820992935836e-953j)  +/-  (2.38e-246, 2.38e-246j)
| (-5.7525664932724817643 + 2.497702912226591961e-948j)  +/-  (1.89e-243, 1.89e-243j)
| (-7.485336286116986494 - 3.5618312562876477691e-960j)  +/-  (2.45e-244, 2.45e-244j)
| (5.9095061421099601502 + 8.6259758873985723503e-966j)  +/-  (2.06e-243, 2.06e-243j)
| (8.7700706471687405716 - 1.0813539692768230562e-976j)  +/-  (5.21e-245, 5.21e-245j)
| (-11.259494195343326536 - 4.7432014012063893322e-979j)  +/-  (1.97e-247, 1.97e-247j)
| (9.4880086483176372037 - 8.5026588072948879945e-978j)  +/-  (1.34e-245, 1.34e-245j)
| (-6.3366586050468119201 + 3.5618706707638407915e-974j)  +/-  (8.37e-244, 8.37e-244j)
| (10.291302765160083694 - 1.1322457465233854308e-981j)  +/-  (2.89e-246, 2.89e-246j)
| (-6.8956391981569169575 - 3.8039279233824442458e-980j)  +/-  (4.34e-244, 4.34e-244j)
| (-8.7700706471687405716 - 5.1589724826129226551e-981j)  +/-  (4.92e-245, 4.92e-245j)
| (4.7888356187420432164 + 2.5543785541127706196e-978j)  +/-  (1.05e-244, 1.05e-244j)
| (-5.9095061421099601502 - 2.7003327893099972211e-980j)  +/-  (2.06e-243, 2.06e-243j)
| (-2.3344142183389772393 + 2.6463449881741692794e-989j)  +/-  (1.64e-248, 1.64e-248j)
| (-5.2676050741688815108 + 5.3389023466135764476e-985j)  +/-  (3.15e-244, 3.15e-244j)
| (5.7525664932724817643 + 2.5549574243956729696e-985j)  +/-  (1.75e-243, 1.75e-243j)
| (0.74196378430272585765 + 1.8074986134789893154e-1003j)  +/-  (2.1e-252, 2.1e-252j)
| (3.0954420462911432479 - 2.9795871992775250641e-997j)  +/-  (6.38e-247, 6.38e-247j)
| (3.9139822016309083791 - 1.1726716209905411928e-994j)  +/-  (9.84e-246, 9.84e-246j)
| (-4.7888356187420432164 + 1.2557438174414670578e-995j)  +/-  (1.06e-244, 1.06e-244j)
| (-1.4697192347651409339 - 1.2171018754973915056e-1001j)  +/-  (1.47e-250, 1.47e-250j)
| (1.4697192347651409339 + 1.9745819416424266872e-1001j)  +/-  (1.47e-250, 1.47e-250j)
| (-4.3407179375549160233 - 4.3792699370618260183e-996j)  +/-  (3.13e-245, 3.13e-245j)
| (3.4954745810572123223 + 1.8235037901719677439e-997j)  +/-  (2.65e-246, 2.65e-246j)
| (5.2676050741688815108 - 4.6301549546566549812e-994j)  +/-  (3.15e-244, 3.15e-244j)
| (-3.0954420462911432479 - 2.5430928026639974302e-1007j)  +/-  (6.29e-247, 6.29e-247j)
| (1.0547260148797809805 - 1.7279932405080006477e-1009j)  +/-  (1.62e-251, 1.62e-251j)
| (4.3407179375549160233 - 5.2819763014187949705e-1002j)  +/-  (3.28e-245, 3.28e-245j)
| (6.8956391981569169575 - 4.5444869273142594852e-1013j)  +/-  (4.22e-244, 4.22e-244j)
| (-2.7228201812104201837 + 1.8301044099109369661e-1032j)  +/-  (1.33e-247, 1.33e-247j)
| (-0.41698724741646768714 + 8.1087137445280613274e-1038j)  +/-  (1.75e-253, 1.75e-253j)
| (7.485336286116986494 + 7.8777469677693084749e-1035j)  +/-  (2.4e-244, 2.4e-244j)
| (1.9090466889022845717 - 4.8448968355364885976e-1051j)  +/-  (1.56e-249, 1.56e-249j)
| (-3.9139822016309083791 - 8.0129349733382474374e-1050j)  +/-  (9.7e-246, 9.7e-246j)
| (-1.9090466889022845717 + 4.4361868338751940262e-1054j)  +/-  (1.77e-249, 1.77e-249j)
| (-1.2002150555245762997e-1062 - 3.0790571849407626338e-1063j)  +/-  (5.82e-1061, 5.82e-1061j)
| (2.7228201812104201837 - 1.9831063602398014965e-1052j)  +/-  (1.29e-247, 1.29e-247j)
| (0.41698724741646768714 + 3.1977595273809563225e-1060j)  +/-  (1.75e-253, 1.75e-253j)
| (2.3344142183389772393 + 1.5889349278801875409e-1055j)  +/-  (1.73e-248, 1.73e-248j)
| (-3.4954745810572123223 - 2.6875671343712506911e-1054j)  +/-  (2.79e-246, 2.79e-246j)
| (-1.0547260148797809805 - 1.252462282371672641e-1058j)  +/-  (1.67e-251, 1.67e-251j)
| (-0.74196378430272585765 + 2.4613368301884802342e-1059j)  +/-  (2.2e-252, 2.2e-252j)
-------------------------------------------------
The weights are:
| (1.3617290716235642728e-15 + 1.0943707376206758578e-933j)  +/-  (6.69e-83, 2.71e-204j)
| (8.5098278923977914525e-21 + 4.9952476927055536978e-939j)  +/-  (1.95e-86, 7.92e-208j)
| (1.3179749310774598101e-28 - 6.0617394264611513629e-943j)  +/-  (4.02e-90, 1.63e-211j)
| (1.3617290716235642728e-15 + 1.2284721020958776782e-935j)  +/-  (1.01e-83, 4.12e-205j)
| (4.1139022621273859927e-10 - 2.2594547537741447957e-930j)  +/-  (8.62e-80, 3.5e-201j)
| (3.4612404346293112488e-24 - 4.1536098066952352373e-941j)  +/-  (1.79e-88, 7.27e-210j)
| (1.0787656158545588984e-08 - 1.0727202497430223076e-929j)  +/-  (6.29e-79, 2.55e-200j)
| (1.6438767302054146989e-13 - 3.7137161675800631996e-934j)  +/-  (1.14e-82, 4.61e-204j)
| (1.4595760102130602227e-09 + 3.6742479446097374597e-929j)  +/-  (5.79e-80, 2.35e-201j)
| (5.4468259851929367945e-18 + 7.8191986940924600473e-936j)  +/-  (4.95e-87, 2.01e-208j)
| (1.3179749310774598101e-28 + 9.8655612796695682852e-944j)  +/-  (4.76e-92, 1.93e-213j)
| (8.5098278923977914525e-21 - 6.3667363634829329129e-938j)  +/-  (6.25e-89, 2.54e-210j)
| (4.1139022621273859927e-10 - 2.7700605021583922141e-931j)  +/-  (3.51e-82, 1.42e-203j)
| (3.4612404346293112488e-24 + 3.4994514774503519562e-940j)  +/-  (4.95e-91, 2.01e-212j)
| (1.0842495357397273447e-11 + 9.7023259685925139572e-933j)  +/-  (2.19e-83, 8.89e-205j)
| (5.4468259851929367945e-18 - 3.0696597494110174989e-937j)  +/-  (2.45e-87, 9.95e-209j)
| (1.9369603897192351198e-06 - 3.8879326943482872308e-928j)  +/-  (3.07e-82, 1.24e-203j)
| (1.4595760102130602227e-09 + 5.7615358511109493633e-930j)  +/-  (1.51e-81, 6.13e-203j)
| (0.010700230333840230299 - 6.1074155149207119826e-926j)  +/-  (7.53e-75, 3.06e-196j)
| (1.8525238359832227166e-07 + 2.3425841539624734438e-929j)  +/-  (1.24e-81, 5.01e-203j)
| (1.0787656158545588984e-08 - 6.3135617435266178754e-929j)  +/-  (2.3e-84, 9.32e-206j)
| (0.082834195091191148888 - 1.0278885924456186375e-924j)  +/-  (1.22e-74, 4.94e-196j)
| (0.0012713967147094986114 - 3.4253652380412134979e-926j)  +/-  (5.11e-80, 2.07e-201j)
| (7.9353306406220496015e-05 - 4.5372375511172672775e-927j)  +/-  (4.27e-82, 1.73e-203j)
| (1.9369603897192351198e-06 - 1.0004950111771371826e-928j)  +/-  (1.01e-82, 4.08e-204j)
| (0.059109215631114557888 - 2.225309007301056882e-925j)  +/-  (1.05e-74, 4.24e-196j)
| (0.059109215631114557888 - 3.2107539063457450435e-925j)  +/-  (1.13e-75, 4.6e-197j)
| (1.4042106365233763143e-05 + 4.2509695009561212627e-928j)  +/-  (1.43e-82, 5.79e-204j)
| (0.0003662447246266273934 + 1.3295985335348635861e-926j)  +/-  (6.7e-82, 2.72e-203j)
| (1.8525238359832227166e-07 + 1.103293718956147098e-928j)  +/-  (2.26e-85, 9.16e-207j)
| (0.0012713967147094986114 - 1.53246469402807287e-926j)  +/-  (1.58e-82, 6.41e-204j)
| (0.086173394249004628042 + 6.8654924174628764651e-925j)  +/-  (3.15e-76, 1.28e-197j)
| (1.4042106365233763143e-05 + 1.4048351184254595019e-927j)  +/-  (5.34e-84, 2.17e-205j)
| (1.0842495357397273447e-11 + 1.2011798391436355517e-931j)  +/-  (1.05e-89, 4.27e-211j)
| (0.0036355401766956980026 + 3.3940061041901772338e-926j)  +/-  (2.46e-83, 9.99e-205j)
| (0.14191227121175667912 + 8.6208341444163053205e-925j)  +/-  (2.48e-80, 1.01e-201j)
| (1.6438767302054146989e-13 - 9.30753738652012257e-933j)  +/-  (3.55e-91, 1.44e-212j)
| (0.028187639015623028386 + 1.7565198100164650095e-925j)  +/-  (7.69e-83, 3.12e-204j)
| (7.9353306406220496015e-05 - 1.5827467230871164923e-927j)  +/-  (1.18e-85, 4.78e-207j)
| (0.028187639015623028386 + 1.0869714618914865577e-925j)  +/-  (4.49e-83, 1.82e-204j)
| (0.17142868511252497273 - 7.8500029354549073752e-925j)  +/-  (1.22e-81, 4.95e-203j)
| (0.0036355401766956980026 + 6.8264414838920779225e-926j)  +/-  (2.18e-84, 8.82e-206j)
| (0.14191227121175667912 + 9.5556955638881089773e-925j)  +/-  (2.12e-82, 8.61e-204j)
| (0.010700230333840230299 - 1.1046631365357616136e-925j)  +/-  (3.68e-84, 1.49e-205j)
| (0.0003662447246266273934 + 5.2849684783897720735e-927j)  +/-  (1.62e-85, 6.58e-207j)
| (0.086173394249004628042 + 5.2848241175789145378e-925j)  +/-  (6.18e-84, 2.53e-205j)
| (0.082834195091191148888 - 8.5552632196798104749e-925j)  +/-  (1.17e-83, 4.67e-205j)
