Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 20 31
-------------------------------------------------
Trying to find an order 20 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 31 Kronrod extension for:
P2 : t^22 - 1181590807/5060457*t^20 + 113450524465/5060457*t^18 - 649682892835/562273*t^16 + 19694384411050/562273*t^14 - 362148733074310/562273*t^12 + 4024456368542610/562273*t^10 - 26133921471007350/562273*t^8 + 92387182004842725/562273*t^6 - 155509398101932875/562273*t^4 + 94224095717476725/562273*t^2 - 8649322961253975/562273
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^53 - 5163279899880145920446043835400887836994552131949118339830795950325427338957036064118581444041725302747497567963664260588628587387183575043549536677131713389/5404159799055435486200467120253998323182160268920284226411178949149693719335043207783008766473831178707447685188889536121822341672840292262825797021749739*t^51 + 2265867571722158887654231805282546235988787618799798516224180923521176221508149692840702568944739332354141727962492507663332873665718209303394732482437453812975/5404159799055435486200467120253998323182160268920284226411178949149693719335043207783008766473831178707447685188889536121822341672840292262825797021749739*t^49 - 202354964828658865628072948746138205970802326380324456531639144415145649021662910390989667447639390414380630816636154981559111495874743423139995357298779157778875/1801386599685145162066822373417999441060720089640094742137059649716564573111681069261002922157943726235815895062963178707274113890946764087608599007249913*t^47 + 12370139340935281628239628721146882414326420347531018186235844080287502647393838059742915945829616111243771255708542976616387725031918825304527132423699120360603575/600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971*t^45 - 1650380319192726146552185947300829852186805837653124107311250008053098098690703056859596078061480412256098852244236914215552325017224242909918581021199710662108864645/600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971*t^43 + 166199205738125459210126020265083697093990694676955617019623539998115703109572064975035565445187570748579125320754205301695677214921930057226308666229925932139542470145/600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971*t^41 - 12937870543632799204859885075421016737064326667596187123420653632619337657453997300651202529585127748143239787504534503262621916346969314317645370396119472272390363192175/600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971*t^39 + 790992930421377828832735407695112372382014138070054877210378751760647036817367784029564047961933548027461880311098236247316703774962091029997604725029542707790001911004300/600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971*t^37 - 38380504637906360156676739275096540969930461918359684169899197187992720560100469037454359938423027722195494790379048813559081682925590146540648777217930864731850404977233000/600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971*t^35 + 1487737116104896964848723942815653345940147965621122600266420270419359113982360139903837319317536916314363572586903094928985135844133505792683467037620555771734965821477893950/600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971*t^33 - 46230708039517158911028200704645873737069832513508755470006706409088674541311249823528259713544975466488865380130419784306772069459486805253816995584256139847023415757906647450/600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971*t^31 + 1152672795581521465777136344482013894184472652838150408518192389657135382510277140422415778125322516235834140003342134409860843944326176028983222606147338108781382527818202494750/600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971*t^29 - 23025653189274955605096820606310229160903222826247200478125020466732178722800674961324258630841636418810227194532216790757690613102428360057986966876298472280704243991217688132250/600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971*t^27 + 367125114500320416478759258411641622853158193252293978644554961731695853952153234403243308094826997671800082323833606631995553788743759384793969422526140219136513677089071716381250/600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971*t^25 - 4643527965614310520932242952516706397838009188161761678251842674310860514689253918594588685596422814405045780012759196214118676528033155404179750662233159095503772414711978060298750/600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971*t^23 + 46186445739183703293799506219348558661592599740000019648176048723641326272319707483808075012060394853675668572099318731194320479077148448139424536202133377262805312543267311979926875/600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971*t^21 - 357020520952150847920974298540747365281814813524811272889718518170370296677393952372525598711503584597792402558805772921961867225735618244409812207267229170019538313107172000354053125/600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971*t^19 + 2111772451905025015481706147121278014198206422359459720025540694089332622642032949096526412575166564637846275681492841991335565151069403155663792050797401784046178700276410279058271875/600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971*t^17 - 9366313377819671837456038061137718072516954727801965372694337790553889472583033331767555377604898635288484934559204526047547475693932984883082545497343790944856965752273839985015078125/600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971*t^15 + 30331014278913628028736403665207220524402789057361136296385690452346791643704133685858234566230879184833925352243885424916386250732673200579358457066204084367266072855524456719267746875/600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971*t^13 - 69218370912653121745074519799696857120673793606664942912031748998223749587236717129713547925928566924560749173758915544189511751118926190312529969474944961820058891328216729633339340625/600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971*t^11 + 106123620801764603315241861471025770216245982475329712523814043250577548261497627164106945242643987424617828315345720512191411221319014813444821129156624503081401094330503343262247078125/600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971*t^9 - 102322561894814494881300820204600771796203970834541423555500493670486341296671482329027492376247458785770558073481051498329429006477572795088721015479876128983074135017059864572083171875/600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971*t^7 + 56236723618242731265776877739536811886366479015729227674114976617109831607180804350648050739794388705300132989190217351752639009267225559756750769726857275272437135429656122947926093750/600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971*t^5 - 14636028398379816839329807739469843006106391184419280656199569029363929010610354324794868592254223581578588756510727152561072044211427528557665987958147111328420146544201897841401718750/600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971*t^3 + 1055275828666165714519266581211709000336426799259512625670416035935519572252492304151008883406595759859137634020594131157358626712692032876326212505889757263227959943881643591844375000/600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971*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
-------------------------------------------------
The nodes are:
| (-8.7263278879859661947 - 1.6998505976066577241e-908j)  +/-  (8.01e-244, 8.01e-244j)
| (-8.1204403159369693153 - 3.9440348363264474137e-931j)  +/-  (1.62e-243, 1.62e-243j)
| (-10.872606009319157473 + 1.0435109935358204996e-947j)  +/-  (1.04e-245, 1.04e-245j)
| (7.0242756563279622323 + 1.6472760548802965989e-948j)  +/-  (4.08e-243, 4.08e-243j)
| (11.827785281029018498 + 3.5900444925847999806e-955j)  +/-  (7.24e-247, 7.24e-247j)
| (10.081252570214272522 - 9.2090168665791339523e-953j)  +/-  (7.1e-245, 7.1e-245j)
| (-7.0242756563279622323 - 5.6204721351237974206e-950j)  +/-  (4.22e-243, 4.22e-243j)
| (-11.827785281029018498 + 9.5435331690301948026e-969j)  +/-  (7.12e-247, 7.12e-247j)
| (-6.5427321157121779218 + 3.5585696572096731761e-964j)  +/-  (5.09e-243, 5.09e-243j)
| (2.2064980528153029741 + 1.1774399432754823208e-977j)  +/-  (1.78e-247, 1.78e-247j)
| (10.872606009319157473 - 1.1836624465440105806e-976j)  +/-  (1.07e-245, 1.07e-245j)
| (3.4784174876676331101 + 2.1082870764508221234e-976j)  +/-  (2.8e-245, 2.8e-245j)
| (-9.3754708935436991357 + 5.0479133486989694036e-973j)  +/-  (2.65e-244, 2.65e-244j)
| (-4.0877721961582127083 - 4.4140011307747734137e-975j)  +/-  (2.21e-244, 2.21e-244j)
| (-7.552553945151188188 + 6.8774210321571523225e-979j)  +/-  (2.65e-243, 2.65e-243j)
| (8.1204403159369693153 - 5.1828914145214480914e-991j)  +/-  (1.71e-243, 1.71e-243j)
| (9.3754708935436991357 + 1.8364787393024410673e-993j)  +/-  (2.59e-244, 2.59e-244j)
| (4.8901363593417857701 - 2.5509219951959683101e-992j)  +/-  (1.44e-243, 1.44e-243j)
| (7.552553945151188188 - 1.0390631448301106271e-993j)  +/-  (2.88e-243, 2.88e-243j)
| (2.5331139555031823092 - 3.8779231571053826098e-996j)  +/-  (8.72e-247, 8.72e-247j)
| (-2.3532617193700997362 - 7.2034039087781713435e-998j)  +/-  (6.36e-247, 6.36e-247j)
| (4.0877721961582127083 + 6.9022491692133473476e-994j)  +/-  (2.16e-244, 2.16e-244j)
| (8.7263278879859661947 + 6.551304456423285259e-994j)  +/-  (7.71e-244, 7.71e-244j)
| (-6.105308445701344896 + 1.4683534226629851963e-991j)  +/-  (5.2e-243, 5.2e-243j)
| (-3.047427742808632157 + 3.0228803774849080119e-1007j)  +/-  (3.2e-246, 3.2e-246j)
| (-10.081252570214272522 - 6.3711062030156644774e-1005j)  +/-  (6.82e-245, 6.82e-245j)
| (3.047427742808632157 + 7.7372679091534839722e-1008j)  +/-  (3.14e-246, 3.14e-246j)
| (2.3532617193700997362 + 3.813662639550268983e-1009j)  +/-  (5.84e-247, 5.84e-247j)
| (3.7602455005259023482 + 9.9650918967524317789e-1007j)  +/-  (1.01e-244, 1.01e-244j)
| (-1.6722472893031764503 + 1.4465057245903069124e-1010j)  +/-  (1.54e-249, 1.54e-249j)
| (-5.6849882482076379676 + 4.8506918651188480945e-1004j)  +/-  (3.85e-243, 3.85e-243j)
| (1 - 4.3711473450495494262e-1016j)  +/-  (8.85e-251, 8.85e-251j)
| (1.6722472893031764503 - 4.8454986474363971701e-1015j)  +/-  (1.69e-249, 1.69e-249j)
| (0.33278598572612987549 + 3.6035156004194533667e-1020j)  +/-  (1.06e-253, 1.06e-253j)
| (6.5427321157121779218 + 1.3959588099816647147e-1008j)  +/-  (5.32e-243, 5.32e-243j)
| (-5.2749131231106767794 - 1.6283489859019682235e-1009j)  +/-  (2.61e-243, 2.61e-243j)
| (4.4991245811000041365 + 3.1045906046033171457e-1009j)  +/-  (6.31e-244, 6.31e-244j)
| (1.1498813987504849841 + 5.0817715118399443021e-1017j)  +/-  (1.82e-250, 1.82e-250j)
| (5.6849882482076379676 + 2.2356395323761785337e-1008j)  +/-  (3.72e-243, 3.72e-243j)
| (-1 + 4.239435356187446926e-1018j)  +/-  (9.69e-251, 9.69e-251j)
| (-0.8027185326625188028 + 1.6534943501219631421e-1020j)  +/-  (1.18e-251, 1.18e-251j)
| (-2.2064980528153029741 - 1.9736686398352012151e-1015j)  +/-  (1.68e-247, 1.68e-247j)
| (6.105308445701344896 - 3.5977540370653474372e-1009j)  +/-  (5.27e-243, 5.27e-243j)
| (5.2749131231106767794 - 4.8373445958816846752e-1013j)  +/-  (2.72e-243, 2.72e-243j)
| (-4.4991245811000041365 + 2.938555505421976902e-1013j)  +/-  (5.38e-244, 5.38e-244j)
| (-2.5331139555031823092 + 1.229096190417391016e-1021j)  +/-  (8.24e-247, 8.24e-247j)
| (-4.8901363593417857701 - 4.7813597979122758528e-1020j)  +/-  (1.3e-243, 1.3e-243j)
| (-3.4784174876676331101 + 3.8922406782137122335e-1031j)  +/-  (2.59e-245, 2.59e-245j)
| (0.8027185326625188028 + 3.2080983653539098765e-1039j)  +/-  (1.12e-251, 1.12e-251j)
| (6.9566601412029587776e-1056 - 7.1397577998778269041e-1056j)  +/-  (5.28e-1054, 5.28e-1054j)
| (-3.7602455005259023482 - 2.3443677269757015879e-1037j)  +/-  (8.78e-245, 8.78e-245j)
| (-1.1498813987504849841 + 6.3043842232587941908e-1047j)  +/-  (1.68e-250, 1.68e-250j)
| (-0.33278598572612987549 - 1.0636277557794226627e-1049j)  +/-  (1.06e-253, 1.06e-253j)
-------------------------------------------------
The weights are:
| (7.2782536018863507406e-18 - 7.3988312269887923471e-925j)  +/-  (2.93e-68, 4.71e-189j)
| (1.122552950368024797e-15 + 7.1738507005417563121e-924j)  +/-  (9.23e-67, 1.48e-187j)
| (7.2707212186492306229e-27 - 9.689453565279151521e-932j)  +/-  (7.71e-74, 1.24e-194j)
| (3.9003367307515820154e-12 + 1.567149313562128584e-922j)  +/-  (2.52e-66, 4.05e-187j)
| (1.8418101991311208824e-31 - 1.7679948203906245071e-935j)  +/-  (4.16e-78, 6.68e-199j)
| (2.5239476859535121958e-23 - 1.728305600580164802e-930j)  +/-  (1.61e-74, 2.59e-195j)
| (3.9003367307515820154e-12 + 1.4502226825680932786e-921j)  +/-  (3.62e-66, 5.8e-187j)
| (1.8418101991311208824e-31 + 1.1716932079110711437e-934j)  +/-  (8.27e-78, 1.33e-198j)
| (9.2266900169473043425e-11 - 1.7412706224823049215e-920j)  +/-  (2.63e-65, 4.22e-186j)
| (0.028261956153201600072 - 1.3362347372048740692e-913j)  +/-  (7.32e-48, 1.18e-168j)
| (7.2707212186492306229e-27 + 1.061091501394983528e-932j)  +/-  (1.84e-77, 2.95e-198j)
| (0.00035015627329404175634 - 2.0574601873436440498e-915j)  +/-  (9.33e-57, 1.5e-177j)
| (2.2012748080539372647e-20 - 3.8880821133720132863e-927j)  +/-  (2.03e-72, 3.25e-193j)
| (3.7520911379416607282e-05 - 7.2422736670370681055e-916j)  +/-  (3.27e-60, 5.25e-181j)
| (8.9975808741672750923e-14 - 9.9956434725999547444e-923j)  +/-  (7.36e-68, 1.18e-188j)
| (1.122552950368024797e-15 + 2.5800479537559636756e-925j)  +/-  (2.45e-73, 3.94e-194j)
| (2.2012748080539372647e-20 + 1.3942930972721213059e-928j)  +/-  (5.6e-76, 8.98e-197j)
| (9.7031388326884994343e-07 - 9.2422757833831055542e-918j)  +/-  (1.17e-66, 1.88e-187j)
| (8.9975808741672750923e-14 - 7.2072676552768674236e-924j)  +/-  (1.63e-72, 2.62e-193j)
| (0.011612230609471495001 - 5.7068623640258465432e-914j)  +/-  (2.17e-57, 3.48e-178j)
| (-0.015952826468452005635 + 2.7679120448618579775e-913j)  +/-  (1.64e-58, 2.63e-179j)
| (3.7520911379416607282e-05 - 2.621619116396396212e-916j)  +/-  (2.28e-64, 3.66e-185j)
| (7.2782536018863507406e-18 - 7.0888602247759241744e-927j)  +/-  (5.19e-75, 8.33e-196j)
| (1.3614716061958142814e-09 + 1.5415830991433977727e-919j)  +/-  (1.15e-70, 1.85e-191j)
| (0.0017919693318520276803 + 1.0036286354187109679e-914j)  +/-  (3.17e-63, 5.09e-184j)
| (2.5239476859535121958e-23 + 2.3990445421520754472e-929j)  +/-  (5.32e-79, 8.54e-200j)
| (0.0017919693318520276803 + 4.8408570570941887859e-915j)  +/-  (4.93e-62, 7.91e-183j)
| (-0.015952826468452005635 + 1.5921245493697434735e-913j)  +/-  (4.91e-59, 7.88e-180j)
| (8.2851085400104528478e-05 + 1.0308859086497001929e-915j)  +/-  (2.17e-64, 3.49e-185j)
| (0.048666608202735063243 + 1.2027879754605563466e-913j)  +/-  (1.31e-59, 2.1e-180j)
| (1.600299543996824305e-08 - 1.0987231372410242653e-918j)  +/-  (2.69e-71, 4.32e-192j)
| (-0.10992229769145817946 + 1.2238226641201030871e-912j)  +/-  (9.65e-59, 1.55e-179j)
| (0.048666608202735063243 + 8.1593518125020141656e-914j)  +/-  (4.74e-59, 7.61e-180j)
| (0.15263338840414719648 + 4.5957212848575924732e-913j)  +/-  (3.65e-59, 5.86e-180j)
| (9.2266900169473043425e-11 - 2.4901540557938823941e-921j)  +/-  (3.37e-73, 5.4e-194j)
| (1.439377545880423455e-07 + 6.7797171538262617237e-918j)  +/-  (1.89e-71, 3.03e-192j)
| (6.5262345856661106924e-06 + 4.5217025695032851082e-917j)  +/-  (3.49e-68, 5.6e-189j)
| (0.14785346165481482325 - 6.645136671822824533e-913j)  +/-  (1.11e-60, 1.78e-181j)
| (1.600299543996824305e-08 - 2.3187266165374195729e-919j)  +/-  (4.16e-72, 6.67e-193j)
| (-0.10992229769145817946 + 1.5406155007334917089e-912j)  +/-  (3.92e-62, 6.29e-183j)
| (0.17820798933122222611 - 9.7022128442591251093e-913j)  +/-  (6.43e-62, 1.03e-182j)
| (0.028261956153201600072 - 2.2406753193322894674e-913j)  +/-  (8.81e-67, 1.41e-187j)
| (1.3614716061958142814e-09 + 2.7242572456923962997e-920j)  +/-  (4.11e-73, 6.6e-194j)
| (1.439377545880423455e-07 + 1.671252988777847316e-918j)  +/-  (3.28e-71, 5.26e-192j)
| (6.5262345856661106924e-06 + 1.4146838481814916585e-916j)  +/-  (1.14e-73, 1.84e-194j)
| (0.011612230609471495001 - 1.037524064194348562e-913j)  +/-  (1.28e-69, 2.05e-190j)
| (9.7031388326884994343e-07 - 3.2805222791589113061e-917j)  +/-  (2.5e-74, 4.02e-195j)
| (0.00035015627329404175634 - 4.784909762474323631e-915j)  +/-  (9.23e-73, 1.48e-193j)
| (0.17820798933122222611 - 8.0676010029216752398e-913j)  +/-  (2.61e-69, 4.18e-190j)
| (0.11273866851088655727 - 5.4249576679931668919e-913j)  +/-  (8.63e-70, 1.38e-190j)
| (8.2851085400104528478e-05 + 2.5920296018529835966e-915j)  +/-  (4.29e-73, 6.88e-194j)
| (0.14785346165481482325 - 8.6622086756811443177e-913j)  +/-  (2.5e-70, 4.03e-191j)
| (0.15263338840414719648 + 4.9601423256323157324e-913j)  +/-  (2.09e-70, 3.3e-191j)
