Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 20 31
-------------------------------------------------
Trying to find an order 20 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 31 Kronrod extension for:
P2 : 4*t^22 - 2363181614/5060457*t^20 + 113450524465/5060457*t^18 - 649682892835/1124546*t^16 + 9847192205525/1124546*t^14 - 181074366537155/2249092*t^12 + 2012228184271305/4498184*t^10 - 13066960735503675/8996368*t^8 + 92387182004842725/35985472*t^6 - 155509398101932875/71970944*t^4 + 94224095717476725/143941888*t^2 - 8649322961253975/287883776
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^53 - 10326559799760291840892087670801775673989104263898236679661591900650854677914072128237162888083450605494995135927328521177257174774367150087099073354263426778/5404159799055435486200467120253998323182160268920284226411178949149693719335043207783008766473831178707447685188889536121822341672840292262825797021749739*t^51 + 2265867571722158887654231805282546235988787618799798516224180923521176221508149692840702568944739332354141727962492507663332873665718209303394732482437453812975/5404159799055435486200467120253998323182160268920284226411178949149693719335043207783008766473831178707447685188889536121822341672840292262825797021749739*t^49 - 202354964828658865628072948746138205970802326380324456531639144415145649021662910390989667447639390414380630816636154981559111495874743423139995357298779157778875/3602773199370290324133644746835998882121440179280189484274119299433129146223362138522005844315887452471631790125926357414548227781893528175217198014499826*t^47 + 12370139340935281628239628721146882414326420347531018186235844080287502647393838059742915945829616111243771255708542976616387725031918825304527132423699120360603575/2401848799580193549422429831223999254747626786186792989516079532955419430815574759014670562877258301647754526750617571609698818521262352116811465342999884*t^45 - 1650380319192726146552185947300829852186805837653124107311250008053098098690703056859596078061480412256098852244236914215552325017224242909918581021199710662108864645/4803697599160387098844859662447998509495253572373585979032159065910838861631149518029341125754516603295509053501235143219397637042524704233622930685999768*t^43 + 166199205738125459210126020265083697093990694676955617019623539998115703109572064975035565445187570748579125320754205301695677214921930057226308666229925932139542470145/9607395198320774197689719324895997018990507144747171958064318131821677723262299036058682251509033206591018107002470286438795274085049408467245861371999536*t^41 - 12937870543632799204859885075421016737064326667596187123420653632619337657453997300651202529585127748143239787504534503262621916346969314317645370396119472272390363192175/19214790396641548395379438649791994037981014289494343916128636263643355446524598072117364503018066413182036214004940572877590548170098816934491722743999072*t^39 + 197748232605344457208183851923778093095503534517513719302594687940161759204341946007391011990483387006865470077774559061829175943740522757499401181257385676947500477751075/9607395198320774197689719324895997018990507144747171958064318131821677723262299036058682251509033206591018107002470286438795274085049408467245861371999536*t^37 - 4797563079738295019584592409387067621241307739794960521237399648499090070012558629681794992302878465274436848797381101694885210365698768317581097152241358091481300622154125/9607395198320774197689719324895997018990507144747171958064318131821677723262299036058682251509033206591018107002470286438795274085049408467245861371999536*t^35 + 743868558052448482424361971407826672970073982810561300133210135209679556991180069951918659658768458157181786293451547464492567922066752896341733518810277885867482910738946975/76859161586566193581517754599167976151924057157977375664514545054573421786098392288469458012072265652728144856019762291510362192680395267737966890975996288*t^33 - 23115354019758579455514100352322936868534916256754377735003353204544337270655624911764129856772487733244432690065209892153386034729743402626908497792128069923511707878953323725/153718323173132387163035509198335952303848114315954751329029090109146843572196784576938916024144531305456289712039524583020724385360790535475933781951992576*t^31 + 576336397790760732888568172241006947092236326419075204259096194828567691255138570211207889062661258117917070001671067204930421972163088014491611303073669054390691263909101247375/307436646346264774326071018396671904607696228631909502658058180218293687144393569153877832048289062610912579424079049166041448770721581070951867563903985152*t^29 - 11512826594637477802548410303155114580451611413123600239062510233366089361400337480662129315420818209405113597266108395378845306551214180028993483438149236140352121995608844066125/614873292692529548652142036793343809215392457263819005316116360436587374288787138307755664096578125221825158848158098332082897541443162141903735127807970304*t^27 + 183562557250160208239379629205820811426579096626146989322277480865847926976076617201621654047413498835900041161916803315997776894371879692396984711263070109568256838544535858190625/1229746585385059097304284073586687618430784914527638010632232720873174748577574276615511328193156250443650317696316196664165795082886324283807470255615940608*t^25 - 2321763982807155260466121476258353198919004594080880839125921337155430257344626959297294342798211407202522890006379598107059338264016577702089875331116579547751886207355989030149375/2459493170770118194608568147173375236861569829055276021264465441746349497155148553231022656386312500887300635392632393328331590165772648567614940511231881216*t^23 + 46186445739183703293799506219348558661592599740000019648176048723641326272319707483808075012060394853675668572099318731194320479077148448139424536202133377262805312543267311979926875/9837972683080472778434272588693500947446279316221104085057861766985397988620594212924090625545250003549202541570529573313326360663090594270459762044927524864*t^21 - 357020520952150847920974298540747365281814813524811272889718518170370296677393952372525598711503584597792402558805772921961867225735618244409812207267229170019538313107172000354053125/19675945366160945556868545177387001894892558632442208170115723533970795977241188425848181251090500007098405083141059146626652721326181188540919524089855049728*t^19 + 2111772451905025015481706147121278014198206422359459720025540694089332622642032949096526412575166564637846275681492841991335565151069403155663792050797401784046178700276410279058271875/39351890732321891113737090354774003789785117264884416340231447067941591954482376851696362502181000014196810166282118293253305442652362377081839048179710099456*t^17 - 9366313377819671837456038061137718072516954727801965372694337790553889472583033331767555377604898635288484934559204526047547475693932984883082545497343790944856965752273839985015078125/78703781464643782227474180709548007579570234529768832680462894135883183908964753703392725004362000028393620332564236586506610885304724754163678096359420198912*t^15 + 30331014278913628028736403665207220524402789057361136296385690452346791643704133685858234566230879184833925352243885424916386250732673200579358457066204084367266072855524456719267746875/157407562929287564454948361419096015159140469059537665360925788271766367817929507406785450008724000056787240665128473173013221770609449508327356192718840397824*t^13 - 69218370912653121745074519799696857120673793606664942912031748998223749587236717129713547925928566924560749173758915544189511751118926190312529969474944961820058891328216729633339340625/314815125858575128909896722838192030318280938119075330721851576543532735635859014813570900017448000113574481330256946346026443541218899016654712385437680795648*t^11 + 106123620801764603315241861471025770216245982475329712523814043250577548261497627164106945242643987424617828315345720512191411221319014813444821129156624503081401094330503343262247078125/629630251717150257819793445676384060636561876238150661443703153087065471271718029627141800034896000227148962660513892692052887082437798033309424770875361591296*t^9 - 102322561894814494881300820204600771796203970834541423555500493670486341296671482329027492376247458785770558073481051498329429006477572795088721015479876128983074135017059864572083171875/1259260503434300515639586891352768121273123752476301322887406306174130942543436059254283600069792000454297925321027785384105774164875596066618849541750723182592*t^7 + 28118361809121365632888438869768405943183239507864613837057488308554915803590402175324025369897194352650066494595108675876319504633612779878375384863428637636218567714828061473963046875/1259260503434300515639586891352768121273123752476301322887406306174130942543436059254283600069792000454297925321027785384105774164875596066618849541750723182592*t^5 - 7318014199189908419664903869734921503053195592209640328099784514681964505305177162397434296127111790789294378255363576280536022105713764278832993979073555664210073272100948920700859375/2518521006868601031279173782705536242546247504952602645774812612348261885086872118508567200139584000908595850642055570768211548329751192133237699083501446365184*t^3 + 131909478583270714314908322651463625042053349907439078208802004491939946531561538018876110425824469982392204252574266394669828339086504109540776563236219657903494992985205448980546875/1259260503434300515639586891352768121273123752476301322887406306174130942543436059254283600069792000454297925321027785384105774164875596066618849541750723182592*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:
| (7.688093438359183177 - 3.1070987508167432241e-906j)  +/-  (7.85e-246, 7.85e-246j)
| (7.128522055252823433 + 1.95269750455000013e-921j)  +/-  (5.01e-245, 5.01e-245j)
| (-8.363507178634053701 + 7.6316085292973965717e-938j)  +/-  (5.45e-247, 5.45e-247j)
| (-5.7420184136196614094 - 1.7140631600564928102e-933j)  +/-  (1.05e-243, 1.05e-243j)
| (6.1704456244521599937 - 2.0308503174664681622e-943j)  +/-  (5.33e-244, 5.33e-244j)
| (5.3404621098936174793 + 4.4989723601277367813e-955j)  +/-  (1.9e-243, 1.9e-243j)
| (-4.9669129495130888888 - 6.9160236635432232639e-966j)  +/-  (3.11e-243, 3.11e-243j)
| (5.7420184136196614094 + 4.3807578958140747974e-970j)  +/-  (1.09e-243, 1.09e-243j)
| (-5.3404621098936174793 + 4.8587912572337437292e-979j)  +/-  (1.95e-243, 1.95e-243j)
| (8.363507178634053701 + 1.1304564685929401853e-982j)  +/-  (4.96e-247, 4.96e-247j)
| (-4.6264102465070881318 - 1.4944588443894769491e-978j)  +/-  (3.4e-243, 3.4e-243j)
| (-7.688093438359183177 - 2.4060581606202569489e-983j)  +/-  (7.94e-246, 7.94e-246j)
| (-1.5602297358206136229 - 3.8422946828536348241e-985j)  +/-  (1.15e-247, 1.15e-247j)
| (4.6264102465070881318 - 1.0820245539558125788e-978j)  +/-  (3.65e-243, 3.65e-243j)
| (-7.128522055252823433 + 1.3792564153546933132e-988j)  +/-  (4.83e-245, 4.83e-245j)
| (2.4596125933276574175 + 1.1150226702333747785e-986j)  +/-  (2.17e-245, 2.17e-245j)
| (3.7299268395214693487 + 5.360932000135233277e-990j)  +/-  (1.8e-243, 1.8e-243j)
| (-6.1704456244521599937 + 2.6760323433896643205e-996j)  +/-  (4.97e-244, 4.97e-244j)
| (-0.81308893461674038758 - 7.9529253516363324281e-1003j)  +/-  (1.35e-250, 1.35e-250j)
| (-4.0198937412734523869 + 1.335408472203712569e-994j)  +/-  (2.85e-243, 2.85e-243j)
| (6.629459045641849664 + 1.5061447372510192498e-1000j)  +/-  (1.79e-244, 1.79e-244j)
| (1.6640073196733117201 - 1.7886049898981830162e-1008j)  +/-  (4.56e-247, 4.56e-247j)
| (4.3171050031909214531 + 5.2359090518588327857e-1003j)  +/-  (3.63e-243, 3.63e-243j)
| (-2.6588950923480691058 - 9.8108931735908849539e-1015j)  +/-  (6.78e-245, 6.78e-245j)
| (-2.4596125933276574175 + 1.5992333561226859499e-1015j)  +/-  (1.74e-245, 1.74e-245j)
| (4.9669129495130888888 - 8.7742024018738115544e-1013j)  +/-  (2.9e-243, 2.9e-243j)
| (0.81308893461674038758 + 1.9321064786558472673e-1023j)  +/-  (1.23e-250, 1.23e-250j)
| (1.1824573980870984249 - 1.3262803831819731722e-1023j)  +/-  (1.09e-249, 1.09e-249j)
| (-4.3171050031909214531 - 4.557480599553798894e-1016j)  +/-  (3.76e-243, 3.76e-243j)
| (-0.7071067811865475244 + 3.2579428726511886352e-1024j)  +/-  (6.58e-251, 6.58e-251j)
| (-2.8904914398492981384 + 1.7864755949349719795e-1017j)  +/-  (1.7e-244, 1.7e-244j)
| (-6.629459045641849664 + 8.656496737970818951e-1018j)  +/-  (1.86e-244, 1.86e-244j)
| (2.1548568221159978848 + 6.3303687203823107074e-1019j)  +/-  (2.21e-246, 2.21e-246j)
| (-3.7299268395214693487 + 7.3710073862163615332e-1016j)  +/-  (1.75e-243, 1.75e-243j)
| (-1.1824573980870984249 - 1.481976291665818951e-1022j)  +/-  (1.08e-249, 1.08e-249j)
| (-3.1813615006988979167 + 9.2563741176876585159e-1019j)  +/-  (3.95e-244, 3.95e-244j)
| (3.4578485806174722465 - 1.0164756702019085854e-1015j)  +/-  (8.79e-244, 8.79e-244j)
| (1.7911820554545786153 - 3.8177969355093869809e-1022j)  +/-  (6.07e-247, 6.07e-247j)
| (2.2027386372411830929e-1050 - 4.8943780948700593011e-1050j)  +/-  (2.84e-1048, 2.84e-1048j)
| (-1.7911820554545786153 + 9.2282020918315230793e-1021j)  +/-  (5.95e-247, 5.95e-247j)
| (-0.56760771782978218506 - 1.3084826600867754085e-1025j)  +/-  (8.52e-252, 8.52e-252j)
| (4.0198937412734523869 - 1.4250093192795857799e-1016j)  +/-  (2.93e-243, 2.93e-243j)
| (3.1813615006988979167 + 1.905379106454153032e-1023j)  +/-  (4.02e-244, 4.02e-244j)
| (0.23531522719079604564 + 2.8709981117298769644e-1038j)  +/-  (7.72e-254, 7.72e-254j)
| (-2.1548568221159978848 + 1.7111421338057216068e-1027j)  +/-  (2.13e-246, 2.13e-246j)
| (-3.4578485806174722465 - 2.5898803423421711341e-1027j)  +/-  (1.04e-243, 1.04e-243j)
| (1.5602297358206136229 + 5.6749166736099057909e-1030j)  +/-  (1.18e-247, 1.18e-247j)
| (0.7071067811865475244 - 5.0279904156890597052e-1033j)  +/-  (6.95e-251, 6.95e-251j)
| (0.56760771782978218506 - 9.6135173100801169653e-1034j)  +/-  (8.45e-252, 8.45e-252j)
| (2.6588950923480691058 + 2.6051870395675814637e-1028j)  +/-  (6.13e-245, 6.13e-245j)
| (-0.23531522719079604564 + 7.2986058263343389004e-1041j)  +/-  (7.72e-254, 7.72e-254j)
| (-1.6640073196733117201 + 1.8493062499139388523e-1033j)  +/-  (5.05e-247, 5.05e-247j)
| (2.8904914398492981384 - 1.2298915196021588329e-1035j)  +/-  (1.58e-244, 1.58e-244j)
-------------------------------------------------
The weights are:
| (7.2707212186492306229e-27 + 2.1109427911531804905e-931j)  +/-  (1.11e-85, 3.21e-207j)
| (2.5239476859535121958e-23 - 6.3102306579241561202e-930j)  +/-  (4.95e-84, 1.43e-205j)
| (1.8418101991311208824e-31 - 2.4592838124727266966e-936j)  +/-  (1.69e-89, 4.89e-211j)
| (1.122552950368024797e-15 + 3.5157016565247449704e-926j)  +/-  (2.82e-81, 8.14e-203j)
| (7.2782536018863507406e-18 - 8.8555226961481877738e-927j)  +/-  (8.01e-82, 2.31e-203j)
| (8.9975808741672750923e-14 - 5.4289093476359109858e-924j)  +/-  (1.61e-79, 4.66e-201j)
| (3.9003367307515820154e-12 + 2.1188122396821701788e-923j)  +/-  (1.51e-79, 4.35e-201j)
| (1.122552950368024797e-15 + 2.4262305350552800075e-925j)  +/-  (6.96e-81, 2.01e-202j)
| (8.9975808741672750923e-14 - 9.7824180253188213819e-925j)  +/-  (6.09e-81, 1.76e-202j)
| (1.8418101991311208824e-31 + 5.8446311064952960531e-935j)  +/-  (3.97e-90, 1.14e-211j)
| (9.2266900169473043425e-11 - 3.3540448804517022992e-922j)  +/-  (7.44e-79, 2.15e-200j)
| (7.2707212186492306229e-27 + 1.4692100842119544997e-933j)  +/-  (5.76e-90, 1.66e-211j)
| (0.028261956153201600072 - 1.7159295725593329659e-914j)  +/-  (8.27e-63, 2.39e-184j)
| (9.2266900169473043425e-11 - 1.3490421918717167562e-921j)  +/-  (2.06e-80, 5.94e-202j)
| (2.5239476859535121958e-23 - 2.3831518733120490581e-931j)  +/-  (1.82e-88, 5.26e-210j)
| (0.00035015627329404175634 - 5.2171329852024068336e-916j)  +/-  (4.29e-72, 1.24e-193j)
| (1.439377545880423455e-07 + 6.4218761190587609674e-919j)  +/-  (4.43e-78, 1.28e-199j)
| (7.2782536018863507406e-18 - 9.6976777998754461718e-928j)  +/-  (1.46e-85, 4.23e-207j)
| (0.14785346165481482325 - 8.3861404939036669209e-914j)  +/-  (7.5e-67, 2.17e-188j)
| (1.600299543996824305e-08 - 3.1004035052172987918e-920j)  +/-  (1.45e-79, 4.17e-201j)
| (2.2012748080539372647e-20 + 2.5898646988599242115e-928j)  +/-  (9.95e-87, 2.87e-208j)
| (-0.015952826468452005635 + 3.1809497330470057369e-914j)  +/-  (4.61e-69, 1.33e-190j)
| (1.3614716061958142814e-09 + 1.3020485706632713706e-920j)  +/-  (2.89e-80, 8.34e-202j)
| (8.2851085400104528478e-05 + 1.35141014377817056e-916j)  +/-  (4.35e-76, 1.26e-197j)
| (0.00035015627329404175634 - 2.6880636662056092625e-916j)  +/-  (2.99e-75, 8.64e-197j)
| (3.9003367307515820154e-12 + 9.8536581964285989848e-923j)  +/-  (7.79e-83, 2.25e-204j)
| (0.14785346165481482325 - 1.036975462419919339e-913j)  +/-  (2.96e-68, 8.55e-190j)
| (0.048666608202735063243 + 1.4167296960164890235e-914j)  +/-  (2.37e-68, 6.85e-190j)
| (1.3614716061958142814e-09 + 3.6560750703980149443e-921j)  +/-  (1.4e-81, 4.04e-203j)
| (-0.10992229769145817946 + 1.5402230004281793138e-913j)  +/-  (7.87e-69, 2.27e-190j)
| (3.7520911379416607282e-05 - 3.4496687679902282474e-917j)  +/-  (6.77e-78, 1.95e-199j)
| (2.2012748080539372647e-20 + 1.9149361217717164749e-929j)  +/-  (1.26e-89, 3.63e-211j)
| (0.0017919693318520276803 + 1.1189361346047945137e-915j)  +/-  (3.52e-77, 1.02e-198j)
| (1.439377545880423455e-07 + 2.2262051509554697884e-919j)  +/-  (6.15e-81, 1.77e-202j)
| (0.048666608202735063243 + 1.0390254156325861568e-914j)  +/-  (5.41e-73, 1.56e-194j)
| (6.5262345856661106924e-06 + 5.9765702574179716042e-918j)  +/-  (1.32e-79, 3.81e-201j)
| (9.7031388326884994343e-07 - 3.231655307536592708e-918j)  +/-  (8.54e-83, 2.47e-204j)
| (0.011612230609471495001 - 1.1836871258000563801e-914j)  +/-  (2.25e-77, 6.49e-199j)
| (0.11273866851088655727 - 6.6889275649066339713e-914j)  +/-  (9.73e-75, 2.81e-196j)
| (0.011612230609471495001 - 7.3635354204899323915e-915j)  +/-  (2.07e-77, 5.97e-199j)
| (0.17820798933122222611 - 1.0115495355503215677e-913j)  +/-  (1.31e-74, 3.78e-196j)
| (1.600299543996824305e-08 - 9.895722013065723528e-920j)  +/-  (4.46e-84, 1.29e-205j)
| (6.5262345856661106924e-06 + 1.4414449761315330966e-917j)  +/-  (1.32e-82, 3.81e-204j)
| (0.15263338840414719648 + 6.0683199233071486512e-914j)  +/-  (1.17e-76, 3.4e-198j)
| (0.0017919693318520276803 + 6.2901246347799416589e-916j)  +/-  (2.05e-79, 5.93e-201j)
| (9.7031388326884994343e-07 - 1.2265175274934284796e-918j)  +/-  (3.28e-82, 9.47e-204j)
| (0.028261956153201600072 - 2.5897232708662771905e-914j)  +/-  (1.95e-78, 5.65e-200j)
| (-0.10992229769145817946 + 1.8522425419705647184e-913j)  +/-  (1.05e-77, 3.04e-199j)
| (0.17820798933122222611 - 1.1728203661876468011e-913j)  +/-  (6.71e-78, 1.95e-199j)
| (8.2851085400104528478e-05 + 2.7803686185979831346e-916j)  +/-  (1.74e-82, 5e-204j)
| (0.15263338840414719648 + 5.7078770528975761788e-914j)  +/-  (3.35e-79, 1.13e-200j)
| (-0.015952826468452005635 + 2.0489851025853761233e-914j)  +/-  (4.08e-80, 1.44e-201j)
| (3.7520911379416607282e-05 - 7.6064279352943410785e-917j)  +/-  (3.94e-83, 1.12e-204j)
