data: - - Lhash: 692432823712997555306394244225,2044001334341525037229018635576 a10: 0 a2: 0 a3: 0 a4: 0 a5: 2 a6: 0 a7: -4 a8: 0 a9: 0 accuracy: 100 algebraic: true analytic_conductor: 428.3750897471616 analytic_normalization: __RealLiteral__: 0 data: '0.5' prec: 10 bad_lfactors: - - 2 - - 1 - - 3 - - 1 bad_primes: - 2 - 3 central_character: '2592.1' coefficient_field: 1.1.1.1 conductor: 6718464 conductor_radical: 6 degree: 4 euler_factors: - - 1 - - 1 - - 1 - -2 - -1 - -10 - 25 - - 1 - 4 - 9 - 28 - 49 - - 1 - 4 - 5 - 44 - 121 - - 1 - -2 - -9 - -26 - 169 - - 1 - -12 - 70 - -204 - 289 - - 1 - -8 - 54 - -152 - 361 - - 1 - 0 - -23 - 0 - 529 - - 1 - -2 - -25 - -58 - 841 - - 1 - -4 - -15 - -124 - 961 - - 1 - 4 - 78 - 148 - 1369 - - 1 - -2 - -37 - -82 - 1681 - - 1 - -4 - -27 - -172 - 1849 - - 1 - 8 - 17 - 376 - 2209 - - 1 - 20 - 206 - 1060 - 2809 - - 1 - -4 - -43 - -236 - 3481 - - 1 - 6 - -25 - 366 - 3721 - - 1 - -4 - -51 - -268 - 4489 - - 1 - 32 - 398 - 2272 - 5041 - - 1 - 12 - 182 - 876 - 5329 - - 1 - -4 - -63 - -316 - 6241 - - 1 - 12 - 61 - 996 - 6889 - - 1 - 20 - 278 - 1780 - 7921 - - 1 - -14 - 99 - -1358 - 9409 - - 1 - 6 - -65 - 606 - 10201 - - 1 - 12 - 41 - 1236 - 10609 - - 1 - 8 - 230 - 856 - 11449 - - 1 - -28 - 414 - -3052 - 11881 - - 1 - -2 - -109 - -226 - 12769 euler_factors_factorization: - - 1 - - 1 - - - - 1 - -2 - -1 - -10 - 25 - 1 - - - - 1 - -1 - 7 - 1 - - - 1 - 5 - 7 - 1 - - - - 1 - 4 - 5 - 44 - 121 - 1 - - - - 1 - -7 - 13 - 1 - - - 1 - 5 - 13 - 1 - - - - 1 - -6 - 17 - 2 - - - - 1 - -4 - 19 - 2 - - - - 1 - 0 - -23 - 0 - 529 - 1 - - - - 1 - -2 - -25 - -58 - 841 - 1 - - - - 1 - -11 - 31 - 1 - - - 1 - 7 - 31 - 1 - - - - 1 - 2 - 37 - 2 - - - - 1 - -2 - -37 - -82 - 1681 - 1 - - - - 1 - -4 - -27 - -172 - 1849 - 1 - - - - 1 - 8 - 17 - 376 - 2209 - 1 - - - - 1 - 10 - 53 - 2 - - - - 1 - -4 - -43 - -236 - 3481 - 1 - - - - 1 - 6 - -25 - 366 - 3721 - 1 - - - - 1 - -4 - -51 - -268 - 4489 - 1 - - - - 1 - 16 - 71 - 2 - - - - 1 - 6 - 73 - 2 - - - - 1 - -17 - 79 - 1 - - - 1 - 13 - 79 - 1 - - - - 1 - 12 - 61 - 996 - 6889 - 1 - - - - 1 - 10 - 89 - 2 - - - - 1 - -19 - 97 - 1 - - - 1 - 5 - 97 - 1 - - - - 1 - 6 - -65 - 606 - 10201 - 1 - - - - 1 - 12 - 41 - 1236 - 10609 - 1 - - - - 1 - 4 - 107 - 2 - - - - 1 - -14 - 109 - 2 - - - - 1 - -2 - -109 - -226 - 12769 - 1 gamma_factors: - [] - - 0 - 0 group: GL2 id: 23580332 index: 9 label: 4-2592e2-1.1-c1e2-0-9 leading_term: '2.43951113518653400349485234566653594622344383170553254964440578368356374901334742306519134' load_key: CMFs-workshop motivic_weight: 1 mu_imag: [] mu_real: [] nu_imag: - __RealLiteral__: 0 data: '0.0' prec: 10 - __RealLiteral__: 0 data: '0.0' prec: 10 nu_real_doubled: - 1 - 1 order_of_vanishing: 0 origin: ModularForm/GL2/Q/holomorphic/2592/2/i/q plot_delta: __RealLiteral__: 0 data: '0.029296875' prec: 37 plot_values: - 2.4395111351865344 - 2.431370223687733 - 2.407990914527491 - 2.3686485138019595 - 2.313573767525506 - 2.243058861362119 - 2.15722998907886 - 2.0563152873158037 - 1.9406575651283682 - 1.8106998786876072 - 1.6669864412439983 - 1.5102049752561295 - 1.3411920660119125 - 1.1609483287925764 - 0.9706581937119527 - 0.771687827656681 - 0.5656047764997636 - 0.3541680680393526 - 0.1393296577832388 - -0.07677241451295799 - -0.2918401009466989 - -0.5034216807089507 - -0.708958399626277 - -0.9058038038320683 - -1.0912777821864055 - -1.2627064619862118 - -1.4174800319655778 - -1.5531062896554437 - -1.6672767612944375 - -1.7579221152553126 - -1.8232851291508303 - -1.8619741646348478 - -1.873029596006225 - -1.8559770706903762 - -1.810874498343875 - -1.7383560561037257 - -1.6396628873951014 - -1.5166521929869703 - -1.3718251819851728 - -1.2082798949978089 - -1.0297358428005952 - -0.8404359767205988 - -0.6451418252738209 - -0.44901577935749326 - -0.25755475228113106 - -0.07647967887637613 - 0.0883971423727649 - 0.2312754881218502 - 0.3465373017550515 - 0.42886084362110544 - 0.4733885416915881 - 0.4758566538633075 - 0.4327391609475457 - 0.34137288079742356 - 0.20007164215602388 - 0.008219251602509383 - -0.23365530066063428 - -0.5238312365622837 - -0.8593814526665681 - -1.2361709098645974 - -1.6489245047074665 - -2.09126615933386 - -2.5558778772083084 - -3.034574553868632 - -3.5185526967162115 - -3.9984858870031523 - -4.464858090043375 - -4.90805482406818 - -5.318764738273236 - -5.688045965792273 - -6.007758200559378 - -6.270594022700964 - -6.470494202536366 - -6.602627409171908 - -6.663760293110255 - -6.652144583384613 - -6.567842543750379 - -6.4124769224124325 - -6.189510863828603 - -5.9038553801991 - -5.562072161859106 - -5.171889663773172 - -4.742276105016639 - -4.282939977057465 - -3.8042521699191965 - -3.316779563081614 - -2.8310930726154937 - -2.3573512719852823 - -1.9050653896838887 - -1.4827485566773961 - -1.0976990635721489 - -0.7557540015140272 - -0.46112437468774287 - -0.2162982770651071 - -0.0219507120735448 - 0.12298149984422187 - 0.22129260218536423 - 0.2772714618936097 - 0.29658480771900747 - 0.2859122489953386 - 0.25272947198146034 - 0.20486450827012104 - 0.15021034028412023 - 0.09626774404018122 - 0.04983096250377722 - 0.01658725193292318 - 0.0008328891272071423 - 0.005189541695198599 - 0.03041241936577349 - 0.07527137556249969 - 0.13649422180988346 - 0.20885071001140737 - 0.28524604839635526 - 0.35701486855346465 - 0.4141726328101489 - 0.44586324802788857 - 0.44078078702724244 - 0.3876670511527636 - 0.2758813284252015 - 0.09586265600559538 - -0.16026327868216447 - -0.4982772531968661 - -0.9213993884487791 - -1.4299398057676405 - -2.02110675624001 - -2.688775393177643 - -3.4235977397593356 - -4.212997002320664 - -5.041540124812392 - -5.891200148312569 - -6.741981391009801 - -7.572370304054075 - -8.360216014987305 - -9.083247567005303 - -9.720122354499022 - -10.250943217906569 - -10.658282900624128 - -10.927657363049224 - -11.048359570055096 - -11.013750356385781 - -10.821884289536623 - -10.475381274329534 - -9.981910476656193 - -9.353506458187503 - -8.606877273622429 - -7.762273742476533 - -6.843459638083751 - -5.876416410161315 - -4.888862408665425 - -3.909023568507056 - -2.964806111260107 - -2.0827164753821323 - -1.286949578664677 - -0.5984970056373734 - -0.03439322548992755 - 0.3928852902774933 - 0.6758883881975337 - 0.8123811634968224 - 0.805458282916402 - 0.6632870039547676 - 0.3988203023210734 - 0.029158153774438655 - -0.42511679910030914 - -0.9408537864049704 - -1.4932617604552665 - -2.056946272541841 - -2.6069746057548246 - -3.1197897392655403 - -3.5743305061359183 - -3.9525602640267015 - -4.240529493594172 - -4.4284045434823325 - -4.511241146896601 - -4.488617198844254 - -4.364857741147265 - -4.1484444934855045 - -3.851625170817774 - -3.4896685391743785 - -3.080056104877123 - -2.641566571471498 - -2.1933648899406384 - -1.7539886984648452 - -1.3405522431770265 - -0.9678527132798783 - -0.6477892431562287 - -0.38882209343409263 - -0.19568112847459823 - -0.06928605098102335 - -0.0068259099248476 - -0.0021052355644915147 - -0.04601672353282904 - -0.12719953707401205 - -0.23282694167274287 - -0.3494073991432329 - -0.4637436895770041 - -0.5636632831105133 - -0.6389748106822705 - -0.681934342645046 - -0.6879935766087135 - -0.6559013425510309 - -0.5880470206069579 - -0.49018210608135676 - -0.37127074546700767 - -0.24285428944567894 - -0.11847617232048628 - -0.012761827925880638 - 0.059416723316859495 - 0.08397235897737214 - 0.04851528085279004 - -0.05674663714912973 - -0.23822126703287402 - -0.49836057187820415 - -0.8352357606534501 - -1.2423797674109838 - -1.7089151365178967 - -2.219814219602622 - -2.7566311590179 - -3.2981156489157604 - -3.8214666328673355 - -4.303119014013732 - -4.720374454627926 - -5.052071923329655 - -5.2803904505141235 - -5.391143168707471 - -5.375427341613966 - -5.229440101670995 - -4.955598120717748 - -4.561884959302277 - -4.062218713674669 - -3.475336052268895 - -2.824456770799631 - -2.1357257613738736 - -1.4373969224721772 - -0.7580197271402092 - -0.12536298502811785 - 0.4352856092106918 - 0.9022432982802857 - 1.25864808500091 - 1.4933538442929706 - 1.601447373787379 - 1.5846259515762073 - 1.450959537241722 - 1.2145963984543204 - 0.8948258095414728 - 0.5151432447795922 - 0.10181977613291412 - -0.3175271057720457 - -0.7154864790828471 - -1.066545779331287 - -1.3483719458532073 - -1.543395467532771 - -1.63956956316807 - -1.6314077494637866 - -1.520101386492419 - -1.3137364356966201 - -1.026680874842469 - -0.6790026777415736 - -0.29511957152920903 - 0.09737015346850802 - 0.4695338319465168 - 0.7926308514022474 - 1.03998561154936 - 1.188589731971245 - 1.220554453889879 - 1.1243690013270995 - 0.8956818244984198 - 0.5377935785674204 - 0.06165337137031624 - -0.5146030696255596 - -1.1664703261543645 - -1.8644127159846402 - -2.575312813327314 - -3.264499879912872 - -3.8973718713354795 - -4.4418441712275865 - -4.869646935570055 - -5.158685025202099 - -5.293770307507852 - -5.268201626323181 - -5.083893997486809 - -4.7517189374309625 - -4.290924501447547 - -3.728310778332634 - -3.096754936317007 - -2.4336755890249595 - -1.7787565081598813 - -1.1721088609028174 - -0.651731885278563 - -0.2516593796667552 - 0.00015448628341828698 - 0.0833503124276232 - -0.013603385420294814 - -0.29269131814650645 - -0.7461365127476143 - -1.3567945925324953 - -2.0989031766670836 - -2.939601288446388 - -3.840386433663035 - -4.759555185414105 - -5.653864497429935 - -6.481551239999604 - -7.203647184754766 - -7.78700000471203 - -8.204947907079294 - -8.439585719362888 - -8.481755074763269 - -8.332020292239449 - -7.999917181697554 - -7.503659210493119 - -6.868510755814331 - -6.125682267923094 - -5.309941113642061 - -4.458143367731355 - -3.606632532682671 - -2.7896930819565453 - -2.037463366076004 - -1.3745875719178942 - -0.8191365072011562 - -0.3818210231581822 - -0.06602325965106172 - 0.13216235775420243 - 0.22294481168853478 - 0.2219764339327803 - 0.14875039328227208 - 0.025166003768247062 - -0.126206958872462 - -0.283770433748988 - -0.42826967061836285 - -0.5441948904657969 - -0.6204759114067219 - -0.6512085942225796 - -0.6355867444556551 - -0.5777453202295197 - -0.48598395933075866 - -0.37186509222895786 - -0.2489081690129099 - -0.13131691128693135 - -0.032511614942029296 - 0.036107682489775556 - 0.06631250544203855 - 0.05387811235875997 - -0.0009493631357039214 - -0.09332930717626273 - -0.21415668444261873 - -0.3507736883603657 - -0.48796988885791187 - -0.6093874552565727 - -0.6988655448575929 - -0.7421904655289521 - -0.7282955642422007 - -0.6509232327439005 - -0.5091857275224986 - -0.30868080632151873 - -0.06112764207345095 - 0.21544989578671175 - 0.49802603225629166 - 0.7594174411210054 - 0.9703596755670523 - 1.1010737695062267 - 1.1237737006961386 - 1.0144408586871914 - 0.7551462093093401 - 0.3355637352582289 - -0.2456182609272201 - -0.9798767019506889 - -1.8487796671354193 - -2.824315048664752 - -3.870086651509501 - -4.943040653128356 - -5.995586124161694 - -6.978415836689224 - -7.843144946166893 - -8.54550461069173 - -9.047845211191712 - -9.322088807652037 - -9.35108592447781 - -9.131004972263614 - -8.670718001548108 - -7.993234618418318 - -7.1331312790975705 - -6.136415892310636 - -5.056842064961078 - -3.9539013504984184 - -2.8889587180713905 - -1.9219565541079688 - -1.1079436640654734 - -0.49371938398571635 - -0.11517307390160403 - 0.00498340496197363 - -0.14143450605722702 - -0.5475372825435825 - -1.1916541438846653 - -2.0387208329519813 - -3.042046496046456 - -4.14647539026875 - -5.2910434623240405 - -6.413267233266879 - -7.45195594659837 - -8.351663220280809 - -9.06480595786017 - -9.555466862535198 - -9.799896967536654 - -9.789217827801993 - -9.527779658932557 - -9.034438374081258 - -8.339085011786551 - -7.482208088323383 - -6.510621059275176 - -5.475405843350441 - -4.427920696156295 - -3.4168886796669278 - -2.485416528382169 - -1.6683363277101992 - -0.9906815224172643 - -0.4661623614524503 - -0.09734173298070388 - 0.12439346302600833 - 0.21707011526529843 - 0.2067459052468557 - 0.1247196220185235 - 0.005184274135593251 - -0.11776879181055792 - -0.21273649153794116 - -0.25337746286428625 - -0.22047602330840782 - -0.10303047568520687 - 0.10074663562292224 - 0.38392611403295307 - 0.7311651431121017 - 1.1205566220555212 - 1.525165183569317 - 1.9155740180085814 - 2.262178626022111 - 2.5376950090570873 - 2.719378278363946 - 2.7909067807595043 - 2.7437245199599034 - 2.5776308003453923 - 2.301142136415214 - 1.9310440310124153 - 1.489765277734059 - 1.00379124613448 - 0.5086482596361512 - 0.03723116773691674 positive_zeros: - '0.54623318411897654023694048050704' - '1.33153106367843797436547517728238' - '1.61243274288161144511544500487756' - '2.75777918642639635223666845749864' - '3.11210321750689923638245189346373' - '3.11594811809659479814376814324550' - '3.49839209218241177546766190159782' - '4.51376439229060954432598363816086' - '4.71883769099416620556295262356760' - '5.51606420923729636508185604889699' - '5.53378037272390217592388190966938' - '6.01006486638016017582975513081965' - '6.10979780039144253905857067493210' - '6.86166440945316610047332621941698' - '7.18481242833963500625169124498180' - '7.55126874611262419808969959610884' - '7.82563842306841597038728593252195' - '8.466770107578634234459457748071287' - '8.523196761884638693677920060892979' - '9.353773918829635163119583115158524' prelabel: 4-2592e2-1.1-c1e2-0 primitive: false rational: true root_analytic_conductor: 4.549420205247685 root_angle: 0.0 root_number: '1' self_dual: true sign_arg: 0 spectral_label: c1e2-0 trace_hash: 1510606611075848379 types: - CMF z1: __RealLiteral__: 0 data: '0.54623318411897654023694048051' prec: 103 z2: __RealLiteral__: 0 data: '1.33153106367843797436547517728' prec: 103 z3: __RealLiteral__: 0 data: '1.61243274288161144511544500488' prec: 103 - - algebraic: true analytic_conductor: 428.3750897471616 bad_primes: - 2 - 3 central_character: '1.1' conductor: 6718464 conductor_radical: 6 degree: 4 dirichlet_coefficients: - 1 - 0 - 0 - 0 - 2 - 0 - -4 - 0 - 0 - 0 - -4 - 0 - 2 - 0 - 0 - 0 - 12 - 0 - 8 - 0 - 0 - 0 - 0 - 0 - 5 - 0 - 0 - 0 - 2 - 0 - 4 - 0 - 0 - 0 - -8 - 0 - -4 - 0 - 0 - 0 - 2 - 0 - 4 - 0 - 0 - 0 - -8 - 0 - 7 - 0 - 0 - 0 - -20 - 0 - -8 - 0 - 0 - 0 - 4 - 0 - -6 - 0 - 0 - 0 - 4 - 0 - 4 - 0 - 0 - 0 - -32 - 0 - -12 - 0 - 0 - 0 - 16 - 0 - 4 - 0 - 0 - 0 - -12 - 0 - 24 - 0 - 0 - 0 - -20 - 0 - -8 - 0 - 0 - 0 - 16 - 0 - 14 - 0 - 0 - 0 euler11: - 1 - 4 - 5 - 44 - 121 euler13: - 1 - -2 - -9 - -26 - 169 euler17: - 1 - -12 - 70 - -204 - 289 euler19: - 1 - -8 - 54 - -152 - 361 euler2: - 1 - 0 - 0 - 0 - 0 euler23: - 1 - 0 - -23 - 0 - 529 euler29: - 1 - -2 - -25 - -58 - 841 euler3: - 1 - 0 - 0 - 0 - 0 euler31: - 1 - -4 - -15 - -124 - 961 euler37: - 1 - 4 - 78 - 148 - 1369 euler41: - 1 - -2 - -37 - -82 - 1681 euler43: - 1 - -4 - -27 - -172 - 1849 euler47: - 1 - 8 - 17 - 376 - 2209 euler5: - 1 - -2 - -1 - -10 - 25 euler53: - 1 - 20 - 206 - 1060 - 2809 euler59: - 1 - -4 - -43 - -236 - 3481 euler61: - 1 - 6 - -25 - 366 - 3721 euler67: - 1 - -4 - -51 - -268 - 4489 euler7: - 1 - 4 - 9 - 28 - 49 euler71: - 1 - 32 - 398 - 2272 - 5041 euler73: - 1 - 12 - 182 - 876 - 5329 euler79: - 1 - -4 - -63 - -316 - 6241 euler83: - 1 - 12 - 61 - 996 - 6889 euler89: - 1 - 20 - 278 - 1780 - 7921 euler97: - 1 - -14 - 99 - -1358 - 9409 euler_factors: - - 1 - 0 - 0 - 0 - 0 - - 1 - 0 - 0 - 0 - 0 - - 1 - -2 - -1 - -10 - 25 - - 1 - 4 - 9 - 28 - 49 - - 1 - 4 - 5 - 44 - 121 - - 1 - -2 - -9 - -26 - 169 - - 1 - -12 - 70 - -204 - 289 - - 1 - -8 - 54 - -152 - 361 - - 1 - 0 - -23 - 0 - 529 - - 1 - -2 - -25 - -58 - 841 - - 1 - -4 - -15 - -124 - 961 - - 1 - 4 - 78 - 148 - 1369 - - 1 - -2 - -37 - -82 - 1681 - - 1 - -4 - -27 - -172 - 1849 - - 1 - 8 - 17 - 376 - 2209 - - 1 - 20 - 206 - 1060 - 2809 - - 1 - -4 - -43 - -236 - 3481 - - 1 - 6 - -25 - 366 - 3721 - - 1 - -4 - -51 - -268 - 4489 - - 1 - 32 - 398 - 2272 - 5041 - - 1 - 12 - 182 - 876 - 5329 - - 1 - -4 - -63 - -316 - 6241 - - 1 - 12 - 61 - 996 - 6889 - - 1 - 20 - 278 - 1780 - 7921 - - 1 - -14 - 99 - -1358 - 9409 id: 23580332 index: 9 instance_types: - CMF instance_urls: - ModularForm/GL2/Q/holomorphic/2592/2/i/q is_instance_Artin: false is_instance_BMF: false is_instance_CMF: true is_instance_DIR: false is_instance_ECNF: false is_instance_ECQ: false is_instance_G2Q: false is_instance_HMF: false is_instance_MaassGL3: false is_instance_MaassGL4: false is_instance_MaassGSp4: false is_instance_NF: false label: 4-2592e2-1.1-c1e2-0-9 motivic_weight: 1 mu_imag: [] mu_real: [] nu_imag: - __RealLiteral__: 0 data: '0.0' prec: 10 - __RealLiteral__: 0 data: '0.0' prec: 10 nu_real_doubled: - 1 - 1 order_of_vanishing: 0 prelabel: 4-2592e2-1.1-c1e2-0 primitive: false rational: true root_analytic_conductor: 4.549420205247685 root_angle: 0.0 self_dual: true spectral_label: c1e2-0 trace_hash: 1510606611075848379 z1: __RealLiteral__: 0 data: '0.54623318411897654023694048051' prec: 103 - - Lhash: 692432823712997555306394244225,2044001334341525037229018635576 Lhash_array: - '692432823712997555306394244225' - '2044001334341525037229018635576' id: 23826704 label: 4-2592e2-1.1-c1e2-0-9 type: CMF url: ModularForm/GL2/Q/holomorphic/2592/2/i/q label_cols: - label - label - label labels: - 4-2592e2-1.1-c1e2-0-9 - 4-2592e2-1.1-c1e2-0-9 - 4-2592e2-1.1-c1e2-0-9 tables: - lfunc_lfunctions - lfunc_search - lfunc_instances timestamp: '2024-05-18T03:45:51.892298'