Formats: - HTML - YAML - JSON - 2026-09-07T01:17:49.293527
  • lfunc_lfunctions • Show schema
    {'Lhash': '652976758936082571159913931676,967286154067257927184298800910,1214167913361086171950424950642,2239841048850358251513068066567', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 301304.68380712083, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 7}, 'bad_lfactors': [[3, [1, 0, 0, 0, 4782969]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '75.1', 'coefficient_field': '1.1.1.1', 'conductor': 31640625, 'conductor_radical': 15, 'degree': 8, 'euler_factors': [[1, 0, 0, 0, 32768, 0, 0, 0, 268435456], [1, 0, 0, 0, 4782969], [1], [1, 0, 0, 0, -1351253357977, 0, 0, 0, 459986536544739960976801], [1, 0, -77948684, 0, 2278499001499446, 0, -29600999777032640404844, 0, 144209936106499234037676064081], [1, 0, 0, 0, -6759928051400497, 0, 0, 0, 15502932802662396215269535105521], [1, 0, 0, 0, 336755653118801858, 0, 0, 0, 28351092476867700887730107366063041], [1, 0, 138181606, 0, 1602786910624953051, 0, 110408027046216295151678326, 0, 638411683925748518131605316913942641], [1, 0, 0, 0, 23185672649077499618, 0, 0, 0, 134393854047545109686936775588697536481], [1, 0, 68999505236, 0, 1785349396054796780886, 0, 20531370833528731370943250286516, 0, 88540901833145211536614766025207452637361], [1, -1325548, 768954519058, -254976032227133896, 52857859025541828939595, -7015057182219034784176006456, 582055459661577341532210667177618, -27605208348747383304441787351277072788, 572964121067545096123347421337293637543041], [1, 0, 0, 0, -5563743051285261331822, 0, 0, 0, 81217248802771228597652036390959994837496721], [1, 0, -779017095524, 0, 227575363169493352812966, 0, -29547516404853032438496894754627364, 0, 1438626275603521989270100382252682485138269921], [1, 0, 0, 0, -6431509767729015169177, 0, 0, 0, 5459046029871041534743397034507955551606171601], [1, 0, 0, 0, 513333972375334818668738, 0, 0, 0, 65877941798660252683780571409941608871644628161], [1, 0, 0, 0, 2759892524114287536773138, 0, 0, 0, 1904251686165483303166544735375573842653419591761], [1, 0, 9954605939276, 0, 37160317277350880324776566, 0, 61652719179082938506074649286877301036, 0, 38358032782038398419973086399760468678777161743121], [1, -7993388, 36531315738538, -107284210177357999136, 225810566130390465741272995, -337166682953063109605682707677856, 360813687772886465671353685918066951258, -248117518735334290986223438692789679201630268, 97551820892064552722266841889541788960852432978481], [1, 0, 0, 0, -54545136337176750865517017, 0, 0, 0, 1349256365417755877454657051946796697206085388680241], [1, 0, -36380480633564, 0, 496327264173421973566253286, 0, -3009437403695163573276254267797829481884, 0, 6842798698940938981814244812733146152009703886272161], [1, 0, 0, 0, 54454581630836951278994018, 0, 0, 0, 14894985451961941943846586557477384171894488107677281], [1, 0, 76766244347236, 0, 2210844308492242563442356486, 0, 28310632491533216689892962226452335801316, 0, 136006152866792691625201101984747368303641150837104961], [1, 0, 0, 0, 1472730526623272972123198258, 0, 0, 0, 542233801012015735135407853098133122208235840693558641], [1, 0, 176925339582116, 0, 11738465919842648480065139046, 0, 346138678173542706064747105069547512483556, 0, 3827543948647425430322045212330289877339037312647605281], [1, 0, 0, 0, 8086854168472409683785834863, 0, 0, 0, 42619520516862344959898006540158454742326868747150111361], [1, 0, -428854140842804, 0, 68968452794257338722789468406, 0, -4929567761389785970910306329872359328408404, 0, 132129096689825080931822600853816049099831724850779782801], [1, 0, 0, 0, 2710265791858466612008247138, 0, 0, 0, 228792767573726113549107350198718474022130892363602038561], [1, 0, 0, 0, 51570683004024932787085105298, 0, 0, 0, 664883836375406516433586250657527435394385613490936917201], [1, 0, 699454530815326, 0, 189143700714247095999430772691, 0, 23373861099484302260809966648965274981347886, 0, 1116713952456127112240969687448211536647543601817400964721], [1, 0, 0, 0, 110695050932695295922881126978, 0, 0, 0, 3063348575248001425954190006610728401266477888045839853121]], 'euler_factors_factorization': [[[[1, -16, 128], 2], [[1, 16, 128], 2]], [[[1, 0, 0, 0, 4782969], 1]], [1], [[[1, 0, 0, 0, -1351253357977, 0, 0, 0, 459986536544739960976801], 1]], [[[1, 0, -19487171], 4]], [[[1, 0, 0, 0, -6759928051400497, 0, 0, 0, 15502932802662396215269535105521], 1]], [[[1, 0, 0, 0, 168377826559400929], 2]], [[[1, 0, 69090803, 0, 799006685782884121], 2]], [[[1, 0, 0, 0, 11592836324538749809], 2]], [[[1, 0, 17249876309], 4]], [[[1, -331387, 27512614111], 4]], [[[1, 0, 0, 0, -5563743051285261331822, 0, 0, 0, 81217248802771228597652036390959994837496721], 1]], [[[1, 0, -194754273881], 4]], [[[1, 0, 0, 0, -6431509767729015169177, 0, 0, 0, 5459046029871041534743397034507955551606171601], 1]], [[[1, 0, 0, 0, 256666986187667409334369], 2]], [[[1, 0, 0, 0, 1379946262057143768386569], 2]], [[[1, 0, 2488651484819], 4]], [[[1, -1998347, 3142742836021], 4]], [[[1, 0, 0, 0, -54545136337176750865517017, 0, 0, 0, 1349256365417755877454657051946796697206085388680241], 1]], [[[1, 0, -9095120158391], 4]], [[[1, 0, 0, 0, 54454581630836951278994018, 0, 0, 0, 14894985451961941943846586557477384171894488107677281], 1]], [[[1, 0, 38383122173618, 0, 368790120348678391253573281], 2]], [[[1, 0, 0, 0, 736365263311636486061599129], 2]], [[[1, 0, 44231334895529], 4]], [[[1, 0, 0, 0, 8086854168472409683785834863, 0, 0, 0, 42619520516862344959898006540158454742326868747150111361], 1]], [[[1, 0, -107213535210701], 4]], [[[1, 0, 0, 0, 2710265791858466612008247138, 0, 0, 0, 228792767573726113549107350198718474022130892363602038561], 1]], [[[1, 0, 0, 0, 25785341502012466393542552649], 2]], [[[1, 0, 349727265407663, 0, 33417270272362569384925825561], 2]], [[[1, 0, 0, 0, 55347525466347647961440563489], 2]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 3, 'label': '8-75e4-1.1-c7e4-0-3', 'load_key': 'CMFs-workshop', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0, 0], 'nu_real_doubled': [7, 7, 7, 7], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/75/8/e/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.03125', 'prec': 14}, 'plot_values': [6.289773048032359, 6.187446958144975, 6.044281776147511, 5.83908880025886, 5.553821084312109, 5.17996910744941, 4.732416463327944, 4.2322132918904405, 3.7003949351438647, 3.156176978574686, 2.614396158418513, 2.088651116745632, 1.5918610775916933, 1.1360039858273014, 0.7319414534511162, 0.3880986184271193, 0.10999460418267783, -0.09988268871385951, -0.2420882190608302, -0.3201172194310789, -0.34021330166549896, -0.3110876955993799, -0.24356728484102053, -0.1501434932170132, -0.04442845999248859, 0.05943149993406428, 0.14737259768235442, 0.20603246000868305, 0.22334130752355477, 0.1890723091348302, 0.09534584215169785, -0.06298273880751393, -0.288037182010321, -0.5787412562440203, -0.9307655413867687, -1.3366259453856082, -1.7858948079630672, -2.2655413054599394, -2.7604353685437113, -3.253877997586031, -3.728202349138842, -4.165477855943878, -4.548349066358653, -4.860647982814471, -5.088020582462495, -5.2185977205420855, -5.243708705904772, -5.1581329921634484, -4.960339534783798, -4.652710548040308, -4.241691600265109, -3.7374366716164733, -3.1534663756178687, -2.506277332563658, -1.8147923778984292, -1.0995498867865225, -0.38196314563949957, 0.31646891064080157, 0.9751251026007882, 1.5750229513459488, 2.099476771153098, 2.534791148125103, 2.871075829568916, 3.1023949654591365, 3.2268602065880745, 3.246767472232039, 3.1687820317717854, 3.0032469158168027, 2.763572888268336, 2.465723614522228, 2.127717273448686, 1.7684134940526397, 1.406555549615074, 1.0599876509481025, 0.7449271634946225, 0.474947755742376, 0.26032770490580714, 0.1076297583998423, 0.019411733511020057, -0.005949933977900861, 0.02589154463053839, 0.1056117212019968, 0.22073875358092934, 0.35639664261157467, 0.49619116116590656, 0.6231793355420228, 0.720935847114254, 0.7746006513863782, 0.7718336003129546, 0.7036848004307025, 0.5654103515339469, 0.3569159493474749, 0.08296653005276909, -0.24679519954579776, -0.6180046911275038, -1.0122379660875456, -1.4078618439856798, -1.7810289286976106, -2.106795186345243, -2.3605199267042805, -2.519254399011905, -2.5630680745242644, -2.476222284296032, -2.2482831309186024, -1.8750127124724387, -1.3589260783580737, -0.7093026558400407, 0.05783660704549722, 0.9200586000643841, 1.8493813493018807, 2.813979654117509, 3.7791948287919674, 4.708804524573924, 5.566880286990924, 6.320518820338231, 6.94063592601277, 7.402990876430187, 7.689757420671816, 7.7917492634246015, 7.707659184645648, 7.443691346143124, 7.013730852497471, 6.439893264405968, 5.74996196095573, 4.975588637488625, 4.15112305240054, 3.312699812106191, 2.4951593100452008, 1.7300853205148439, 1.0445798483322861, 0.4603455034709887, -0.008007690730081046, -0.35351992623995654, -0.5767674785524792, -0.6854097858379503, -0.6936103229671273, -0.6207677529039869, -0.4899204588933236, -0.3260069393712043, -0.1540305593880535, 0.002786919547999342, 0.124690947221881, 0.1968412622882098, 0.21032514417511133, 0.16272871176798986, 0.0582468076133457, -0.09269510157304071, -0.2744219613848619, -0.4673572382261379, -0.649696469037557, -0.7993652592282935, -0.8960284108003408, -0.9230081717434228, -0.8690488134373208, -0.7297633434975229, -0.5084599342369116, -0.21651971933584852, 0.12679129424095914, 0.49534093940592233, 0.8575880303675676, 1.178387231955083, 1.4213315479278745, 1.5518300946490802, 1.5394041038912691, 1.3599163115159396, 0.9979012228166074, 0.44890986772788005, -0.2800960223006069, -1.1706271688806063, -2.1928655144878104, -3.3066134197450445, -4.463864235678878, -5.611342046730491, -6.693364020714811, -7.655611263605029, -8.448465948103822, -9.029802183010657, -9.367784071919111, -9.444075631941143, -9.254373524352582, -8.808353195195023, -8.129480771030968, -7.254719595365746, -6.231099679474597, -5.112422778838925, -3.95620147179976, -2.820584076041714, -1.7598342392146609, -0.8208723036573005, -0.040639647682905726, 0.5559740277973106, 0.9575729377276533, 1.166430041039096, 1.197705528778521, 1.0778280669985099, 0.841891305818184, 0.5305709142593403, 0.18669579664162228, -0.1484613821556199, -0.4383975924469413, -0.6540867433486751, -0.7762165042362925, -0.7967771288608876, -0.718898247223057, -0.556059841517731, -0.330654036726969, -0.0716087985487466, 0.18893559276079397, 0.4187393029572803, 0.5886136054206554, 0.6758178159161699, 0.6662196854948692, 0.5555442741161086, 0.35007637166737665, 0.06679404065385065, -0.2687793231193828, -0.6251661584135099, -0.9677715470399466, -1.2621425306003604, -1.478145101276177, -1.593304704169233, -1.5954402490309734, -1.484741622360163, -1.2746998076396359, -0.9915858922086687, -0.6728268679490802, -0.36439289663447283, -0.11688748891020889, 0.01891534089592067, -0.003269497239198689, -0.22065840365108041, -0.657282770563811, -1.320806144914595, -2.2005784253206246, -3.2674437781393126, -4.474738913889305, -5.7606391946833515, -7.052170753135949, -8.271330701776392, -9.340061478300312, -10.18560582129201, -10.746505008556037, -10.979112645271728, -10.859745696221928, -10.386349870483821, -9.579569765028676, -8.482407885655379, -7.1557782961635805, -5.674093188382049, -4.120152743229946, -2.5783400281583626, -1.1284546498903543, 0.15934227035799825, 1.2295650758751124, 2.046895136914567, 2.5960982976570124, 2.881201196175423, 2.9246518016936474, 2.7661469389274758, 2.455589413224201, 2.04746098673253, 1.5963719299340389, 1.1529988603134078, 0.7580002857673094, 0.43903285829912386, 0.20978771068011112, 0.0702424729078846, 0.00785720932031783, 0.0009131371366732698, 0.022815752463169612, 0.04675560858907423, 0.050504414319818364, 0.02067759133754248, -0.044123123611219325, -0.1315758833400805, -0.2156061969938358, -0.25817785071530636, -0.2127426257888526, -0.02901951750564567, 0.3413341425704167, 0.9386280924914546, 1.7893463052516974, 2.901850446045393, 4.262995065860902, 5.836241212016642, 7.562424832310651, 9.364876515200857, 11.1530958538379, 12.827913420262078, 14.289623119506052, 15.450294346526269, 16.237604799119932, 16.59912583048081, 16.508391810640607, 15.97266137076847, 15.027169325696567, 13.730667434412643, 12.162596267224739, 10.420590425217638, 8.60727241153255, 6.821189677092572, 5.150769702031764, 3.6695691664555716, 2.428331943410749, 1.4524749143931928, 0.7429349377179449, 0.2788765576808944, 0.021280018277267172, -0.08074523795651829, -0.08273068190671788, -0.037745501432363986, 0.009927456864567632, 0.02983870766727818, 0.008434829989097243, -0.05021153271278291, -0.12606290155342117, -0.1868557377948234, -0.1935729130475349, -0.10693610850092304, 0.10604316845012701, 0.46591555759868886, 0.9759481626790157, 1.6202023046662766, 2.3631832180264065, 3.151402691833821, 3.917976230658767, 4.5916932108757065, 5.10311676424652, 5.391141940195385, 5.411085587030502, 5.144382592670671, 4.5987783119708405, 3.8078454152304335, 2.8302758994148225, 1.7476693211258383, 0.6536904503402289, -0.3552740383671076, -1.1886586324797497, -1.7709146665796085, -2.0508008749785986, -2.0065177827471397, -1.6481830530229942, -1.0183275060158135, -0.18708689454811123, 0.755200129113146, 1.7068671645293791, 2.5651668967876655, 3.2376359789962605, 3.6515608539408473, 3.761523415216628, 3.5548561932535185, 3.0522100221690316, 2.304972730284291, 1.389990399850138, 0.40128754411074047, -0.5607316823294716, -1.3996132629917861, -2.0329043360885155, -2.4020073253944254, -2.4770192236105926, -2.258522343931805, -1.7771973409039583, -1.091128998183492, -0.27675596302260586, 0.5804050893058412, 1.3948003817481684, 2.089703281741074, 2.6063240197697337, 2.9092175104646545, 2.988588762343401, 2.859614938669355, 2.558901261896787, 2.1384033961041116, 1.657754644846185, 1.175500934971926, 0.7418074391871405, 0.3928362705836659, 0.14700702681221178, 0.0036460300108909897, -0.05382908103280471, -0.05282300729322413, -0.025079997238994966, 0.0009451348805350064, 0.007951636677506055, -0.004396765534696084, -0.015999103443716134, 0.014229847917537737, 0.14516939092622894, 0.4471440871249011, 0.9930789164264721, 1.8479817605240738, 3.0580620176424507, 4.640724125472097, 6.57719895139179, 8.81084751009779, 11.246776115645531, 13.755163837235445, 16.18108845832965, 18.364233974739417, 20.148395692131004, 21.392877641522333, 21.988913951141086, 21.88198806147191, 21.067989922024374, 19.590922055822325, 17.543757155921526, 15.070011679986047, 12.33885742405603, 9.527484907782215, 6.808901939395034, 4.341117676963369, 2.2462464176654673, 0.6014637434125936, -0.5628877917211581, -1.2616924112245282, -1.551064696665893, -1.5174552669759114, -1.264272073802062, -0.8982885744764197, -0.5160430654835878, -0.1926547479964598, 0.02548970804592026, 0.12372435607830824, 0.11757148319675481, 0.046968059112888795, -0.03271105135728644, -0.061458550519884796, 0.014390737961759976, 0.23241658145465427, 0.6069230553854562, 1.1263135767115169, 1.7538648723964319, 2.4316400734785812, 3.088276786100443, 3.6515249625005346, 4.0569647784372815, 4.255868198495594, 4.223000685840035, 3.9637626705052273, 3.5101503487044075, 2.9152531203324306, 2.247040704835339, 1.5805742904527764, 0.9843844724651273, 0.5107803541267298, 0.18956178508738705, 0.024462738944136656, -0.007294672351934857, 0.050025938081238695, 0.1391640388024448, 0.20047869328866147, 0.18365535650109488, 0.058499355715911465, -0.1770002689580729, -0.4929129800004728, -0.8281630100068089, -1.09626091813165, -1.195952957523812, -1.025984267303706, -0.4996044151597147, 0.44070905791661313, 1.8103659861314214, 3.576040386827238, 5.6543942050018305, 7.914832008555401, 10.189878809633125, 12.298224465002178, 14.059527076277142, 15.309999868371877, 15.922954246953115, 15.83573730032692, 15.047587317766904, 13.616779251900258, 11.659467818969707, 9.34743102129911, 6.878471276026999, 4.453862433296616, 2.2609980468721553, 0.4570130821257627, -0.8517874867023485, -1.617849144258974, -1.8527601618284986, -1.623290046652615, -1.0390560139277367, -0.23555972618018048, 0.6435922971911839, 1.4639299525133078, 2.1171725208901555, 2.532022206065089, 2.6790682277488327, 2.570328235507723, 2.2524774199565134, 1.7957990152974206, 1.2810583941328055, 0.7858013240202847, 0.3721349053745529, 0.07853898162434976, -0.08397107958118685, -0.13099834166568397, -0.09859163369643854, -0.03416481676744362, 0.014058528820160806, 0.007471665936968515, -0.0746283187911744, -0.23045155489605304, -0.43544299858496605, -0.6475301718887406, -0.815418267597273, -0.8887415839936011, -0.829517017759049, -0.6237860845526296, -0.2866931870416133, 0.13648656024019454, 0.5733681115102088, 0.9329542940942345, 1.1202602896891527, 1.0515307532015143, 0.6692227511567452, -0.04402292143828971, -1.0573174712571953, -2.290001043313918, -3.616949067186485, -4.881717486893868, -5.913805089402874, -6.549064490183677, -6.652416947635501, -6.140357609640658, -4.991404362081683, -3.252443076039845, -1.0389234383397525, 1.4762744578924776, 4.083393881985235, 6.556581511201557, 8.678758672689149, 10.273855188515526, 11.222070509309678, 11.468722286881137, 11.031298040000934, 10.004137557331669, 8.53520625988957, 6.80395995200281, 5.00174525939523, 3.3121785789531923, 1.883273609006101, 0.8123294711715404, 0.13996949048460866, -0.14954695886083152, -0.12113725220151834, 0.12620333965193684, 0.4777923941359578, 0.822456046395638, 1.0696959000764685, 1.1618198476923107, 1.0801680165397896, 0.8448184742143175, 0.5063579485671624, 0.13372937807284374, -0.20018158739626696, -0.43367870074773596, -0.5282015839891903, -0.4751029216421039, -0.2971169770138039, -0.04361041875145823, 0.22032312530708636, 0.4270067951424079, 0.5203486889937283, 0.4696572999661997, 0.2772380194467221, -0.019707766871237528, -0.35259549265450885, -0.6312450787571006, -0.7601116416216678, -0.6551736833337878, -0.2601566399437824, 0.43970601268990345, 1.4110662200071247, 2.5731408734107033, 3.8056003387553243, 4.965209713735844, 5.90599296051979, 6.5000098576002, 6.657953372027808, 6.348474996627819, 5.603572864249642, 4.5163044694446555, 3.2315612039332344, 1.9295957623331834, 0.7998797315254256, 0.014842360152331861, -0.2945044633010394, -0.05724651045978544, 0.7269403070859273, 1.9853637035604899, 3.580469467332686, 5.333380394315514, 7.045265050550861, 8.51944576492081, 9.588209835488719, 10.145433981566093, 10.148496182825339, 9.61640569723567, 8.628055528220747, 7.318111355505794, 5.843508790126728, 4.35881889213639, 2.999380242208963, 1.8682166777826372, 1.019446147457148, 0.4574463016023083, 0.14522997666470797, 0.017473979708146757, -0.0037345806802191604, 0.008905741618518441, 0.002724086052060922, -0.04562258491264349, -0.12774986235602728, -0.2085072597884257, -0.2372624942012636, -0.16291707345648115, 0.0502338750451889, 0.4084940857022643, 0.8799942956703259, 1.3956880765601418, 1.8560168266898744, 2.143613242639058, 2.1433211483163337, 1.7691172322495323, 0.979854895162284, -0.20854279087481467, -1.7145984139433594, -3.3917735907382727, -5.048701815080565, -6.471651806858741, -7.450018123695884, -7.808507640248305, -7.435079255875048, -6.297500034850434, -4.451252951150275, -2.0391356161353027, 0.7259367362700718, 3.5869046210284052, 6.274355481381705, 8.543314683204303, 10.200018432087143, 11.122572547670059, 11.27549102358562, 10.716182302023979, 9.574194809687892, 8.02855651567983, 6.28363956034715, 4.542622113592143, 2.975649779958406, 1.7013261368652504, 0.7780051094842018, 0.2036782299380025, -0.07417629135861353, -0.1410972274749419, -0.09507120676003554, -0.025675497123270496, 0.002778798252954316, -0.039179326234106894, -0.144129219860404, -0.2744049944286956, -0.37517374950328614, -0.38973361446511606, -0.2753088057408275, -0.01778367215497581, 0.36335097373284236, 0.8171683200951585, 1.2693570658741884, 1.636228185608516, 1.84399493046994, 1.845794139519874, 1.6346387098781032, 1.25060204328623, 0.7773234177804418, 0.33006465417937714, 0.0371233765959436, 0.01664254996037846, 0.35294389252930786, 1.0771798108502337, 2.1555305489602956, 3.490201855105337, 4.929526363589954, 6.286035212231278, 7.364256171134441, 7.999213281396486, 8.078147645001021, 7.557344824949112, 6.475545357971312, 4.959527260788318, 3.197470303053669, 1.4112735328760304, -0.17225145967807534, -1.3551270950730292, -2.0029856498774357, -2.0632665414932205, -1.5720430832053875, -0.6515465098796901, 0.5125942679977371, 1.702890807742232, 2.703697017962909, 3.334453343047315, 3.480766820146112, 3.111851068431542, 2.28377381002729, 1.1285949354673768, -0.16748557712480824, -1.3946089367143426, -2.354282597819887, -2.893365372312769, -2.925000779590099, -2.4410987022961588, -1.5136507088650852, -0.27939856526168577, 1.0853304905463872, 2.390763279670108, 3.4632916988913136, 4.179092089391016, 4.475043762535292, 4.350735710311376, 3.865875169090959, 3.131583598583373, 2.280197506467195, 1.4405535202437618, 0.719304515804717, 0.18647210484203386, -0.13424002878722827, -0.2619335621653282, -0.24724181786364224, -0.1569059277325127, -0.05584680821258567, 0.00817385513651007, 0.013925522857903747, -0.03165159216379933, -0.09966122443064092, -0.15169149598028164, -0.1559884227233509, -0.10371097796725808, -0.019216139939922276, 0.036471484085367996, -0.02923117155796872, -0.3245115059048622, -0.9512056434725141, -1.9813987792188632, -3.4343004284113565, -5.258264003568724, -7.328405093158094, -9.454541271483478, -11.400311808162426, -12.91806851637507, -13.786391810129492, -13.843875897396725, -13.019589164549716, -11.358613310390943, -9.01863827280457, -6.252195707564377, -3.377620504683058, -0.7380696180179345, 1.3487684266815148, 2.6350024461971553, 2.9781916232962984, 2.3638664111206413, 0.9039117273968125, -1.1798710568744797, -3.5876385394481076, -5.991196518082654, -8.07913498394543, -9.595591307342088, -10.37554595212848, -10.373802154402965, -9.651768074023105, -8.357053473469426, -6.6988832920623755, -4.916081810061642, -3.2287646602151723, -1.807530179365401, -0.7552674632046501, -0.09853031659110748, 0.206180242173698, 0.2524035323821005, 0.15843784089396595, 0.04059756697733787, -0.012042811012092003, 0.04719355674487586, 0.21817895910303728, 0.4601806053787971, 0.7072956125883029, 0.8885698986722247, 0.9485536618636118, 0.8646395499268666, 0.6542479207545273, 0.3726692836936368, 0.10228408767065976, -0.06579524852846069, -0.053728166111684614, 0.18362728551667493, 0.6450396459801464, 1.2795933366163128, 1.9937796424350989, 2.6665573070404704, 3.1723841605781637, 3.4115125675655116, 3.3277898873337604, 2.919809681328679, 2.2458274262065254, 1.4187275631475211, 0.5787813129667234, -0.13389995210301855, -0.6059577061900503, -0.7762984625728139, -0.6524744962492677, -0.3106478399704097, 0.11707891486472463, 0.4674068816828623, 0.5814385527889571, 0.3399333023858288, -0.3068239274073339, -1.317966878855514, -2.5598972005836567, -3.8218505968440524, -4.846469796965165, -5.371274559346769, -5.174964324791334, -4.12062520062382, -2.187958594427989, 0.5183297079304193, 3.7754868388670526, 7.263870165349546, 10.609627294472201, 13.456121590108772, 15.502500385533853, 16.536562165790485, 16.469822183756346, 15.37093718996926, 13.426794419277842, 10.90476312324228, 8.119644315833252, 5.397670679606321, 3.012313609609897, 1.1507144207112299, -0.0986532444840953, -0.7458609476341883, -0.8874464093259367, -0.6758400375346129, -0.283636253556071, 0.1296423390165141, 0.4446438520653975, 0.5977390803747666, 0.5829386094260192, 0.4410197209597828, 0.24003717720942397, 0.05270788684732399, -0.06505271989359925, -0.08860591767743249, -0.028199068104379832, 0.07598641356014689, 0.16710640215371603, 0.19274390192410948, 0.1212916707400504, -0.047708564355203605, -0.2797095955594316, -0.5109915483099965, -0.6690176580778807, -0.6954086906328125, -0.5689050448840698, -0.3256220559469717, -0.06602895777336726, 0.052072085486742976, -0.1669688379680316, -0.9235192897034332, -2.381707190394437, -4.63161746773061, -7.659351549277966, -11.330645217325884, -15.395059076916532, -19.50855639530797, -23.275351178508217, -26.310456383679803, -28.2868178353003, -28.97828699676171, -28.29875178027157, -26.33086638906066, -23.296236026609346, -19.520111806862204, -15.391213845140022, -11.31173936784385, -7.630045021027172, -4.599365789487131, -2.3549719616622924, -0.9067947006193448, -0.15547960301667585, 0.07401466776532004, -0.00800138619284646, -0.1985509443150673, -0.33924595041804473, -0.33767218518324027, -0.17346943501388068, 0.11061987062219476, 0.4324915510346151, 0.6993021903201098, 0.8350825083722981, 0.8031023975743148, 0.6146947999330192, 0.3247251582745627, 0.0159789070995241, -0.2246736589302957, -0.33148465981703035, -0.2798078934575813, -0.09692315791614824, 0.14091833977829404, 0.32606422703654164, 0.34463846150866595, 0.10687484561240805, -0.42318548648411924, -1.2116065038674042, -2.150739335008572, -3.0697927494715933, -3.7671741087497255, -4.048509196984707, -3.7628246588168963, -2.8380122883013175, -1.3144531374465016, 0.6597668394083136, 2.8496897594876995, 4.964901248236604, 6.701949864255151, 7.801707696993865, 8.094405697971107, 7.529546171236983, 6.187443194933124, 4.265146725529521, 2.0443553554059055, -0.15532934197697182, -2.0349851777056993, -3.3627899016812965, -4.006684971693386, -3.953905950972483, -3.3117596570984023, -2.2723308008627927, -1.0721603282795646, 0.0509976772643098, 0.9049272683002826, 1.3770247402683862, 1.445927265895344, 1.1778991894360074, 0.7091576564870303, 0.20609267311523266, -0.17399256406457966, -0.3155519237317337, -0.16913444917743653, 0.23946023689110396, 0.8195487205548315, 1.439104831895097, 1.9560786535041912, 2.2519631898990866, 2.258623914875712, 1.973134401849081, 1.4565537201273386, 0.8178685662497549, 0.18882900648222753, -0.3069731710890382, -0.5853841053543706, -0.6178442118934657, -0.4355923096914828, -0.12172456878155512, 0.21116280111793406, 0.4527264878244176, 0.5228106888410861, 0.39361221052030954, 0.10203336929883253, -0.2596891752775222, -0.5661997226870019, -0.6896447717864617, -0.536057259493942, -0.07661917582936072, 0.6359761501006209, 1.467525519534395, 2.22171792029483, 2.6785232214244976, 2.6401818285396685, 1.9782400273410707, 0.6734829329511893, -1.166651104994111, -3.312335396112587, -5.438997488487077, -7.181244076152044, -8.192866772718746, -8.206657229194448, -7.087966059448358, -4.868042583282559, -1.7416032143633584, 1.954077648015577, 5.786821750980982, 9.31572410597888, 12.146096826754079, 13.975638582216705, 14.64434815707319, 14.185228996465039, 12.773515740128069, 10.679703389894417, 8.23271623667531, 5.782257262246049, 3.6133945389729303, 1.9090477498020109, 0.743621991484358, 0.09241630961908401, -0.15197350017189107, -0.14011442121190146, -0.023434017747638966, 0.07972339484143486, 0.10582311113455181, 0.05226299798493598, -0.034269245362409335, -0.08248980100168338, -0.023551046163115513, 0.1856603884344215, 0.545530574002218, 1.0012534705453944, 1.4452364860607372, 1.7407162253985675, 1.7778821750371332, 1.561787635734435, 1.1627569094393388], 'positive_zeros': ['0.51510783714260050662429927666489', '0.76305423110524817856720216019585', '0.957809599224333471992722726301887', '1.76692303734727413390453388788684', '2.45209306092126336171779485861251', '2.48081779188899308855263052699728', '2.88333098512087756508732556490984', '3.34153123051256104667015057056254', '4.09314184501363984964519300960441', '4.37438941127491511963557531482937', '4.54431658249328599439511447027658', '4.89510612831368179892121918955862', '5.20759614301632545135376167470246', '5.90810090013092891687380781698320', '6.17331797534105332116258953721145', '6.44593989692216236574455233093101', '6.69404845482672026131120249334532', '7.11778032868994693899629600569791', '7.15533360002861009485123078020769', '7.87085441230304205755861889407920', '8.355823144415181067062732741756872', '8.372367819203288381806323777071489', '8.511780635309880095552932667015145', '8.690745060066492999943298834893135', '9.597897021881650634476510055250852', '9.711149113898568939655705125290401', '9.787027472693325515445645222200090', '9.955684349795889594555756593528303', '10.48850827667707676077501831605498', '10.72515238241282722342597776198465', '11.07524276050473054560282378406923', '11.35386162322091961651606869850573', '11.81363746650167802197299951563692', '11.93592266495712620630891945736898', '11.99174528767181433576195623068589', '12.05482680270366066945674120644143', '12.88953519676765021063881571859242', '13.15148645042099826179644944204342', '13.26734284321356153017560167052173', '13.34040470074284232635116018266816'], 'prelabel': '8-75e4-1.1-c7e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.84033851205772, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c7e4-0', 'trace_hash': 1051391604190531617, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.51510783714260050662429927666489', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '0.76305423110524817856720216019585', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '0.957809599224333471992722726301887', 'prec': 110}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 301304.68380712083, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 31640625, 'conductor_radical': 15, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32768, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1325548, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7993388, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4782969, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -77948684, 0, 2278499001499446, 0, -29600999777032640404844, 0, 144209936106499234037676064081], 'euler13': [1, 0, 0, 0, -6759928051400497, 0, 0, 0, 15502932802662396215269535105521], 'euler17': [1, 0, 0, 0, 336755653118801858, 0, 0, 0, 28351092476867700887730107366063041], 'euler19': [1, 0, 138181606, 0, 1602786910624953051, 0, 110408027046216295151678326, 0, 638411683925748518131605316913942641], 'euler2': [1, 0, 0, 0, 32768, 0, 0, 0, 268435456], 'euler23': [1, 0, 0, 0, 23185672649077499618, 0, 0, 0, 134393854047545109686936775588697536481], 'euler29': [1, 0, 68999505236, 0, 1785349396054796780886, 0, 20531370833528731370943250286516, 0, 88540901833145211536614766025207452637361], 'euler3': [1, 0, 0, 0, 4782969, 0, 0, 0, 0], 'euler31': [1, -1325548, 768954519058, -254976032227133896, 52857859025541828939595, -7015057182219034784176006456, 582055459661577341532210667177618, -27605208348747383304441787351277072788, 572964121067545096123347421337293637543041], 'euler37': [1, 0, 0, 0, -5563743051285261331822, 0, 0, 0, 81217248802771228597652036390959994837496721], 'euler41': [1, 0, -779017095524, 0, 227575363169493352812966, 0, -29547516404853032438496894754627364, 0, 1438626275603521989270100382252682485138269921], 'euler43': [1, 0, 0, 0, -6431509767729015169177, 0, 0, 0, 5459046029871041534743397034507955551606171601], 'euler47': [1, 0, 0, 0, 513333972375334818668738, 0, 0, 0, 65877941798660252683780571409941608871644628161], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 0, 0, 0, 2759892524114287536773138, 0, 0, 0, 1904251686165483303166544735375573842653419591761], 'euler59': [1, 0, 9954605939276, 0, 37160317277350880324776566, 0, 61652719179082938506074649286877301036, 0, 38358032782038398419973086399760468678777161743121], 'euler61': [1, -7993388, 36531315738538, -107284210177357999136, 225810566130390465741272995, -337166682953063109605682707677856, 360813687772886465671353685918066951258, -248117518735334290986223438692789679201630268, 97551820892064552722266841889541788960852432978481], 'euler67': [1, 0, 0, 0, -54545136337176750865517017, 0, 0, 0, 1349256365417755877454657051946796697206085388680241], 'euler7': [1, 0, 0, 0, -1351253357977, 0, 0, 0, 459986536544739960976801], 'euler71': [1, 0, -36380480633564, 0, 496327264173421973566253286, 0, -3009437403695163573276254267797829481884, 0, 6842798698940938981814244812733146152009703886272161], 'euler73': [1, 0, 0, 0, 54454581630836951278994018, 0, 0, 0, 14894985451961941943846586557477384171894488107677281], 'euler79': [1, 0, 76766244347236, 0, 2210844308492242563442356486, 0, 28310632491533216689892962226452335801316, 0, 136006152866792691625201101984747368303641150837104961], 'euler83': [1, 0, 0, 0, 1472730526623272972123198258, 0, 0, 0, 542233801012015735135407853098133122208235840693558641], 'euler89': [1, 0, 176925339582116, 0, 11738465919842648480065139046, 0, 346138678173542706064747105069547512483556, 0, 3827543948647425430322045212330289877339037312647605281], 'euler97': [1, 0, 0, 0, 8086854168472409683785834863, 0, 0, 0, 42619520516862344959898006540158454742326868747150111361], 'euler_factors': [[1, 0, 0, 0, 32768, 0, 0, 0, 268435456], [1, 0, 0, 0, 4782969, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, -1351253357977, 0, 0, 0, 459986536544739960976801], [1, 0, -77948684, 0, 2278499001499446, 0, -29600999777032640404844, 0, 144209936106499234037676064081], [1, 0, 0, 0, -6759928051400497, 0, 0, 0, 15502932802662396215269535105521], [1, 0, 0, 0, 336755653118801858, 0, 0, 0, 28351092476867700887730107366063041], [1, 0, 138181606, 0, 1602786910624953051, 0, 110408027046216295151678326, 0, 638411683925748518131605316913942641], [1, 0, 0, 0, 23185672649077499618, 0, 0, 0, 134393854047545109686936775588697536481], [1, 0, 68999505236, 0, 1785349396054796780886, 0, 20531370833528731370943250286516, 0, 88540901833145211536614766025207452637361], [1, -1325548, 768954519058, -254976032227133896, 52857859025541828939595, -7015057182219034784176006456, 582055459661577341532210667177618, -27605208348747383304441787351277072788, 572964121067545096123347421337293637543041], [1, 0, 0, 0, -5563743051285261331822, 0, 0, 0, 81217248802771228597652036390959994837496721], [1, 0, -779017095524, 0, 227575363169493352812966, 0, -29547516404853032438496894754627364, 0, 1438626275603521989270100382252682485138269921], [1, 0, 0, 0, -6431509767729015169177, 0, 0, 0, 5459046029871041534743397034507955551606171601], [1, 0, 0, 0, 513333972375334818668738, 0, 0, 0, 65877941798660252683780571409941608871644628161], [1, 0, 0, 0, 2759892524114287536773138, 0, 0, 0, 1904251686165483303166544735375573842653419591761], [1, 0, 9954605939276, 0, 37160317277350880324776566, 0, 61652719179082938506074649286877301036, 0, 38358032782038398419973086399760468678777161743121], [1, -7993388, 36531315738538, -107284210177357999136, 225810566130390465741272995, -337166682953063109605682707677856, 360813687772886465671353685918066951258, -248117518735334290986223438692789679201630268, 97551820892064552722266841889541788960852432978481], [1, 0, 0, 0, -54545136337176750865517017, 0, 0, 0, 1349256365417755877454657051946796697206085388680241], [1, 0, -36380480633564, 0, 496327264173421973566253286, 0, -3009437403695163573276254267797829481884, 0, 6842798698940938981814244812733146152009703886272161], [1, 0, 0, 0, 54454581630836951278994018, 0, 0, 0, 14894985451961941943846586557477384171894488107677281], [1, 0, 76766244347236, 0, 2210844308492242563442356486, 0, 28310632491533216689892962226452335801316, 0, 136006152866792691625201101984747368303641150837104961], [1, 0, 0, 0, 1472730526623272972123198258, 0, 0, 0, 542233801012015735135407853098133122208235840693558641], [1, 0, 176925339582116, 0, 11738465919842648480065139046, 0, 346138678173542706064747105069547512483556, 0, 3827543948647425430322045212330289877339037312647605281], [1, 0, 0, 0, 8086854168472409683785834863, 0, 0, 0, 42619520516862344959898006540158454742326868747150111361]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/8/e/b'], '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': '8-75e4-1.1-c7e4-0-3', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0, 0], 'nu_real_doubled': [7, 7, 7, 7], 'order_of_vanishing': 0, 'prelabel': '8-75e4-1.1-c7e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.84033851205772, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7e4-0', 'trace_hash': 1051391604190531617, 'z1': {'__RealLiteral__': 0, 'data': '0.51510783714260050662429927666489', 'prec': 107}}
  • lfunc_instances • Show schema
    {'Lhash': '652976758936082571159913931676,967286154067257927184298800910,1214167913361086171950424950642,2239841048850358251513068066567', 'Lhash_array': ['652976758936082571159913931676', '967286154067257927184298800910', '1214167913361086171950424950642', '2239841048850358251513068066567'], 'factors': ['2-75-15.8-c7-0-7', '2-75-15.2-c7-0-17', '2-75-15.2-c7-0-21', '2-75-15.8-c7-0-29'], 'label': '8-75e4-1.1-c7e4-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/8/e/b'}