-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1797147335023405308674917776033', 'a10': [0, -0.05929777487380054], 'a2': [-0.8090169943749475, -0.5877852522924731], 'a3': [0, 0], 'a4': [0.30901699437494745, 0.9510565162951535], 'a5': [0.03485435756457913, 0.047972907601524395], 'a6': [0, 0], 'a7': [0.9510565162951535, -0.30901699437494745], 'a8': [0.30901699437494745, -0.9510565162951535], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.067265720149466, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8090169943749475, 0.5877852522924731]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.9510565162951535, 0.30901699437494745]]], [11, [[1.0, 0], [-0.7648963126728322, 3.227217629918922]]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '1386.953', 'coefficient_field': 'CDF', 'conductor': 1386, 'conductor_radical': 462, 'conjugate': '533450895218093810597741900432', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.03485435756457913, -0.047972907601524395], [-1.545084971874737, 4.755282581475768]], [[1.0, 0], [-0.9510565162951535, 0.30901699437494745]], [[1.0, 0], [-0.7648963126728322, 3.227217629918922]], [[1.0, 0], [2.7614277679858334, -3.800779254542768], [-4.017220926874317, -12.363734711836996]], [[1.0, 0], [-0.020612091141190548, 0.014975560805197486], [5.253288904374106, -16.167960777017612]], [[1.0, 0], [5.332006327562916, 1.7324738762636773], [15.371322893124, 11.16791979355699]], [[1.0, 0], [0, 7.575429530884615], [-23.0, 0]], [[1.0, 0], [1.0307487721138102, 3.1723185268982808], [-23.461492836873475, 17.04577231648172]], [[1.0, 0], [-3.6164767274558756, -2.6275241440383463], [9.57952682562337, 29.48275200514976]], [[1.0, 0], [-1.3453180562384266, -4.1404632339496175], [-29.933628791873055, 21.748054334821507]], [[1.0, 0], [0.8843778487929252, -2.7218351458724515], [-33.16969676937284, -24.099195343991397]], [[1.0, 0], [0, 1.7633502014595015], [-43.0, 0]], [[1.0, 0], [6.785888218169826, 2.204868738518198], [38.02379873562253, 27.625906857746237]], [[1.0, 0], [-5.4735949973044065, 7.533757194271247], [-16.377900701872214, -50.405995363643136]], [[1.0, 0], [-2.528597560689037, 0.8215911513143498], [47.7320026681219, -34.67932988525592]], [[1.0, 0], [-1.10935572582624, -1.526897164398413], [-18.850036656871794, 58.014447494004365]], [[1.0, 0], [6.35317504417985, 0], [67.0, 0]], [[1.0, 0], [8.200062953866325, 11.286418396427056], [-21.940206600621266, 67.52501265695591]], [[1.0, 0], [-0.9751693113314943, 0.3168517164134816], [59.05824058937116, -42.90832341735054]], [[1.0, 0], [-7.609832026748779, 10.474035219439529], [-24.412342555620846, -75.13346478731714]], [[1.0, 0], [-13.699563182742438, 9.953315267358859], [25.648410533120636, -78.93769085249775]], [[1.0, 0], [0, -1.5806516316544579], [-89.0, 0]], [[1.0, 0], [13.514700222718515, 9.819004465048524], [29.974648454369902, 92.2524820806299]], [[1.0, 0], [-0.2358785577181106, -0.1713758036267745], [31.210716431869688, 96.05670814581052]], [[1.0, 0], [2.8923379144299366, 8.901700783188822], [-83.32875042061958, 60.54188098612473]], [[1.0, 0], [5.379187445274754, -16.55543664370192], [-86.56481839811937, -62.893021995294625]], [[1.0, 0], [0, -2.1741433350193202], [-109.0, 0]], [[1.0, 0], [9.258791861249676, 3.00836383904095], [91.41892036436906, 66.41973350904946]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 20, 'label': '2-1386-33.29-c1-0-20', 'leading_term': '0.846687983350269899899654151090110487023035522199657308', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1386/2/bu/a/953/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.8466879833502698, 0.9471466641928845, 1.0431131670762488, 1.1342574596553008, 1.220053116452376, 1.2997575443052014, 1.37240697552871, 1.4368261814718672, 1.49165201991416, 1.5353693497358818, 1.5663575225323492, 1.5829455399178793, 1.5834739714163932, 1.56636178769229, 1.5301763218482254, 1.4737045952743981, 1.396024223315481, 1.2965720553343316, 1.175208619291748, 1.0322763533690875, 0.868649538198888, 0.6857738133710345, 0.4856931887426449, 0.2710625589228114, 0.045143908534896734, -0.18821533709448304, -0.4246230039483032, -0.659202646521279, -0.886674024539829, -1.1014531928751667, -1.2977711592306114, -1.469809364536811, -1.6118495221894924, -1.7184346387629907, -1.7845373575057795, -1.8057311452981601, -1.778359313078279, -1.6996964479396783, -1.5680965695977902, -1.3831222294180257, -1.1456488674212177, -0.8579390471526506, -0.5236817091797275, -0.1479923230585586, 0.2626292315230277, 0.7003850762252067, 1.156310740032514, 1.6204508023881157, 2.082076459286029, 2.5299410928909616, 2.9525683273211656, 3.338565522999122, 3.6769542625984433, 3.9575081766810567, 4.171087508111033, 4.309959177941524, 4.368090840860363, 4.3414075444108775, 4.228000159363416, 4.028275740247319, 3.7450414000482013, 3.3835151185878596, 2.9512591090491824, 2.458033882385431, 1.9155738988623419, 1.3372885884562464, 0.7378954534759989, 0.13299482465956944, -0.4614014918869821, -1.0293730836614365, -1.5556087917108166, -2.025921633361174, -2.4277420741306304, -2.7505708373135263, -2.98637307485064, -3.1298971090345833, -3.178903078662254, -3.1342896407925855, -3.000110313484814, -2.783474988022625, -2.49433645516958, -2.1451663188589345, -1.7505292337443892, -1.3265688097594088, -0.8904225826985226, -0.45958696463397064, -0.05125588462567194, 0.3183412465547665, 0.6345756891558662, 0.8850032472434296, 1.0598707550408737, 1.1525224864671133, 1.1596872838840502, 1.0816316524897507, 0.9221693262806292, 0.6885236806950954, 0.39104560911699693, 0.04279583014298222, -0.3409932327617141, -0.743555145597772, -1.1473009087029342, -1.534574358534236, -1.888418984422168, -2.1933222664400565, -2.4359038011854515, -2.605515204891022, -2.6947230449062496, -2.6996507535855785, -2.6201614519463376, -2.459870614647422, -2.2259852436049625, -1.9289743378590523, -1.5820835723672066, -1.2007148331581516, -0.8016982094136985, -0.40248984676111915, -0.02033339560921173, 0.3285746196875758, 0.6298745168513794, 0.8717486145675243, 1.0455055608248538, 1.146012838124392, 1.1719534388294797, 1.1258910929124692, 1.0141378373024375, 0.8464276892341509, 0.6354102280836695, 0.39598748242366705, 0.1445261478096298, -0.10201565507278598, -0.3270025547533755, -0.5150293956739813, -0.652773681174103, -0.7297465484982399, -0.7389002291206652, -0.677056712561898, -0.5451311724513735, -0.34813421585476095, -0.09494866232058288, 0.20211125090110124, 0.5279382553479346, 0.8654367314394186, 1.1964524834686028, 1.5027785150934603, 1.7671823186776086, 1.9743976793543259, 2.112024590561986, 2.171284644530682, 2.147586085561448, 2.0408623068483354, 1.8556594779559983, 1.6009626084476432, 1.2897639645757353, 0.9383925605074679, 0.5656376051757415, 0.19171147084169002, -0.1628918135233832, -0.47857902234175725, -0.737813550322222, -0.9261767022185338, -1.0332702087812609, -1.0534031977078349, -0.9860178498234043, -0.8358219698372408, -0.6126129766237988, -0.33079549122769086, -0.008612781076194169, 0.3328702419556881, 0.6709790199734161, 0.9827698115714321, 1.2464225303240397, 1.4426045208647784, 1.555723141436418, 1.5749891777992375, 1.4952220276407244, 1.3173408904786352, 1.0485032250860087, 0.7018715998396141, 0.29601166686379493, -0.14605389651889275, -0.5980893220246551, -1.0321221905628977, -1.4200711147918812, -1.7354318844906254, -1.9549229864243367, -2.0599908516916603, -2.0380805881548123, -1.8835891832926488, -1.5984347168218647, -1.192196167558709, -0.6818028015206126, -0.09077851522533918, 0.5519266566793752, 1.213459987816811, 1.858863658480094, 2.4530470057316616, 2.9628207055192273, 3.3588733863435185, 3.6175714264349286, 3.722470153765561, 3.665439095761908, 3.447324624635083, 3.0780992219347194, 2.5764762008626647, 1.9690003662245221, 1.2886568776575533, 0.5730705706807461, -0.13760569948676735, -0.8029941978944364, -1.3848533078137333, -1.8493564538174123, -2.1691511050249317, -2.3250705589680134, -2.307389747978591, -2.1165418776336504, -1.7632438706027111, -1.268013537691028, -0.6600980427256248, 0.0241306706116715, 0.7432245172996381, 1.4530346192806365, 2.1092744056734487, 2.6701181541026147, 3.0986785359354747, 3.3652122409589103, 3.448917719042818, 3.3392126950263665, 3.03641003178728, 2.5517468905041447, 1.9067617429180612, 1.1320541615884538, 0.26550089630466556, -0.6499639408817343, -1.5688689543588799, -2.4458707376674935, -3.238399530969844, -3.9091211460283892, -4.428062225973317, -4.774266962555759, -4.936883045923916, -4.915611018919024, -4.72049203253982, -4.371051616619358, -3.8948587072488166, -3.3255970627845626, -2.700777825195352, -2.0592452059604187, -1.4386404981844854, -0.872991895458969, -0.3905887155423993, -0.012279115098635981, 0.24969850468067614, 0.3922765615618263, 0.4214793923371604, 0.35171562130657236, 0.2044959813261234, 0.006670066721003164], 'positive_zeros': ['1.41769927352209248508749940596977', '2.54117430344791805679367795919174', '3.93874671815685696095933815687135', '5.04678398885629011988441524024709', '5.69035759162504198405670920926245', '6.80011983668374261913407255992789', '7.53394804878213790305415663874983', '8.105490461625468684692559693100287', '9.113100071417796929985269661070131', '9.728065488858708752987836222315017'], 'prelabel': '2-1386-33.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.326750023694216, 'root_angle': 0.6921235230123925, 'root_number': '-0.5675884856329359286217143746989083979274272968797492080 + 0.8233124018116759092054780847392319827828403402032266113*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3460617615061963', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.41769927352209248508749940597', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.54117430344791805679367795919', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.93874671815685696095933815687', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 11.067265720149466, 'bad_primes': [2, 3, 7, 11], 'central_character': '33.29', 'conductor': 1386, 'conductor_radical': 462, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1386/2/bu/a/953/6'], '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': '2-1386-33.29-c1-0-20', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1386-33.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.326750023694216, 'root_angle': 0.3460617615061963, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.41769927352209248508749940597', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1797147335023405308674917776033', 'Lhash_array': ['1797147335023405308674917776033'], 'label': '2-1386-33.29-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1386/2/bu/a/953/6'}