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  • lfunc_lfunctions • Show schema
    {'Lhash': '432201138368372288186181628339,753615415752887179800849774506,1175546034770184843990066865453', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 3, 'a6': 0, 'a7': -3, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 380137.2649529088, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, 3, 3, 1]]], 'bad_primes': [2, 3, 7], 'central_character': '9072.1', 'coefficient_field': '1.1.1.1', 'conductor': 746636341248, 'conductor_radical': 42, 'degree': 6, 'euler_factors': [[1], [1], [1, -3, 15, -27, 75, -75, 125], [1, 3, 3, 1], [1, 6, 42, 135, 462, 726, 1331], [1, 3, 6, -29, 78, 507, 2197], [1, -6, 60, -207, 1020, -1734, 4913], [1, -3, 51, -97, 969, -1083, 6859], [1, 12, 96, 549, 2208, 6348, 12167], [1, -9, 51, -189, 1479, -7569, 24389], [1, -3, 15, 137, 465, -2883, 29791], [1, 3, 33, -101, 1221, 4107, 50653], [1, 0, 114, -9, 4674, 0, 68921], [1, -3, 123, -259, 5289, -5547, 79507], [1, 3, 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'5.08021543544621423272514686227159', '5.17420839596661862399340767630095', '5.60819761697063157258232597281656', '5.72101095716759272766771176287068', '5.72646314981267686523808582316267', '6.24589951324699001683968805853484', '6.34397593266677109621226637689563', '6.35246626872389726915041649498465', '6.80687196623650056496650641523605', '7.08731649850744577077508550577514', '7.29186216031743523174339118433287', '7.62625747103468896183696965403877', '7.77227611550640979702695844006751', '7.81586846372024088728746033368472'], 'prelabel': '6-9072e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.511185858251809, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e3-0', 'trace_hash': 268345804329543705, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.34094658125082594052727031676', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '0.59449773905933174064225209636', 'prec': 97}, 'z3': {'__RealLiteral__': 0, 'data': '0.927342309117779034536445153365', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 380137.2649529088, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 746636341248, 'conductor_radical': 42, 'degree': 6, 'dirichlet_coefficients': [1, 0, 0, 0, 3, 0, -3, 0, 0, 0, -6, 0, -3, 0, 0, 0, 6, 0, 3, 0, 0, 0, -12, 0, -6, 0, 0, 0, 9, 0, 3, 0, 0, 0, -9, 0, -3, 0, 0, 0, 0, 0, 3, 0, 0, 0, -3, 0, 6, 0, 0, 0, 6, 0, -18, 0, 0, 0, 3, 0, 6, 0, 0, 0, -9, 0, 12, 0, 0, 0, -9, 0, -21, 0, 0, 0, 18, 0, 21, 0, 0, 0, 18, 0, 18, 0, 0, 0, 12, 0, 9, 0, 0, 0, 9, 0, -3, 0, 0, 0], 'euler11': [1, 6, 42, 135, 462, 726, 1331], 'euler13': [1, 3, 6, -29, 78, 507, 2197], 'euler17': [1, -6, 60, -207, 1020, -1734, 4913], 'euler19': [1, -3, 51, -97, 969, -1083, 6859], 'euler2': [1, 0, 0, 0, 0, 0, 0], 'euler23': [1, 12, 96, 549, 2208, 6348, 12167], 'euler29': [1, -9, 51, -189, 1479, -7569, 24389], 'euler3': [1, 0, 0, 0, 0, 0, 0], 'euler31': [1, -3, 15, 137, 465, -2883, 29791], 'euler37': [1, 3, 33, -101, 1221, 4107, 50653], 'euler41': [1, 0, 114, -9, 4674, 0, 68921], 'euler43': [1, -3, 123, -259, 5289, -5547, 79507], 'euler47': [1, 3, 87, 333, 4089, 6627, 103823], 'euler5': [1, -3, 15, -27, 75, -75, 125], 'euler53': [1, -6, 150, -639, 7950, -16854, 148877], 'euler59': [1, -3, 105, -405, 6195, -10443, 205379], 'euler61': [1, -6, 168, -713, 10248, -22326, 226981], 'euler67': [1, -12, 222, -1591, 14874, -53868, 300763], 'euler7': [1, 3, 3, 1, 0, 0, 0], 'euler71': [1, 9, 159, 1305, 11289, 45369, 357911], 'euler73': [1, 21, 303, 2797, 22119, 111909, 389017], 'euler79': [1, -21, 357, -3499, 28203, -131061, 493039], 'euler83': [1, -18, 294, -2997, 24402, -124002, 571787], 'euler89': [1, -12, 204, -1323, 18156, -95052, 704969], 'euler97': [1, 3, 123, 259, 11931, 28227, 912673], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, -3, 15, -27, 75, -75, 125], [1, 3, 3, 1, 0, 0, 0], [1, 6, 42, 135, 462, 726, 1331], [1, 3, 6, -29, 78, 507, 2197], [1, -6, 60, -207, 1020, -1734, 4913], [1, -3, 51, -97, 969, -1083, 6859], [1, 12, 96, 549, 2208, 6348, 12167], [1, -9, 51, -189, 1479, -7569, 24389], [1, -3, 15, 137, 465, -2883, 29791], [1, 3, 33, -101, 1221, 4107, 50653], [1, 0, 114, -9, 4674, 0, 68921], [1, -3, 123, -259, 5289, -5547, 79507], [1, 3, 87, 333, 4089, 6627, 103823], [1, -6, 150, -639, 7950, -16854, 148877], [1, -3, 105, -405, 6195, -10443, 205379], [1, -6, 168, -713, 10248, -22326, 226981], [1, -12, 222, -1591, 14874, -53868, 300763], [1, 9, 159, 1305, 11289, 45369, 357911], [1, 21, 303, 2797, 22119, 111909, 389017], [1, -21, 357, -3499, 28203, -131061, 493039], [1, -18, 294, -2997, 24402, -124002, 571787], [1, -12, 204, -1323, 18156, -95052, 704969], [1, 3, 123, 259, 11931, 28227, 912673]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9072/2/a/ca'], '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': '6-9072e3-1.1-c1e3-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '6-9072e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.511185858251809, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 268345804329543705, 'z1': {'__RealLiteral__': 0, 'data': '0.34094658125082594052727031676', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '432201138368372288186181628339,753615415752887179800849774506,1175546034770184843990066865453', 'Lhash_array': ['432201138368372288186181628339', '753615415752887179800849774506', '1175546034770184843990066865453'], 'factors': ['2-9072-1.1-c1-0-3', '2-9072-1.1-c1-0-23', '2-9072-1.1-c1-0-65'], 'label': '6-9072e3-1.1-c1e3-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9072/2/a/ca'}