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lfunc_lfunctions • Show schema
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{'Lhash': '1119226384098857378155975907131,1171246233114293713935723250161', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -3, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.7650154372309097, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '3888.1', 'coefficient_field': '1.1.1.1', 'conductor': 15116544, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1], [1, 0, -1, 0, 1], [1, 3, 4, 3, 1], [1, 0, 1, 0, 1], [1, -2, 3, -2, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 0, -1, 0, 1], [1, -3, 4, -3, 1], [1, 2, 3, 2, 1], [1, 0, -1, 0, 1], [1, -3, 4, -3, 1], [1, 0, 1, 0, 1], [1, 0, 2, 0, 1], [1, 0, 1, 0, 1], [1, -1, 0, -1, 1], [1, -3, 4, -3, 1], [1, 0, -2, 0, 1], [1, -2, 3, -2, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 2, 0, 1], [1, -2, 3, -2, 1], [1, 0, -1, 0, 1], [1, 3, 4, 3, 1], [1, 0, -2, 0, 1], [1, -2, 3, 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'2.24074128708659151087413854058307', '2.52842567183140256887380358063290', '3.17965225083913818140546369183574', '3.30592738899883602610862650808036', '3.80603310195016664122215192452232', '4.01775139991821207683535937786533', '4.61328014363655551597136191387270', '5.21697786526327794730513257426623', '5.68886278334389292373831424057143', '5.97047825872641130853218933186790', '6.41855240996943048222842169617180', '6.55707343940855613197475359218578', '6.87313905309341377822002747553169', '7.07239592447533887768093004535146', '7.897092670168725190807200455329206', '8.103745366275860782080250283309380', '8.702877284728050058747689794088843', '8.724462949810673403297307668936307'], 'prelabel': '4-3888e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3929697660455929, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e2-0', 'trace_hash': 1117749215937513948, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.882913938507464484612179626193', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '0.923950363691241952173422111122', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '2.24074128708659151087413854058', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.7650154372309097, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 15116544, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 2, 0, 0, 0], 'euler11': [1, 0, 1, 0, 1], 'euler13': [1, -2, 3, -2, 1], 'euler17': [1, 0, 2, 0, 1], 'euler19': [1, 0, -2, 0, 1], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 1, 0, 1], 'euler29': [1, 0, -1, 0, 1], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -3, 4, -3, 1], 'euler37': [1, 2, 3, 2, 1], 'euler41': [1, 0, -1, 0, 1], 'euler43': [1, -3, 4, -3, 1], 'euler47': [1, 0, 1, 0, 1], 'euler5': [1, 0, -1, 0, 1], 'euler53': [1, 0, 2, 0, 1], 'euler59': [1, 0, 1, 0, 1], 'euler61': [1, -1, 0, -1, 1], 'euler67': [1, -3, 4, -3, 1], 'euler7': [1, 3, 4, 3, 1], 'euler71': [1, 0, -2, 0, 1], 'euler73': [1, -2, 3, -2, 1], 'euler79': [1, 0, 1, 0, 1], 'euler83': [1, 0, 1, 0, 1], 'euler89': [1, 0, 2, 0, 1], 'euler97': [1, -2, 3, -2, 1], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -1, 0, 1], [1, 3, 4, 3, 1], [1, 0, 1, 0, 1], [1, -2, 3, -2, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 0, -1, 0, 1], [1, -3, 4, -3, 1], [1, 2, 3, 2, 1], [1, 0, -1, 0, 1], [1, -3, 4, -3, 1], [1, 0, 1, 0, 1], [1, 0, 2, 0, 1], [1, 0, 1, 0, 1], [1, -1, 0, -1, 1], [1, -3, 4, -3, 1], [1, 0, -2, 0, 1], [1, -2, 3, -2, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 2, 0, 1], [1, -2, 3, -2, 1]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3888/1/o/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': '4-3888e2-1.1-c0e2-0-7', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0], 'order_of_vanishing': 0, 'prelabel': '4-3888e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3929697660455929, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 1117749215937513948, 'z1': {'__RealLiteral__': 0, 'data': '0.882913938507464484612179626193', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1119226384098857378155975907131,1171246233114293713935723250161', 'Lhash_array': ['1119226384098857378155975907131', '1171246233114293713935723250161'], 'factors': ['2-3888-36.31-c0-0-2', '2-3888-36.7-c0-0-0'], 'label': '4-3888e2-1.1-c0e2-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3888/1/o/b'}