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lfunc_lfunctions • Show schema
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{'Lhash': '428108690819289434087886842979', 'a10': [0.5, -0.8660254037844386], 'a2': [-0.7071067811865476, 0.7071067811865476], 'a3': [-0.5, -0.8660254037844386], 'a4': [0.0, -1.0], 'a5': [-0.9659258262890683, 0.25881904510252074], 'a6': [0.9659258262890683, 0.25881904510252074], 'a7': [-1.224744871391589, -1.224744871391589], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7785414197074838, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [3, [[1.0, 0], [0.5, 0.8660254037844386]]], [5, [[1.0, 0], [0.9659258262890683, -0.25881904510252074]]], [13, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1560.467', 'coefficient_field': 'CDF', 'conductor': 1560, 'conductor_radical': 390, 'conjugate': '1256598705466767574331932820398', 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4.183648898559911, 2.8813404370957585, 1.7677892852171324, 0.8698529528123019], 'positive_zeros': ['0.33771820937268692910193092819132', '2.65007174436710436220478710794442', '3.25239770704115588825129588253568', '4.25034984568747819746263077056816', '5.16386838129367475050927464789359', '6.22176428299551150821333765458170', '7.16620615272404515806460097240495', '8.211978454130485024358988711243316', '8.924381518418183991234583780645941', '9.492939663466584911317802781284906'], 'prelabel': '2-1560-1560.467-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8823499417507114, 'root_angle': -0.42620819117478337, 'root_number': '0.22975292054736118352393736938184 - 0.97324898946773016378805774830813*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.21310409558739168', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.33771820937268692910193092819', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.65007174436710436220478710794', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.25239770704115588825129588254', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7785414197074838, 'bad_primes': [2, 3, 5, 13], 'central_character': '1560.467', 'conductor': 1560, 'conductor_radical': 390, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1560/1/cs/c/467/1'], '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': '2-1560-1560.467-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1560-1560.467-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8823499417507114, 'root_angle': -0.21310409558739168, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.33771820937268692910193092819', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '428108690819289434087886842979', 'Lhash_array': ['428108690819289434087886842979'], 'label': '2-1560-1560.467-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1560/1/cs/c/467/1'}