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lfunc_lfunctions • Show schema
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{'Lhash': '493899746993384955698267308558', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.4310554463476353, 2.636679788954049], 'a4': [0, 0], 'a5': [5.520483789100713, 0], 'a6': [0, 0], 'a7': [0.8384169858989075, 1.4521808175056667], 'a8': [0, 0], 'a9': [-4.90416061895754, -7.546469944514852], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.63765008224431, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.4310554463476353, -2.636679788954049]]], [19, [[1.0, 0], [16.150892572090008, 10.007430695478627]]]], 'bad_primes': [2, 3, 19], 'central_character': '684.373', 'coefficient_field': 'CDF', 'conductor': 684, 'conductor_radical': 114, 'conjugate': '2208509706707002125443764345673', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.4310554463476353, -2.636679788954049]], [[1.0, 0], [-5.520483789100713, 0], [25.0, 0]], [[1.0, 0], [-0.8384169858989075, -1.4521808175056667], [-24.5, 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'9.167253089833697475201129539493135', '10.01203983218560177179827166629998'], 'prelabel': '2-684-171.31-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.317134475811972, 'root_angle': -0.8645902970595828, 'root_number': '-0.91087285357381182666068596924041922044988187527305663230 - 0.4126871025635537830329697797720044870614078036392890361*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4322951485297914', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.38961820150163035994092402230', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.87198711481880901466333336444', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.76499133562258852376755951556', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.63765008224431, 'bad_primes': [2, 3, 19], 'central_character': '171.31', 'conductor': 684, 'conductor_radical': 114, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/684/3/bl/a/373/15'], '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': '2-684-171.31-c2-0-4', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-684-171.31-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.317134475811972, 'root_angle': -0.4322951485297914, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.38961820150163035994092402230', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '493899746993384955698267308558', 'Lhash_array': ['493899746993384955698267308558'], 'label': '2-684-171.31-c2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/684/3/bl/a/373/15'}