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lfunc_lfunctions • Show schema
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{'Lhash': '2447984253428283914870565928884', 'a10': [0.0, 0.0], 'a2': [1.445041867912629, 0.0], 'a3': [2.246979603717467, 0.0], 'a4': [0.08814600002041936, 0.0], 'a5': [0.0, 0.0], 'a6': [3.246979603717467, 0.0], 'a7': [1.3568958678922094, 0.0], 'a8': [-2.762709075306724, 0.0], 'a9': [2.0489173395223053, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [5, 19], 'central_character': '475.1', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '2447984253428283914870565928884', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.445041867912629, 0], [2.0, 0]], [[1.0, 0], [-2.246979603717467, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.3568958678922094, 0], [7.0, 0]], [[1.0, 0], [-4.850855075327144, 0], [11.0, 0]], [[1.0, 0], [-0.19806226419516174, 0], [13.0, 0]], 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'5.04681577413845035166651753039929', '6.26549343364618694049305406831102', '7.32160862972903769704896201968989', '8.605273715917640134969947995798776', '8.936452791670042375929658128086827', '9.885012626712489645555879755953851', '11.37360375378468570780435606661425'], 'prelabel': '2-475-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.93111907412621882115140510710', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.33189380874357887448436890150', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.97416433603683473675128906019', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/a/h/1/2'], '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': '2-475-1.1-c1-0-15', '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': '2-475-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.93111907412621882115140510710', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2447984253428283914870565928884', 'Lhash_array': ['2447984253428283914870565928884'], 'label': '2-475-1.1-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/a/h/1/2'}