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lfunc_lfunctions • Show schema
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{'Lhash': '1107124659061483935988167755016', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [3.0, 0], 'a6': [0, 0], 'a7': [0.5, 0.8660254037844386], 'a8': [0, 0], 'a9': [1.5, 2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.62621853429843, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.5, -0.8660254037844386]]], [13, [[1.0, 0], [2.5, 2.598076211353316]]]], 'bad_primes': [2, 7, 13], 'central_character': '1456.113', 'coefficient_field': 'CDF', 'conductor': 1456, 'conductor_radical': 182, 'conjugate': '2094897503818252556611331220005', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-1.5, -2.598076211353316]], [[1.0, 0], [-3.0, 0], [5.0, 0]], [[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [1.0, -1.7320508075688772], [-5.5, -9.526279441628825]], [[1.0, 0], [2.5, 2.598076211353316]], [[1.0, 0], [-3.5, -6.06217782649107], 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{'__RealLiteral__': 0, 'data': '0.873367360739746288101611102650', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.14986935362268315041604883913', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.14746800526403503142794500086', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.62621853429843, 'bad_primes': [2, 7, 13], 'central_character': '13.9', 'conductor': 1456, 'conductor_radical': 182, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1456/2/s/d/113/1'], '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': '2-1456-13.9-c1-0-22', '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': '2-1456-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4097241141034313, 'root_angle': -0.16258476388153328, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.873367360739746288101611102650', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1107124659061483935988167755016', 'Lhash_array': ['1107124659061483935988167755016'], 'label': '2-1456-13.9-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1456/2/s/d/113/1'}