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lfunc_lfunctions • Show schema
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{'Lhash': '1372056380787499539940167610131', 'a10': [-0.8099601858596767, 0.0], 'a2': [0.7000165891104687, 0.0], 'a3': [-1.0, 0.0], 'a4': [-1.5099767749701454, 0.0], 'a5': [-1.1570585589820328, 0.0], 'a6': [-0.7000165891104687, 0.0], 'a7': [1.0, 0.0], 'a8': [-2.457041969871564, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [23, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 7, 23], 'central_character': '483.1', 'coefficient_field': 'CDF', 'conductor': 483, 'conductor_radical': 483, 'conjugate': '1372056380787499539940167610131', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7000165891104687, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.1570585589820328, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-3.667035333952178, 0], [11.0, 0]], [[1.0, 0], [-2.347098373122356, 0], [13.0, 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'6.00430580177124077695535307342277', '7.33753146973104786101675728605984', '8.230549114441965978979785307525703', '9.320812417925288448947507920263340', '9.990255747821353218482091201632797', '11.41542281002759819845602597215249'], 'prelabel': '2-483-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, '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': '1.08236163856229215760881166669', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.46742188186919482396754776148', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.15548279852060529630866474558', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'bad_primes': [3, 7, 23], 'central_character': '1.1', 'conductor': 483, 'conductor_radical': 483, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/483/2/a/i/1/3'], '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': '2-483-1.1-c1-0-3', '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': '2-483-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.08236163856229215760881166669', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1372056380787499539940167610131', 'Lhash_array': ['1372056380787499539940167610131'], 'label': '2-483-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/483/2/a/i/1/3'}