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lfunc_lfunctions • Show schema
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{'Lhash': '809442742990920953397213474731', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-0.8090169943749475, -0.5877852522924731], 'a6': [0, 0], 'a7': [0.1775948840377707, -0.5465808508895951], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.810379600213524, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.8090169943749475, 0.5877852522924731]]], [11, [[1.0, 0], [-3.0431018321821743, -1.318912900448507]]]], 'bad_primes': [2, 3, 5, 11], 'central_character': '1980.1081', 'coefficient_field': 'CDF', 'conductor': 1980, 'conductor_radical': 330, 'conjugate': '1458832921735288078480258888481', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [-0.1775948840377707, 0.5465808508895951], [-5.663118960624632, -4.114496766047312]], [[1.0, 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'2.15436860369261766578021466653', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.19802959280764197380568771928', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.810379600213524, 'bad_primes': [2, 3, 5, 11], 'central_character': '11.3', 'conductor': 1980, 'conductor_radical': 330, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1980/2/z/g/1081/3'], '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': '2-1980-11.3-c1-0-5', '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': '2-1980-11.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9762268044231988, 'root_angle': -0.13112619405615697, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.63853773496039671208623388393', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '809442742990920953397213474731', 'Lhash_array': ['809442742990920953397213474731'], 'factors': ['2-1980-11.3-c1-0-5'], 'label': '2-1980-11.3-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1980/2/z/g/1081/3'}