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lfunc_lfunctions • Show schema
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{'Lhash': '2131881632219598697601923734117', 'a10': [0.0, 0.0], 'a2': [0.8090169943749475, 0.5877852522924731], 'a3': [0.0, 0.0], 'a4': [0.30901699437494745, 0.9510565162951535], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.30901699437494745, 0.9510565162951535], 'a9': [-0.8090169943749475, 0.5877852522924731], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.2495325063165012, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8090169943749475, -0.5877852522924731]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '500.451', 'coefficient_field': 'CDF', 'conductor': 500, 'conductor_radical': 10, 'conjugate': '3175225914156019563370313315754', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], 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'10.95785539591166485099844598629058'], 'prelabel': '2-500-100.91-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.49953228756157614, 'root_angle': -0.36, 'root_number': '0.42577929156507264886250244574455 - 0.90482705246601952771366864793250*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.18', 'prec': 17}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.68175807421680079578803111696', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.22864378461474225646871697236', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.98718938395307868810508543941', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.2495325063165012, 'bad_primes': [2, 5], 'central_character': '100.91', 'conductor': 500, 'conductor_radical': 10, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/500/1/j/a/451/1'], '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': '2-500-100.91-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-500-100.91-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.49953228756157614, 'root_angle': -0.18, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.68175807421680079578803111696', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2131881632219598697601923734117', 'Lhash_array': ['2131881632219598697601923734117'], 'label': '2-500-100.91-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/500/1/j/a/451/1'}