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lfunc_lfunctions • Show schema
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{'Lhash': '1214789936590554113132680463878', 'a10': [0.0, 0.0], 'a2': [0.0, 2.0], 'a3': [0.0, -1.0], 'a4': [-2.0, 0.0], 'a5': [0.0, 0.0], 'a6': [2.0, 0.0], 'a7': [0.0, 2.0], 'a8': [0.0, 0.0], 'a9': [2.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.188406156649233, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [31, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [5, 31], 'central_character': '775.249', 'coefficient_field': 'CDF', 'conductor': 775, 'conductor_radical': 155, 'conjugate': '1899191751964906650886640240329', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -2.0], [-2.0, 0]], [[1.0, 0], [0, 1.0], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -2.0], [-7.0, 0]], [[1.0, 0], [-2.0, 0], [11.0, 0]], [[1.0, 0], [0, 6.0], [-13.0, 0]], [[1.0, 0], [0, -7.0], [-17.0, 0]], [[1.0, 0], [-5.0, 0], [19.0, 0]], [[1.0, 0], [0, -4.0], [-23.0, 0]], [[1.0, 0], [0, 0], [29.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], 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False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.323791808825', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.958300289032200049219196324017', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.22230345840774583369564136537', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.57856937666683524762731395444', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.188406156649233, 'bad_primes': [5, 31], 'central_character': '5.4', 'conductor': 775, 'conductor_radical': 155, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/775/2/b/a/249/2'], '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': '2-775-5.4-c1-0-13', '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': '2-775-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.487650730438104, 'root_angle': -0.32379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.958300289032200049219196324017', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1214789936590554113132680463878', 'Lhash_array': ['1214789936590554113132680463878'], 'factors': ['2-775-5.4-c1-0-13'], 'label': '2-775-5.4-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/775/2/b/a/249/2'}