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lfunc_lfunctions • Show schema
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{'Lhash': '3261761739176548370254271580688', 'a10': [0.5187863224222116, 0.0], 'a2': [1.5487946532357122, 0.0], 'a3': [2.8108682216217566, 0.0], 'a4': [0.39876487789153, 0.0], 'a5': [0.33496133353661384, 0.0], 'a6': [4.353457672597952, 0.0], 'a7': [-4.246233717858174, 0.0], 'a8': [-2.479984395694831, 0.0], 'a9': [4.9009801593230575, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9243946887128582, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[241, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [241], 'central_character': '241.1', 'coefficient_field': 'CDF', 'conductor': 241, 'conductor_radical': 241, 'conjugate': '3261761739176548370254271580688', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.5487946532357122, 0], [2.0, 0]], [[1.0, 0], [-2.8108682216217566, 0], [3.0, 0]], [[1.0, 0], [-0.33496133353661384, 0], [5.0, 0]], [[1.0, 0], [4.246233717858174, 0], [7.0, 0]], [[1.0, 0], [-0.9154175087094248, 0], [11.0, 0]], [[1.0, 0], 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.9243946887128582, 'bad_primes': [241], 'central_character': '1.1', 'conductor': 241, 'conductor_radical': 241, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/241/2/a/b/1/8'], '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': '2-241-1.1-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': '2-241-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3872255363540775, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.57307631818207375293336840940', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3261761739176548370254271580688', 'Lhash_array': ['3261761739176548370254271580688'], 'label': '2-241-1.1-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/241/2/a/b/1/8'}