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lfunc_lfunctions • Show schema
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{'Lhash': '2563401140339964097121348006381', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.5, -0.8660254037844386], 'a6': [0.0, 0.0], 'a7': [-2.5, -0.8660254037844386], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.024460261872533, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.5, 0.8660254037844386]]]], 'bad_primes': [2, 3, 7], 'central_character': '504.289', 'coefficient_field': 'CDF', 'conductor': 504, 'conductor_radical': 42, 'conjugate': '734418178856007626907754285510', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386], [-2.5, -4.330127018922194]], [[1.0, 0], [2.5, 0.8660254037844386]], [[1.0, 0], [2.5, 4.330127018922194], [-5.5, 9.526279441628825]], [[1.0, 0], [-2.0, 0], [13.0, 0]], [[1.0, 0], [3.0, 5.196152422706632], 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3.867096567952133, 3.9416179392160617], 'positive_zeros': ['2.02216694401315799934367373563008', '3.20927906090790748271329320923438', '4.46963355997569490413701889847485', '5.71777337773346049355343596544298', '6.60662639000712338966927795390030', '7.40941563614987038053699705727407', '8.627389753104547939759017785006317', '9.463200845042747180078195950763333', '10.33153665707918213721554771598382', '10.95634341454770104950836846532046'], 'prelabel': '2-504-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0061057454363, 'root_angle': 0.5859748544508822, 'root_number': '-0.26682585713848145 + 0.9637447597586795*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.292987427225', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.02216694401315799934367373563', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.20927906090790748271329320923', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.46963355997569490413701889847', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.024460261872533, 'bad_primes': [2, 3, 7], 'central_character': '7.2', 'conductor': 504, 'conductor_radical': 42, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/504/2/s/f/289/1'], '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': '2-504-7.2-c1-0-8', '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': '2-504-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0061057454363, 'root_angle': 0.2929874272254411, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.02216694401315799934367373563', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2563401140339964097121348006381', 'Lhash_array': ['2563401140339964097121348006381'], 'label': '2-504-7.2-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/504/2/s/f/289/1'}