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lfunc_lfunctions • Show schema
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{'Lhash': '1704587399838766923204514272252', 'a10': [36.14580082539492, 0.0], 'a2': [-2.3472707383523574, 0.0], 'a3': [3.0, 0.0], 'a4': [-2.4903200808747794, 0.0], 'a5': [-15.399076141837433, 0.0], 'a6': [-7.041812215057072, 0.0], 'a7': [10.131734592999134, 0.0], 'a8': [24.623621361787503, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.913968372910507, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-3.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '507.1', 'coefficient_field': 'CDF', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.3472707383523574, 0], [8.0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [15.399076141837433, 0], [125.0, 0]], [[1.0, 0], [-10.131734592999134, 0], [343.0, 0]], [[1.0, 0], [15.066897200355514, 0], [1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-90.83522507308638, 0], [4913.0, 0]], [[1.0, 0], 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'4.98158075863797044703669918717605', '6.82658749436413270091609591412020', '7.80801832707127741347145780308369', '8.275293458692667804101950265074724', '8.810482304865378117154100269785894', '10.14831092475841799606375156338187'], 'prelabel': '2-507-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.469366359361064, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.34468235926514046784362854010', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.08057219316364011108262262170', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.23683336992381572977028875538', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.913968372910507, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'index': 46, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/4/a/o/1/4'], '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': '2-507-1.1-c3-0-46', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-507-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.469366359361064, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.34468235926514046784362854010', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1704587399838766923204514272252', 'Lhash_array': ['1704587399838766923204514272252'], 'label': '2-507-1.1-c3-0-46', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/4/a/o/1/4'}