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lfunc_lfunctions • Show schema
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{'Lhash': '2400644776231612954411597197149', 'a10': [-0.5, -0.8660254037844386], 'a2': [0.8660254037844386, -0.5], 'a3': [0, 0], 'a4': [0.5, -0.8660254037844386], 'a5': [0, -1.0], 'a6': [0, 0], 'a7': [-2.598076211353316, -1.5], 'a8': [0, -1.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.34249703648981, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, 0.5]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 1.0]]], [13, [[1.0, 0], [0.8660254037844386, -3.5]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1170.361', 'coefficient_field': 'CDF', 'conductor': 1170, 'conductor_radical': 390, 'conjugate': '745646099310578443269061923805', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, 0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [2.598076211353316, 1.5], [3.5, 6.06217782649107]], [[1.0, 0], [-3.232050807568877, 1.8660254037844386], [5.5, 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3.0565498583353437, 'root_angle': 0.7479590486074333, 'root_number': '-0.70255842307352351146774235171970078989339523815855744943 + 0.7116260690618661887795231289920187813089018818453366619*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.37397952430371667', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.89377481129216352097404021403', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.26499436897199950569818017737', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.73511570805105454268350055854', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.34249703648981, 'bad_primes': [2, 3, 5, 13], 'central_character': '13.10', 'conductor': 1170, 'conductor_radical': 390, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1170/2/bs/d/361/2'], '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': '2-1170-13.10-c1-0-18', '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': '2-1170-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0565498583353437, 'root_angle': 0.37397952430371667, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.89377481129216352097404021403', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2400644776231612954411597197149', 'Lhash_array': ['2400644776231612954411597197149'], 'label': '2-1170-13.10-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1170/2/bs/d/361/2'}