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lfunc_lfunctions • Show schema
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{'Lhash': '1531834715954539450627284246536', 'a10': [0.0, 1.0], 'a2': [-0.9659258262890683, 0.25881904510252074], 'a3': [0.0, 0.0], 'a4': [0.8660254037844386, -0.5], 'a5': [0.25881904510252074, -0.9659258262890683], 'a6': [0.0, 0.0], 'a7': [0.8660254037844386, 0.5], 'a8': [-0.7071067811865476, 0.7071067811865476], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6467882563723711, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9659258262890683, -0.25881904510252074]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1296.269', 'coefficient_field': 'CDF', 'conductor': 1296, 'conductor_radical': 6, 'conjugate': '1823243551778826455288783583263', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9659258262890683, -0.25881904510252074]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.25881904510252074, 0.9659258262890683], [-0.8660254037844386, -0.5]], [[1.0, 0], [-0.8660254037844386, -0.5], 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{'__RealLiteral__': 0, 'data': '-0.034722222222222224', 'prec': 70}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.20840452067686948604551744019', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.55175205032466610677713587452', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.34176612729955676184232078924', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6467882563723711, 'bad_primes': [2, 3], 'central_character': '144.29', 'conductor': 1296, 'conductor_radical': 6, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1296/1/x/a/269/1'], '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': '2-6e4-144.29-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-6e4-144.29-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.804231469399433, 'root_angle': -0.034722222222222224, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.20840452067686948604551744019', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1531834715954539450627284246536', 'Lhash_array': ['1531834715954539450627284246536'], 'factors': ['2-6e4-144.29-c0-0-0'], 'label': '2-6e4-144.29-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1296/1/x/a/269/1'}