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lfunc_lfunctions • Show schema
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{'Lhash': '934656753135795620975393620866', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.1133407984528387, 1.3268278963378768], 'a4': [0, 0], 'a5': [1.4396926207859084, 2.493620766483186], 'a6': [0, 0], 'a7': [0.5, -0.8660254037844386], 'a8': [0, 0], 'a9': [-0.520944533000791, -2.9544232590366244], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.048920523745066, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.1133407984528387, -1.3268278963378768]]], [7, [[1.0, 0], [-0.5, 0.8660254037844386]]]], 'bad_primes': [2, 3, 7], 'central_character': '1008.673', 'coefficient_field': 'CDF', 'conductor': 1008, 'conductor_radical': 42, 'conjugate': '2045636171082309980861641953427', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.1133407984528387, -1.3268278963378768]], [[1.0, 0], [-1.4396926207859084, -2.493620766483186], [-2.5, 4.330127018922194]], [[1.0, 0], [-0.5, 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'8.303575907121097860854599106018486', '8.486577329500815367990121950283991', '9.766530501157270606624426460854365'], 'prelabel': '2-1008-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.837061952750603, 'root_angle': -0.6666666666666667, 'root_number': '-0.50000000000000000000000000000000000000000000000000000000 - 0.8660254037844386467637231707529361834714026269051903141*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.33333333333333337', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.73731417234963549790849247879', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.74668054940701417677491024070', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.15562331937802466851616446493', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.048920523745066, 'bad_primes': [2, 3, 7], 'central_character': '9.7', 'conductor': 1008, 'conductor_radical': 42, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1008/2/r/i/673/1'], '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': '2-1008-9.7-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': '2-1008-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.837061952750603, 'root_angle': -0.33333333333333337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.73731417234963549790849247879', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '934656753135795620975393620866', 'Lhash_array': ['934656753135795620975393620866'], 'label': '2-1008-9.7-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1008/2/r/i/673/1'}