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lfunc_lfunctions • Show schema
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{'Lhash': '2183294356452957551108890025855', 'a10': [-2.046344099707047, 0.9013744092185865], 'a2': [-0.5, -0.8660254037844386], 'a3': [-0.1765290801329452, -0.6588154960695491], 'a4': [-0.5, 0.8660254037844386], 'a5': [0.2425589131490373, -2.222873179839992], 'a6': [-0.48228641593660393, 0.48228641593660393], 'a7': [1.0992978943438672, 4.102635594344796], 'a8': [1.0, 0.0], 'a9': [2.1952008696245335, -1.267399813003025], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [5, [[1.0, 0], [-0.2425589131490373, 2.222873179839992]]], [37, [[1.0, 0], [-2.8260388526661666, -5.386418513559942]]]], 'bad_primes': [2, 5, 37], 'central_character': '370.103', 'coefficient_field': 'CDF', 'conductor': 370, 'conductor_radical': 370, 'conjugate': '1306600940383603005746852735737', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 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'7.47462485139777652025019653887755', '8.924660036570524370418447543886168', '9.964559904646434047878249409183957', '10.83983620274391753372329844495890', '10.91291683028528591279926583584127'], 'prelabel': '2-370-185.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7188556875978203, 'root_angle': 0.5467789695024065, 'root_number': '-0.14643204440141286 + 0.989220731875562*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.273389484751', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.72231556239540651115924893827', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.93590317825874163599101634835', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.53613197076115745149847063743', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'bad_primes': [2, 5, 37], 'central_character': '185.103', 'conductor': 370, 'conductor_radical': 370, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/370/2/q/d/103/1'], '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': '2-370-185.103-c1-0-11', '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': '2-370-185.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7188556875978203, 'root_angle': 0.2733894847512032, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.72231556239540651115924893827', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2183294356452957551108890025855', 'Lhash_array': ['2183294356452957551108890025855'], 'label': '2-370-185.103-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/370/2/q/d/103/1'}