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lfunc_lfunctions • Show schema
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{'Lhash': '2578121946464257136952302764067', 'a10': [0.0, 0.0], 'a2': [0.8312538755549068, 0.8312538755549068], 'a3': [-0.14497350536459938, 0.06004999210678571], 'a4': [0.0, 0.38196601125010515], 'a5': [0.0, 0.0], 'a6': [-0.1704265768529105, -0.07059299952129612], 'a7': [0.744219717332704, -1.7967053349700852], 'a8': [0.5137431483730078, -0.5137431483730078], 'a9': [-0.689695465480873, 0.689695465480873], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.39875294509376896, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[17, [[1.0, 0], [0.30901699437494745, -0.9510565162951535]]], [47, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [17, 47], 'central_character': '799.563', 'coefficient_field': 'CDF', 'conductor': 799, 'conductor_radical': 799, 'conjugate': '1966601353450617284485130843310', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8312538755549068, -0.8312538755549068], [0, 1.0]], [[1.0, 0], [0.14497350536459938, 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'2-799-799.563-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6314688789590259, 'root_angle': -0.135188948910427, 'root_number': '0.91115884094536528930765574476507 - 0.41205529552124253502304183036431*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.06759447445521348', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.03377961245795082116856778826', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.76180661304722172829474014509', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.88564385904656786407428291302', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.39875294509376896, 'bad_primes': [17, 47], 'central_character': '799.563', 'conductor': 799, 'conductor_radical': 799, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/799/1/h/b/563/3'], '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': '2-799-799.563-c0-0-2', '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': '2-799-799.563-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6314688789590259, 'root_angle': -0.0675944744552135, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.03377961245795082116856778826', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2578121946464257136952302764067', 'Lhash_array': ['2578121946464257136952302764067'], 'label': '2-799-799.563-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/799/1/h/b/563/3'}