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lfunc_lfunctions • Show schema
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{'Lhash': '2105946236284408475286158644646', 'a10': [3.2642113604202163, 1.8845933076304464], 'a2': [0.5, 0.8660254037844386], 'a3': [1.7313115631968465, 0.05059912193795112], 'a4': [-0.5, 0.8660254037844386], 'a5': [3.2642113604202163, -1.8845933076304464], 'a6': [0.8218356565909711, 1.5246593565631923], 'a7': [-0.38510764866188735, 2.617573704586389], 'a8': [-1.0, 0.0], 'a9': [2.9948794577182167, 0.17520568979756404], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [3, [[1.0, 0], [-1.7313115631968465, -0.05059912193795112]]], [7, [[1.0, 0], [0.38510764866188735, -2.617573704586389]]], [13, [[1.0, 0], [2.902739447795325, 2.1387154317984645]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.311', 'coefficient_field': 'CDF', 'conductor': 546, 'conductor_radical': 546, 'conjugate': 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'3.54770572011249087477888466150736', '4.87211996601839146283838574872298', '6.13574750733949932521206607143058', '6.99143505148236732164403622349628', '8.017086456281176114212306926381323', '9.414438069382260767540390613271864', '9.721550979189503323225893820923547', '10.61369197401714548696126348551418'], 'prelabel': '2-546-273.38-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.2824232759904526, 'root_number': '0.6315396991772774 - 0.7753435421560394*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.141211637995', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.66129865430210128698516107530', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.71426731280374709259835439109', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.54770572011249087477888466151', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '273.38', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/bg/b/311/18'], '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': '2-546-273.38-c1-0-25', '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': '2-546-273.38-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.1412116379952263, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.66129865430210128698516107530', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2105946236284408475286158644646', 'Lhash_array': ['2105946236284408475286158644646'], 'label': '2-546-273.38-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/bg/b/311/18'}