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lfunc_lfunctions • Show schema
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{'Lhash': '2049757064147672807066387182629', 'a10': [-2.8111678088726912, -1.6230284911898587], 'a2': [-1.5213803361495164, 0.0], 'a3': [-1.6432372069914951, -0.5475139099226523], 'a4': [0.31459812722241526, 0.0], 'a5': [1.8477745124454, 1.0668131121620812], 'a6': [2.499988774346113, 0.8329768963246608], 'a7': [-2.4676374053522343, -0.9543404191935357], 'a8': [2.5641372677533862, 0.0], 'a9': [2.4004570368824196, 1.7993904562605845], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.6432372069914951, 0.5475139099226523]]], [7, [[1.0, 0], [2.4676374053522343, 0.9543404191935357]]], [13, [[1.0, 0], [-1.003893952142094, 3.462975156256904]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.257', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '434461774308080433984418269055', 'degree': 2, 'euler_factors': 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'6.20216628226476882481247876243400', '7.35857066319022352667201585708724', '8.916793542915183940525869140834209', '9.342067735298909071601900911022450', '10.13023716641089720330700229168297', '11.01778061793488930531382773169365', '12.00211022228565864514893298590467'], 'prelabel': '2-273-273.257-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.687415648013289, 'root_number': '-0.5553498744152708 + 0.8316168089853301*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.343707824007', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.61697321310669673362900207681', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.96793859371719836924070092426', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.38450865509861416189682026671', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '273.257', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/br/b/257/9'], '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': '2-273-273.257-c1-0-15', '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': '2-273-273.257-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.3437078240066445, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.61697321310669673362900207681', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2049757064147672807066387182629', 'Lhash_array': ['2049757064147672807066387182629'], 'label': '2-273-273.257-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/br/b/257/9'}