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lfunc_lfunctions • Show schema
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{'Lhash': '1060522384906858833998889706467', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.44573835577653825, 0.8951632913550623], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.05050087027954597, 0.5449911840037233], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.46263326671079325, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [103, [[1.0, 0], [-0.9829730996839018, -0.18374951781657034]]]], 'bad_primes': [3, 103], 'central_character': '927.415', 'coefficient_field': 'CDF', 'conductor': 927, 'conductor_radical': 309, 'conjugate': '2548740263588903727021541259724', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0.44573835577653825, -0.8951632913550623]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.7390089172206591, 0.6736956436465572]], [[1.0, 0], [0.05050087027954597, -0.5449911840037233], [-0.9829730996839018, -0.18374951781657034]], [[1.0, 0], 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'6.66358372443232912271682564736182', '7.41424291509970737579663635580209', '8.602489354017380199805228936106561', '9.256625746952853509669635657921717', '10.09691614792657793698508351191902'], 'prelabel': '2-927-103.3-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6801714980141356, 'root_angle': -0.5073317236783107, 'root_number': '-0.023031252648866880726938306185818 - 0.99973474552074264810054528359309*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25366586183915535', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.836604648564770967463425890609', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.47198849379318853711675659031', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.86461256116506590996766697421', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.46263326671079325, 'bad_primes': [3, 103], 'central_character': '103.3', 'conductor': 927, 'conductor_radical': 309, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/927/1/v/a/415/1'], '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': '2-927-103.3-c0-0-0', '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': '2-927-103.3-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6801714980141356, 'root_angle': -0.25366586183915535, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.836604648564770967463425890609', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1060522384906858833998889706467', 'Lhash_array': ['1060522384906858833998889706467'], 'label': '2-927-103.3-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/927/1/v/a/415/1'}