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lfunc_lfunctions • Show schema
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{'Lhash': '785355222372988283253543366337', 'a10': [1.7972692859976, -2.0741593250056667], 'a2': [-1.1971255511644243, 0.7693458765045058], 'a3': [0.9898214418809327, 0.14231483827328514], 'a4': [0.01038648155246748, -0.02274322218403066], 'a5': [-1.8505175213187517, 0.5433609699058243], 'a6': [-1.2944298731570343, 0.5911463155800576], 'a7': [2.007564878758435, -1.7232768952131956], 'a8': [-0.3999719149688565, -2.781865773027186], 'a9': [0.9594929736144974, 0.28173255684142967], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.9898214418809327, -0.14231483827328514]]], [7, [[1.0, 0], [-2.007564878758435, 1.7232768952131956]]], [23, [[1.0, 0], [4.5728880759022825, 1.4452316925914415]]]], 'bad_primes': [3, 7, 23], 'central_character': '483.34', 'coefficient_field': 'CDF', 'conductor': 483, 'conductor_radical': 483, 'conjugate': 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1.9638672097745928, 'root_angle': -0.7401262198998898, 'root_number': '-0.6848361111337079 - 0.728697125620281*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.37006310995', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.61953603164120456026797026710', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.23847415182015011807538487328', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.39776929641527341811805856068', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'bad_primes': [3, 7, 23], 'central_character': '161.34', 'conductor': 483, 'conductor_radical': 483, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/483/2/r/a/34/10'], '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': '2-483-161.34-c1-0-5', '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': '2-483-161.34-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': -0.3700631099499449, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.61953603164120456026797026710', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '785355222372988283253543366337', 'Lhash_array': ['785355222372988283253543366337'], 'label': '2-483-161.34-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/483/2/r/a/34/10'}