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lfunc_lfunctions • Show schema
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{'Lhash': '1000026180096919988789437339937', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.6149753320250624, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [2.2459808736495237, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.6218053410006643, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 77.29518915659945, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5, 11], 'central_character': '9680.1', 'coefficient_field': 'CDF', 'conductor': 9680, 'conductor_radical': 110, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.6149753320250624, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.2459808736495237, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-5.194472371131779, 0], [13.0, 0]], [[1.0, 0], [3.2299506640501248, 0], [17.0, 0]], [[1.0, 0], [-7.194472371131779, 0], [19.0, 0]], [[1.0, 0], [5.113767088299711, 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'5.01345446703866898173053257844601', '5.71541974557285538754161035880820', '6.17552078642226912621702421707893', '6.85784332567369613649223781989913', '7.86954311299612431794326407575122'], 'prelabel': '2-9680-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.791768261083742, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.788881557675966881591240100463', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.60536645389069388044071939879', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.60221139490202071013830942343', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 77.29518915659945, 'bad_primes': [2, 5, 11], 'central_character': '1.1', 'conductor': 9680, 'conductor_radical': 110, 'degree': 2, 'index': 81, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9680/2/a/db/1/3'], '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': '2-9680-1.1-c1-0-81', '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': '2-9680-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.791768261083742, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.788881557675966881591240100463', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1000026180096919988789437339937', 'Lhash_array': ['1000026180096919988789437339937'], 'factors': ['2-9680-1.1-c1-0-81'], 'label': '2-9680-1.1-c1-0-81', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9680/2/a/db/1/3'}