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lfunc_lfunctions • Show schema
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{'Lhash': '1743417430916511665047611831646', 'a10': [0, 0], 'a2': [0, -2.2226442383332636], 'a3': [0, 2.7517327072046696], 'a4': [-2.940147410196054, 0], 'a5': [0, 0], 'a6': [6.116122847101653, 0], 'a7': [0, -1.2824968281372098], 'a8': [0, 2.089613224456199], 'a9': [-4.57203289189994, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.583918217287646, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [43, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [5, 43], 'central_character': '1075.474', 'coefficient_field': 'CDF', 'conductor': 1075, 'conductor_radical': 215, 'conjugate': '783362166201046734124212078562', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.2226442383332636], [-2.0, 0]], [[1.0, 0], [0, -2.7517327072046696], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.2824968281372098], [-7.0, 0]], [[1.0, 0], [-0.6935557694618579, 0], [11.0, 0]], [[1.0, 0], [0, 4.645211315973058], [-13.0, 0]], [[1.0, 0], [0, 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'4.38553236032962417402832125327', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.583918217287646, 'bad_primes': [5, 43], 'central_character': '5.4', 'conductor': 1075, 'conductor_radical': 215, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1075/2/b/j/474/3'], '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': '2-1075-5.4-c1-0-38', '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': '2-1075-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.929832455497694, 'root_angle': 0.32379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.37531385273089020552565174252', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1743417430916511665047611831646', 'Lhash_array': ['1743417430916511665047611831646'], 'label': '2-1075-5.4-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1075/2/b/j/474/3'}