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lfunc_lfunctions • Show schema
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{'Lhash': '3423630973610838372715725229335', 'a10': [2.0, 3.4641016151377544], 'a2': [-0.5, 0.8660254037844386], 'a3': [0.5, -0.8660254037844386], 'a4': [-0.5, -0.8660254037844386], 'a5': [2.0, -3.4641016151377544], 'a6': [0.5, 0.8660254037844386], 'a7': [-3.0, 0.0], 'a8': [1.0, 0.0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [3, [[1.0, 0], [-0.5, 0.8660254037844386]]], [19, [[1.0, 0], [4.0, -1.7320508075688772]]]], 'bad_primes': [2, 3, 19], 'central_character': '114.49', 'coefficient_field': 'CDF', 'conductor': 114, 'conductor_radical': 114, 'conjugate': '1963756491579052101232446815560', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [-2.0, 3.4641016151377544], [-2.5, -4.330127018922194]], [[1.0, 0], 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'data': '2.70076862898533993905049973728', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.56266624530711247778126453860', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.91093817892060880743479689853', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'bad_primes': [2, 3, 19], 'central_character': '19.11', 'conductor': 114, 'conductor_radical': 114, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/114/2/e/a/49/1'], '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': '2-114-19.11-c1-0-0', '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': '2-114-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': 0.06775328806227679, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.70076862898533993905049973728', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3423630973610838372715725229335', 'Lhash_array': ['3423630973610838372715725229335'], 'label': '2-114-19.11-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/2/e/a/49/1'}