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lfunc_lfunctions • Show schema
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{'Lhash': '618800346037156150642361684300', 'a10': [0.0, 0.0], 'a2': [0.6180339887498949, 0.0], 'a3': [0.38196601125010515, 0.0], 'a4': [-1.618033988749895, 0.0], 'a5': [0.0, 0.0], 'a6': [0.2360679774997897, 0.0], 'a7': [-3.8541019662496847, 0.0], 'a8': [-2.23606797749979, 0.0], 'a9': [-2.8541019662496847, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.15474661143733, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 11], 'central_character': '3025.1', 'coefficient_field': 'CDF', 'conductor': 3025, 'conductor_radical': 55, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6180339887498949, 0], [2.0, 0]], [[1.0, 0], [-0.38196601125010515, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.8541019662496847, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.7639320225002102, 0], [13.0, 0]], [[1.0, 0], [1.618033988749895, 0], [17.0, 0]], [[1.0, 0], 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'4.77824801031410966214136859996489', '5.70333016856872046537591203534640', '6.32657147907866032854651657737204', '7.04122266132773873598011453079196', '8.201446986708997187654314901167779', '8.827885907428486798157694586700557'], 'prelabel': '2-55e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.914747868552092, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.48814740112594634628912402620', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.51347707589512151158421849282', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.10436538494088498147198008226', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 24.15474661143733, 'bad_primes': [5, 11], 'central_character': '1.1', 'conductor': 3025, 'conductor_radical': 55, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3025/2/a/i/1/2'], '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': '2-55e2-1.1-c1-0-14', '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': '2-55e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.914747868552092, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.48814740112594634628912402620', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '618800346037156150642361684300', 'Lhash_array': ['618800346037156150642361684300'], 'label': '2-55e2-1.1-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3025/2/a/i/1/2'}