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lfunc_lfunctions • Show schema
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{'Lhash': '1899177416877799303598783010336', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [2.3234042760864777, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.3982074301369292, 0.0], 'a8': [0.0, 0.0], 'a9': [2.398207430136929, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.068630553617312, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5, 19], 'central_character': '760.1', 'coefficient_field': 'CDF', 'conductor': 760, 'conductor_radical': 190, 'conjugate': '1899177416877799303598783010336', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.3234042760864777, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.3982074301369292, 0], [7.0, 0]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], [-4.323404276086477, 0], [13.0, 0]], [[1.0, 0], [-0.6017925698630708, 0], [17.0, 0]], [[1.0, 0], [-1.0, 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'8.009450292800877235090905566131337', '8.681384638026606490842714315350361', '9.339608443846956485332514463947681', '10.10682727889120896639420226429993'], 'prelabel': '2-760-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4634590627037647, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.49818681625352366274665120402', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.90155047877099722007122839638', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.46187234887498844093351198676', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.068630553617312, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 760, 'conductor_radical': 190, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/760/2/a/j/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': '2-760-1.1-c1-0-7', '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': '2-760-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4634590627037647, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.49818681625352366274665120402', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1899177416877799303598783010336', 'Lhash_array': ['1899177416877799303598783010336'], 'factors': ['2-760-1.1-c1-0-7'], 'label': '2-760-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/760/2/a/j/1/3'}