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lfunc_lfunctions • Show schema
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{'Lhash': '1688321251621647735289575528872', 'a10': [0.0, 0.0], 'a2': [0.6691306063588582, 1.1589682071129128], 'a3': [-0.9781476007338057, 0.20791169081775934], 'a4': [-0.39547153673234653, 0.6849767945677657], 'a5': [0.0, 0.0], 'a6': [-0.8954715367323465, -0.9945218953682733], 'a7': [-0.8090169943749475, -1.4012585384440734], 'a8': [0.2797727760321784, -5.842691974408547e-79], 'a9': [0.9135454576426009, -0.4067366430758002], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6422966712586741, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.9781476007338057, -0.20791169081775934]]], [11, [[1.0, 0], [-0.5, -0.8660254037844386]]], [13, [[1.0, 0], [-0.5, 0.8660254037844386]]]], 'bad_primes': [3, 11, 13], 'central_character': '1287.571', 'coefficient_field': 'CDF', 'conductor': 1287, 'conductor_radical': 429, 'conjugate': '1519465080086270930226112502525', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0.6180339887498949, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0.10452846326765347, 0.18104860921667293], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0.9135454576426009, -1.5823071476607464], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.3382612127177165, 0], [1.0, 0]], [[1.0, 0], [0.6691306063588582, -1.1589682071129128], [-0.5, -0.8660254037844386]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-1287-1287.571-c0-0-3', 'leading_term': '1.1774772641297270824913059028339', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1287/1/ba/d/571/3', 'plot_delta': 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'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.17777777777777778', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.33185063085812467798762461849', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.55482670968959648255201064366', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.49497865283038354677690618182', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6422966712586741, 'bad_primes': [3, 11, 13], 'central_character': '1287.571', 'conductor': 1287, 'conductor_radical': 429, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1287/1/ba/d/571/3'], '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': '2-1287-1287.571-c0-0-3', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1287-1287.571-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8014341340738327, 'root_angle': -0.17777777777777778, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.33185063085812467798762461849', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1688321251621647735289575528872', 'Lhash_array': ['1688321251621647735289575528872'], 'label': '2-1287-1287.571-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1287/1/ba/d/571/3'}