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lfunc_lfunctions • Show schema
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{'Lhash': '1100601790441957444443397234320', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-12.731369278381807, 0.0], 'a4': [0.0, 0.0], 'a5': [-83.6516705026033, 0.0], 'a6': [0.0, 0.0], 'a7': [121.59483774866708, 0.0], 'a8': [0.0, 0.0], 'a9': [-80.9122362974759, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 164.8745667677441, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [257, [[1.0, 0], [-66049.0, 0]]]], 'bad_primes': [2, 257], 'central_character': '1028.1', 'coefficient_field': 'CDF', 'conductor': 1028, 'conductor_radical': 514, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [12.731369278381807, 0], [243.0, 0]], [[1.0, 0], [83.6516705026033, 0], [3125.0, 0]], [[1.0, 0], [-121.59483774866708, 0], [16807.0, 0]], [[1.0, 0], [-227.54941834444975, 0], [161051.0, 0]], [[1.0, 0], [501.9623016521337, 0], [371293.0, 0]], [[1.0, 0], [1301.4543204802671, 0], [1419857.0, 0]], [[1.0, 0], 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{'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.868221724695908888340063522196', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.32426824376478280632400973541', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.62538647628427462132853202559', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 164.8745667677441, 'bad_primes': [2, 257], 'central_character': '1.1', 'conductor': 1028, 'conductor_radical': 514, 'degree': 2, 'index': 54, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1028/6/a/a/1/16'], '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': '2-1028-1.1-c5-0-54', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-1028-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.84034916845115, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.868221724695908888340063522196', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1100601790441957444443397234320', 'Lhash_array': ['1100601790441957444443397234320'], 'label': '2-1028-1.1-c5-0-54', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1028/6/a/a/1/16'}