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lfunc_lfunctions • Show schema
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{'Lhash': '2192228731827581843376352396097', 'a10': [1.0, 0.0], 'a2': [0.9238795325112867, 0.3826834323650898], 'a3': [0.0, 0.0], 'a4': [0.7071067811865476, 0.7071067811865476], 'a5': [0.9238795325112867, -0.3826834323650898], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.3826834323650898, 0.9238795325112867], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7186536181915235, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9238795325112867, -0.3826834323650898]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.9238795325112867, 0.3826834323650898]]]], 'bad_primes': [2, 3, 5], 'central_character': '1440.739', 'coefficient_field': 'CDF', 'conductor': 1440, 'conductor_radical': 30, 'conjugate': '2393205858258939637737337264777', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9238795325112867, -0.3826834323650898]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.9238795325112867, 0.3826834323650898]], [[1.0, 0], 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'sign_arg': {'__RealLiteral__': 0, 'data': '-0.09375', 'prec': 27}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.72936354184101694682411560930', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.48603981667718517981696148874', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.65056406088643831899936314046', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7186536181915235, 'bad_primes': [2, 3, 5], 'central_character': '160.99', 'conductor': 1440, 'conductor_radical': 30, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1440/1/cm/a/739/2'], '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': '2-1440-160.99-c0-0-1', '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': '2-1440-160.99-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8477344030954055, 'root_angle': -0.09375, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.72936354184101694682411560930', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2192228731827581843376352396097', 'Lhash_array': ['2192228731827581843376352396097'], 'label': '2-1440-160.99-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1440/1/cm/a/739/2'}