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lfunc_lfunctions • Show schema
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{'Lhash': '635306030945034367006483167642', 'a10': [1.0, 0.0], 'a2': [-0.3826834323650898, -0.9238795325112867], 'a3': [0.7071067811865476, 0.7071067811865476], 'a4': [-0.7071067811865476, 0.7071067811865476], 'a5': [-0.3826834323650898, 0.9238795325112867], 'a6': [0.3826834323650898, -0.9238795325112867], 'a7': [0.0, 0.0], 'a8': [0.9238795325112867, 0.3826834323650898], 'a9': [0.0, 1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7785414197074838, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.3826834323650898, 0.9238795325112867]]], [3, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]], [5, [[1.0, 0], [0.3826834323650898, -0.9238795325112867]]], [13, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1560.1403', 'coefficient_field': 'CDF', 'conductor': 1560, 'conductor_radical': 390, 'conjugate': '2895617731954904819916990847437', 'degree': 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-1.0714992322697632], 'positive_zeros': ['0.50116809066366794890095799436897', '2.06247559250676054708604681768482', '3.35002569589319896260021749475196', '4.71263030396386845163028434845193', '5.30774906205377968519676344973292', '6.25365602202958854978562653833789', '7.45693842169225021191702170417311', '7.76489383967042580730359538971031', '8.347094738593597890012457271959646', '9.114980989339304345571118340503661'], 'prelabel': '2-1560-1560.1403-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8823499417507114, 'root_angle': -0.5737918088252166, 'root_number': '-0.22975292054736118352393736938184 - 0.97324898946773016378805774830813*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2868959044126083', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.50116809066366794890095799437', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.06247559250676054708604681768', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.35002569589319896260021749475', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7785414197074838, 'bad_primes': [2, 3, 5, 13], 'central_character': '1560.1403', 'conductor': 1560, 'conductor_radical': 390, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1560/1/cs/e/1403/2'], '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': '2-1560-1560.1403-c0-0-2', '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': '2-1560-1560.1403-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8823499417507114, 'root_angle': -0.2868959044126083, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.50116809066366794890095799437', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '635306030945034367006483167642', 'Lhash_array': ['635306030945034367006483167642'], 'label': '2-1560-1560.1403-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1560/1/cs/e/1403/2'}