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lfunc_lfunctions • Show schema
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{'Lhash': '3666257701083921556202425803634', 'a10': [-8.744562646538029, 0.0], 'a2': [2.715194527703128, 0.0], 'a3': [0.0, 0.0], 'a4': [5.372281323269014, 0.0], 'a5': [-3.2206026335561817, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.3722813232690143, 0.0], 'a8': [9.156399794815492, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 19], 'central_character': '171.1', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '3666257701083921556202425803634', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.715194527703128, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.2206026335561817, 0], [5.0, 0]], [[1.0, 0], [2.3722813232690143, 0], [7.0, 0]], [[1.0, 0], [2.2097864218500747, 0], [11.0, 0]], [[1.0, 0], [-2.0, 0], [13.0, 0]], [[1.0, 0], 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[-5.255437353461971, 0], [109.0, 0]], [[1.0, 0], [11.87159432251862, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-171-1.1-c1-0-6', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/171/2/a/e/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.5613072861540926, 2.57711182376058, 2.6230435553081928, 2.6948657532186684, 2.7861238794583465, 2.8888111728870034, 2.993987730234474, 3.0922796726812596, 3.1742747884548685, 3.2308694491852554, 3.253617899489368, 3.2351125041534208, 3.1693985537259013, 3.05240659495949, 2.882370359859252, 2.6601888090627495, 2.3896860904546178, 2.0777232138907116, 1.734120096434629, 1.371356498052841, 1.0040351795698654, 0.6481098919491203, 0.31990352881506917, 0.034966334583525, -0.19315170574788298, 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'7.13413028488371389295620299903419', '8.238365858967256567168450837137290', '10.27061200076407566688849681077470', '11.38999826050231165427198056276440', '11.87074489719162000192938990034491', '13.04183876456383678813676835785898'], 'prelabel': '2-171-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, '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': '2.89216736885056807339606496549', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.84105804025055284632284483666', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.84767825282947347246593092996', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'bad_primes': [3, 19], 'central_character': '1.1', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/2/a/e/1/4'], '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': '2-171-1.1-c1-0-6', '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': '2-171-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.89216736885056807339606496549', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3666257701083921556202425803634', 'Lhash_array': ['3666257701083921556202425803634'], 'label': '2-171-1.1-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/2/a/e/1/4'}