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lfunc_lfunctions • Show schema
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{'Lhash': '396357152286270223797813579404', 'a10': [3.8993716582937217, 0], 'a2': [0, -1.0], 'a3': [0, -0.7653668647301796], 'a4': [-1.0, 0], 'a5': [0, 3.8993716582937217], 'a6': [-0.7653668647301796, 0], 'a7': [0, 0], 'a8': [0, 1.0], 'a9': [2.414213562373095, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.607873337894029, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-0.21488185092355414, -3.309656445938712]]]], 'bad_primes': [2, 7, 11], 'central_character': '1078.1077', 'coefficient_field': 'CDF', 'conductor': 1078, 'conductor_radical': 154, 'conjugate': '2635982898903217823157024716075', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0.7653668647301796], [-3.0, 0]], [[1.0, 0], [0, -3.8993716582937217], [-5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.21488185092355414, -3.309656445938712]], [[1.0, 0], [1.8190261538471002, 0], [13.0, 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['0.31267066194336955763433577779963', '1.88499082017537163409391836131100', '3.93289988331120565968746248165003', '4.45943330691746207204178382052774', '5.24435499710239500428176449199880', '6.14886076880716232446240901835800', '7.14216899279154893625469644275699', '8.280408365054436947015957563102559', '8.744753939898263998046780080911921', '9.330725004561281183489008661406504'], 'prelabel': '2-1078-77.76-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': -0.570677351594479, 'root_number': '-0.2202194604870939139113519933432511897311830517336043501 - 0.9754503520029982963095192371009631831486816384650650508*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2853386757972395', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.31267066194336955763433577780', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.88499082017537163409391836131', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.93289988331120565968746248165', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.607873337894029, 'bad_primes': [2, 7, 11], 'central_character': '77.76', 'conductor': 1078, 'conductor_radical': 154, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1078/2/c/c/1077/4'], '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': '2-1078-77.76-c1-0-4', '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': '2-1078-77.76-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': -0.2853386757972395, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.31267066194336955763433577780', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '396357152286270223797813579404', 'Lhash_array': ['396357152286270223797813579404'], 'label': '2-1078-77.76-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1078/2/c/c/1077/4'}