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lfunc_lfunctions • Show schema
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{'Lhash': '840961935759271261635080268748', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [2.6626918942115068, -1.1029230950033124], 'a4': [0.0, 0.0], 'a5': [-5.507881164791315, 13.297201407978513], 'a6': [0.0, 0.0], 'a7': [6.480551375543508, 6.480551375543508], 'a8': [0.0, 0.0], 'a9': [-13.218394322028807, 13.218394322028807], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.552244480734802, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]]], 'bad_primes': [2], 'central_character': '128.49', 'coefficient_field': 'CDF', 'conductor': 128, 'conductor_radical': 2, 'conjugate': '2940065708170907727157838406808', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.6626918942115068, 1.1029230950033124], [19.091883092036785, -19.091883092036785]], [[1.0, 0], [5.507881164791315, -13.297201407978513], [-88.38834764831844, -88.38834764831844]], [[1.0, 0], [-6.480551375543508, -6.480551375543508], [0, 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[-915723.7877332334, 915723.7877332334]], [[1.0, 0], [0, -1651.2910099886778], [-1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-2e7-32.21-c3-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/128/4/g/a/49/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.3756841766220291, 1.1484637011982006, 0.9042889635873725, 0.6448782894358761, 0.37220945245924447, 0.08876707031316422, -0.20222632967698606, -0.49661927547544854, -0.7892020183335127, -1.07365765217214, -1.3426087953909234, -1.5877705812554204, -1.8002154578080516, -1.970748993688463, -2.0903884351867896, -2.1509272586682906, -2.145559742854528, -2.06953022582042, -1.9207630136979987, -1.7004218434354268, -1.413343432476455, -1.0682890249265466, -0.6779618880892796, 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'8.323364566827366309458808498951889', '9.216121544123117964837922191831044', '10.46305667577933194502354953505703', '11.61109050376782705412986569088756', '12.77907172677324161520880791149197'], 'prelabel': '2-2e7-32.21-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.748134727544267, 'root_angle': -0.5667278770694776, 'root_number': '-0.20809978294826337 - 0.9781076016149173*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.283363938535', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.66340199389947310529863983884', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.95039680324672352761605531410', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.50321165334236459703558934187', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.552244480734802, 'bad_primes': [2], 'central_character': '32.21', 'conductor': 128, 'conductor_radical': 2, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/128/4/g/a/49/8'], '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': '2-2e7-32.21-c3-0-2', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-2e7-32.21-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.748134727544267, 'root_angle': -0.2833639385347388, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.66340199389947310529863983884', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '840961935759271261635080268748', 'Lhash_array': ['840961935759271261635080268748'], 'label': '2-2e7-32.21-c3-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/128/4/g/a/49/8'}