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lfunc_lfunctions • Show schema
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{'Lhash': '515806073905409915594619836545', 'a10': [25353.581106037956, -18899.627644468426], 'a2': [-19.10477835010012, 12.124662642463326], 'a3': [-48.34121704755135, -48.34121704755135], 'a4': [217.98511161290847, -463.2779847080021], 'a5': [-1393.605774745107, 104.82339718349948], 'a6': [1509.669185295207, 337.4272884398927], 'a7': [5614.4166611251185, -5614.4166611251185], 'a8': [1452.532033278357, 11493.819151713682], 'a9': [0.0, -15009.253468723062], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.300716723277466, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [19.10477835010012, -12.124662642463326]]], [5, [[1.0, 0], [1393.605774745107, -104.82339718349948]]]], 'bad_primes': [2, 5], 'central_character': '20.7', 'coefficient_field': 'CDF', 'conductor': 20, 'conductor_radical': 10, 'conjugate': '1685749827265857395427496651155', 'degree': 2, 'euler_factors': [[[1.0, 0], [19.10477835010012, 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[-478075013.4409189, 478075013.4409189], [0, -3004041937984268300]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-20-20.7-c9-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/20/10/e/b/7/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [0.5725862716634585, 0.35035644137853217, 0.08836945306888606, -0.19854794860422084, -0.49447230343147014, -0.7828908775830499, -1.0472578111645952, -1.2716006732129772, -1.4411740046265233, -1.5431493428564087, -1.5673225982574523, -1.5068101273345111, -1.3586952634923173, -1.124578444888442, -0.8109775839518102, -0.4295221841946866, 0.0031138748941322647, 0.4655889563804905, 0.9326144290879642, 1.376034401626337, 1.766253112098742, 2.073967396407785, 2.2721272026828534, 2.338012217654195, 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'10.59674286934224955900790273032139', '11.46353765346561351762257604525068', '12.60839303476431978278529700924418', '14.88085530280437570276820353452038', '16.13258865374670642628163896832488'], 'prelabel': '2-20-20.7-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.209472966590849, 'root_angle': -0.5601151724923102, 'root_number': '-0.18773671845148016 - 0.9822193871763424*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.280057586246', 'prec': 50}, 'spectral_label': 'c9-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.40689924637951778204811555687', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.81128732685819964902362039412', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.02447757532476813370335696201', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.300716723277466, 'bad_primes': [2, 5], 'central_character': '20.7', 'conductor': 20, 'conductor_radical': 10, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/20/10/e/b/7/5'], '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': '2-20-20.7-c9-0-2', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-20-20.7-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.209472966590849, 'root_angle': -0.2800575862461551, 'self_dual': False, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '0.40689924637951778204811555687', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '515806073905409915594619836545', 'Lhash_array': ['515806073905409915594619836545'], 'label': '2-20-20.7-c9-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/20/10/e/b/7/5'}