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lfunc_lfunctions • Show schema
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{'Lhash': '4867501393974572285882506943821', 'a10': [6.403882032022076, 11.091849045139659], 'a2': [2.280776406404415, 3.950420616596809], 'a3': [-4.342329219213245, -7.521134830868234], 'a4': [-6.403882032022076, 11.091849045139659], 'a5': [2.8077640640441515, 0.0], 'a6': [19.80776406404415, -34.30805374326146], 'a7': [-4.780776406404415, 8.280547635519003], 'a8': [-21.93086968966181, 0.0], 'a9': [-24.21164609606623, 41.935801173263364], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7670248300746283, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[13, [[1.0, 0], [-40.52698765763974, -23.54916710623789]]]], 'bad_primes': [13], 'central_character': '13.3', 'coefficient_field': 'CDF', 'conductor': 13, 'conductor_radical': 13, 'conjugate': '7160242585993072847561087725692', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.280776406404415, -3.950420616596809], [-4.0, 6.928203230275509]], [[1.0, 0], [4.342329219213245, 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[896.0037313302959, 0], [1295029.0, 0]], [[1.0, 0], [-167.44124568491307, 290.0167448088925], [-721448.5, -1249585.457044355]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-13-13.3-c3-0-1', '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/13/4/c/b/3/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [1.0831803764026384, 1.0631494982239582, 1.0522820984318282, 1.0493567967292745, 1.0529215044978775, 1.0613075399022154, 1.0726418473237556, 1.0848581839163454, 1.0957105128369253, 1.1027937078651964, 1.1035775966175536, 1.0954603382780561, 1.0758463305343346, 1.0422524540771627, 0.9924445968929472, 0.9246040881222581, 0.8375209188679188, 0.7308074611106878, 0.6051228966516125, 0.4623948926766236, 0.3060214516463708, 0.1410326478122347, 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'13.37139333206078506665771272036561', '15.09259625175710776437642716566407', '16.47930155832714051475863650637092', '18.06018248216009198275540077030250', '20.06374713047679510172826553572134'], 'prelabel': '2-13-13.3-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.875799537608138, 'root_angle': -0.25115347835724794, 'root_number': '0.7045397594107957 - 0.7096645175076588*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.125576739179', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.83978155581531791135561886183', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.36503335546656995246130403068', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '9.876914585513506265401796361910', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7670248300746283, 'bad_primes': [13], 'central_character': '13.3', 'conductor': 13, 'conductor_radical': 13, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/13/4/c/b/3/2'], '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': '2-13-13.3-c3-0-1', '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': '2-13-13.3-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.875799537608138, 'root_angle': -0.12557673917862397, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '3.83978155581531791135561886183', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4867501393974572285882506943821', 'Lhash_array': ['4867501393974572285882506943821'], 'label': '2-13-13.3-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/13/4/c/b/3/2'}