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lfunc_lfunctions • Show schema
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{'Lhash': '1969741202376454181626454818983', 'a10': [1.6852099743038522, 2.9188692969161143], 'a2': [-1.4624302015370778, -0.8443344705284705], 'a3': [-1.545929324956522, 0.781090597971498], 'a4': [0.4258013962451853, 0.7375096522304287], 'a5': [-1.7285029800389344, -0.9979516608205491], 'a6': [2.9203154507312763, 0.16299093745142637], 'a7': [0.0, -1.0], 'a8': [0.0, 1.9392626963180342], 'a9': [1.7797949555210553, -2.415021721703928], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.545929324956522, -0.781090597971498]]], [7, [[1.0, 0], [0, 1.0]]], [13, [[1.0, 0], [-2.533739712034024, 2.56518285345543]]]], 'bad_primes': [3, 7, 13], 'central_character': '819.400', 'coefficient_field': 'CDF', 'conductor': 819, 'conductor_radical': 273, 'conjugate': '190630897474357583039632860336', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.4624302015370778, 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[-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 49, 'label': '2-819-117.49-c1-0-49', '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/819/2/dk/a/400/21', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.1521705418238315, 0.2909335448989068, 0.43897896576900614, 0.5931414547637076, 0.7474645241516357, 0.8923035983577176, 1.0140432123815606, 1.0954579135893558, 1.1167009749732069, 1.0568875574675232, 0.8962122167113651, 0.6184889825095266, 0.21392930550920977, -0.31810739920363157, -0.9667269132726132, -1.707857423384721, -2.503732443098075, -3.303827753896707, -4.047466673512093, -4.668135561274011, -5.0993326626138575, -5.2815303407184695, -5.169594608155913, -4.739813839725147, -3.9955790916227607, -2.9707652629269004, 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'7.934935334044294825487930908384698', '8.927919842143956460502552368709112', '9.873701127334427749306922241191909', '10.74828803827490589634171907116511'], 'prelabel': '2-819-117.49-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': -0.7679418287444248, 'root_number': '-0.7458194190405364 - 0.6661481773464796*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.383970914372', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.55385182795781385573996866786', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.40784203735211469414811886209', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.63995466883469135410310949050', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'bad_primes': [3, 7, 13], 'central_character': '117.49', 'conductor': 819, 'conductor_radical': 273, 'degree': 2, 'index': 49, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/819/2/dk/a/400/21'], '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': '2-819-117.49-c1-0-49', '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': '2-819-117.49-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': -0.3839709143722124, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.55385182795781385573996866786', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1969741202376454181626454818983', 'Lhash_array': ['1969741202376454181626454818983'], 'label': '2-819-117.49-c1-0-49', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/819/2/dk/a/400/21'}