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lfunc_lfunctions • Show schema
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{'Lhash': '2433816946408213947503611449959', 'a10': [0, 0], 'a2': [0.8660254037844386, -0.5], 'a3': [-0.5, -0.8660254037844386], 'a4': [0.5, -0.8660254037844386], 'a5': [0, 0], 'a6': [-0.8660254037844386, -0.5], 'a7': [0.7494816955549555, 0.4327134586813507], 'a8': [0, -1.0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.570828394149682, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, 0.5]]], [3, [[1.0, 0], [0.5, 0.8660254037844386]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [3.341310909099541, 1.354858446012866]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1950.751', 'coefficient_field': 'CDF', 'conductor': 1950, 'conductor_radical': 390, 'conjugate': '216036215416305606764123256373', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, 0.5]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.7494816955549555, 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'0.6291328622695106411050483570606168698984304470817205913', '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/1950/2/bc/i/751/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.6291328622695106, 0.8518396915470344, 1.0779772504041603, 1.3074911924440096, 1.54009554064122, 1.7751907333390111, 2.011797726025739, 2.2485114727026243, 2.483475609239609, 2.714378849981523, 2.9384726056290393, 3.15260865362443, 3.3532952877676196, 3.5367701516177776, 3.6990878273564265, 3.8362201332247756, 3.9441669304683433, 4.019075034007999, 4.057362560969262, 4.055845754441754, 4.011865012495048, 3.9234065650950867, 3.789216005581006, 3.608899728631389, 3.383010279773861, 3.1131117046453434, 2.801821216254269, 2.4528238862764224, 2.0708576161816583, 1.6616663529333922, 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'7.945026201049029660954384266396269', '8.924696384578938236272873566831025', '9.511017493222334882473410748480651'], 'prelabel': '2-1950-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9459888993951417, 'root_angle': -0.8732963242667607, 'root_number': '-0.92181808992346278433893107327855545813510079620867706238 - 0.3876227664751629109389972639845585319728690938886355283*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.43664816213338037', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.91994303948582243142866101005', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.05755690870974486394960422417', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.09318927449226179811658622905', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.570828394149682, 'bad_primes': [2, 3, 5, 13], 'central_character': '13.10', 'conductor': 1950, 'conductor_radical': 390, 'degree': 2, 'index': 42, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1950/2/bc/i/751/5'], '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': '2-1950-13.10-c1-0-42', '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': '2-1950-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9459888993951417, 'root_angle': -0.43664816213338037, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.91994303948582243142866101005', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2433816946408213947503611449959', 'Lhash_array': ['2433816946408213947503611449959'], 'label': '2-1950-13.10-c1-0-42', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1950/2/bc/i/751/5'}