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lfunc_lfunctions • Show schema
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{'Lhash': '1449693465911390628356015565933', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.8284271247461903, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 49.826650861278985, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '6240.1', 'coefficient_field': 'CDF', 'conductor': 6240, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.8284271247461903, 0], [7.0, 0]], [[1.0, 0], [4.0, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-4.82842712474619, 0], [17.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [19.0, 0]], [[1.0, 0], [2.8284271247461903, 0], [23.0, 0]], [[1.0, 0], 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'2-6240-1.1-c1-0-60', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/6240/2/a/bn/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-3.877230221948641e-61, 0.148569105105248, 0.29589321501126487, 0.4406948390711201, 0.5816341694063151, 0.717284416730513, 0.8461144319412431, 0.9664802619577306, 1.0766267366846702, 1.174699612596026, 1.2587682514081113, 1.3268583208996256, 1.3769935862297056, 1.4072455187907182, 1.4157891815478405, 1.400963646012955, 1.3613350463247282, 1.2957602715760905, 1.2034492325534387, 1.084023610659308, 0.9375700051438223, 0.7646854422445798, 0.5665133001131709, 0.34476784056253107, 0.1017457263345243, -0.15967685674187881, -0.43606255883283684, -0.7234474454678582, -1.0173921401180173, -1.3130494337295826, -1.6052477911314647, 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'prelabel': '2-6240-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.058799534005693, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.14360649981184563108810772519', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.46412081208854751346991094724', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.09048257757754632206312473517', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 49.826650861278985, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 6240, 'conductor_radical': 390, 'degree': 2, 'index': 60, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6240/2/a/bn/1/1'], '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': '2-6240-1.1-c1-0-60', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-6240-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.058799534005693, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.14360649981184563108810772519', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1449693465911390628356015565933', 'Lhash_array': ['1449693465911390628356015565933'], 'label': '2-6240-1.1-c1-0-60', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6240/2/a/bn/1/1'}