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lfunc_lfunctions • Show schema
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{'Lhash': '1131639787166505795849895669919', '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': [2.742521361354168, 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], [-2.742521361354168, 0], [7.0, 0]], [[1.0, 0], [5.767634668719238, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.7425213613541677, 0], [17.0, 0]], [[1.0, 0], [-2.263944778838085, 0], [19.0, 0]], [[1.0, 0], [-2.742521361354168, 0], [23.0, 0]], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 37, 'label': '2-6240-1.1-c1-0-37', 'leading_term': '2.99983683453702390404283927112', '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/6240/2/a/cf/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.999836834537024, 2.9898760853491195, 2.959929507445103, 2.909814481173995, 2.839260440603644, 2.7479569617594177, 2.6356161567323033, 2.5020450715626135, 2.3472233171789125, 2.171381070391349, 1.9750728024978066, 1.7592425401067722, 1.5252770490722278, 1.2750439855300042, 1.0109127277678218, 0.7357562614516427, 0.45293312904678734, 0.1662490741573763, -0.12010137988900116, -0.4016125735070761, -0.6735631290478414, -0.9311270955281183, -1.169498181577401, -1.3840238725278418, -1.570345704466088, 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'5.20337203521141644535697029702292', '5.68432078848289423721347690700618', '6.83120072221359479545967399189349', '7.44081859109034377711509422444011', '8.254933358833290128908754720498832'], 'prelabel': '2-6240-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.058799534005693, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.892706386888282900239307649799', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.04156239707215546311898311221', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.60113212216177839746706904842', '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': 37, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6240/2/a/cf/1/3'], '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-c1-0-37', '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': '2-6240-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.058799534005693, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.892706386888282900239307649799', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1131639787166505795849895669919', 'Lhash_array': ['1131639787166505795849895669919'], 'label': '2-6240-1.1-c1-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6240/2/a/cf/1/3'}