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lfunc_lfunctions • Show schema
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{'Lhash': '746827956319262293358590719999', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.735489498215868, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33.058066436810094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [23, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '4140.1', 'coefficient_field': 'CDF', 'conductor': 4140, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [3.735489498215868, 0], [7.0, 0]], [[1.0, 0], [4.844685644748453, 0], [11.0, 0]], [[1.0, 0], [2.8446856447484534, 0], [13.0, 0]], [[1.0, 0], [0.8908038534674149, 0], [17.0, 0]], [[1.0, 0], [-6.844685644748453, 0], [19.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-4140-1.1-c1-0-3', 'leading_term': '1.19563484352800447579351175002', '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/4140/2/a/s/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.1956348435280044, 1.1869535996266338, 1.1608639035190116, 1.1172352414391624, 1.05587418740859, 0.976558849605351, 0.8790838839118141, 0.7633132607508583, 0.62923764842858, 0.477033190078028, 0.3071185606585644, 0.12020743967572549, -0.0826461314651086, -0.3000116671151525, -0.5300572110549243, -0.7705367773034109, -1.0187913118177052, -1.271763879807044, -1.5260294347923695, -1.7778391692362772, -2.0231790765466826, -2.2578419680453816, -2.477511787693425, -2.6778586576263823, -2.854642678152548, 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'6.35782044232975906956561047433613', '6.82168432893485571516960758664986', '7.71202951961405956826639303019113', '8.315980577922586045499568997226022'], 'prelabel': '2-4140-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.749614459840772, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58914337766637151662930508360', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.18772630102367677477184677524', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.94138419891333984158036316766', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 33.058066436810094, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 4140, 'conductor_radical': 690, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4140/2/a/s/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': '2-4140-1.1-c1-0-3', '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': '2-4140-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.749614459840772, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.58914337766637151662930508360', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '746827956319262293358590719999', 'Lhash_array': ['746827956319262293358590719999'], 'label': '2-4140-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4140/2/a/s/1/1'}