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lfunc_lfunctions • Show schema
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{'Lhash': '987238031084042295492743060620', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 1.0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-2.6426489071648906, 0], 'a8': [0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.1640964851073, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, -1.0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '2400.1201', 'coefficient_field': 'CDF', 'conductor': 2400, 'conductor_radical': 30, 'conjugate': '943108181414647339830276482331', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.6426489071648906, 0], [7.0, 0]], [[1.0, 0], [0, 1.513632775490905], [-11.0, 0]], [[1.0, 0], [0, 3.8708646639400595], [-13.0, 0]], [[1.0, 0], [-3.31415045623155, 0], [17.0, 0]], [[1.0, 0], [0, -7.085815495070426], [-19.0, 0]], [[1.0, 0], [4.827783231722455, 0], [23.0, 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'4.09126826011184126008985000217171', '4.92944873048515401704111303829410', '6.12636039955725407700081250723316', '6.54735641707656188606800181012829', '7.31192131440921268728700779225658', '8.055143406604106310796091804194371', '9.045157984358803352914362327837203'], 'prelabel': '2-2400-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.377681633594122, 'root_angle': -0.10310842525638832, 'root_number': '0.9479935403481846906075276049209189307420059680888130614 - 0.318289565424496322794780600939341186416071250318430685*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.05155421262819416', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77879348686956699590168710429', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.17599943435635160806574549861', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.97894481934235703887237635005', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.1640964851073, 'bad_primes': [2, 3, 5], 'central_character': '8.5', 'conductor': 2400, 'conductor_radical': 30, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2400/2/k/f/1201/8'], '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': '2-2400-8.5-c1-0-17', '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': '2-2400-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.377681633594122, 'root_angle': -0.05155421262819416, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.77879348686956699590168710429', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '987238031084042295492743060620', 'Lhash_array': ['987238031084042295492743060620'], 'label': '2-2400-8.5-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2400/2/k/f/1201/8'}