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lfunc_lfunctions • Show schema
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{'Lhash': '980749986900531043774775578611', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.8060634335253696, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.3502617411332922, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.3502617411332922, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.137261107234623, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5, 19], 'central_character': '1520.1', 'coefficient_field': 'CDF', 'conductor': 1520, 'conductor_radical': 190, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.8060634335253696, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [3.3502617411332922, 0], [7.0, 0]], [[1.0, 0], [0.9623886081840313, 0], [11.0, 0]], [[1.0, 0], [-6.156325174658662, 0], [13.0, 0]], [[1.0, 0], [6.312650349317323, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], 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'5.59562810747179178073161718668348', '6.28561856886506231686131666840128', '6.63144874542798838372369477283176', '7.932160086340054580401837564388727', '8.954524838498873351040686739129633', '9.256535066609790094058231845723047'], 'prelabel': '2-1520-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77367532246184838943517958557', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.48525198776378497071493119436', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.33193957116151940061608630837', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.137261107234623, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 1520, 'conductor_radical': 190, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1520/2/a/p/1/2'], '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': '2-1520-1.1-c1-0-5', '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': '2-1520-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.77367532246184838943517958557', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '980749986900531043774775578611', 'Lhash_array': ['980749986900531043774775578611'], 'label': '2-1520-1.1-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1520/2/a/p/1/2'}