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lfunc_lfunctions • Show schema
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{'Lhash': '2876699260269675892749711141166', 'a10': [-2.2244253173690702, -0.2278859527208959], 'a2': [1.0, 0.0], 'a3': [0.7071067811865476, -0.7071067811865476], 'a4': [1.0, 0.0], 'a5': [-2.2244253173690702, -0.2278859527208959], 'a6': [0.7071067811865476, -0.7071067811865476], 'a7': [0.0, -4.0533617152242885], 'a8': [1.0, 0.0], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [5, [[1.0, 0], [2.2244253173690702, 0.2278859527208959]]], [13, [[1.0, 0], [-3.1867536412581434, 1.6865945659606416]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '390.187', 'coefficient_field': 'CDF', 'conductor': 390, 'conductor_radical': 390, 'conjugate': '1511907903365693304748065952307', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.7071067811865476, 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{'__RealLiteral__': 0, 'data': '0.178879910896', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.26931558250495156595000518431', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.55202264316065212124950670226', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.31293856440506382695455931706', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'bad_primes': [2, 3, 5, 13], 'central_character': '65.57', 'conductor': 390, 'conductor_radical': 390, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/390/2/j/b/187/5'], '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': '2-390-65.57-c1-0-12', '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': '2-390-65.57-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': 0.17887991089607172, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.26931558250495156595000518431', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2876699260269675892749711141166', 'Lhash_array': ['2876699260269675892749711141166'], 'label': '2-390-65.57-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/390/2/j/b/187/5'}