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lfunc_lfunctions • Show schema
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{'Lhash': '2286587020484325695820265790936', 'a10': [1.0, 0], 'a2': [-0.5, 0.8660254037844386], 'a3': [0.5, 0.8660254037844386], 'a4': [-0.5, -0.8660254037844386], 'a5': [-0.5, -0.8660254037844386], 'a6': [-1.0, 0], 'a7': [-1.5, -2.598076211353316], 'a8': [1.0, 0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.863394624362128, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [3, [[1.0, 0], [-0.5, -0.8660254037844386]]], [5, [[1.0, 0], [0.5, 0.8660254037844386]]], [37, [[1.0, 0], [0.5, 6.06217782649107]]]], 'bad_primes': [2, 3, 5, 37], 'central_character': '1110.121', 'coefficient_field': 'CDF', 'conductor': 1110, 'conductor_radical': 1110, 'conjugate': '2284387103563538012575202203490', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], 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{'__RealLiteral__': 0, 'data': '0.3801574000852811', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.80379910684588143234779557876', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.95283374525383741297836899869', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43510292531433566086146437629', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.863394624362128, 'bad_primes': [2, 3, 5, 37], 'central_character': '37.10', 'conductor': 1110, 'conductor_radical': 1110, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1110/2/i/b/121/1'], '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': '2-1110-37.10-c1-0-21', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1110-37.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9771453817981626, 'root_angle': 0.38015740008528104, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.80379910684588143234779557876', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2286587020484325695820265790936', 'Lhash_array': ['2286587020484325695820265790936'], 'factors': ['2-1110-37.10-c1-0-21'], 'label': '2-1110-37.10-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1110/2/i/b/121/1'}