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lfunc_lfunctions • Show schema
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{'Lhash': '1157877293270322462584544721313', 'a10': [7.051528751793421, 0.0], 'a2': [-2.5541224714634825, 0.0], 'a3': [1.0, 0.0], 'a4': [4.523541599234728, 0.0], 'a5': [-2.7608420624219234, 0.0], 'a6': [-2.5541224714634825, 0.0], 'a7': [-1.0, 0.0], 'a8': [-6.445434306278314, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.22367834571584, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [383, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 7, 383], 'central_character': '8043.1', 'coefficient_field': 'CDF', 'conductor': 8043, 'conductor_radical': 8043, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.5541224714634825, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.7608420624219234, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [5.115311968344985, 0], [11.0, 0]], [[1.0, 0], [-1.4448656931910193, 0], [13.0, 0]], [[1.0, 0], [-2.550782821087106, 0], [17.0, 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103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.22367834571584, 'bad_primes': [3, 7, 383], 'central_character': '1.1', 'conductor': 8043, 'conductor_radical': 8043, 'degree': 2, 'index': 173, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8043/2/a/q/1/3'], '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': '2-8043-1.1-c1-0-173', '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': '2-8043-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.013967703061688, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.913404129704081538507192064988', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1157877293270322462584544721313', 'Lhash_array': ['1157877293270322462584544721313'], 'label': '2-8043-1.1-c1-0-173', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8043/2/a/q/1/3'}