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lfunc_lfunctions • Show schema
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{'Lhash': '1822082313850366146041415773456', 'a10': [2.301029316856628, 0.0], 'a2': [0.7518235434087973, 0.0], 'a3': [1.0, 0.0], 'a4': [-1.4347613595762403, 0.0], 'a5': [3.0605975790857403, 0.0], 'a6': [0.7518235434087973, 0.0], 'a7': [-2.0207762967834038, 0.0], 'a8': [-2.5823344561202273, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 63.936216898439234, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [17, [[1.0, 0], [1.0, 0]]], [157, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 17, 157], 'central_character': '8007.1', 'coefficient_field': 'CDF', 'conductor': 8007, 'conductor_radical': 8007, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7518235434087973, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-3.0605975790857403, 0], [5.0, 0]], [[1.0, 0], [2.0207762967834038, 0], [7.0, 0]], [[1.0, 0], [2.874189080509175, 0], [11.0, 0]], [[1.0, 0], [0.8536557919136603, 0], [13.0, 0]], 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'2.97586600389741487276287735235', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 63.936216898439234, 'bad_primes': [3, 17, 157], 'central_character': '1.1', 'conductor': 8007, 'conductor_radical': 8007, 'degree': 2, 'index': 358, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8007/2/a/e/1/29'], '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': '2-8007-1.1-c1-0-358', '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': '2-8007-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.9960125624238, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.43736950349119557434044267329', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1822082313850366146041415773456', 'Lhash_array': ['1822082313850366146041415773456'], 'label': '2-8007-1.1-c1-0-358', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8007/2/a/e/1/29'}