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lfunc_lfunctions • Show schema
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{'Lhash': '1891477762070109338814555300957', 'a10': [2894.4571359560005, 0.0], 'a2': [-2.2559822477611493, 0.0], 'a3': [127.43756396416411, 0.0], 'a4': [-506.91054409778656, 0.0], 'a5': [-1283.014145536153, 0.0], 'a6': [-287.49688200108017, 0.0], 'a7': [6707.916258328662, 0.0], 'a8': [2298.64409954126, 0.0], 'a9': [-3442.6672908795795, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 56.138906141862186, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[109, [[1.0, 0], [141158161.0, 0]]]], 'bad_primes': [109], 'central_character': '109.1', 'coefficient_field': 'CDF', 'conductor': 109, 'conductor_radical': 109, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.2559822477611493, 0], [512.0, 0]], [[1.0, 0], [-127.43756396416411, 0], [19683.0, 0]], [[1.0, 0], [1283.014145536153, 0], [1953125.0, 0]], [[1.0, 0], [-6707.916258328662, 0], [40353607.0, 0]], [[1.0, 0], [-42989.12419717751, 0], [2357947691.0, 0]], [[1.0, 0], 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{'__RealLiteral__': 0, 'data': '4.22960776039040236399255069771', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 56.138906141862186, 'bad_primes': [109], 'central_character': '1.1', 'conductor': 109, 'conductor_radical': 109, 'degree': 2, 'index': 56, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/109/10/a/a/1/20'], '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': '2-109-1.1-c9-0-56', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 1, 'prelabel': '2-109-1.1-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.492590082332156, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '1.49211285959204004155745254865', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1891477762070109338814555300957', 'Lhash_array': ['1891477762070109338814555300957'], 'label': '2-109-1.1-c9-0-56', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/109/10/a/a/1/20'}