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lfunc_lfunctions • Show schema
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{'Lhash': '3158168346482381433696566905951', 'a10': [-42.53393259026993, 0.0], 'a2': [0.0, -2.2231973033913377], 'a3': [2.898268816291124, 0.0], 'a4': [3.0573937501934845, 0.0], 'a5': [0.0, -19.13187485671527], 'a6': [0.0, -6.443423416881631], 'a7': [0.0, 4.295940484234749], 'a8': [0.0, -24.582767967966387], 'a9': [-18.60003786851445, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.437273130820913, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [0, -11.0]]], [13, [[1.0, 0], [-35.79685511858442, -30.25863783482457]]]], 'bad_primes': [11, 13], 'central_character': '143.12', 'coefficient_field': 'CDF', 'conductor': 143, 'conductor_radical': 143, 'conjugate': '1292310708033549420790986788075', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.2231973033913377], [-8.0, 0]], [[1.0, 0], [-2.898268816291124, 0], [27.0, 0]], [[1.0, 0], [0, 19.13187485671527], [-125.0, 0]], [[1.0, 0], [0, -4.295940484234749], [-343.0, 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'5.83785658509240032309828912520', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.437273130820913, 'bad_primes': [11, 13], 'central_character': '13.12', 'conductor': 143, 'conductor_radical': 143, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/143/4/b/a/12/13'], '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': '2-143-13.12-c3-0-31', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-143-13.12-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.904698457812947, 'root_angle': 0.36168728447084564, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.49135554064643747239131590840', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3158168346482381433696566905951', 'Lhash_array': ['3158168346482381433696566905951'], 'label': '2-143-13.12-c3-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/143/4/b/a/12/13'}