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lfunc_lfunctions • Show schema
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{'Lhash': '2079354627380573761138447242803', 'a10': [1.361263593058203, 3.8628159776209237], 'a2': [0.9158161891654139, -1.5862401700286068], 'a3': [1.914324066322514, -0.5129415876225806], 'a4': [-0.6774385846749224, -1.1733580476645165], 'a5': [-1.4548033774459466, 1.6981010373272454], 'a6': [0.939520420081938, -3.506337942494248], 'a7': [3.0647815637641878, -1.769452460846656], 'a8': [1.18162786461926, 0.0], 'a9': [0.8034513472354754, -0.46387285160716923], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.747358970798196, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [1.4548033774459466, -1.6981010373272454]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 13], 'central_character': '845.488', 'coefficient_field': 'CDF', 'conductor': 845, 'conductor_radical': 65, 'conjugate': '2031630596009500329349593861277', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9158161891654139, 1.5862401700286068], [-1.0, 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'5.13269475021819877710358263238291', '5.76920243333591464881916221700673', '7.03941288138552790235508061011719', '8.060791113377232438456854063682355', '8.503324610473645608422338843114658', '8.857783240001120634396615417641543', '10.26578347542730635842501488536072'], 'prelabel': '2-845-65.33-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5975678953201964, 'root_angle': 0.20699257281045583, 'root_number': '0.2669469625523159 + 0.9637112218834502*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.20699257281', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.64032157363093911691954204858', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.31336784933127025960214804576', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.17279983744360490316144516291', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.747358970798196, 'bad_primes': [5, 13], 'central_character': '65.33', 'conductor': 845, 'conductor_radical': 65, 'degree': 2, 'index': 47, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/845/2/o/g/488/4'], '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': '2-845-65.33-c1-0-47', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-845-65.33-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5975678953201964, 'root_angle': 0.20699257281045583, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.64032157363093911691954204858', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2079354627380573761138447242803', 'Lhash_array': ['2079354627380573761138447242803'], 'factors': ['2-845-65.33-c1-0-47'], 'label': '2-845-65.33-c1-0-47', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/845/2/o/g/488/4'}