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lfunc_lfunctions • Show schema
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{'Lhash': '3533062248779719187029021350923', 'a10': [-1.1385477169812965, 0.3343077731802022], 'a2': [0.4608281674185715, 0.5318240555955169], 'a3': [0.8412535328311812, 0.5406408174555976], 'a4': [0.2141554503228658, -1.4894838739034764], 'a5': [-0.7004893866492367, 1.53385780137781], 'a6': [0.10014753170928087, 0.6965413827540766], 'a7': [-3.1174668867821707, -0.9153708688173371], 'a8': [2.07481929758739, -1.3334053972352224], 'a9': [0.41541501300188644, 0.9096319953545183], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5509677739468349, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.8412535328311812, -0.5406408174555976]]], [23, [[1.0, 0], [0.7792947609461249, -4.73209252609899]]]], 'bad_primes': [3, 23], 'central_character': '69.13', 'coefficient_field': 'CDF', 'conductor': 69, 'conductor_radical': 69, 'conjugate': '3917922236040025461572104467708', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[-2.67666435172188, -5.861077377913701], [-54.35344091745866, 62.72721467140344]], [[1.0, 0], [-2.11081580842416, -1.3565389500642315], [36.97193615716789, 80.95724758655213]], [[1.0, 0], [-0.7539203230461119, 1.6508552323014951], [-63.52149119269265, -73.30770871236305]], [[1.0, 0], [0.9967372249183155, 2.182550082133058], [-66.14093412847379, 76.33070700978008]], [[1.0, 0], [2.6915380273408016, -3.1062004684053424], [-14.658428342148369, -101.95160851373608]], [[1.0, 0], [-11.32035547051796, 7.275150708575934], [44.44940639120185, -97.33062350293346]], [[1.0, 0], [2.2524062657548938, 15.66582968242509], [-104.58473412398021, 30.708848695715837]], [[1.0, 0], [-8.470217214372811, -9.77515175766396], [-16.08157672488122, 111.8498229325454]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-69-23.13-c1-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': 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-0.13361286192507202, 'root_number': '0.9131879235653333 - 0.4075387297600499*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0668064309625', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.78709468377455288976040547982', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.16850659623982714120888986580', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.23083740558236525576155175982', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5509677739468349, 'bad_primes': [3, 23], 'central_character': '23.13', 'conductor': 69, 'conductor_radical': 69, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/69/2/e/c/13/2'], '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': '2-69-23.13-c1-0-1', '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': '2-69-23.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7422720350025555, 'root_angle': -0.06680643096253601, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.78709468377455288976040547982', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3533062248779719187029021350923', 'Lhash_array': ['3533062248779719187029021350923'], 'label': '2-69-23.13-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/69/2/e/c/13/2'}