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lfunc_lfunctions • Show schema
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{'Lhash': '1246416658161302403200548366189', 'a10': [-28.0, 0.0], 'a2': [-2.6457513110645907, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.0, 0.0], 'a5': [10.583005244258363, 0.0], 'a6': [0.0, 0.0], 'a7': [22.0, 0.0], 'a8': [23.811761799581316, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 89.74190511873151, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': 'CDF', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.6457513110645907, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-10.583005244258363, 0], [125.0, 0]], [[1.0, 0], [-22.0, 0], [343.0, 0]], [[1.0, 0], [-5.291502622129181, 0], [1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-116.41305768684198, 0], [4913.0, 0]], [[1.0, 0], [-126.0, 0], [6859.0, 0]], [[1.0, 0], [-31.74901573277509, 0], [12167.0, 0]], 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'group': 'GL2', 'index': 95, 'label': '2-39e2-1.1-c3-0-95', 'leading_term': '2.1376262724268201028354415305107', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1521/4/a/p/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.1376262724268202, 2.125262927843264, 2.0883965934939606, 2.027696711401514, 1.9442733793059026, 1.8396684866534, 1.7158425246850715, 1.575156360608435, 1.420347159211553, 1.2544975938581855, 1.0809975199022115, 0.9034973909163125, 0.72585288179151, 0.5520604391403849, 0.3861838014836323, 0.23227190920440607, 0.09426904419528293, -0.024081513922931872, -0.11933857153385123, -0.18846665382911737, -0.22893957737677884, -0.23884098387542338, -0.21695855636016428, -0.1628684271998168, -0.07700618109499965, 0.039279128735674955, 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'6.92442745339876701374555524087201', '7.918886333176190709910924481554659', '8.132493870776209318655748984016860', '9.316259147983626776363914704936796'], 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.983249373239673445682942248340', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.44663337187210115042919382354', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.72653866790398621540479129883', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 89.74190511873151, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'index': 95, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/4/a/p/1/1'], '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': '2-39e2-1.1-c3-0-95', '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': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.983249373239673445682942248340', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1246416658161302403200548366189', 'Lhash_array': ['1246416658161302403200548366189'], 'label': '2-39e2-1.1-c3-0-95', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/4/a/p/1/1'}