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lfunc_lfunctions • Show schema
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{'Lhash': '1752420733356836424522419640221', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0473937938715371, -0.08208845894894876], 'a4': [0.0, 0.0], 'a5': [0.0, 1.0], 'a6': [0.0, 0.0], 'a7': [0.7160630551645101, -0.41341919765597573], 'a8': [0.0, 0.0], 'a9': [1.4955076566049246, 2.5902952443479985], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.076110452553291, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, -1.0]]], [13, [[1.0, 0], [-3.322346051916876, 1.4007200688618502]]]], 'bad_primes': [2, 5, 13], 'central_character': '260.121', 'coefficient_field': 'CDF', 'conductor': 260, 'conductor_radical': 130, 'conjugate': '2274108159891665456060824880418', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.0473937938715371, 0.08208845894894876], [-1.5, -2.598076211353316]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [-0.7160630551645101, 0.41341919765597573], [3.5, 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[-30.5, 52.827549630850754]], [[1.0, 0], [11.912215477871142, 6.877520812793731], [33.5, 58.023702053557386]], [[1.0, 0], [-8.467038155750629, 4.888446758461457], [35.5, -61.48780366869514]], [[1.0, 0], [0, 11.180590488695998], [-73.0, 0]], [[1.0, 0], [0.25238725842048826, 0], [79.0, 0]], [[1.0, 0], [0, 5.671646164204205], [-83.0, 0]], [[1.0, 0], [-3.9805151859358543, -2.2981515141134587], [44.5, 77.07626093681505]], [[1.0, 0], [-8.256982884465037, 4.767171291040022], [48.5, -84.00446416709055]], [[1.0, 0], [2.90072006886185, -5.024194537803417], [-50.5, -87.4685657822283]], [[1.0, 0], [-10.075966577375306, 0], [103.0, 0]], [[1.0, 0], [8.139773942044943, -14.09850202974705], [-53.5, -92.66471820493493]], [[1.0, 0], [0, 3.1297939735194955], [-109.0, 0]], [[1.0, 0], [-5.085377082559191, -8.808131482638908], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-260-13.4-c1-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 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True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': -0.13108504696868375, 'root_number': '0.9163955082373361 - 0.40027399676026243*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0655425234843', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.38241620604394333990585995176', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.43960957350700788253176807088', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.55419633479545802237819638477', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.076110452553291, 'bad_primes': [2, 5, 13], 'central_character': '13.4', 'conductor': 260, 'conductor_radical': 130, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/260/2/x/a/121/3'], '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': '2-260-13.4-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': '2-260-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': -0.06554252348434188, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.38241620604394333990585995176', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1752420733356836424522419640221', 'Lhash_array': ['1752420733356836424522419640221'], 'label': '2-260-13.4-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/260/2/x/a/121/3'}