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lfunc_lfunctions • Show schema
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{'Lhash': '1416688833951023228012867599301', 'a10': [1.2572826749743826, -6.160333876637806e-61], 'a2': [0.6286413374871913, -1.0888387362658687], 'a3': [-0.9336689455332245, -1.4588565043028998], 'a4': [0.20962013760463055, 0.36307272862079953], 'a5': [0.5, 0.8660254037844386], 'a6': [-2.175402367228674, 0.09951741067821918], 'a7': [-2.284449727408436, 3.9567829952082834], 'a8': [3.041668884620861, 0.0], 'a9': [-1.2565246002937531, 2.724178028113549], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.9336689455332245, 1.4588565043028998]]], [5, [[1.0, 0], [-0.5, -0.8660254037844386]]], [13, [[1.0, 0], [0.5, 0.8660254037844386]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.196', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '1814636849937089255435594153134', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'7.80812752617182777852100404375769', '9.496288747073445984666664429516503', '9.874014519927218630296043734987763', '10.52125163695344749148619875209059'], 'prelabel': '2-585-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.19311927909910484, 'root_number': '0.8215328118790179 + 0.5701612394806878*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0965596395496', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.11757043596710386622440427230', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.50605008934240935409820579885', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.53424625979503550598418042709', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '9.7', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/i/h/196/11'], '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': '2-585-9.7-c1-0-21', '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': '2-585-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.09655963954955242, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.11757043596710386622440427230', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1416688833951023228012867599301', 'Lhash_array': ['1416688833951023228012867599301'], 'label': '2-585-9.7-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/i/h/196/11'}