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lfunc_lfunctions • Show schema
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{'Lhash': '1571528263116353159779261386041', 'a10': [-1.6514774436119968, -1.2155108916706623], 'a2': [0.41632906506962164, 0.8170917968527769], 'a3': [-0.9876883405951378, 0.15643446504023087], 'a4': [0.6812613905225919, -0.9376758610303472], 'a5': [-1.998578126768922, 1.002838706473193], 'a6': [-0.5390246815495648, -0.7419038263725528], 'a7': [-1.956033288971205, -1.7815537523287053], 'a8': [2.8613026402728536, 0.4531858172787339], 'a9': [0.9510565162951535, -0.30901699437494745], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.192146106117222, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.9876883405951378, -0.15643446504023087]]], [5, [[1.0, 0], [1.998578126768922, -1.002838706473193]]], [7, [[1.0, 0], [1.956033288971205, 1.7815537523287053]]]], 'bad_primes': [3, 5, 7], 'central_character': '525.328', 'coefficient_field': 'CDF', 'conductor': 525, 'conductor_radical': 105, 'conjugate': 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[-24.412342555620846, -75.13346478731714]], [[1.0, 0], [1.2514609750335126, -7.901413626674547], [-78.93769085249775, -25.648410533120636]], [[1.0, 0], [1.7522788670526213, -5.392959821667957], [-72.00251249937033, -52.31288745403011]], [[1.0, 0], [-0.7411180057919402, -4.67923493162181], [-92.2524820806299, 29.974648454369902]], [[1.0, 0], [0, 16.984087775051393], [-101.0, 0]], [[1.0, 0], [-6.6943170168277275, 1.060275654065279], [97.95882117840081, -31.828750420619585]], [[1.0, 0], [-0.7090727584173333, 0.7090727584173333], [0, -107.0]], [[1.0, 0], [-4.607416366364822, 1.497040326177779], [88.18285238686927, -64.06859249987957]], [[1.0, 0], [1.2098679286115321, -2.3744995069667483], [-66.41973350904946, -91.41892036436906]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 13, 'label': '2-525-175.153-c1-0-13', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/525/2/bh/a/328/25', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.4123549954590429, 1.4146221038575255, 1.4000968852405937, 1.3643373515572, 1.300358020974175, 1.200055974202163, 1.0557138722965675, 0.8614027198399629, 0.6141998204212964, 0.31517621939524715, -0.029896870565576255, -0.41019261756135145, -0.8099055395708299, -1.2088346778546264, -1.583516944331551, -1.9089044397972545, -2.160513868570165, -2.316902329519728, -2.3622511906249413, -2.288779443814766, -2.098671403065239, -1.8052014416629505, -1.4327785911137354, -1.0157197154287154, -0.5956891007704105, -0.21790516253659725, 0.07360498520307673, 0.2412477179217086, 0.2590036398074052, 0.11678453710690744, -0.176677969261988, -0.5930015922745375, -1.0857745414037112, -1.5947388608708446, -2.052301062014946, -2.3917710130591865, -2.5563990686811975, -2.5080395567125833, -2.2341671549492914, -1.7520485870361002, 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'root_angle': -0.09091983445290405, 'root_number': '0.9594834640762713 - 0.28176494133266217*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0454599172265', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.23971720822237077260998095116', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.21359658200882497645606010929', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.68220218762076752869487991121', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.192146106117222, 'bad_primes': [3, 5, 7], 'central_character': '175.153', 'conductor': 525, 'conductor_radical': 105, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/525/2/bh/a/328/25'], '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': '2-525-175.153-c1-0-13', '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': '2-525-175.153-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0474731026602577, 'root_angle': -0.045459917226452026, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.23971720822237077260998095116', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1571528263116353159779261386041', 'Lhash_array': ['1571528263116353159779261386041'], 'label': '2-525-175.153-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/525/2/bh/a/328/25'}