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lfunc_lfunctions • Show schema
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{'Lhash': '2611574503062467176054908099978', 'a10': [5.37386354243376, 0.0], 'a2': [1.79128784747792, 0.0], 'a3': [-1.0, 0.0], 'a4': [1.20871215252208, 0.0], 'a5': [3.0, 0.0], 'a6': [-1.79128784747792, 0.0], 'a7': [1.0, 0.0], 'a8': [-1.41742430504416, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8445442866915778, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 7, 11], 'central_character': '231.1', 'coefficient_field': 'CDF', 'conductor': 231, 'conductor_radical': 231, 'conjugate': '2611574503062467176054908099978', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.79128784747792, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-3.0, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0], [13.0, 0]], [[1.0, 0], [-7.58257569495584, 0], [17.0, 0]], [[1.0, 0], [6.58257569495584, 0], 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[113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-231-1.1-c1-0-6', '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/231/2/a/b/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.153673043928826, 2.1623950159668435, 2.186912036227053, 2.2225113960258245, 2.262028661146445, 2.296636727055979, 2.3166318329490316, 2.3121342322286487, 2.273707764002804, 2.1929383203673094, 2.063004828735643, 1.8792510271995442, 1.6397388699184872, 1.3457425232441702, 1.0021278549436698, 0.6175563631546278, 0.20445456831767284, -0.2213000534286285, -0.6410076833965495, -1.0340954400383888, -1.3793626860579926, -1.6564633646715945, -1.8475314586345872, -1.9388239844851682, -1.9222316974620866, -1.7964951294607308, -1.5679664514168683, -1.2507785993502833, 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'10.36938564096962006674759496066119', '11.50530040163972206601299999110492', '12.47963995589029819295526310647534'], 'prelabel': '2-231-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3581400099737795, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.06016902653797192392454285505', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.75271478128334122181597471475', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.11749517832103761916153067282', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8445442866915778, 'bad_primes': [3, 7, 11], 'central_character': '1.1', 'conductor': 231, 'conductor_radical': 231, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/231/2/a/b/1/2'], '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': '2-231-1.1-c1-0-6', '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': '2-231-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3581400099737795, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.06016902653797192392454285505', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2611574503062467176054908099978', 'Lhash_array': ['2611574503062467176054908099978'], 'label': '2-231-1.1-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/231/2/a/b/1/2'}