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lfunc_lfunctions • Show schema
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{'Lhash': '2287742824765365723266769583836', 'a10': [-0.05609488113743001, -0.03238639472485528], 'a2': [0.0, -0.12234446238196733], 'a3': [-0.9376565414722243, -1.4562967452529538], 'a4': [1.9850318325244674, 0.0], 'a5': [0.2647148395138871, -0.4584995515554939], 'a6': [-0.17816984236658148, 0.11471708546535414], 'a7': [0.0, 0.0], 'a8': [0.0, -0.48754657712523203], 'a9': [-1.241600420468694, 2.7310123390222834], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.9376565414722243, 1.4562967452529538]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '441.227', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'conjugate': '1446683005253257088981494008823', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0.12234446238196733], [-2.0, 0]], [[1.0, 0], [0.9376565414722243, 1.4562967452529538]], [[1.0, 0], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 25, 'label': '2-21e2-63.38-c1-0-25', '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/441/2/i/d/227/11', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.5304577529193033, 1.6375285686683632, 1.7453287298767848, 1.850838740296972, 1.947496010438122, 2.02578893933179, 2.0741607847870824, 2.0800756709010724, 2.0311733692693097, 1.9164842183635609, 1.727677629226064, 1.460291953580708, 1.1148589949403505, 0.6978066907429306, 0.2220065903294403, -0.2931665978077372, -0.8223753290540974, -1.3355297040262715, -1.799677316972489, -2.181505177134474, -2.4503012607136476, -2.5811388364205667, -2.557974363985406, -2.3763016618954533, -2.0449926353843777, -1.586987080890565, -1.03857549131919, -0.44714793773003825, 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'10.63044783463003724664430190754817', '11.10114486994123231242759116854018'], 'prelabel': '2-21e2-63.38-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': 0.41841198001995844, 'root_number': '0.2535189483366936 + 0.9673304207116908*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.20920599001', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.80471087565728098913132466129', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.47053563898301788791896491065', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.41693884929319407707494381735', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'bad_primes': [3, 7], 'central_character': '63.38', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/2/i/d/227/11'], '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': '2-21e2-63.38-c1-0-25', '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': '2-21e2-63.38-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': 0.20920599000997922, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.80471087565728098913132466129', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2287742824765365723266769583836', 'Lhash_array': ['2287742824765365723266769583836'], 'label': '2-21e2-63.38-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/2/i/d/227/11'}