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lfunc_lfunctions • Show schema
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{'Lhash': '186821058677446655961662705096', 'a10': [1.5415534228052126, 0.8900162836267784], 'a2': [-0.8660254037844386, 0.5], 'a3': [-1.5439324865364636, 0.7850302395559885], 'a4': [0.5, -0.8660254037844386], 'a5': [-0.8900162836267784, -1.5415534228052126], 'a6': [0.9445696352906591, -1.4518223734627014], 'a7': [-1.5172661665494076, -2.16746473554807], 'a8': [0.0, 1.0], 'a9': [1.7674550459653346, -2.424067379527986], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, -0.5]]], [3, [[1.0, 0], [1.5439324865364636, -0.7850302395559885]]], [7, [[1.0, 0], [1.5172661665494076, 2.16746473554807]]], [13, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.521', 'coefficient_field': 'CDF', 'conductor': 546, 'conductor_radical': 546, 'conjugate': '1825185522265601322167608734666', 'degree': 2, 'euler_factors': 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8.940450903361201], [-54.5, -94.39676901250381]], [[1.0, 0], [0, -0.3623825405815582], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-546-21.17-c1-0-1', '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/546/2/z/a/521/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.18083944996290005, 0.028203225600978588, -0.1332473895537449, -0.304761647460554, -0.48587804910512805, -0.6735059189275064, -0.8614546408516287, -1.040405532974561, -1.198291451616081, -1.3210547755272644, -1.3937598567074245, -1.4020232058323001, -1.3336921400143678, -1.1806572846261916, -0.9406358143972262, -0.6187206256006116, -0.22846526403849599, 0.20772619359214683, 0.6591045651915932, 1.0881115158596937, 1.4529826222717799, 1.7113279021734373, 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'4.74365727752674938268948692490575', '6.23150296664961188553859719142809', '6.66514347125800246593006504003823', '7.59207445233467407040305991285596', '8.873982519359519653909866411933192', '9.436915319828194648146774531464357', '10.77961777652831210460145203589462'], 'prelabel': '2-546-21.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.8844810667673858, 'root_number': '-0.9348665261243888 - 0.3549994061010772*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.442240533384', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.14737582946263833157837385153', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.06660173435060752356409562029', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.32394708937258439854469664913', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '21.17', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/z/a/521/2'], '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': '2-546-21.17-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': '2-546-21.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.4422405333836929, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.14737582946263833157837385153', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '186821058677446655961662705096', 'Lhash_array': ['186821058677446655961662705096'], 'label': '2-546-21.17-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/z/a/521/2'}