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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_547.99', 'a10': [0.9154080085253663, -0.40252723873996754], 'a2': [-0.31120506203571086, -0.9503427851903488], 'a3': [0.6234898018587335, 0.7818314824680298], 'a4': [-0.8063028187266987, 0.5915029708407055], 'a5': [0.09765925109799801, 0.9952199107106822], 'a6': [0.5489747261320865, -0.8358389498391425], 'a7': [0.9244290506050568, 0.38135407484047346], 'a8': [0.8130560994785325, 0.5821853477207707], 'a9': [-0.2225209339563144, 0.9749279121818236], 'algebraic': True, 'analytic_conductor': 2.540257320534655, 'analytic_normalization': 0, 'bad_lfactors': [[547, [1]]], 'bad_primes': [547], 'central_character': '547.99', 'coeff_info': ['x^273 - 1', '0.999735158965141 + 0.0230132989583119*I', '\\\\zeta_{273}'], 'conductor': 547, 'conductor_radical': 547, 'conjugate': 'dirichlet_L_547.326', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^191', 'a^39', 'a^109', 'a^64', 'a^230', 'a^17', 'a^27', 'a^78', 'a^255', 'a^266', 'a^148', 'a^26', 'a^208', 'a^103', 'a^218', 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[1, 'a^29'], [1, 'a^170'], [1, 'a^213'], [1, 'a^77'], [1, 'a^69'], [1, 'a^124'], [1, 'a^183']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-547-547.99-r0-0-0', 'leading_term': '1.57943256201063052934133271563+0.531563154995159884274599765791*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/547/99', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.6664833049532395, 2.0718716917149704, 2.4217925672582683, 2.1669331195062647, 1.2112675057989855, -0.0178526302062492, -0.8513117200162945, -0.8442872928706742, -0.13453438409734522, 0.6085929546191203, 0.685989363050544, -0.018996140912703425, -0.8431897409519074, -0.8389909104598405, 0.33222338990712574, 1.8519663560653103, 2.151544917218902, 0.14388151233018234, -3.646829407834119, -7.101316052254413, -7.889040010913153, 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lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.540257320534655, 'bad_primes': [547], 'central_character': '547.99', 'conductor': 547, 'conductor_radical': 547, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/547/99'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-547-547.99-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-547-547.99-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.540257320534655, 'root_angle': 0.10333792650937967, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.55762167861', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_547.99', 'Lhash_array': ['dirichlet_L_547.99'], 'label': '1-547-547.99-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/547/99'}
Lfunction data - 1-547-547.99-r0-0-0