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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3751.224', 'a10': [0.009519833939576644, 0.9999546853541729], 'a2': [-0.9983691039261356, -0.057088810862767986], 'a3': [-0.9781476007338057, -0.20791169081775934], 'a4': [0.9934817353485502, 0.11399140989054063], 'a5': [-0.0665905319833038, -0.9977803871845651], 'a6': [0.9646829124588557, 0.2634138918316567], 'a7': [0.7976796275621554, -0.6030814304654896], 'a8': [-0.985353835847693, -0.17052219263262378], 'a9': [0.9135454576426009, 0.4067366430758002], 'algebraic': True, 'analytic_conductor': 17.41957076659139, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [31, [1]]], 'bad_primes': [11, 31], 'central_character': '3751.224', 'coeff_info': ['x^165 - 1', '0.999275047800474 + 0.0380707084693900*I', '\\\\zeta_{165}'], 'conductor': 3751, 'conductor_radical': 341, 'conjugate': 'dirichlet_L_3751.2830', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^84', 'a^88', 'a^3', 'a^122', 'a^7', 'a^148', 'a^87', 'a^11', 'a^41', 0, 'a^91', 'a^47', 'a^67', 'a^45', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-3751-3751.224-r0-0-0', 'leading_term': '-0.0605486312039389319416134734518-0.323616191609170607881582006467*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/3751/224', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.329231797085722, 0.2603453200954863, 0.6363018509414942, 0.40790847884599424, -0.1265532453240409, 0.11633299303815156, 1.6015575094486665, 2.9189208166635616, 1.6904810464166624, -2.6408778154798798, -7.22463760352412, -7.994544314274103, -3.96177234466913, 1.2875123755048044, 3.2337274029617147, 1.3610655171634096, -0.5787422937337442, 0.5339095185154545, 3.2867710091180844, 3.883010457033862, 1.3871454765193234, -1.105322188760417, -0.8858930371370888, 0.7321264138145754, 0.7293433981702828, 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{'__RealLiteral__': 0, 'data': '1.51845985784', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 17.41957076659139, 'bad_primes': [11, 31], 'central_character': '3751.224', 'conductor': 3751, 'conductor_radical': 341, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3751/224'], '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': '1-3751-3751.224-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': '1-3751-3751.224-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.41957076659139, 'root_angle': 0.44112488410320483, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.170235168135', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3751.224', 'Lhash_array': ['dirichlet_L_3751.224'], 'factors': ['1-3751-3751.224-r0-0-0'], 'label': '1-3751-3751.224-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3751/224'}
Lfunction data - 1-3751-3751.224-r0-0-0