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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3751.105', 'a10': [0.8308078967080545, 0.5565592859413437], 'a2': [-0.08557500847883974, -0.9963317308626913], 'a3': [0.5, -0.8660254037844386], 'a4': [-0.985353835847693, 0.17052219263262378], 'a5': [-0.6256140694947214, 0.7801327041281206], 'a6': [-0.9056360937630308, -0.42405573415960174], 'a7': [-0.9971012423132775, 0.07608621805109508], 'a8': [0.25421833419348694, 0.9671468547019572], 'a9': [-0.5, -0.8660254037844386], 'algebraic': True, 'analytic_conductor': 17.41957076659139, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [31, [1]]], 'bad_primes': [11, 31], 'central_character': '3751.105', 'coeff_info': ['x^330 - 1', '0.999818745523526 + 0.0190388051033467*I', '\\\\zeta_{330}'], 'conductor': 3751, 'conductor_radical': 341, 'conjugate': 'dirichlet_L_3751.1036', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^243', 'a^275', 'a^156', 'a^118', 'a^188', 'a^161', 'a^69', 'a^220', 'a^31', 0, 'a^101', 'a^46', 'a^74', 'a^63', 'a^312', 'a^236', 'a^133', 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[1, 'a^285']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-3751-3751.105-r0-0-0', 'leading_term': '0.822043656205008190045021226190-0.227770019767379451418569509737*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/3751/105', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.8530152135875017, 0.9643087486837638, 0.3442629426671196, -0.828259772709128, -1.458780438723675, -0.772779283081719, 0.5971288010853228, 1.2201934059426471, 0.6011591179459471, -0.1645250934849874, 0.09605494074273782, 0.8077639059087451, 0.26032682104089283, -1.6491201952710715, -2.288290146556885, 0.8351315988893606, 6.229825231325335, 9.003223362368491, 6.227994174539857, 0.7360760259916823, -1.9529443866280414, -0.17906435856553773, 2.2280499727512133, 1.4069729049202662, -1.4288781961516954, 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'195.141474275888202345007405155608', '195.59250556228748435442897115893', '196.30638243151053576634644660485', '196.903141136946084523305647883602', '197.54956615497333231888868765083', '198.00212853006672787728219662624', '198.422863289205969550158508107329', '199.33457871163510619647051298428', '199.68060677814302183965388776921'], 'prelabel': '1-3751-3751.105-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.41957076659139, 'root_angle': -0.08603816445276938, 'root_number': '0.857403271857615930865774510155-0.514645149018092999155149623877*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(330)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.672431963520652730531760679692-0.426394131011228752926312089470*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.721865797068', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.7367912398', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.71291809711', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 17.41957076659139, 'bad_primes': [11, 31], 'central_character': '3751.105', 'conductor': 3751, 'conductor_radical': 341, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3751/105'], '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': '1-3751-3751.105-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': '1-3751-3751.105-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.41957076659139, 'root_angle': -0.08603816445276938, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.721865797068', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3751.105', 'Lhash_array': ['dirichlet_L_3751.105'], 'factors': ['1-3751-3751.105-r0-0-0'], 'label': '1-3751-3751.105-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3751/105'}
Lfunction data - 1-3751-3751.105-r0-0-0