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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_143.48', 'a10': [-0.5, -0.8660254037844386], 'a2': [0.6691306063588582, -0.7431448254773942], 'a3': [-0.10452846326765347, 0.9945218953682733], 'a4': [-0.10452846326765347, -0.9945218953682733], 'a5': [0.30901699437494745, -0.9510565162951535], 'a6': [0.6691306063588582, 0.7431448254773942], 'a7': [-0.10452846326765347, -0.9945218953682733], 'a8': [-0.8090169943749475, -0.5877852522924731], 'a9': [-0.9781476007338057, -0.20791169081775934], 'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [13, [1]]], 'bad_primes': [11, 13], 'central_character': '143.48', 'coeff_info': ['x^15 - 1', '0.913545457642601 + 0.406736643075800*I', '\\\\zeta_{15}'], 'conductor': 143, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_143.3', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^13', 'a^4', 'a^11', 'a^12', 'a^2', 'a^11', 'a^9', 'a^8', 'a^10', 0, 'a^0', 0, 'a^9', 'a^1', 'a^7', 'a^2', 'a^6', 'a^14', 'a^8', 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'192.10721202067262367481688641030', '192.61413778192570481287936824397', '193.29992343200261452839965081356', '193.98696873384031310787854414794', '194.73702721140976532720791368247', '195.261841798985381059792344780631', '196.35412827857961159643438086301', '197.07400767647190002945720439209', '197.59059263759850095607132834059', '198.91672883103849109669370852509', '199.30266217619166791687536293855'], 'prelabel': '1-143-143.48-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': -0.2389034052607783, 'root_number': '0.0696654865801999681195034969856-0.997570408532422325957485213126*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.238903405261', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(15)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.20949564090509421997145102598-0.605803154793756774437803995618*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.12959939952', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.10452718486', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.29402796528', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'bad_primes': [11, 13], 'central_character': '143.48', 'conductor': 143, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/143/48'], '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': '1-143-143.48-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': '1-143-143.48-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': -0.2389034052607783, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.12959939952', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_143.48', 'Lhash_array': ['dirichlet_L_143.48'], 'factors': ['1-143-143.48-r0-0-0'], 'label': '1-143-143.48-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/143/48'}
Lfunction data - 1-143-143.48-r0-0-0