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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_837.689', 'a10': [-0.10452846326765347, -0.9945218953682733], 'a2': [-0.5591929034707468, 0.8290375725550417], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.374606593415912, -0.9271838545667874], 'a5': [-0.766044443118978, 0.6427876096865394], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.03489949670250097, 0.9993908270190958], 'a8': [0.9781476007338057, 0.20791169081775934], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 89.94814205310114, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [31, [1]]], 'bad_primes': [3, 31], 'central_character': '837.689', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.164', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^31', 0, 'a^62', 'a^35', 0, 'a^22', 'a^3', 0, 'a^66', 'a^67', 0, 'a^74', 'a^53', 0, 'a^34', 'a^63', 0, 'a^6', 'a^7', 0, 'a^8', 'a^53', 0, 'a^70', 'a^15', 0, 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'192.51787341693442712760722064723', '193.69902886460569518228780073209', '194.065000034286587925008534253245', '194.97190061467151756845283909223', '195.37040672028125286886566220433', '195.933993503832540734156887168030', '196.62703522342704481271975318062', '197.31550826405536037032031300780', '197.65578941849605407690585632326', '198.541972148009907848707162854233', '199.03391498104908418479144566436', '199.52613174310108246194267632065', '199.85860252433254118414695356877'], 'prelabel': '1-837-837.689-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 89.94814205310114, 'root_angle': -0.8807744129995898, 'root_number': '-0.930669339966714822245318589523-0.365861421368691712494636840211*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4403872065', 'prec': 44}, 'spectral_label': 'r1-0', 'st_group': 'mu(90)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.565756046958479607609790370771+0.279746682328701455198878264745*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.97243502328', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.57157958908', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.50413569561', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 89.94814205310114, 'bad_primes': [3, 31], 'central_character': '837.689', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/689'], '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': '1-837-837.689-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-837-837.689-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 89.94814205310114, 'root_angle': -0.4403872064997949, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.97243502328', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_837.689', 'Lhash_array': ['dirichlet_L_837.689'], 'label': '1-837-837.689-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/689'}