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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1375.328', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.9048270524660196, 0.42577929156507266], 'a3': [0.8443279255020151, 0.5358267949789967], 'a4': [0.6374239897486897, 0.7705132427757893], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.5358267949789967, 0.8443279255020151], 'a7': [0.5877852522924731, 0.8090169943749475], 'a8': [0.2486898871648548, 0.9685831611286311], 'a9': [0.42577929156507266, 0.9048270524660196], 'algebraic': True, 'analytic_conductor': 147.76427159260942, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]]], 'bad_primes': [5, 11], 'central_character': '1375.328', 'coeff_info': ['x^100 - 1', '0.998026728428272 + 0.0627905195293134*I', '\\\\zeta_{100}'], 'conductor': 1375, 'conductor_radical': 55, 'conjugate': 'dirichlet_L_1375.742', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^7', 'a^9', 'a^14', 0, 'a^16', 'a^15', 'a^21', 'a^18', 0, 0, 'a^23', 'a^93', 'a^22', 0, 'a^28', 'a^71', 'a^25', 'a^26', 0, 'a^24', 0, 'a^57', 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'186.54298517120210317910491240718', '187.21413785009183911402657124648', '187.63119373807996927078498748411', '188.34277685054424761845428513393', '189.03323425884858533200926408561', '189.52921060275018315630772588056', '190.10226778346422089108220879100', '190.95874742137720313241428006650', '191.66900802036604577242093362962', '192.34340793807093323847312726641', '192.48313038823134566821528640735', '193.31238176519195030160175093885', '193.76135118975891431673173182852', '194.250282089608197944538147660892', '195.27241153822819085276679087365', '195.55365891743632660037721198907', '196.18100336000953610103062862143', '196.76362019305044189205979820987', '197.26433467207117189947977224971', '197.8101082815567121490567423333', '198.38694625294843255328938471660', '198.952303498692376691902400254830', '199.395577148837638780322320396399'], 'prelabel': '1-1375-1375.328-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 147.76427159260942, 'root_angle': 0.8705657398607866, 'root_number': '-0.918459036327015786143741744007+0.395516116725032453507737997845*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.43528286993', 'prec': 44}, 'spectral_label': 'r1-0', 'st_group': 'mu(100)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.96949507274259376973312677817+1.71124790274699517899375561322*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.6193951941', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.46930281516', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.33398687398', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 147.76427159260942, 'bad_primes': [5, 11], 'central_character': '1375.328', 'conductor': 1375, 'conductor_radical': 55, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1375/328'], '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': '1-1375-1375.328-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': '1-1375-1375.328-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 147.76427159260942, 'root_angle': 0.4352828699303933, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.6193951941', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1375.328', 'Lhash_array': ['dirichlet_L_1375.328'], 'label': '1-1375-1375.328-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1375/328'}
Lfunction data - 1-1375-1375.328-r1-0-0