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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.1062', 'a10': [-0.7806463958627762, 0.6249729631163717], 'a2': [-0.589074657562223, 0.8080786148747842], 'a3': [0.9918730395931648, -0.12723157362941068], 'a4': [-0.30598209563589956, -0.9520372666814378], 'a5': [0.9648862946893156, 0.26266792404236017], 'a6': [-0.4814741573567515, 0.8764602876329344], 'a7': [-0.44377793167127955, -0.8961367905412438], 'a8': [0.9495672539760007, 0.3135634388389013], 'a9': [0.9676242533435677, -0.25239513533605024], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.1062', 'coeff_info': ['x^1182 - 1', '0.999985871574519 + 0.00531569857584313*I', '\\\\zeta_{1182}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.3736', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^414', 'a^1158', 'a^828', 'a^50', 'a^390', 'a^800', 'a^60', 'a^1134', 'a^464', 'a^657', 'a^804', 'a^356', 'a^32', 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0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(1182)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.16318111891646785210331572339+0.349956120242577214006478633633*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.93364048364', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.68276046667', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.59458962952', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.1062', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/1062'], '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': '1-4729-4729.1062-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': '1-4729-4729.1062-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': 0.17116579632389875, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.93364048364', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.1062', 'Lhash_array': ['dirichlet_L_4729.1062'], 'label': '1-4729-4729.1062-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/1062'}
Lfunction data - 1-4729-4729.1062-r0-0-0