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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1045.43', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.6427876096865394, 0.766044443118978], 'a3': [0.3420201433256687, -0.9396926207859084], 'a4': [-0.17364817766693036, 0.984807753012208], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.9396926207859084, -0.3420201433256687], 'a7': [-0.8660254037844386, -0.5], 'a8': [-0.8660254037844386, 0.5], 'a9': [-0.766044443118978, -0.6427876096865394], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.43', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.802', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 'a^29', 'a^10', 0, 'a^34', 'a^21', 'a^15', 'a^22', 0, 0, 'a^3', 'a^7', 'a^26', 0, 'a^20', 'a^5', 'a^27', 0, 0, 'a^14', 0, 'a^1', 'a^8', 0, 'a^12', 'a^15', 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'190.23950261640653893481469499408', '190.88127491496358682714390277397', '191.50623530039238752836836616577', '192.2356631571579844414676259445', '193.01256706136451409087852403952', '193.72474776599370191607211235307', '194.17523723975206266382615613775', '194.92683153806548192848437919129', '195.33882210300043408311967256189', '195.800083315962960490179211590508', '196.69251853077794051792725882418', '196.99260858975768687799910844144', '197.44377829170875546892029265271', '197.99488537462992932520315863479', '198.73309368758218651599000048487', '199.471108796252947416478237792375'], 'prelabel': '1-1045-1045.43-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': 0.3361973032499449, 'root_number': '0.492187866624582205304896989298+0.870489002772316749771091105534*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.168098651625', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.38737241849629022602059786552+0.379319645060219841055672659294*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.12129991381', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.5127009479', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.42462432614', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.43', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/43'], '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': '1-1045-1045.43-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': '1-1045-1045.43-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': 0.16809865162497245, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.12129991381', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1045.43', 'Lhash_array': ['dirichlet_L_1045.43'], 'label': '1-1045-1045.43-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/43'}
Lfunction data - 1-1045-1045.43-r0-0-0