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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2580.1187', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.8660254037844386, -0.5], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 11.981469628847185, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [43, [1]]], 'bad_primes': [2, 3, 5, 43], 'central_character': '2580.1187', 'coeff_info': ['x^84 - 1', '0.997203797181180 + 0.0747300935864243*I', '\\\\zeta_{84}'], 'conductor': 2580, 'conductor_radical': 1290, 'conjugate': 'dirichlet_L_2580.263', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 0, 0, 'a^77', 0, 0, 0, 'a^96', 0, 'a^59', 0, 0, 0, 'a^11', 0, 'a^58', 0, 0, 0, 'a^103', 0, 0, 0, 0, 0, 'a^50', 0, 'a^106', 0, 0, 0, 0, 0, 'a^7', 0, 0, 0, 'a^78', 0, 0, 0, 0, 0, 'a^93', 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'191.84617989237606968855951449588', '192.30712225727710244711663649339', '192.748755129692578482452687273566', '193.57661131740671001866949231163', '194.13838123272257052710746266040', '194.45390986404939769761139581202', '195.30371172598007373518962236962', '195.562735540710159718631076864261', '196.28415988497495963604189815385', '196.69747580371753304227448117922', '197.458014725481128928424483556696', '198.01669198855990063970584378534', '198.49589761181404904293083211869', '198.9733091461577218831210270804', '199.37225650307237825016781665105'], 'prelabel': '1-2580-2580.1187-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.981469628847185, 'root_angle': 0.004718365072039751, 'root_number': '0.999560578792883873474874294533+0.0296420195539202365004067053788*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.00471836507204', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(84)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.25862914398172100574876023653+0.0172545870158975582337623836018*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.919293021852', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.69819500298', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.69532077414', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 11.981469628847185, 'bad_primes': [2, 3, 5, 43], 'central_character': '2580.1187', 'conductor': 2580, 'conductor_radical': 1290, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2580/1187'], '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': '1-2580-2580.1187-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': '1-2580-2580.1187-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.981469628847185, 'root_angle': 0.004718365072039751, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.919293021852', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2580.1187', 'Lhash_array': ['dirichlet_L_2580.1187'], 'factors': ['1-2580-2580.1187-r0-0-0'], 'label': '1-2580-2580.1187-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2580/1187'}
Lfunction data - 1-2580-2580.1187-r0-0-0