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Income Taxes - Rate (Details) - USD ($)
$ in Thousands
12 Months Ended
Sep. 30, 2023
Sep. 30, 2022
Sep. 30, 2021
Effective income tax rate reconciliation      
Statutory federal tax rate (as a percent) 21.00% 21.00% 21.00%
Tax provision for income taxes at the statutory rate $ 10,899 $ 12,099 $ (2,054)
Foreign tax rate differentials 102 (307) (59)
Provision for state taxes, net of federal taxes 822 974 (84)
U.S. tax on distributed and undistributed earnings of foreign subsidiaries 54 984 198
Foreign derived intangible income deduction (693) (966)  
Tax credits (724) (702) (691)
Federal and state tax rate change impact on deferred tax asset 81 (206) 790
Change in valuation allowance 355 804 415
Stock compensation 46 191 138
Other, net (1,015) (344) 247
Total provision for (benefit from) income taxes $ 9,927 $ 12,527 $ (1,100)
Effective tax rate (as a percent) 19.10% 21.70% 11.20%