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Stock-Based Compensation (Stock-Based Compensation Expense) (Details) - USD ($)
$ in Thousands
3 Months Ended 6 Months Ended
Mar. 31, 2024
Mar. 31, 2023
Mar. 31, 2024
Mar. 31, 2023
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]        
Stock-based compensation before income taxes $ 3,473 $ 3,465 $ 6,579 $ 6,333
Income tax benefit (751) (737) (1,414) (1,336)
Stock-based compensation after income taxes 2,722 2,728 5,165 4,997
Cost of Sales        
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]        
Stock-based compensation before income taxes 175 161 356 303
Sales and Marketing        
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]        
Stock-based compensation before income taxes 1,208 1,072 2,376 1,923
Research and Development        
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]        
Stock-based compensation before income taxes 501 469 931 917
General and Administrative        
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]        
Stock-based compensation before income taxes $ 1,589 $ 1,763 $ 2,916 $ 3,190