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Income Taxes - Narrative (Details) - USD ($)
$ / shares in Units, $ in Thousands
12 Months Ended
Sep. 30, 2023
Sep. 30, 2022
Sep. 30, 2021
Sep. 30, 2020
Operating Loss Carryforwards [Line Items]        
Income Tax Holiday, Aggregate Dollar Amount $ 6,000 $ 8,500 $ 6,000  
Income Tax Holiday, Income Tax Benefits Per Share $ 0.10 $ 0.14 $ 0.10  
Deferred Tax Assets, Operating Loss Carryforwards $ 40,201 $ 42,849    
Deferred Tax Assets, Tax Credit Carryforwards 23,883 28,858    
Valuation Allowance, Deferred Tax Asset, Change in Amount (2,200) 5,700    
Unrecognized Tax Benefits 79,167 66,840 $ 70,814 $ 51,767
Unrecognized Tax Benefits that Would Impact Effective Tax Rate 51,200 43,200 39,200  
Unrecognized Tax Benefits, Period Increase (Decrease) 3,300 (1,500) $ 1,400  
Unrecognized Tax Benefits, Income Tax Penalties and Interest Accrued 6,200 $ 2,900    
Foreign [Member]        
Operating Loss Carryforwards [Line Items]        
Deferred Tax Assets, Operating Loss Carryforwards, Not Subject to Expiration 56,900      
Deferred Tax Assets, Operating Loss Carryforwards, Subject to Expiration 300      
Deferred Tax Assets, Tax Credit Carryforwards 200      
Deferred Tax Assets, Tax Credit Carryforwards, Subject to Expiration 3,200      
Domestic Tax Authority [Member]        
Operating Loss Carryforwards [Line Items]        
Deferred Tax Assets, Operating Loss Carryforwards, Not Subject to Expiration 56,400      
Deferred Tax Assets, Operating Loss Carryforwards, Subject to Expiration 23,400      
Deferred Tax Assets, Operating Loss Carryforwards 79,800      
Deferred Tax Assets, Tax Credit Carryforwards, Subject to Expiration 3,200      
State and Local Jurisdiction [Member]        
Operating Loss Carryforwards [Line Items]        
Deferred Tax Assets, Operating Loss Carryforwards, Not Subject to Expiration 47,000      
Deferred Tax Assets, Operating Loss Carryforwards, Subject to Expiration 191,800      
Deferred Tax Assets, Operating Loss Carryforwards 238,800      
Deferred Tax Assets, Tax Credit Carryforwards 30,200      
Deferred Tax Assets, Tax Credit Carryforwards, Subject to Expiration $ 3,700