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Income Taxes - Schedule of Deferred Tax Assets and Liabilities (Details) - USD ($)
$ in Thousands
Sep. 30, 2023
Sep. 30, 2022
Deferred tax assets/(liabilities):    
Costs deductible in future periods $ 37,036 $ 36,604
Deferred revenue 8,712 7,273
Stock compensation 6,212 4,918
Capital loss carryforward 2,391 2,391
Net operating loss carryforwards 33,278 6,666
Amortization of goodwill and intangibles (189,316) (198,903)
Capitalized software (28,246) (15,445)
Accounts receivable - unbilled (7,963) (12,087)
Property and equipment (3,437) (2,577)
Prepaid expenses (10,906) (11,522)
Financial instruments (8,158) (8,261)
Valuation allowance (34,643) (8,075)
Other (6,399) (2,111)
Net deferred tax liability $ (201,439) $ (201,129)