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Stock Award Plans - Narrative (Details) - USD ($)	12 Months Ended
Stock Award Plans - Narrative (Details) - USD ($)	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Contractual term of award (in years)	10 years
Options granted (in shares)	352,043	0	1,043,349
Compensation cost for stock options	$ 1,296,000	$ 1,676,000	$ 1,344,000
Stock Option Awards
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Unrecognized compensation cost for stock options, net of forfeitures	$ 1,851,364
Restricted Stock Awards
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Equity instruments other than options, nonvested (in shares)	489,777	522,991	409,469	435,838
Fair market value at date of grant at restricted stock	$ 10,598,774
Compensation cost for stock options	$ 4,367,000	$ 4,473,000	$ 4,453,000
Minimum
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Award vesting period (in years)	3 years
Minimum \| Restricted Stock Awards
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Award vesting period (in years)	1 year
Maximum
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Award vesting period (in years)	5 years
Maximum \| Restricted Stock Awards
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Award vesting period (in years)	7 years
2020 Incentive Plan
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares available for grant (in shares)	3,200,000
Shares available for issuance (in shares)	1,882,283