Securities (Amortized Cost, Estimated Fair Value, and Gross Unrealized Gains and Losses of AFS and HTM Securities) (Details) - USD ($) $ in Thousands	Jun. 30, 2023	Sep. 30, 2022
Marketable Securities [Line Items]
Available-for-sale Securities, Amortized Cost	$ 1,624,837	$ 1,768,490
Available-for-sale Securities, Gross Unrealized Gains	66	365
Available-for-sale Securities, Gross Unrealized Losses	180,036	205,548
Available-for-sale Securities, Estimated Fair Value	1,444,867	1,563,307
MBS [Member]
Marketable Securities [Line Items]
Available-for-sale Securities, Amortized Cost	1,099,824	1,243,270
Available-for-sale Securities, Gross Unrealized Gains	66	365
Available-for-sale Securities, Gross Unrealized Losses	135,171	155,011
Available-for-sale Securities, Estimated Fair Value	964,719	1,088,624
GSE Debentures [Member]
Marketable Securities [Line Items]
Available-for-sale Securities, Amortized Cost	519,983	519,977
Available-for-sale Securities, Gross Unrealized Gains	0	0
Available-for-sale Securities, Gross Unrealized Losses	44,224	50,150
Available-for-sale Securities, Estimated Fair Value	475,759	469,827
Corporate Bonds [Member]
Marketable Securities [Line Items]
Available-for-sale Securities, Amortized Cost	4,000	4,000
Available-for-sale Securities, Gross Unrealized Gains	0	0
Available-for-sale Securities, Gross Unrealized Losses	623	305
Available-for-sale Securities, Estimated Fair Value	3,377	3,695
Municipal Bonds [Member]
Marketable Securities [Line Items]
Available-for-sale Securities, Amortized Cost	1,030	1,243
Available-for-sale Securities, Gross Unrealized Gains	0	0
Available-for-sale Securities, Gross Unrealized Losses	18	82
Available-for-sale Securities, Estimated Fair Value	$ 1,012	$ 1,161

Amount, before tax, of unrealized gain in accumulated other comprehensive income (AOCI) on investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 320
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481800/320-10-50-2

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- Definition

Amount, before tax, of unrealized loss in accumulated other comprehensive income (AOCI) on investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 320
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481800/320-10-50-2

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Amortized cost excluding accrued interest, after allowance for credit loss, of investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 326
-SubTopic 30
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479130/326-30-45-1

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Amount excluding accrued interest, of investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).

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