Securities (Amortized Cost, Estimated Fair Value, and Gross Unrealized Gains and Losses of AFS and HTM Securities) (Details) - USD ($) $ in Thousands	Jun. 30, 2022	Sep. 30, 2021
Marketable Securities [Line Items]
Available-for-sale Securities, Amortized Cost	$ 1,830,262	$ 2,008,456
Available-for-sale Securities, Gross Unrealized Gains	1,071	18,705
Available-for-sale Securities, Gross Unrealized Losses	137,173	12,553
Available-for-sale Securities, Estimated Fair Value	1,694,160	2,014,608
MBS [Member]
Marketable Securities [Line Items]
Available-for-sale Securities, Amortized Cost	1,306,076	1,484,211
Available-for-sale Securities, Gross Unrealized Gains	1,052	18,690
Available-for-sale Securities, Gross Unrealized Losses	100,381	8,908
Available-for-sale Securities, Estimated Fair Value	1,206,747	1,493,993
GSE Debentures [Member]
Marketable Securities [Line Items]
Available-for-sale Securities, Amortized Cost	519,976	519,971
Available-for-sale Securities, Gross Unrealized Gains	0	0
Available-for-sale Securities, Gross Unrealized Losses	36,783	3,645
Available-for-sale Securities, Estimated Fair Value	483,193	516,326
Corporate Bonds [Member]
Marketable Securities [Line Items]
Available-for-sale Securities, Amortized Cost	4,000
Available-for-sale Securities, Gross Unrealized Gains	19
Available-for-sale Securities, Gross Unrealized Losses	9
Available-for-sale Securities, Estimated Fair Value	4,010
Municipal Bonds [Member]
Marketable Securities [Line Items]
Available-for-sale Securities, Amortized Cost	210	4,274
Available-for-sale Securities, Gross Unrealized Gains	0	15
Available-for-sale Securities, Gross Unrealized Losses	0	0
Available-for-sale Securities, Estimated Fair Value	$ 210	$ 4,289

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://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=126970911&loc=d3e27161-111563

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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://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)
-URI https://asc.fasb.org/extlink&oid=126970911&loc=d3e27161-111563

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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
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 30
-Section 45
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=124258926&loc=SL82898722-210454

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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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