Securities (Amortized Cost, Estimated Fair Value, and Gross Unrealized Gains and Losses of AFS and HTM Securities) (Details) - USD ($) $ in Thousands	Dec. 31, 2021	Sep. 30, 2021
Marketable Securities [Line Items]
Available-for-sale Securities, Amortized Cost	$ 1,899,027	$ 2,008,456
Available-for-sale Securities, Gross Unrealized Gains	14,111	18,705
Available-for-sale Securities, Gross Unrealized Losses	22,485	12,553
Available-for-sale Securities, Estimated Fair Value	1,890,653	2,014,608
MBS [Member]
Marketable Securities [Line Items]
Available-for-sale Securities, Amortized Cost	1,375,711	1,484,211
Available-for-sale Securities, Gross Unrealized Gains	14,105	18,690
Available-for-sale Securities, Gross Unrealized Losses	13,577	8,908
Available-for-sale Securities, Estimated Fair Value	1,376,239	1,493,993
GSE Debentures [Member]
Marketable Securities [Line Items]
Available-for-sale Securities, Amortized Cost	519,972	519,971
Available-for-sale Securities, Gross Unrealized Gains	0	0
Available-for-sale Securities, Gross Unrealized Losses	8,908	3,645
Available-for-sale Securities, Estimated Fair Value	511,064	516,326
Municipal Bonds [Member]
Marketable Securities [Line Items]
Available-for-sale Securities, Amortized Cost	3,344	4,274
Available-for-sale Securities, Gross Unrealized Gains	6	15
Available-for-sale Securities, Gross Unrealized Losses	0	0
Available-for-sale Securities, Estimated Fair Value	$ 3,350	$ 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 http://asc.fasb.org/extlink&oid=123581744&loc=d3e27161-111563

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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://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)
-URI http://asc.fasb.org/extlink&oid=123581744&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 http://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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