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Selected Quarterly Financial Data (Unaudited) (Details) - USD ($)
$ / shares in Units, $ in Thousands
 3 Months Ended 12 Months Ended
Sep. 30, 2019
Jun. 30, 2019
Mar. 31, 2019
Dec. 31, 2018
Sep. 30, 2018
Jun. 30, 2018
Mar. 31, 2018
Dec. 31, 2017
Sep. 30, 2019
Sep. 30, 2018
Sep. 30, 2017
Quarterly Financial Information Disclosure [Abstract]                      
Interest income $ 169,436 $ 171,826 $ 167,582 $ 162,622 $ 157,152 $ 155,072 $ 149,079 $ 145,780 $ 671,466 $ 607,083 $ 548,918
Interest expense 49,264 50,160 47,512 43,470 37,901 35,220 31,778 30,045 190,406 134,944 116,992
Net interest income 120,172 121,666 120,070 119,152 119,251 119,852 117,301 115,735 481,060 472,139 431,926
Provision (release) for loan losses (1,900) 0 750 (500) (5,500) 1,000 (950) 0 (1,650) (5,450) (2,100)
Other operating income (including REO gain (loss), net) 15,786 14,395 13,618 19,329 12,207 12,619 12,309 6,841      
Other operating expense 72,526 70,898 67,967 71,672 69,617 66,977 65,787 61,941 283,063 264,322 231,519
Income before income taxes 65,332 65,163 64,971 67,309 67,341 64,494 64,773 60,635 262,775 257,243 256,216
Income tax expense 12,970 11,309 13,873 14,367 15,826 13,100 15,502 8,965 52,519 53,393 82,684
Net income $ 52,362 $ 53,854 $ 51,098 $ 52,942 $ 51,515 $ 51,394 $ 49,271 $ 51,670 $ 210,256 $ 203,850 $ 173,532
Basic earnings per share (in dollars per share) $ 0.66 $ 0.67 $ 0.63 $ 0.65 $ 0.62 $ 0.61 $ 0.58 $ 0.59 $ 2.61 $ 2.40 $ 1.95
Diluted earnings per share (in dollars per share) 0.66 0.67 0.63 0.65 0.62 0.61 0.57 0.59 2.61 2.40 1.94
Cash dividends per share (in dollars per share) $ 0.21 $ 0.20 $ 0.20 $ 0.18 $ 0.18 $ 0.17 $ 0.17 $ 0.15 $ 0.79 $ 0.67 $ 0.84