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Selected Quarterly Financial Data (Unaudited) (Details) - USD ($)
$ / shares in Units, $ in Thousands
 3 Months Ended 12 Months Ended
Sep. 30, 2018
Jun. 30, 2018
Mar. 31, 2018
Dec. 31, 2017
Sep. 30, 2017
Jun. 30, 2017
Mar. 31, 2017
Dec. 31, 2016
Sep. 30, 2018
Sep. 30, 2017
Sep. 30, 2016
Quarterly Financial Information Disclosure [Abstract]                      
Interest income $ 157,152 $ 155,072 $ 149,079 $ 145,780 $ 142,240 $ 137,716 $ 136,198 $ 132,764 $ 607,083 $ 548,918 $ 536,793
Interest expense 37,901 35,220 31,778 30,045 29,808 29,101 28,471 29,612 134,944 116,992 116,544
Net interest income 119,251 119,852 117,301 115,735 112,432 108,615 107,727 103,152 472,139 431,926 420,249
Provision (release) for loan losses (5,500) 1,000 (950) 0 (500) 0 (1,600) 0 (5,450) (2,100) (6,250)
Other operating income (including REO gain (loss), net) 12,207 12,619 12,309 6,841 16,686 13,798 10,931 12,294      
Other operating expense 69,617 66,977 65,787 61,941 62,649 57,062 57,467 54,341 264,322 231,519 235,447
Income before income taxes 67,341 64,494 64,773 60,635 66,969 65,351 62,791 61,105 257,243 256,216 248,134
Income tax expense 15,826 13,100 15,502 8,965 20,865 21,239 20,721 19,859 53,393 82,684 84,085
NET INCOME $ 51,515 $ 51,394 $ 49,271 $ 51,670 $ 46,104 $ 44,112 $ 42,070 $ 41,246 $ 203,850 $ 173,532 $ 164,049
Basic earnings per share (in dollars per share) $ 0.62 $ 0.61 $ 0.58 $ 0.59 $ 0.53 $ 0.49 $ 0.47 $ 0.46 $ 2.40 $ 1.95 $ 1.79
Diluted earnings per share (in dollars per share) 0.62 0.61 0.57 0.59 0.52 0.49 0.47 0.46 2.40 1.94 1.78
Cash dividends per share (in dollars per share) $ 0.18 $ 0.17 $ 0.17 $ 0.15 $ 0.15 $ 0.15 $ 0.4 $ 0.14 $ 0.67 $ 0.84 $ 0.55