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Goodwill and Intangible Assets - Schedule of Goodwill and Acquired Intangible Assets (Details) - USD ($) $ in Thousands | Dec. 31, 2023 | Sep. 30, 2023
--- | --- | ---
Goodwill (not amortized) | $ 3,458,463 | $ 3,358,511
Intangible assets with finite lives (amortized), Gross Carrying Amount | 1,834,464 | 1,795,627
Intangible assets with finite lives (amortized), Accumulated Amortization | 881,094 | 854,378
Intangible assets with finite lives (amortized), Net Book Value | 953,370 | 941,249
Intangible Assets, Net (Including Goodwill) | 4,411,833 | 4,299,760
Purchased Software |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 629,554 | 615,915
Intangible assets with finite lives (amortized), Accumulated Amortization | 406,952 | 395,109
Intangible assets with finite lives (amortized), Net Book Value | 222,602 | 220,806
Capitalized Software |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 22,877 | 22,877
Intangible assets with finite lives (amortized), Accumulated Amortization | 22,877 | 22,877
Intangible assets with finite lives (amortized), Net Book Value | 0 | 0
Customer Lists and Relationships |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 1,140,213 | 1,116,117
Intangible assets with finite lives (amortized), Accumulated Amortization | 427,224 | 413,125
Intangible assets with finite lives (amortized), Net Book Value | 712,989 | 702,992
Trademarks and Trade Names |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 37,892 | 36,851
Intangible assets with finite lives (amortized), Accumulated Amortization | 20,113 | 19,400
Intangible assets with finite lives (amortized), Net Book Value | 17,779 | 17,451
Other |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 3,928 | 3,867
Intangible assets with finite lives (amortized), Accumulated Amortization | 3,928 | 3,867
Intangible assets with finite lives (amortized), Net Book Value | $ 0 | $ 0

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