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Goodwill and Intangible Assets (Tables)
3 Months Ended
Mar. 31, 2023
Goodwill and Intangible Assets Disclosure [Abstract]  
Changes in Carrying Amounts of Goodwill The changes in carrying amounts of goodwill for the three months ended March 31, 2023 are as follows (in thousands):
Amount
Balance as of January 1, 2023$346,585 
Foreign exchange translation1,167 
Balance as of March 31, 2023$347,752 
Intangible Assets with Indefinite Lives
Intangible assets are summarized as of March 31, 2023 and December 31, 2022 as follows (in thousands):
March 31, 2023December 31, 2022
Trade names$27,353 $27,337 
Other4,045 4,045 
Total$31,398 $31,382 
Intangible Assets Subject to Amortization
As of March 31, 2023, intangible assets subject to amortization are summarized as follows (in thousands):
Weighted-Average Remaining
  Amortization
Period
Historical
Cost
Accumulated
Amortization
Net
Trade names0.4 years$8,178 $7,666 $512 
Patent and patent licenses0.0 years54,341 54,341 — 
Customer relationships (1)
3.0 years107,512 93,788 13,724 
Other purchased intangibles 2.0 years11,936 9,474 2,462 
Total
 $181,967 $165,269 $16,698 
(1) Historically, the Company has amortized its customer relationship assets in a pattern that best reflects the pace in which the assets’ benefits are consumed. This pattern results in a substantial majority of the amortization expense being recognized in the first four to five years, despite the overall life of the asset.

    As of December 31, 2022, intangible assets subject to amortization are summarized as follows (in thousands):
Weighted-Average Remaining
  Amortization
Period
Historical
Cost
Accumulated
Amortization
Net
Trade names0.5 years$8,151 $7,605 $546 
Patent and patent licenses0.0 years54,341 54,341 — 
Customer relationships (1)
3.1 years107,175 92,573 14,602 
Other purchased intangibles 2.0 years11,937 9,311 2,626 
Total$181,604 $163,830 $17,774 
(1) Historically, the Company has amortized its customer relationship assets in a pattern that best reflects the pace in which the assets’ benefits are consumed. This pattern results in a substantial majority of the amortization expense being recognized in the first four to five years, despite the overall life of the asset.
Estimated Intangible Assets Amortization Expense
Expected amortization expenses for intangible assets subject to amortization at March 31, 2023 are as follows (in thousands):
Fiscal Year:Amount
2023 (remainder)$3,177 
20243,520 
20252,629 
20262,119 
20271,416 
Thereafter3,837 
Total$16,698