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Goodwill and Acquired Intangibles (Tables)
 12 Months Ended
Dec. 31, 2022
Goodwill and Intangible Assets Disclosure [Abstract]  
Changes in the carrying amount of goodwill
The changes in the carrying amount of goodwill during fiscal 2022 and 2021 were as follows:
 Gross Carrying
Amount
 (In thousands)
Balance as of January 2, 2021$782,087 
Goodwill resulting from acquisitions154,362 
Effect of foreign currency translation(8,091)
Balance as of January 1, 2022928,358 
Goodwill resulting from acquisitions456,323 
Effect of foreign currency translation(10,413)
Balance as of December 31, 2022$1,374,268 
Acquired intangibles with finite lives (excluding goodwill), excluding intangibles fully amortized at end of prior fiscal year
Acquired intangibles as of December 31, 2022 were as follows, excluding intangibles that were fully amortized as of January 1, 2022:
Gross Carrying
Amount		Accumulated
Amortization		Acquired
Intangibles, Net
 (In thousands)
Existing technology$479,796 $(278,851)$200,945 
Agreements and relationships274,624 (137,847)136,777 
Tradenames, trademarks and patents12,979 (2,884)10,095 
Total acquired intangibles with definite lives767,399 (419,582)347,817 
In-process technology6,800 — 6,800 
Total acquired intangibles$774,199 $(419,582)$354,617 
Acquired intangibles as of January 1, 2022 were as follows, excluding intangibles that were fully amortized as of January 2, 2021:
Gross Carrying
Amount		Accumulated
Amortization		Acquired
Intangibles, Net
 (In thousands)
Existing technology$405,481 $(254,599)$150,882 
Agreements and relationships205,057 (130,187)74,870 
Tradenames, trademarks and patents10,666 (3,153)7,513 
Total acquired intangibles$621,204 $(387,939)$233,265 
Amortization of acquired intangibles Amortization expense for fiscal 2022, 2021 and 2020, by consolidated income statement caption, was as follows:
202220212020
 (In thousands)
Cost of product and maintenance$41,348 $47,576 $46,184 
Amortization of acquired intangibles18,470 19,640 18,009 
Total amortization of acquired intangibles$59,818 $67,216 $64,193 
Estimated amortization expense
As of December 31, 2022, the estimated amortization expense for intangible assets with definite lives was as follows for the following five fiscal years and thereafter:
 (In thousands)
2023$58,307 
202456,563 
202544,481 
202638,314 
202735,881 
Thereafter114,271 
Total estimated amortization expense$347,817