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Goodwill and Acquired Intangibles (Tables)
 3 Months Ended
Apr. 03, 2021
Goodwill and Intangible Assets Disclosure [Abstract]  
Changes in the carrying amount of goodwill
The changes in the carrying amount of goodwill during the three months ended April 3, 2021 were as follows:
 Gross Carrying
Amount
 (In thousands)
Balance as of January 2, 2021$782,087 
Goodwill resulting from acquisitions133,326 
Effect of foreign currency translation(2,810)
Balance as of April 3, 2021$912,603 
Schedule of acquired intangibles with finite and indefinite lives (excluding goodwill)
Acquired intangibles as of April 3, 2021 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$393,026 $(219,061)$173,965 
Agreements and relationships198,546 (115,650)82,896 
Tradenames, trademarks and patents10,290 (2,480)7,810 
Total acquired intangibles$601,862 $(337,191)$264,671 
Acquired intangibles as of January 2, 2021 were as follows, excluding intangibles that were fully amortized as of December 28, 2019:
Gross Carrying
Amount		Accumulated
Amortization		Acquired
Intangibles, Net
 (In thousands)
Existing technology$370,838 $(230,654)$140,184 
Agreements and relationships180,023 (113,629)66,394 
Tradenames, trademarks and patents10,590 (6,578)4,012 
Total acquired intangibles with definite lives$561,451 $(350,861)$210,590 
Amortization of acquired intangibles Amortization expense for the three months ended April 3, 2021 and March 28, 2020 by condensed consolidated income statement caption was as follows:
 Three Months Ended
 April 3,
2021		March 28,
2020
 (In thousands)
Cost of product and maintenance$11,768 $10,860 
Amortization of acquired intangibles4,631 4,206 
Total amortization of acquired intangibles$16,399 $15,066 
Estimated amortization expense
As of April 3, 2021, the estimated amortization expense for acquired intangible assets with definite lives was as follows for the following five fiscal years and thereafter:
 (In thousands)
2021 - remaining period$49,424 
202248,187 
202332,657 
202431,194 
202520,645 
Thereafter82,564 
Total estimated amortization expense$264,671