July 4 (Reuters) - Canada's main stock index opened muted on Thursday as gains in technology shares were offset by losses in real estate and utilities, while investors awaited U.S. employment data on Friday to gauge the Federal Reserve's rate cut trajectory.

At 9:35 a.m. ET (1335 GMT), the Toronto Stock Exchange's S&P/TSX composite index was up 20.84 points, or 0.09%, at 22,244.51.

(Reporting by Nikhil Sharma in Bengaluru; Editing by Andrew Heavens)