276 Days from The Annunciation to The Nativity of The Lord ≈ 40 Weeks.
From Annunciation to Nativity there are 40 Week Cycles if Annunciation happens on Sunday thru Thursday.
If Annunciation happens on Friday or Saturday (as in the image below) then there are 41 Week Cycles
See:
Saint Augustine's remarks on the significance of 276 Days being 6 x 46 (TWO x THREE x 46) where 46 years is the number of years it took to build the Old Testament Temple