Just went out to grab something and checked, 80 mph equals appx 3100 RPM. 03 .. yours might be the five speed which could be different. Would be probably totally different actually.
235 65 17 stock tires

This is really the same on my other bimmers, 80 mph is above 3K. Pretty sure my Subaru WRX it was like two and a half.

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'05 E53 3.0 6mt
'17 F30 340ix 6mt
'96 E36 328is, in progress