#1
I've always noticed how my low e on my Dean wouldn't be in tune by ear. So I brought an electronic tuner and it showed it was in tune but as a G#...
#2
Then you need to tune it to E

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#4
what gauge strings do you have? maybe you have to tune up to the E? You likely haven't tuned above the E to a G# as you'd notice how tight the string is. Also try another tuner to make sure.
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#5
Check the tuning against the A string (which I assume is in tune).
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#7
It's either the frequency, the string gauge or you.

Only two of those can be fixed.
#12
What kind of tuner is it? My clip-on tuner thinks my lowest string is a B when I tune it to E (I guess it only picks up the 3rd harmonic)