We determine the exact shape of the G2 equidistribution law for the one parameter family of exponential sums over Ép ≠, ‡x mod p, x ± 0 ç2(x)exp(2πi(x 7 + tx)/p). Here ç2(x) denotes the quadratic character (x/p), t in Ép is the parameter, and p is any prime other than 2 or 7. This answers a question raised in [K-L-R, page 2943, footnote 3] and in [Se]. We also analyze the analogous families whe...