Character sums over Galois rings and primitive polynomials over finite fields

Using the estimates of character sums over Galois rings and Cohen's sieve, we prove that there exists a primitive polynomial f(x)=x^n-a"1x^n^-^1+...+(-1)^na"n over F"q of degree n with the first three coefficients a"1,a"2,a"3 prescribed when n>=8.