f(x) = a3 x3 + a2 x2 + a1 x + a0
Zeros at 4 and +/- 2i. That says you have factors that look like this:
(x - 4) (x2 + 4) <-- that second factor accommodates the complex zeros
And the constant coefficient of -128. So
f(x) = -128 (x - 4) (x2 + 4)
We'll multiply this through to find all the integer coefficients.
f(x) = -128 (x3 - 4x2 + 4x - 16)
a3 = -128
a2 = 512
a1 = -512
a0 = 2048
All integers! Cheers!