I don't understand the formula for the Zech logarithm. How do you compute it by hand?

On Wikipedia: the Zech logarithm of an integer n may be defined such that
α^[Z(n)] = 1 + α^n

Given q=2^3 and an irreducible polynomial α^3 + α + 1, how do you find the Zech log vector {-infinity,0,3,6,1,5,4,2} ?

Thanks for any kind of help provided.