> This is somewhat off-topic, but could you explain why q^(1/2)
> is -2[mod 17] and why q^(1/3) is 2[mod 17]?
>
> If I square -2[mod 17], I think I get 4[mod 17]. Likewise,
> the cube of 2[mod 17] is 8[mod 17].
>
> I must be missing something here.
You're missing nothing. The choice was completely arbitrary, the first
roots I found. Perhaps there is some more sensible way of choosing
roots.
-s