Estimating special values of the Riemann zeta function on the critical line

Question

If $p,q$ are primes, is it necessarily true that $$\left|\zeta\left(\frac{1}{2} + i\frac{p}{q}\right)\right| > (p+q)^{–(p+q)} ?$$ (Here $\zeta$ is the Riemann zeta function.)