Find the frequency of a pole (Discrete Form)
Usually a discrete-time notch filter is implemented by an IIR (infinite impulse response) filter, which has a numerator as well as a denominator polynomial. The notch frequency - the frequency where the input signal should be completely suppressed - is determined by the numerator polynomial, i.e. by the zeros of the filter's transfer function, not (directly) by its poles. Of course, a practical design will also place the poles close to the notch-frequency, but the actual notch is implemented by a zero on the unit circle of the complex plane, i.e. by the numerator polynomial.

The numerator of a second order notch filter looks like this:

$$N(z)=z^2-2\cos(\omega_0)z+1\tag{1}$$

You can verify that this polynomial has two complex conjugate zeros at $z=e^{j\omega_0}$ and at $z=e^{-j\omega_0}$, so the notch frequency is given by the normalized angular frequency $\omega_0$.