Doubts about Notch filter design
This Octave / Matlab code gives you a 2nd ord notch filter at $\omega_n = \pi/6$

r = 0.99;          % notch radius (closer to 1 stiffer)
wn = pi/6;         % notch radian frequency...  

% Create the 2nd order NOTCH filter coefficients b() and a()
b = r*conv([1,  -exp(j*wn)],[1,  -exp(-j*wn)]);      
a = conv([1,  -r*exp(j*wn)],[1,  -r*exp(-j*wn)]);    

figure,freqz(b,a,2048);


with the following result: