import numpy as np

coeff_list = []

for y in range(16):
    coeff = 0
    coeff += np.exp(-np.pi * 1j * 3 * y / 8)
    coeff += np.exp(-np.pi * 1j * 7 * y / 8)
    coeff += np.exp(-np.pi * 1j * 11 * y / 8)
    coeff += np.exp(-np.pi * 1j * 15 * y / 8)
    
    if np.abs(coeff.real) > 1e-14 or np.abs(coeff.imag) > 1e-14:
        coeff_list.append(coeff)
    else:
        coeff_list.append(0)
    
for c in range(len(coeff_list)):
    print(f'{c} : {coeff_list[c]}')



