{\hat{a}}_2=\frac{1}{N}\cdot\left(a_0+a_1{\cdot\zeta}_N^2+a_2{\cdot\zeta}_N^4+a_3{\cdot\zeta}_N^6\right)=\frac{1}{4}\cdot\left(3,28-1,41\cdot e^{-\pi i}+1,41\cdot e^{-2\pi i}-3,28\cdot e^{-3\pi i}\right)=\frac{1}{4}\cdot\left(3,28-1,41\cdot(-1)+1,41\cdot1-3,28\cdot(-1)\right)=\frac{1}{4}\cdot9,38=2,35