  In the present paper the optimal quadrature formulas in the sense of Sard are
constructed for numerical integration of the integral $\int_a^b e^{2\pi i\omega
x}\varphi(x)d x$ with $\omega\in \mathbb{R}$ in the Hilbert space
$W_2^{(2,1)}[a,b]$ of complex-valued functions. Furthermore, the explicit
expressions for coefficients of the constructed optimal quadrature formulas are
obtained. At the end of the paper some numerical results are presented.
