  The precise calculations of the Wigner's d-matrix are important in various
research fields. Due to the presence of large numbers, direct calculations of
the matrix using the Wigner's formula suffer from loss of precision. We present
a simple method to avoid this problem by expanding the d-matrix into a complex
Fourier series and calculate the Fourier coefficients by exactly diagonalizing
the angular-momentum operator $J_{y}$ in the eigenbasis of $J_{z}$. This method
allows us to compute the d-matrix and its various derivatives for spins up to a
few thousand. The precision of the d-matrix from our method is about $10^{-14}$
for spins up to $100$.
