High-precision evaluation of Wigner's d matrix by exact diagonalization

The precise calculations of Wigner's d matrix are important in various research fields. Due to the presence of large numbers, direct calculations of the matrix using Wigner's formula suffer from a 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.