Maaß cusp forms for large eigenvalues

We investigate the numerical computation of Maaß cusp forms for the modular group corresponding to large eigenvalues. We present Fourier coefficients of two cusp forms whose eigenvalues exceed r = 40000 r=40000 . These eigenvalues are the largest that have so far been found in the case of the modular group. They are larger than the 130 130 millionth eigenvalue.