The database contains data for Maass forms on $\Gamma_0(N)$ with trivial character and Laplace eigenvalue $\lambda = \frac14 + R^2$ in three ranges:
$1\le N \le 10$ and $0<R\le 10$,
prime $100 < N < 250$ and $0<R\le 2$, and
prime $250 < N < 1000$ and $0<R\le 1$,
as well as many additional examples for small $N$.
It is believed that each database entry corresponds to an actual Maass form and the given decimal numbers are reasonable approximations to the true value. However, some eigenvalues may be missing.
Using current methods it is not feasible to prove that the data for an individual Maass form is correct, nor that the list of Maass eigenvalues in a given range is compete. You can read about the reasons for this difficulty.