We present a numerical test for determining whether a given set of numbers is the set of Fourier coefficients of a Maass form, without knowing its eigenvalue. Our method extends directly to consideration of holomorphic newforms. The test is applied to show that the Kloosterman sums $\pm S(1,1;p)\big/\hskip-1pt\sqrt p$ are not the coefficients of a Maass form with small level and eigenvalue. Source code and the calculated Kloosterman sums are available electronically.
"A test for identifying Fourier coefficients of automorphic forms and application to Kloosterman sums." Experiment. Math. 9 (4) 571 - 581, October 2000.