Let q be a prime power. Following a paper by Coons, Jenkins, Knowles, Luke and Rault (case q a prime ) we define the numerical range 052ff434eb" title="Click to view the MathML source">Num(M)⊆Fq2 of an n×n-matrix M with coefficients in Fq2 in terms of the usual Hermitian form. We prove that e40956e3d6d5ebbd3c9e51f" title="Click to view the MathML source">♯(Num(M))>q (case 05" title="Click to view the MathML source">q≠2), unless M is unitarily equivalent to a diagonal matrix with eigenvalues contained in an affine Fq-line. We study in details Num(M) when n=2.