Let q be a prime power. Following a paper by Coons, Jenkins, Knowles, Luke and Rault (case q a prime bb17e3476be127e79e336e5f69">) we define the numerical range Num(M)⊆Fq2 of an bc1469f714e" title="Click to view the MathML source">n×n-matrix M with coefficients in bbd3c790c27ad8318997e7951" title="Click to view the MathML source">Fq2 in terms of the usual Hermitian form. We prove that e40956e3d6d5ebbd3c9e51f" title="Click to view the MathML source">♯(Num(M))>q (case q≠2), unless M is unitarily equivalent to a diagonal matrix with eigenvalues contained in an affine e4987a090b74b5d87ac42c86a73d92" title="Click to view the MathML source">Fq-line. We study in details 98" title="Click to view the MathML source">Num(M) when n=2.