Summary: We significantly extend the range of published tables of primitive normal polynomials over finite fields. For each \(p^ n < 10^{50}\) with \(p \leq 97\), we provide a primitive normal polynomial of degree \(n\) over \(\mathbb{F}_ p\). Moreover, each polynomial has the minimal number of nonzero coefficients among all primitive normal polynomials of degree \(n\) over \(\mathbb{F}_ p\). The roots of such a polynomial generate a primitive normal basis of \(\mathbb{F}_{p^ n}\) over \(\mathbb{F}_ p\), and so are of importance in many computational problems. We also raise several conjectures concerning the distribution of such primitive normal polynomials, including a refinement of the primitive normal basis theorem. In the tables on pp. S 19–S 23 only the nonzero terms are represented so that, for example, the polynomial \(x^ 8 + x^ 7 + 3\) over \(\mathbb{F}_ 7\) is listed as 8:1, 7:1, 0:3. An asterisk denotes the fact that for the given polynomial \(f(x)\), the reciprocal polynomial \(f(x)^* = x^ n f(1/x)\) is also primitive normal. Copies of the tables, either in electronic or hardcopy form, are available upon request from the authors [mullen@math.psu.edu].