Determinants of prime alternating achiral knots

Definitions and mathematical statement

For a smooth knot $K\subset S^3$, define $\det(K)=|\Delta_K(-1)|$, where $\Delta_K$ is its Alexander polynomial. This value is independent of multiplying the polynomial by $\pm t^j$. A knot is prime if it is nontrivial and has no decomposition as a connected sum of two nontrivial knots. It is alternating if it admits a diagram whose crossings alternate over and under along the knot. It is achiral if the unoriented knot is ambient isotopic to its mirror image.

Let \[ A=\{n\in\mathbb Z_{>0}:n\text{ is odd},\ n=a^2+b^2 \text{ for some }a,b\in\mathbb Z\}\setminus\{1,9,49\}. \] Is every $n\in A$ equal to $\det(K)$ for some knot $K$ which is simultaneously prime, alternating and achiral? Zero is allowed as one of $a,b$; coprimality is not assumed.

Short English statement

Do prime alternating achiral knots realize every odd sum of two squares other than 1, 9 and 49 as a determinant?

Sources

A. Stoimenow, Problem 12.25 in T. Ohtsuki (ed.), Problems on invariants of knots and 3-manifolds, Geometry and Topology Monographs 4 (2002), p. 541, https://msp.org/gtm/2002/04/gtm-2002-04-024s.pdf. See also A. Stoimenow, Square numbers, spanning trees and invariants of achiral knots, Communications in Analysis and Geometry 13 (2005), 591--631, https://arxiv.org/abs/math/0003172.