The determinant characterization conjecture for prime alternating achiral knots

Let $n$ be an odd natural number. The determinant characterization conjecture for prime alternating achiral knots. Then $n$ is the determinant of a prime alternating achiral knot if and only if $n$ is the sum of two squares and $n\not\in\{1,\ 9,\ 49\}$.

The conjecture asserts that the listed values are the only exceptions to the determinant characterization for prime alternating achiral knots. The source reports only a possibility based on computations up to 16 crossings and gives no resolution, so the conjecture remains open.