Allen's non-orientable surface realizability conjecture for torus knots

For a positive torus knot $T(3,6n+1)$, let $(e,h)$ denote the normal Euler number and non-orientable genus of a smoothly and properly embedded surface in $D^4$ bounded by the knot. The exceptional pairs are

$$(e,h)=\left(\frac{8}{3}(1-n)+2+2m,1+m\right),$$

where $m$ is a non-negative integer. For a positive torus knot $T(3,6n+2)$, the exceptional pairs are

$$(e,h)=\left(\frac{8}{3}(2-n)+2+2m,3+m\right),$$

where $m$ is a non-negative integer. Allen's conjecture. Both of these families of pairs are not realizable. This concerns the unresolved realizability question for non-orientable surfaces bounded by torus knots; the supplied text gives no resolution status.