Cylindrical-strip Beraha-zero pattern conjecture

Let $L$ be the width of a triangular-lattice strip with cylindrical boundary conditions, let $B_k$ denote the Beraha numbers, and let $D(q)$ be the amplitude matrix. Cylindrical-strip Beraha-zero pattern conjecture. The Beraha numbers where $\det D(q)$ vanishes are given by the union of the sets

$$\{B_2,B_3,\ldots,B_{L+1}\}\quad\text{and}\quad\{B_{4k-2}\mid k=1,2,\ldots,\lfloor L/2\rfloor\}.$$

The upper limit on $k$ is the integer part of $L/2$. This conjecture is based on systematic checks through $B_{50}$ and the observed cylindrical-boundary examples; unlike the free and zig-zag cases, the cylindrical data exhibit additional zeros beyond $B_{L+1}$, and the proposed general pattern remains open.