  Let $ \chi $ be a virtual (generalized) character of a finite group $ G $ and
$ L=L(\chi)$ be the image of $ \chi $ on $ G-\lbrace 1 \rbrace $. The pair $
(G, \chi) $ is said to be sharp of type $ L $ if $|G|=\prod _{ l \in L}
(\chi(1) - l) $. If the principal character of $G$ is not an irreducible
constituent of $\chi$, the pair $(G,\chi)$ is called normalized. In this paper,
we first provide some counterexamples to a conjecture that was proposed by
Cameron and Kiyota in $1988$. This conjecture states that if $(G,\chi)$ is
sharp and $|L|\geq 2$, then the inner product $(\chi,\chi)_G$ is uniquely
determined by $ L $. We then prove that this conjecture is true in the case
that $(G,\chi) $ is normalized, $\chi$ is a character of $ G $, and $ L $
contains at least an irrational value.
