Jill Smith has $$137,000$ invested in a $3-$stock portfolio consisting of stocks A$,$ B and C$.$ The amounts invested in stocks A and $B$ and their betas are shown in the table below. If the portfolio overall is market neutral i$.$e$.$ it's beta is equal to that of the market, what is the beta of stock $C?$

Item Amount $($$$)$ Beta

Stock A $,38,000,1\mathrm{.}75$

Stock $B47,000,1\mathrm{.}25$

$0\mathrm{.}23$

$2\mathrm{.}41$

$-0\mathrm{.}23$

$-2\mathrm{.}41$

$-5\mathrm{.}04$