A polynomial $P(x)=c_{2023}{x}^{2023}+c_{2022}{x}^{2022}+\dots +c_{1}x+c_0$ has real coefficients with $c_{2023}\ne 0$ and $2023$ distinct complex zeroes $z_k=a_k+b_{k}i$, $1\le k\le 2023$ with $a_k$ and $b_k$ real. Given that $a_1=b_1=0$, one of the roots is $1$, and ${\sum }_{k=1}^{2023}{a}_k=0$. Which of the following quantities can be a nonzero number?