Dirichlet character tables modulo 3, 4, and 5

For $q=3$, the unit group is $\{1,2\}\cong C_2$, so there are two characters with values on the classes $(0,1,2)$ given by ${\chi }_0=(0,1,1)$ and the nonprincipal character $(0,1,-1)$. For $q=4$, the unit group is also $C_2$, giving ${\chi }_0=(0,1,0,1)$ and ${\chi }_4=(0,1,0,-1)$.

For $q=5$, the unit group is cyclic of order $4$, generated by $2$, so the four characters are determined by $\chi (2)\in \{1,-1,i,-i\}$. Writing values on the classes $0,1,2,3,4$ gives ${\chi }_0=(0,1,1,1,1)$, ${\chi }_1=(0,1,i,-i,-1)$, ${\chi }_2=(0,1,-1,-1,1)$, and ${\chi }_3=(0,1,-i,i,-1)$. Each table is zero exactly off the units and multiplicative on the unit classes, so these are exactly the Dirichlet characters for the three moduli.