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        Cycle type of $\sigma\in S_4$ &amp; $\chi_{t\Pi_4}(\sigma)$ &amp; $\sum\limits_{t \geq 0} \chi_{t\Pi_4}(\sigma)z^t$ &amp; $\phi[z](\sigma)$ \\
    \hline
        $(1,1,1,1)$ &amp; $16t^3 + 15t^2 + 6t +1$ &amp; $\dfrac{1 + 34z + 55z^2 + 6z^3}{(1-z)^4}$ &amp; $1 + 34z + 55z^2 + 6z^3$\\
   \hline
        $(2,1,1)$ &amp; $\begin{cases} 4t^2 + 3t + 1 &amp; \text{if $t$ is even}\\4t^2 + 2t &amp; \text{if $t$ is odd} \end{cases}$ &amp; $\dfrac{1 + 6z + 20z^2 + 24z^3 + 11z^4 + 2z^5}{(1-z)^2(1-z^2){\color{red}(1+z)^2}}$ &amp; $1+4z+11z^2-2z^3+\displaystyle\sum_{i=4}^\infty 4(-1)^i z^i$ \\
    \hline
        $(3,1)$ &amp;  $t+1$ &amp; $\dfrac{1}{(1-z)^2} = \dfrac{1+z+z^2}{(1-z)(1-z^3)}$ &amp; $1+z+z^2$\\
    \hline
        $(4)$ &amp; $\begin{cases} 1 &amp; \text{if $t$ is even}\\0 &amp; \text{if $t$ is odd} \end{cases}$ &amp; $\dfrac{1}{1-z^2}=\dfrac{1+z^2}{1-z^4}$ &amp; $1+z^2$\\
    \hline
        $(2,2)$ &amp;  $\begin{cases} 2t+1 &amp; \text{if $t$ is even}\\ 2t &amp; \text{if $t$ is odd} \end{cases}$ &amp; $\dfrac{1+2z+3z^2+2z^3}{(1-z^2)^2}$ &amp; $1+2z+3z^2+2z^3$\\
    \hline
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