Riemann Zeta Function of 4/Proof 5

Proof

 * $\begin{array}{r|cccccccccc}

\paren {\map \zeta 2}^2 & \paren {\frac {1} {1}} & \paren {\frac {1} {4}} & \paren {\frac {1} {9}} & \paren {\frac {1} {16}} & \paren {\frac {1} {25}} & \paren {\frac {1} {36}} & \paren {\frac {1} {49}} & \paren {\frac {1} {64}} & \cdots \\ \hline

\paren {\frac {1} {1}} & \paren {\frac {1} {1}} \paren {\frac {1} {1}} & \paren {\frac {1} {1}} \paren {\frac {1} {4}} & \paren {\frac {1} {1}} \paren {\frac {1} {9}} & \paren {\frac {1} {1}} \paren {\frac {1} {16}} & \paren {\frac {1} {1}} \paren {\frac {1} {25}} & \paren {\frac {1} {1}} \paren {\frac {1} {36}} & \paren {\frac {1} {1}} \paren {\frac {1} {49}} & \paren {\frac {1} {1}} \paren {\frac {1} {64}} & \cdots \\

\paren {\frac {1} {4}} & \paren {\frac {1} {4}} \paren {\frac {1} {1}} & \paren {\frac {1} {4}} \paren {\frac {1} {4}} & \paren {\frac {1} {4}} \paren {\frac {1} {9}} & \paren {\frac {1} {4}} \paren {\frac {1} {16}} & \paren {\frac {1} {4}} \paren {\frac {1} {25}} & \paren {\frac {1} {4}} \paren {\frac {1} {36}} & \paren {\frac {1} {4}} \paren {\frac {1} {49}} & \paren {\frac {1} {4}} \paren {\frac {1} {64}} & \cdots \\

\paren {\frac {1} {9}} & \paren {\frac {1} {9}} \paren {\frac {1} {1}} & \paren {\frac {1} {9}} \paren {\frac {1} {4}} & \paren {\frac {1} {9}} \paren {\frac {1} {9}} & \paren {\frac {1} {9}} \paren {\frac {1} {16}} & \paren {\frac {1} {9}} \paren {\frac {1} {25}} & \paren {\frac {1} {9}} \paren {\frac {1} {36}} & \paren {\frac {1} {9}} \paren {\frac {1} {49}} & \paren {\frac {1} {9}} \paren {\frac {1} {64}} & \cdots \\

\paren {\frac {1} {16}} & \paren {\frac {1} {16}} \paren {\frac {1} {1}} & \paren {\frac {1} {16}} \paren {\frac {1} {4}} & \paren {\frac {1} {16}} \paren {\frac {1} {9}} & \paren {\frac {1} {16}} \paren {\frac {1} {16}} & \paren {\frac {1} {16}} \paren {\frac {1} {25}} & \paren {\frac {1} {16}} \paren {\frac {1} {36}} & \paren {\frac {1} {16}} \paren {\frac {1} {49}} & \paren {\frac {1} {16}} \paren {\frac {1} {64}} & \cdots \\

\paren {\frac {1} {25}} & \paren {\frac {1} {25}} \paren {\frac {1} {1}} & \paren {\frac {1} {25}} \paren {\frac {1} {4}} & \paren {\frac {1} {25}} \paren {\frac {1} {9}} & \paren {\frac {1} {25}} \paren {\frac {1} {16}} & \paren {\frac {1} {25}} \paren {\frac {1} {25}} & \paren {\frac {1} {25}} \paren {\frac {1} {36}} & \paren {\frac {1} {25}} \paren {\frac {1} {49}} & \paren {\frac {1} {25}} \paren {\frac {1} {64}} & \cdots \\

\paren {\frac {1} {36}} & \paren {\frac {1} {36}} \paren {\frac {1} {1}} & \paren {\frac {1} {36}} \paren {\frac {1} {4}} & \paren {\frac {1} {36}} \paren {\frac {1} {9}} & \paren {\frac {1} {36}} \paren {\frac {1} {16}} & \paren {\frac {1} {36}} \paren {\frac {1} {25}} & \paren {\frac {1} {36}} \paren {\frac {1} {36}} & \paren {\frac {1} {36}} \paren {\frac {1} {49}} & \paren {\frac {1} {36}} \paren {\frac {1} {64}} & \cdots \\

\paren {\frac {1} {49}} & \paren {\frac {1} {49}} \paren {\frac {1} {1}} & \paren {\frac {1} {49}} \paren {\frac {1} {4}} & \paren {\frac {1} {49}} \paren {\frac {1} {9}} & \paren {\frac {1} {49}} \paren {\frac {1} {16}} & \paren {\frac {1} {49}} \paren {\frac {1} {25}} & \paren {\frac {1} {49}} \paren {\frac {1} {36}} & \paren {\frac {1} {49}} \paren {\frac {1} {49}} & \paren {\frac {1} {49}} \paren {\frac {1} {64}} & \cdots \\

\paren {\frac {1} {64}} & \paren {\frac {1} {64}} \paren {\frac {1} {1}} & \paren {\frac {1} {64}} \paren {\frac {1} {4}} & \paren {\frac {1} {64}} \paren {\frac {1} {9}} & \paren {\frac {1} {64}} \paren {\frac {1} {16}} & \paren {\frac {1} {64}} \paren {\frac {1} {25}} & \paren {\frac {1} {64}} \paren {\frac {1} {36}} & \paren {\frac {1} {64}} \paren {\frac {1} {49}} & \paren {\frac {1} {64}} \paren {\frac {1} {64}} & \cdots \\

\cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots \\

\end{array}$