An entry in row \( k \) and column \( n \) of the table below is an element of \( H_n( \underline{\mathrm{H}\mathbb{F}}_k ; \mathbb{F}_2) \), where \( \underline{\mathrm{H}\mathbb{F}}_k = K(\mathbb{Z}/2,k) \) denotes the \(k\)th space in the mod 2 Eilenberg-Mac Lane spectrum. Only some \(*\)-indecomposable elements are shown. Juxtaposition and exponentiation denote circle products (\( xy = x \circ y\) and \(x^n = x \circ x \circ \cdots x\) with \( n \) factors).