Calculate the Chern classes $$ c_n \in H^{2n}(S^{2n})$$ for the generator of the group $$ K(S^{2n})$$ where $S^{2n} $ - sphere of dimension $ 2n $, $ K(S^{2n})$ - group from [K-theory][1].

I found the following fact about the K-group $$ K(S^0) = K(S^{2k})= \mathbb{Z} \times \mathbb{Z},\quad K(S^1) = K(S^{2k+1}) =\mathbb{Z} $$ How to calculate the Chern classes for sphere $S^{2n}$ if we know that $\eta$ is generator for $K(S^{2n})$? [1]: https://en.wikipedia.org/wiki/K-theory

Calculate the Chern classes $$ c_n \in H^{2n}(S^{2n})$$ for the generator of the group $$ K(S^{2n})$$ where $S^{2n} $ - sphere of dimension $ 2n $, $ K(S^{2n})$ - group from K-theory.

I found the following fact about the K-group $$ K(S^0) = K(S^{2k})= \mathbb{Z} \times \mathbb{Z},\quad K(S^1) = K(S^{2k+1}) =\mathbb{Z} $$ How to calculate the Chern classes for sphere $S^{2n}$ if we know that $\eta$ is generator for $K(S^{2n})$?