Weight spaces appearing in the first fundamental representation of $\frak{sl}_n$ Where can I find a table of the non-trivial weight spaces appearing in the first fundamental representation of $\frak{sl}_n$?

The fundamental representation with highest weight $\Lambda_1$ is the representation of $\mathfrak{sl}_n$ on $\mathbb{C}^{n-1}$. A weight basis is the standard basis $\{e_1,e_2,\ldots,e_{n-1}\}$ with $e_1$ the highest weight vector with weight $\Lambda_1$ ( $\langle \Lambda_1,\alpha_j\rangle = \delta_{1j}$).
Let $\{E_{ji}\mid 1\leq i< j\leq n-1\}$ be the standard basis of $\mathfrak{n}^-\subset\mathfrak{sl}_n$. Then, $E_{ji}$ is a basis for the $-(\alpha_i+\alpha_{i+1}+\cdots+\alpha_j)$-root space of $\mathfrak{n}^-$.
Note $E_{21}e_1=e_2$ has weight $\Lambda_1-\alpha_1$, $E_{31}e_1=e_3$ has weight $\Lambda_1-\alpha_1-\alpha_2$, and so on.
