Done in SymPy. General formula is
$$\chi^{(2)}_{(\ell n m)_{\text{curv}}}= R_{\ell i} R_{n j} R_{m k} \chi^{(2)}_{(ijk)_{\text{cart}}}$$
where rotation matrix $\hat{R}$ is defined as
$$\mathbf{A}^{\text{curv}} = \hat{R}^{-1} \mathbf{A}^{\text{cart}}$$