As part of a project in a quantum computing course we were asked to classically simulate the quantum phase estimation algorithm, which has inverse QFT as one of its components. On the Wikipedia page of QFT, the quantum circuit implementation presented uses a controlled version of the phase gate $$R_N = \begin{pmatrix}1 & 0\\ 0 & \omega_{N} \end{pmatrix}$$ with $\omega_N=e^{2\pi i/N}$. However, in the instructions of the project we are instructed to only use the single-qubit gates in the set $\{X,Z,S,T,H\}$, the 2-qubit gates $\{CNOT,SWAP\}$ and the 3-qubit Toffoli gate.
My question is - is there a way to construct a circuit that calculates controlled-$R_N$ using only the given gates?