What is the Fourier series expansion of the $e^{-2i\pi ax}, x\in(0, 1)$ and $a\in\mathbb{R}$

Question

I am trying to find the Fourier series of the function $f(x)=e^{-2i\pi ax}$, over the interval $(0,1)$ and $a\in\mathbb{R}$. As we know the Fourier series $$f(x)=\sum\limits_{n\in\mathbb{Z}}c_ne^{2i\pi nx/T}$$ First I tried to find the Fourier coefficient $C_n$ of the function. The period $T$ of the function $f(x)$ is $1/a$. So $c_n=\frac{1}{T}\int\limits_{0}^{T}e^{-2i\pi ax}e^{-2i\pi nx/T}dx=a\int\limits_{0}^\frac{1}{a}e^{-2i\pi ax(n+1)} dx.$ but after integration, I am getting $c_n =0$. Did I understand something wrong? I do not know why I am getting my Fourier coefficient as zero.