Let $\zeta_n = e^{i2\pi/n}$. What is the group of all units in the cyclotomic field $\mathbb{Q}[\zeta_n]$?

Here I like to know all the group elements for small $n$'s. For $n=1$ and $n=2$, the group is given by $\{1,-1\}$. For $n=3$, the group appears to be $\{\pm 1,\pm \zeta_3, \pm \zeta_3^2\}$. For $n=4$, the group is $\{\pm 1,\pm \zeta_4\}$. What are the groups for larger $n$?

Let $\zeta_n = e^{i2\pi/n}$. What is the group of all units in the integral cyclotomic ring $\mathbb{Z}[\zeta_n]$?

Here I like to know all the group elements for small $n$'s. For $n=1$ and $n=2$, the group is given by $\{1,-1\}$. For $n=3$, the group appears to be $\{\pm 1,\pm \zeta_3, \pm \zeta_3^2\}$. For $n=4$, the group is $\{\pm 1,\pm \zeta_4\}$. What are the groups for larger $n$?