Galois invariant of Tate twists

Question

let $k$ be the maximal extension of $\mathbb{Q}$ unramified outside a set $T$ of primes in $\mathbb{Z}$. Take a $p\in T$ and set $G=Gal(k/\mathbb{Q})$. I would like to now if there is a classical result in order to compute the cohomology group $H^0(G,\mathbb{Q}_p(n))$ for $n\geq 1$?