number theory – Show that 2020 divides $pleft( n right)$ for every integer $n$

Consider:
$$pleft( n right)=800n+400{{n}^{2}}+400{{n}^{4}}+200{{n}^{5}}+100{{n}^{10}}+100{{n}^{20}}+8{{n}^{101}}+4{{n}^{202}}+4{{n}^{404}}+2{{n}^{505}}+{{n}^{1010}}+{{n}^{2020}}$$
Show that: $2020$ divides $pleft( n right)$ for every positive integer $n$?

Work: the statement is indeed true for $n=1,2..100$ , of course using a computer!!