Frank Calegari Point counts IMU lecture

https://www.youtube.com/watch?v=L0Z4Ng6ZJbY

"Mathematica:"
(*start*)
Clear[n, k];
nn = 45;
LeftHandSide = n^2;
RightHandSide = 2;
TableForm[{Table[
   Count[Table[Mod[LeftHandSide, Prime[k]], {n, 1, Prime[k]}],
    RightHandSide], {k, 1, nn}],
  Table[Prime[k], {k, 1, nn}]}]
Table[Count[Table[Mod[LeftHandSide, Prime[k]], {n, 1, Prime[k]}],
  RightHandSide], {k, 1, nn}]
(*end*)

0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, \
2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0