Murmurations of L-functions of products of elliptic curves over Q ordered by conductor

Each blue/red dot at (p,a_p) records the average of a_p(A) over abelian surfaces isogenous to a product of non-CM elliptic curves over Q whose L-functions have root number w(A)=+1/-1 with the conductor of A in a varying dyadic interval.

Each purple dot at (p,a_p) records the average of w(A)a_p(A) over abelian surfaces isogenous to a product of non-CM elliptic curves with the conductor of A in a varying dyadic interval.

Each purple dot at (p,a_p) records the average of w(A)a_p(A) over abelian surfaces isogenous to a product of non-CM elliptic curves with the conductor of A in a varying dyadic interval. The green line shows a least squares fit using a piecewise polynomial function.