Murmurations of L-functions of generic genus 2 curves over Q ordered by conductor

Each blue/red dot at (p,a_p) records the average of a_p(X) over genus 2 curves X/Q with Sato-Tate group USp(4) whose L-functions have root number w(X)=+1/-1 with conductor in a varying dyadic interval.

Each purple dot at (p,a_p) records the average of w(X)a_p(X) over genus 2 curves X/Q with Sato-Tate group USp(4) and conductor in a varying dyadic interval.

Each purple dot at (p,a_p) records the average of w(X)a_p(X) over genus 2 curves X/Q with Sato-Tate group USp(4) and conductor in a varying dyadic interval. The green line shows a least squares fit using a piecewise polynomial function.