range (10 5 < T < 10 30 ). Firstly, it is observed that there is extended mesoscale structure surrounding the

large peaks of the L-function on the line S=1+i*T reflecting closely the product function of (i) a truncated

Riemann Zeta function near the real axis with (ii) simple Euler factor type terms arising from the absent

lower modulo primes of the L-function. A second self-similarity pattern mimicking a version of the L-function

near the real axis (S=1) occurs around points known to correspond to large Riemann Zeta function peaks.

Following previous work, simple expressions are provided to approximate the known lower bound height and

local structure of the self-similarity features about large 1st degree L-function peaks for σ ≥ 1.}, publisher={figshare}, author={Martin, John}, year={2020}, month={Nov} }