I gave my talk on our project to a packed room... and it went very
well. There were a billion questions, many of which I couldn't
answer -- I've probably never said "I don't know" so many times in a
talk before! But that's fine. (Many questions would have been
easier to answer if I fully understood Sarnak's letter...) Some of
the questions were exactly things we already plan to do, e.g., to
apply random matrix heuristics and see what we get (one of Jordan
Ellenberg's questions). Tonghai Yang was very interested in the CM
case. People wanted to know *how* we compute the zeros -- I can only
say "by using Rubinstein's code". Robert Heron pointed out that in
our formula for the raw mean the term outside the sum *is* what would
be in the sum if we started the sum at k=0 instead of k=1. Right
when I wrote down the formula for the raw mean, Jordan instantly asked
if we could reverse engineer it to 'deduce' something about
exceptional zeros, so it's a natural question.
Soroosh Yazdani plans to give a version of our talk at his department
("Lethbridge"), and I'll share our write-up with him.