Hi all, 

Happy new year! 

I am interested in trying to recreate a numerical experiment from the end 
of William Stein's talk on sato tate convergence 
<http://wstein.org/talks/20071016-convergence/>. 

The details are in this public sage worksheet 
<https://cloud.sagemath.com/projects/e1c3e3c5-3723-436b-bf8f-a3c09f35d685/files/2017-01-19%20R_E%20test%202.sagews>,
 
but the gist of my problem is that I have tried to calculate values of 
Stein's R_E(C) function, and am getting negative values for certain inputs. 
Stein immediately calculates the logarithm of these values, and after 
seeing this, surely I have made a mistake because the usual logarithm 
function is not defined for negative input (although I suppose Stein could 
have used the complex logarithm, but it doesn't look like that to me).

I would really love any advice on how I could move forward trying to run 
his experiments for myself. 

Further, in the spirit of the new year, I will include a neat factoid with 
my post, completely irrelevant from my problem: 

        2017 is the first integer whose cube root's first ten digits are 
unique: 
        2017^(1/3) = 12.63480759...

--Christian

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