How I learned to stop worrying and love the

Using our -series, and in fact using any -series one can define the notion of a function that is very similar to , except that it has more symmetries. It is defined as follows:

Where is the conductor of the curve and is the complete function evaluated at .

However, when only considering those -series that come from elliptic curves the associated -series obeys the following symmetry:

where is the root number of (which can be found using ellrootno in PARI). Because of this symmetry, the graphs of can look ``nicer'' then those of and in the graphs below we produce graphs of both and for this reason.