[[This is a sample data directory created as a followup to the
design group meeting.]]

Maass forms and eigenvalues of the Laplacian for Hecke congruence groups

David Farmer and Stefan Lemurell
2000 and 2001
Mathematica on a PC running Linux

Cite this data as  [[need a format for referencing this project]]

Data is made avaiable under the Creative Commons License
Attribution-NonCommercial-ShareAlike 3.0
http://creativecommons.org/licenses/by-nc-sa/3.0/

The file  eigsNx.txt, where N is an integer (padded with initial zeros)
and  x  is "e" or "o", contains the initial "even"  or  "odd" 
newform eigenvalues for the Hecke congruence group $\Gamma_0(N)$.
The format of the file is

R	 s
(tab separated)

where  R  is the eigenvalue  and s  is a string of +  or  -.
There are  $\nu(N)$   +'s or -'s, where $\nu(N)$ is the number
of distinct prime divisors of $N$, and  +/- refers to the
eigenvalues under the Atkin-Lehner involutions.  (Note that the
eigenvalue of the Fricke involution, which determines the sign in
the functional equation of the associated L-function, is the product
of the Atkin-Lehner eigenvalues).

For level 1 we omit the +/- because it is always +.

The file firsteigs107.txt gives the first eigenvalue in each
symmetry type for $\Gamma_0(p)$ for prime level up to $p=107$.
The format is

p x y R

where
p  is the level
x is 0 for even forms and 1 for odd forms
y is the Fricke eigenvalue
R is the eigenvalue



Here "eigenvalue" refers to the number $R$, where the "real"
eigenvalue is  $\frac14 + R^2$.

We believe that all lists of eigenvalues are complete, meaning that
the list starts with the smallest eigenvallue of the particular
symmetry type and there are no missing eigenvalues in the range
covered by the data.

Note that some files interlace the different Fricke eigenvalues,
while others first list one sign, then the other.

We believe that the first 7 or 8 digits after the decimal point are
correct (or all but the last one or two, if fewer digits are given).

File list:

firsteigs107.txt
eigsNe.txt  for N=1,2,11,65-67,100
eigsNo.txt  for N=1,2,11,65-67,100