Mathematica 8.0 for Mac OS X x86 (64-bit)
Copyright 1988-2011 Wolfram Research, Inc.

In[1]:= 

             SALEM 6

		Picard group 
Glue group {3, 3, 3, 3, 3, 3, 13}, Signature {9, 1}, lambda 1.40127

Positivity verified.  Crossing: 4 Cyclic: 4 Fixed: 2
                   2           2        2    3    4    6
Char poly  (-1 + x)  (1 + x + x ) (1 - x  - x  - x  + x )
                             2    3                2    3
Localization at 3: (2 + x + x  + x ) (2 + 2 x + 2 x  + x )
Localization at 13: 12 + x

		Transcendental cycles
Glue group {3, 3, 3, 3, 3, 3, 13}, Signature {10, 2}, lambda = 1.
                    2    3    4    5    6    7    8    9    10    11    12
Char poly  1 + x + x  + x  + x  + x  + x  + x  + x  + x  + x   + x   + x
 
>     Period 1
                             2    3                2    3
Localization at 3: (2 + x + x  + x ) (2 + 2 x + 2 x  + x )
Localization at 13: 12 + x
Rotation of T(X): 1/13

		Periodic factor of Pic
Glue group {2, 2, 13}, Signature {4, 0}

Positivity verified.  Cyclic: 4 Fixed: 2
                   2           2
Char poly  (-1 + x)  (1 + x + x )  Period 1
                            2
Localization at 2: 1 + x + x
Localization at 13: 12 + x

		Salem factor of Pic
Glue group {2, 2, 3, 3, 3, 3, 3, 3}, Signature {5, 1}, lambda 1.40127

Positivity verified.  Crossing: 6 Cyclic: Infinity Fixed: Infinity
                2    3    4    6
Char poly  1 - x  - x  - x  + x
                            2
Localization at 2: 1 + x + x
                             2    3                2    3
Localization at 3: (2 + x + x  + x ) (2 + 2 x + 2 x  + x )

		Field Information
A/Z[x], h(K), B/Z[y], h(k), Ramif: {1, 1, 1, 1, 1}

In[2]:= 