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In[1]:=  			SALEM 12:  Twisting at 13
                                        2       3      5
Fixing signature; twist is 2 + 7 x - 3 x  - 17 x  + 4 x
Salem part: 
At prime 7 : Glue group {7}, Period 2, Char poly 1 + x
                 q = 1/7 * 4   f = 6
Gluing to cyclotomic of order 12
Cyclo part: 
Glue group {13, 13}, Signature {2, 2}, lambda = 1.
                2    4
Char poly  1 - x  + x   Period 1
Localization at 13: (2 + x) (7 + x)

 Result of gluing Salem + cyclo:
Glue group {7}, Signature {13, 3}, lambda = 1.24073
                 2    4            2    3    6    9    10    11    12
Char poly  (1 - x  + x ) (1 - x + x  - x  - x  - x  + x   - x   + x  )
Localization at 7: 1 + x
At prime 7 : Glue group {7}, Period 2, Char poly 1 + x
                 q = 1/7 * 1   f = 6

		Picard group 
Glue group {13, 13}, Signature {17, 1}, lambda 1.24073

* * * * POSITIVITY FAILED:  Cyclic root {1, 1, -1, 0, 1, 0}
                  6           2    3    6    9    10    11    12
Char poly  (1 + x)  (1 - x + x  - x  - x  - x  + x   - x   + x  )
Localization at 13: (2 + x) (7 + x)

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

		Periodic factor of Pic
Glue group {7}, Signature {6, 0}

* * * * POSITIVITY FAILED:  Cyclic root {1, 1, -1, 0, 1, 0}
                  6
Char poly  (1 + x)   Period 2
Localization at 7: 1 + x

		Salem factor of Pic
Glue group {7, 13, 13}, Signature {11, 1}, lambda 1.24073

Positivity verified.  Crossing: 4 Cyclic: Infinity Fixed: Infinity
                    2    3    6    9    10    11    12
Char poly  1 - x + x  - x  - x  - x  + x   - x   + x
Localization at 7: 1 + x
Localization at 13: (2 + x) (7 + x)

		Field Information
A/Z[x], h(K), B/Z[y], h(k), Ramif: {1, 1, 1, 1, -7}

In[2]:= 