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In[1]:=  			SALEM 12:  Twisting at 31
                                        2       3      5
Fixing signature; twist is 1 + 6 x - 2 x  - 13 x  + 3 x
Salem part: 
At prime 7 : Glue group {7}, Period 2, Char poly 1 + x
                 q = 1/7 * 1   f = 6
Gluing to cyclotomic of order 30
Cyclo part: 
Glue group {31, 31}, Signature {8, 0}

Positivity verified.  Cyclic: 4 Fixed: Infinity
                    3    4    5    7    8
Char poly  1 + x - x  - x  - x  + x  + x   Period 1
Localization at 31: (7 + x) (9 + x)

 Result of gluing Salem + cyclo:
Glue group {7}, Signature {19, 1}, lambda 1.24073

* * * * POSITIVITY FAILED:  Obstructing root 
 
>   {0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 1, 1, -1, 0}
                     3    4    5    7    8
Char poly  (1 + x - x  - x  - x  + x  + x ) 
 
               2    3    6    9    10    11    12
>    (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 {7}, Signature {19, 1}, lambda 1.24073

* * * * POSITIVITY FAILED:  Obstructing root 
 
>   {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0}
                     3    4    5    7    8
Char poly  (1 + x - x  - x  - x  + x  + x ) 
 
               2    3    6    9    10    11    12
>    (1 - x + x  - x  - x  - x  + x   - x   + x  )
Localization at 7: 1 + x

		Transcendental cycles
Glue group {7}, Signature {0, 2}, lambda = 1.
Char poly  (-1 + x) (1 + x)  Period 2
Localization at 7: 1 + x
Rotation of T(X): 1/2

		Periodic factor of Pic
Glue group {31, 31}, Signature {8, 0}

Positivity verified.  Cyclic: 4 Fixed: Infinity
                    3    4    5    7    8
Char poly  1 + x - x  - x  - x  + x  + x   Period 1
Localization at 31: (7 + x) (9 + x)

		Salem factor of Pic
Glue group {7, 31, 31}, 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 31: (7 + x) (9 + x)

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

In[2]:= 