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             LEHMER'S NUMBER - two prime approach

Twisting Salem by -2 x^4-x^3+8 x^2+4 x
Twisting Cyclo by -2 x-1

		Picard group 
Glue group {7, 13, 13}, Signature {15, 1}, lambda 1.17628

Positivity verified.  Crossing: 4 Cyclic: 4 Fixed: 2
                   2        2       2
Char poly  (-1 + x)  (1 + x)  (1 + x ) 
 
               3    4    5    6    7    9    10
>    (1 + x - x  - x  - x  - x  - x  + x  + x  )
Localization at 7: 1 + x
                               2
Localization at 13: 1 + 7 x + x

		Transcendental cycles
Glue group {7, 13, 13}, Signature {4, 2}, lambda = 1.
                    2    3    4    5    6
Char poly  1 - x + x  - x  + x  - x  + x   Period 1
Localization at 7: 1 + x
                               2
Localization at 13: 1 + 7 x + x
Rotation of T(X): 1/14

		Periodic factor of Pic
Glue group {3, 3, 7}, Signature {6, 0}

Positivity verified.  Cyclic: 4 Fixed: 2
                   2        2       2
Char poly  (-1 + x)  (1 + x)  (1 + x )  Period 4
                        2
Localization at 3: 1 + x
Localization at 7: 1 + x

		Salem factor of Pic
Glue group {3, 3, 13, 13}, Signature {9, 1}, lambda 1.17628

Positivity verified.  Crossing: 4 Cyclic: Infinity Fixed: Infinity
                    3    4    5    6    7    9    10
Char poly  1 + x - x  - x  - x  - x  - x  + x  + x
                        2
Localization at 3: 1 + x
                               2
Localization at 13: 1 + 7 x + x

		Field Information
A/Z[x], h(K), B/Z[y], h(k), Ramif: {1, 1, 1, 1, 1}
                    2    3      4
Twisted by 4 x + 8 x  - x  - 2 x
Prime 3^1  <-  (x), inert in K
Prime 13^1  <-  (7 + x), inert in K

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