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             SALEM 14  


		Salem number 1.2000265239873915189 of degree 14

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

		Primes and Twists

Feasible Primes: {5, 13, 19, 41}
                     2      3      4    5    6
Prime 5^6  <-  (1 + x  + 3 x  + 4 x  + x  + x ), inert in K
Prime 5^1  <-  (4 + x), inert in K
                              2    3    4
Prime 13^4  <-  (2 + 7 x + 4 x  + x  + x ), splits in K
                            2
Prime 13^2  <-  (2 + 9 x + x ), inert in K
Prime 13^1  <-  (3 + x), inert in K
                              2
Prime 19^2  <-  (15 + 10 x + x ), inert in K
                           2
Prime 19^2  <-  (14 + x + x ), splits in K
                              2
Prime 19^2  <-  (13 + 11 x + x ), inert in K
Prime 19^1  <-  (16 + x), splits in K
                                2    3
Prime 41^3  <-  (19 + 33 x + 9 x  + x ), splits in K
                                 2    3
Prime 41^3  <-  (18 + 23 x + 35 x  + x ), splits in K
Prime 41^1  <-  (38 + x), splits in K
All twists:  those with dim'n small enough: 9
All twists:  those with period small enough: 6
All twists:  those with right signature: 3
Twists found: 3
Obstruction found after 22669 trials
Ideal 5          Periods {6}            Min 2  OBSTRUCTED
Obstruction found after 21561 trials
Ideal 13         Periods {7}            Min 2  OBSTRUCTED
Ideal 5 19       Periods {6, 9}         Min 4  


             Obstruction over 5x19:  

Glue group {5, 5, 19, 19}, Signature {5, 9}, lambda = 1.20003
                3    4    7    10    11    14
Char poly  1 - x  - x  + x  - x   - x   + x
                              2
Localization at 5: 1 + 4 x + x
Localization at 19: (3 + x) (13 + x)
                                                               2
At prime 5 : Glue group {5, 5}, Period 6, Char poly 1 + 4 x + x
                 q = 1/5 * 1   2   f = 1   4

                           2   1       1   0
At prime 19 : Glue group {19, 19}, Period 9, Char poly (3 + x) (13 + x)
                 q = 1/19 * 17   3    f = 3    18

                            3    17       1    0
Glue group {3, 5, 5}, Signature {2, 0}

Positivity verified.  Cyclic: 10 Fixed: Infinity
                    2
Char poly  1 - x + x   Period 1
Localization at 3: 1 + x
                              2
Localization at 5: 1 + 4 x + x
Glue group {3, 19, 19}, Signature {4, 2}, lambda = 1.
                3    6
Char poly  1 + x  + x   Period 1
Localization at 3: 2 + x
Localization at 19: (14 + x) (15 + x)
Gluing is impossible because of different actions mod 3

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