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Properties

Modulus $16$
Structure \(C_{2}\times C_{4}\)
Order $8$

Learn more

Show commands: Pari/GP / SageMath

Copy content sage:H = DirichletGroup(16)
 
Copy content pari:g = idealstar(,16,2)
 

Character group

Copy content sage:G.order()
 
Copy content pari:g.no
 
Order = 8
Copy content sage:H.invariants()
 
Copy content pari:g.cyc
 
Structure = \(C_{2}\times C_{4}\)
Copy content sage:H.gens()
 
Copy content pari:g.gen
 
Generators = $\chi_{16}(15,\cdot)$, $\chi_{16}(5,\cdot)$

Characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character Orbit Order Primitive \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\)
\(\chi_{16}(1,\cdot)\) 16.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{16}(3,\cdot)\) 16.f 4 yes \(-1\) \(1\) \(-i\) \(-i\) \(1\) \(-1\) \(i\) \(i\)
\(\chi_{16}(5,\cdot)\) 16.e 4 yes \(1\) \(1\) \(-i\) \(i\) \(-1\) \(-1\) \(i\) \(-i\)
\(\chi_{16}(7,\cdot)\) 16.d 2 no \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\)
\(\chi_{16}(9,\cdot)\) 16.b 2 no \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\)
\(\chi_{16}(11,\cdot)\) 16.f 4 yes \(-1\) \(1\) \(i\) \(i\) \(1\) \(-1\) \(-i\) \(-i\)
\(\chi_{16}(13,\cdot)\) 16.e 4 yes \(1\) \(1\) \(i\) \(-i\) \(-1\) \(-1\) \(-i\) \(i\)
\(\chi_{16}(15,\cdot)\) 16.c 2 no \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\)