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Properties

Modulus $15$
Structure \(C_{2}\times C_{4}\)
Order $8$

Learn more

Show commands: Pari/GP / SageMath

Copy content sage:H = DirichletGroup(15)
 
Copy content pari:g = idealstar(,15,2)
 

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 = $\chi_{15}(11,\cdot)$, $\chi_{15}(7,\cdot)$

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 \(-1\) \(1\) \(2\) \(4\) \(7\) \(8\) \(11\) \(13\)
\(\chi_{15}(1,\cdot)\) 15.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{15}(2,\cdot)\) 15.e 4 yes \(1\) \(1\) \(-i\) \(-1\) \(i\) \(i\) \(-1\) \(-i\)
\(\chi_{15}(4,\cdot)\) 15.b 2 no \(1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(1\) \(-1\)
\(\chi_{15}(7,\cdot)\) 15.f 4 no \(-1\) \(1\) \(i\) \(-1\) \(i\) \(-i\) \(1\) \(-i\)
\(\chi_{15}(8,\cdot)\) 15.e 4 yes \(1\) \(1\) \(i\) \(-1\) \(-i\) \(-i\) \(-1\) \(i\)
\(\chi_{15}(11,\cdot)\) 15.c 2 no \(-1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(1\)
\(\chi_{15}(13,\cdot)\) 15.f 4 no \(-1\) \(1\) \(-i\) \(-1\) \(-i\) \(i\) \(1\) \(i\)
\(\chi_{15}(14,\cdot)\) 15.d 2 yes \(-1\) \(1\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\)