Properties

Modulus $10$
Structure \(C_{4}\)
Order $4$

Learn more

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(10)
 
pari: g = idealstar(,10,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 4
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{4}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{10}(7,\cdot)$

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 \(-1\) \(1\) \(3\) \(7\)
\(\chi_{10}(1,\cdot)\) 10.a 1 no \(1\) \(1\) \(1\) \(1\)
\(\chi_{10}(3,\cdot)\) 10.c 4 no \(-1\) \(1\) \(i\) \(-i\)
\(\chi_{10}(7,\cdot)\) 10.c 4 no \(-1\) \(1\) \(-i\) \(i\)
\(\chi_{10}(9,\cdot)\) 10.b 2 no \(1\) \(1\) \(-1\) \(-1\)