Properties

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

Learn more about

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(15)
 
pari: g = idealstar(,15,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 8
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{4}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{15}(7,\cdot)$, $\chi_{15}(11,\cdot)$

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.

orbit label 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 \(-1\) \(1\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\)