Properties

Modulus 1169
Conductor 1169
Order 6
Real no
Primitive yes
Minimal yes
Parity odd
Orbit label 1169.f

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1169)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([4,3]))
 
pari: [g,chi] = znchar(Mod(333,1169))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 1169
Conductor = 1169
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 6
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = odd
Orbit label = 1169.f
Orbit index = 6

Galois orbit

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{1169}(333,\cdot)\) \(\chi_{1169}(667,\cdot)\)

Values on generators

\((836,673)\) → \((e\left(\frac{2}{3}\right),-1)\)

Values

-112345689101112
\(-1\)\(1\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{5}{6}\right)\)\(1\)\(1\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{1}{3}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{3})\)