# Properties

 Modulus 1169 Conductor 7 Order 3 Real no Primitive no Minimal yes Parity even Orbit label 1169.e

# Related objects

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([2,0]))

pari: [g,chi] = znchar(Mod(669,1169))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Modulus = 1169 Conductor = 7 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 3 Real = no sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = no Minimal = yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = even Orbit label = 1169.e Orbit index = 5

## 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 ]

## Values on generators

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

## Values

 -1 1 2 3 4 5 6 8 9 10 11 12 $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$
value at  e.g. 2

## Related number fields

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