# Properties

 Label 2268.163 Modulus $2268$ Conductor $28$ Order $6$ Real no Primitive no Minimal yes Parity odd

# Related objects

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter

sage: H = DirichletGroup(2268, base_ring=CyclotomicField(6))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([3,0,2]))

pari: [g,chi] = znchar(Mod(163,2268))

## Basic properties

 Modulus: $$2268$$ Conductor: $$28$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$6$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{28}(23,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 2268.y

sage: chi.galois_orbit()

pari: order = charorder(g,chi)

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

## Related number fields

 Field of values: $$\Q(\sqrt{-3})$$ Fixed field: 6.0.153664.1

## Values on generators

$$(1135,1541,325)$$ → $$(-1,1,e\left(\frac{1}{3}\right))$$

## Values

 $$-1$$ $$1$$ $$5$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$ $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$
 value at e.g. 2