# Properties

 Label 1110.bm Modulus $1110$ Conductor $555$ Order $12$ Real no Primitive no Minimal yes Parity odd

# Learn more about

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

sage: H = DirichletGroup(1110, base_ring=CyclotomicField(12))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([6,9,5]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(23,1110))

pari: order = charorder(g,chi)

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

## Basic properties

 Modulus: $$1110$$ Conductor: $$555$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$12$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 555.be sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Related number fields

 Field of values: $$\Q(\zeta_{12})$$ Fixed field: 12.0.253324113822708283353515625.2

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$41$$ $$43$$
$$\chi_{1110}(23,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$1$$ $$-i$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$
$$\chi_{1110}(347,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$1$$ $$i$$ $$i$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$
$$\chi_{1110}(563,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$1$$ $$-i$$ $$-i$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$
$$\chi_{1110}(917,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$1$$ $$i$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$