Properties

 Label 1110.t Modulus $1110$ Conductor $37$ Order $4$ 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(1110, base_ring=CyclotomicField(4))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,0,1]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(31,1110))

pari: order = charorder(g,chi)

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

Basic properties

 Modulus: $$1110$$ Conductor: $$37$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$4$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 37.d 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: $$\Q(\sqrt{-1})$$ Fixed field: 4.0.50653.1

Characters in Galois orbit

Character $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$41$$ $$43$$
$$\chi_{1110}(31,\cdot)$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-i$$ $$-i$$ $$-i$$ $$-i$$ $$i$$ $$i$$ $$-1$$ $$-i$$
$$\chi_{1110}(931,\cdot)$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$i$$ $$i$$ $$i$$ $$i$$ $$-i$$ $$-i$$ $$-1$$ $$i$$