Properties

 Label 1110.31 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]))

pari: [g,chi] = znchar(Mod(31,1110))

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 $$\chi_{37}(31,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

Galois orbit 1110.t

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: $$\Q(\sqrt{-1})$$ Fixed field: 4.0.50653.1

Values on generators

$$(371,667,631)$$ → $$(1,1,i)$$

Values

 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$41$$ $$43$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-i$$ $$-i$$ $$-i$$ $$-i$$ $$i$$ $$i$$ $$-1$$ $$-i$$
 value at e.g. 2