# Properties

 Label 1840.459 Modulus $1840$ Conductor $1840$ Order $4$ Real no Primitive yes Minimal yes Parity even

# Related objects

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

sage: H = DirichletGroup(1840, base_ring=CyclotomicField(4))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([2,1,2,2]))

pari: [g,chi] = znchar(Mod(459,1840))

## Basic properties

 Modulus: $$1840$$ Conductor: $$1840$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$4$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1840.bj

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: 4.4.27084800.2

## Values on generators

$$(1151,1381,737,1201)$$ → $$(-1,i,-1,-1)$$

## Values

 $$-1$$ $$1$$ $$3$$ $$7$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$21$$ $$27$$ $$29$$ $$1$$ $$1$$ $$-i$$ $$1$$ $$-1$$ $$i$$ $$i$$ $$1$$ $$-i$$ $$-i$$ $$i$$ $$-i$$
 value at e.g. 2