# Properties

 Label 1380.737 Modulus $1380$ Conductor $15$ Order $4$ Real no Primitive no Minimal yes Parity even

# Learn more

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

sage: H = DirichletGroup(1380, base_ring=CyclotomicField(4))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,2,1,0]))

pari: [g,chi] = znchar(Mod(737,1380))

## Basic properties

 Modulus: $$1380$$ Conductor: $$15$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$4$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{15}(2,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1380.r

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: $$\Q(\zeta_{15})^+$$

## Values on generators

$$(691,461,277,1201)$$ → $$(1,-1,i,1)$$

## Values

 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$ $$1$$ $$1$$ $$i$$ $$-1$$ $$-i$$ $$-i$$ $$-1$$ $$1$$ $$1$$ $$i$$ $$-1$$ $$-i$$
 value at e.g. 2