# Properties

 Conductor 1 Order 1 Real Yes Primitive No Parity Even

# Related objects

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(88400)
sage: chi = H[1]
pari: [g,chi] = znchar(Mod(1,88400))

## Basic properties

 sage: chi.conductor() pari: znconreyconductor(g,chi) Conductor = 1 sage: chi.multiplicative_order() pari: charorder(g,chi) Order = 1 Real = Yes sage: chi.is_primitive() pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = No sage: chi.is_odd() pari: zncharisodd(g,chi) Parity = Even

## Galois orbit

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

## Inducingprimitive character

sage: chi.primitive_character()
pari: znconreyconductor(g,chi,&chi0)
pari: chi0

## Values on generators

sage: chi(k) for k in H.gens()
pari: [ chareval(g,chi,x) | x <- g.gen ] \\ value in Q/Z

$$(40177,33457,64193,22101,33151)$$ → $$(1,1,1,1,1)$$

## First values

 1 3 7 9 11 19 21 23 27 29 31 33 37 41 43 47 49 53 57 59 61 63 67 69 71 73 77 79 81 83 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
value at  e.g. 2

## Related number fields

 Field of values $$\Q$$