# Properties

 Modulus 4410 Conductor 735 Order 42 Real no Primitive no Minimal yes Parity even Orbit label 4410.dc

# Related objects

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

sage: H = DirichletGroup(4410)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([21,21,23]))

pari: [g,chi] = znchar(Mod(89,4410))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Modulus = 4410 Conductor = 735 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 42 Real = no sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = no Minimal = yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = even Orbit label = 4410.dc Orbit index = 81

## Galois orbit

sage: chi.galois_orbit()

pari: order = charorder(g,chi)

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

## Values on generators

$$(3431,2647,1081)$$ → $$(-1,-1,e\left(\frac{23}{42}\right))$$

## Values

 -1 1 11 13 17 19 23 29 31 37 41 43 $$1$$ $$1$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{21})$$