# Properties

 Modulus 6017 Conductor 6017 Order 42 Real no Primitive yes Minimal yes Parity even Orbit label 6017.bd

# Related objects

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

sage: H = DirichletGroup(6017)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([21,31]))

pari: [g,chi] = znchar(Mod(3651,6017))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Modulus = 6017 Conductor = 6017 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 = yes Minimal = yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = even Orbit label = 6017.bd Orbit index = 30

## 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

$$(3830,2190)$$ → $$(-1,e\left(\frac{31}{42}\right))$$

## Values

 -1 1 2 3 4 5 6 7 8 9 10 12 $$1$$ $$1$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{5}{42}\right)$$
value at  e.g. 2

## Related number fields

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