# Properties

 Conductor 3004 Order 150 Real No Primitive Yes Parity Even Orbit Label 3004.y

# 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(3004)

sage: chi = H[223]

pari: [g,chi] = znchar(Mod(223,3004))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 3004 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 150 Real = No sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = Yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = Even Orbit label = 3004.y Orbit index = 25

## 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 ]

## Values on generators

$$(1503,1505)$$ → $$(-1,e\left(\frac{101}{150}\right))$$

## Values

 -1 1 3 5 7 9 11 13 15 17 19 21 $$1$$ $$1$$ $$e\left(\frac{13}{75}\right)$$ $$e\left(\frac{43}{75}\right)$$ $$e\left(\frac{21}{25}\right)$$ $$e\left(\frac{26}{75}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{4}{75}\right)$$ $$e\left(\frac{56}{75}\right)$$ $$e\left(\frac{79}{150}\right)$$ $$e\left(\frac{143}{150}\right)$$ $$e\left(\frac{1}{75}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{75})$$