# Properties

 Label 2880.367 Modulus $2880$ Conductor $720$ Order $12$ Real no Primitive no Minimal no Parity even

# Related objects

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

sage: H = DirichletGroup(2880, base_ring=CyclotomicField(12))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([6,9,8,3]))

pari: [g,chi] = znchar(Mod(367,2880))

## Basic properties

 Modulus: $$2880$$ Conductor: $$720$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$12$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{720}(547,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 2880.df

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: $$\Q(\zeta_{12})$$ Fixed field: 12.12.722204136308736000000000.1

## Values on generators

$$(2431,901,641,577)$$ → $$(-1,-i,e\left(\frac{2}{3}\right),i)$$

## Values

 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$i$$ $$i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$
 value at e.g. 2