# Properties

 Label 3584.545 Modulus $3584$ Conductor $448$ Order $16$ Real no Primitive no Minimal no Parity odd

# Related objects

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3584, base_ring=CyclotomicField(16))

M = H._module

chi = DirichletCharacter(H, M([0,15,8]))

pari: [g,chi] = znchar(Mod(545,3584))

## Basic properties

 Modulus: $$3584$$ Conductor: $$448$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$16$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{448}(13,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 3584.bf

sage: chi.galois_orbit()

order = charorder(g,chi)

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

## Related number fields

 Field of values: $$\Q(\zeta_{16})$$ Fixed field: 16.0.3484608386920116940487669055488.4

## Values on generators

$$(1023,1541,1025)$$ → $$(1,e\left(\frac{15}{16}\right),-1)$$

## First values

 $$a$$ $$-1$$ $$1$$ $$3$$ $$5$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$19$$ $$23$$ $$25$$ $$\chi_{ 3584 }(545, a)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 3584 }(545,a) \;$$ at $$\;a =$$ e.g. 2