# Properties

 Label 1792.bf Modulus $1792$ Conductor $448$ Order $16$ Real no Primitive no Minimal no Parity odd

# Related objects

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

sage: H = DirichletGroup(1792, base_ring=CyclotomicField(16))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,11,8]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(209,1792))

pari: order = charorder(g,chi)

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

## Basic properties

 Modulus: $$1792$$ 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 448.bf sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Related number fields

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

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$3$$ $$5$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$19$$ $$23$$ $$25$$
$$\chi_{1792}(209,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{1792}(433,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$i$$ $$i$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$
$$\chi_{1792}(657,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{1792}(881,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$i$$ $$i$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{1792}(1105,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{1792}(1329,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$i$$ $$i$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$
$$\chi_{1792}(1553,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{1792}(1777,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$i$$ $$i$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$