# Properties

 Label 3332.bp Modulus $3332$ Conductor $476$ Order $24$ Real no Primitive no Minimal no Parity odd

# Related objects

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

H = DirichletGroup(3332, base_ring=CyclotomicField(24))

M = H._module

chi = DirichletCharacter(H, M([12,16,15]))

chi.galois_orbit()

[g,chi] = znchar(Mod(263,3332))

order = charorder(g,chi)

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

## Basic properties

 Modulus: $$3332$$ Conductor: $$476$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$24$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 476.bg 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: $$\Q(\zeta_{24})$$ Fixed field: Number field defined by a degree 24 polynomial

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$3$$ $$5$$ $$9$$ $$11$$ $$13$$ $$15$$ $$19$$ $$23$$ $$25$$ $$27$$
$$\chi_{3332}(263,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{3332}(655,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{3332}(1243,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{3332}(1647,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{8}\right)$$
$$\chi_{3332}(2235,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{3332}(2627,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{3332}(3007,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{8}\right)$$
$$\chi_{3332}(3215,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{8}\right)$$