# Properties

 Label 3332.2787 Modulus $3332$ Conductor $3332$ Order $14$ Real no Primitive yes Minimal yes Parity odd

# Related objects

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

H = DirichletGroup(3332, base_ring=CyclotomicField(14))

M = H._module

chi = DirichletCharacter(H, M([7,2,7]))

pari: [g,chi] = znchar(Mod(2787,3332))

## Basic properties

 Modulus: $$3332$$ Conductor: $$3332$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$14$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 3332.be

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: $$\Q(\zeta_{7})$$ Fixed field: Number field defined by a degree 14 polynomial

## Values on generators

$$(1667,885,785)$$ → $$(-1,e\left(\frac{1}{7}\right),-1)$$

## First values

 $$a$$ $$-1$$ $$1$$ $$3$$ $$5$$ $$9$$ $$11$$ $$13$$ $$15$$ $$19$$ $$23$$ $$25$$ $$27$$ $$\chi_{ 3332 }(2787, a)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$-1$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 3332 }(2787,a) \;$$ at $$\;a =$$ e.g. 2