# Properties

 Label 3267.838 Modulus $3267$ Conductor $11$ Order $10$ 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(3267, base_ring=CyclotomicField(10))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,1]))

pari: [g,chi] = znchar(Mod(838,3267))

## Basic properties

 Modulus: $$3267$$ Conductor: $$11$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$10$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{11}(2,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 3267.l

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: $$\Q(\zeta_{5})$$ Fixed field: $$\Q(\zeta_{11})$$

## Values on generators

$$(3026,244)$$ → $$(1,e\left(\frac{1}{10}\right))$$

## Values

 $$a$$ $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$7$$ $$8$$ $$10$$ $$13$$ $$14$$ $$16$$ $$17$$ $$\chi_{ 3267 }(838, a)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$-1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 3267 }(838,a) \;$$ at $$\;a =$$ e.g. 2