# Properties

 Label 4830.659 Modulus $4830$ Conductor $345$ Order $22$ Real no Primitive no Minimal yes Parity even

# Related objects

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

sage: H = DirichletGroup(4830, base_ring=CyclotomicField(22))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([11,11,0,17]))

pari: [g,chi] = znchar(Mod(659,4830))

## Basic properties

 Modulus: $$4830$$ Conductor: $$345$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$22$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{345}(314,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 4830.cd

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: $$\Q(\zeta_{11})$$ Fixed field: 22.22.341419566026798986253349758444608447265625.1

## Values on generators

$$(3221,967,2761,1891)$$ → $$(-1,-1,1,e\left(\frac{17}{22}\right))$$

## Values

 $$-1$$ $$1$$ $$11$$ $$13$$ $$17$$ $$19$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$ $$47$$ $$1$$ $$1$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$1$$
sage: chi.jacobi_sum(n)

$$\chi_{ 4830 }(659,a) \;$$ at $$\;a =$$ e.g. 2