# Properties

 Label 1380.361 Modulus $1380$ Conductor $23$ Order $11$ 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(1380, base_ring=CyclotomicField(22))

sage: M = H._module

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

pari: [g,chi] = znchar(Mod(361,1380))

## Basic properties

 Modulus: $$1380$$ Conductor: $$23$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$11$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{23}(16,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1380.y

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: $$\Q(\zeta_{23})^+$$

## Values on generators

$$(691,461,277,1201)$$ → $$(1,1,1,e\left(\frac{4}{11}\right))$$

## Values

 $$a$$ $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$ $$\chi_{ 1380 }(361, a)$$ $$1$$ $$1$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 1380 }(361,a) \;$$ at $$\;a =$$ e.g. 2