# Properties

 Label 1805.293 Modulus $1805$ Conductor $95$ Order $12$ Real no Primitive no Minimal no Parity even

# Related objects

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

sage: H = DirichletGroup(1805, base_ring=CyclotomicField(12))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([9,2]))

pari: [g,chi] = znchar(Mod(293,1805))

## Basic properties

 Modulus: $$1805$$ Conductor: $$95$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$12$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{95}(8,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1805.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: $$\Q(\zeta_{12})$$ Fixed field: 12.12.11974738784767578125.1

## Values on generators

$$(362,1446)$$ → $$(-i,e\left(\frac{1}{6}\right))$$

## Values

 $$a$$ $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$6$$ $$7$$ $$8$$ $$9$$ $$11$$ $$12$$ $$13$$ $$\chi_{ 1805 }(293, a)$$ $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$i$$ $$e\left(\frac{1}{12}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 1805 }(293,a) \;$$ at $$\;a =$$ e.g. 2