# Properties

 Label 2268.229 Modulus $2268$ Conductor $567$ Order $54$ Real no Primitive no Minimal yes Parity odd

# Related objects

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

sage: H = DirichletGroup(2268, base_ring=CyclotomicField(54))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,44,45]))

pari: [g,chi] = znchar(Mod(229,2268))

## Basic properties

 Modulus: $$2268$$ Conductor: $$567$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$54$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{567}(229,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 2268.dj

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: $$\Q(\zeta_{27})$$ Fixed field: Number field defined by a degree 54 polynomial

## Values on generators

$$(1135,1541,325)$$ → $$(1,e\left(\frac{22}{27}\right),e\left(\frac{5}{6}\right))$$

## Values

 $$-1$$ $$1$$ $$5$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$ $$-1$$ $$1$$ $$e\left(\frac{49}{54}\right)$$ $$e\left(\frac{25}{27}\right)$$ $$e\left(\frac{1}{54}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{17}{27}\right)$$ $$e\left(\frac{22}{27}\right)$$ $$e\left(\frac{4}{27}\right)$$ $$e\left(\frac{7}{54}\right)$$ $$e\left(\frac{8}{9}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 2268 }(229,a) \;$$ at $$\;a =$$ e.g. 2