# Properties

 Label 2736.625 Modulus $2736$ Conductor $171$ Order $9$ Real no Primitive no Minimal no Parity even

# Related objects

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

sage: H = DirichletGroup(2736, base_ring=CyclotomicField(18))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,0,6,10]))

pari: [g,chi] = znchar(Mod(625,2736))

## Basic properties

 Modulus: $$2736$$ Conductor: $$171$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$9$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{171}(112,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 2736.dl

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: $$\Q(\zeta_{9})$$ Fixed field: 9.9.9025761726072081.1

## Values on generators

$$(1711,2053,1217,1009)$$ → $$(1,1,e\left(\frac{1}{3}\right),e\left(\frac{5}{9}\right))$$

## Values

 $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$17$$ $$23$$ $$25$$ $$29$$ $$31$$ $$35$$ $$1$$ $$1$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$1$$ $$e\left(\frac{2}{9}\right)$$
 value at e.g. 2