# Properties

 Label 1944.7 Modulus $1944$ Conductor $972$ Order $162$ Real no Primitive no Minimal no Parity odd

# Related objects

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

sage: H = DirichletGroup(1944, base_ring=CyclotomicField(162))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([81,0,70]))

pari: [g,chi] = znchar(Mod(7,1944))

## Basic properties

 Modulus: $$1944$$ Conductor: $$972$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$162$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{972}(7,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1944.bi

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: $\Q(\zeta_{81})$ Fixed field: Number field defined by a degree 162 polynomial (not computed)

## Values on generators

$$(487,973,1217)$$ → $$(-1,1,e\left(\frac{35}{81}\right))$$

## Values

 $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$-1$$ $$1$$ $$e\left(\frac{76}{81}\right)$$ $$e\left(\frac{121}{162}\right)$$ $$e\left(\frac{127}{162}\right)$$ $$e\left(\frac{37}{81}\right)$$ $$e\left(\frac{7}{27}\right)$$ $$e\left(\frac{49}{54}\right)$$ $$e\left(\frac{95}{162}\right)$$ $$e\left(\frac{71}{81}\right)$$ $$e\left(\frac{80}{81}\right)$$ $$e\left(\frac{23}{162}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 1944 }(7,a) \;$$ at $$\;a =$$ e.g. 2