# Properties

 Label 1323.20 Modulus $1323$ Conductor $1323$ Order $126$ Real no Primitive yes Minimal yes Parity even

# Related objects

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

sage: H = DirichletGroup(1323, base_ring=CyclotomicField(126))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([49,117]))

pari: [g,chi] = znchar(Mod(20,1323))

## Basic properties

 Modulus: $$1323$$ Conductor: $$1323$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$126$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1323.ce

sage: chi.galois_orbit()

pari: order = charorder(g,chi)

pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

## Values on generators

$$(785,1081)$$ → $$(e\left(\frac{7}{18}\right),e\left(\frac{13}{14}\right))$$

## Values

 $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$8$$ $$10$$ $$11$$ $$13$$ $$16$$ $$17$$ $$19$$ $$1$$ $$1$$ $$e\left(\frac{67}{126}\right)$$ $$e\left(\frac{4}{63}\right)$$ $$e\left(\frac{55}{63}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{25}{126}\right)$$ $$e\left(\frac{95}{126}\right)$$ $$e\left(\frac{8}{63}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{1}{6}\right)$$
 value at e.g. 2

## Related number fields

 Field of values: $\Q(\zeta_{63})$ Fixed field: Number field defined by a degree 126 polynomial (not computed)