# Properties

 Label 1323.62 Modulus $1323$ Conductor $441$ Order $42$ 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(1323, base_ring=CyclotomicField(42))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([7,33]))

pari: [g,chi] = znchar(Mod(62,1323))

## Basic properties

 Modulus: $$1323$$ Conductor: $$441$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$42$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{441}(209,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1323.bt

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

$$(785,1081)$$ → $$(e\left(\frac{1}{6}\right),e\left(\frac{11}{14}\right))$$

## Values

 $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$8$$ $$10$$ $$11$$ $$13$$ $$16$$ $$17$$ $$19$$ $$1$$ $$1$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$-1$$
 value at e.g. 2