Properties

 Label 1323.37 Modulus $1323$ Conductor $441$ Order $21$ 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([14,32]))

pari: [g,chi] = znchar(Mod(37,1323))

Basic properties

 Modulus: $$1323$$ Conductor: $$441$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$21$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{441}(184,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

Galois orbit 1323.bk

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

$$(785,1081)$$ → $$(e\left(\frac{1}{3}\right),e\left(\frac{16}{21}\right))$$

Values

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

Related number fields

 Field of values: $$\Q(\zeta_{21})$$ Fixed field: 21.21.2972491714150324080426899160865869074720055489.1