Properties

 Label 1224.53 Modulus $1224$ Conductor $408$ Order $8$ Real no Primitive no Minimal yes Parity odd

Related objects

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

sage: H = DirichletGroup(1224)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,4,4,7]))

pari: [g,chi] = znchar(Mod(53,1224))

Basic properties

 Modulus: $$1224$$ Conductor: $$408$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$8$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{408}(53,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

Galois orbit 1224.bu

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

$$(919,613,137,649)$$ → $$(1,-1,-1,e\left(\frac{7}{8}\right))$$

Values

 $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$35$$ $$-1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$1$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$1$$
 value at e.g. 2

Related number fields

 Field of values: $$\Q(\zeta_{8})$$ Fixed field: Number field defined by a degree %d polynomial (not computed)