Properties

 Label 3024.1189 Modulus $3024$ Conductor $112$ Order $4$ 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(3024, base_ring=CyclotomicField(4))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,1,0,2]))

pari: [g,chi] = znchar(Mod(1189,3024))

Basic properties

 Modulus: $$3024$$ Conductor: $$112$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$4$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{112}(69,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

Galois orbit 3024.u

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

$$(1135,757,785,2593)$$ → $$(1,i,1,-1)$$

Values

 $$-1$$ $$1$$ $$5$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$ $$-1$$ $$1$$ $$-i$$ $$i$$ $$i$$ $$-1$$ $$i$$ $$-1$$ $$-1$$ $$-i$$ $$-1$$ $$i$$
 value at e.g. 2

Related number fields

 Field of values: $$\Q(\sqrt{-1})$$ Fixed field: 4.0.100352.5