Properties

 Label 145.j Modulus $145$ Conductor $145$ Order $4$ Real no Primitive yes Minimal yes Parity even

Learn more

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

sage: H = DirichletGroup(145, base_ring=CyclotomicField(4))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([1,3]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(17,145))

pari: order = charorder(g,chi)

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

Basic properties

 Modulus: $$145$$ Conductor: $$145$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$4$$ 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)

Related number fields

 Field of values: $$\Q(\sqrt{-1})$$ Fixed field: 4.4.3048625.1

Characters in Galois orbit

Character $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$6$$ $$7$$ $$8$$ $$9$$ $$11$$ $$12$$ $$13$$
$$\chi_{145}(17,\cdot)$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$i$$ $$1$$ $$1$$ $$-i$$ $$-1$$ $$i$$
$$\chi_{145}(128,\cdot)$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-i$$ $$1$$ $$1$$ $$i$$ $$-1$$ $$-i$$