Properties

 Label 153.f Modulus $153$ Conductor $17$ Order $4$ Real no Primitive no Minimal yes Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(4))

M = H._module

chi = DirichletCharacter(H, M([0,3]))

chi.galois_orbit()

[g,chi] = znchar(Mod(55,153))

order = charorder(g,chi)

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

Basic properties

 Modulus: $$153$$ Conductor: $$17$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$4$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 17.c 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: 4.4.4913.1

Characters in Galois orbit

Character $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$7$$ $$8$$ $$10$$ $$11$$ $$13$$ $$14$$ $$16$$
$$\chi_{153}(55,\cdot)$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-i$$ $$i$$ $$-1$$ $$i$$ $$i$$ $$1$$ $$-i$$ $$1$$
$$\chi_{153}(64,\cdot)$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$i$$ $$-i$$ $$-1$$ $$-i$$ $$-i$$ $$1$$ $$i$$ $$1$$