Properties

 Label 104.m Modulus $104$ Conductor $104$ Order $4$ Real no Primitive yes Minimal yes Parity even

Related objects

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

H = DirichletGroup(104, base_ring=CyclotomicField(4))

M = H._module

chi = DirichletCharacter(H, M([2,2,3]))

chi.galois_orbit()

[g,chi] = znchar(Mod(83,104))

order = charorder(g,chi)

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

Basic properties

 Modulus: $$104$$ Conductor: $$104$$ 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: 4.4.140608.1

Characters in Galois orbit

Character $$-1$$ $$1$$ $$3$$ $$5$$ $$7$$ $$9$$ $$11$$ $$15$$ $$17$$ $$19$$ $$21$$ $$23$$
$$\chi_{104}(83,\cdot)$$ $$1$$ $$1$$ $$1$$ $$i$$ $$-i$$ $$1$$ $$i$$ $$i$$ $$-1$$ $$-i$$ $$-i$$ $$1$$
$$\chi_{104}(99,\cdot)$$ $$1$$ $$1$$ $$1$$ $$-i$$ $$i$$ $$1$$ $$-i$$ $$-i$$ $$-1$$ $$i$$ $$i$$ $$1$$