# Properties

 Label 104.p Modulus $104$ Conductor $104$ Order $6$ Real no Primitive yes Minimal yes Parity odd

# Related objects

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

sage: H = DirichletGroup(104, base_ring=CyclotomicField(6))

sage: M = H._module

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

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(43,104))

pari: order = charorder(g,chi)

pari: [ 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: $$6$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Related number fields

 Field of values: $$\Q(\sqrt{-3})$$ Fixed field: 6.0.190102016.1

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$3$$ $$5$$ $$7$$ $$9$$ $$11$$ $$15$$ $$17$$ $$19$$ $$21$$ $$23$$
$$\chi_{104}(43,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{104}(75,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$