# Properties

 Label 91.bd Modulus $91$ Conductor $91$ Order $12$ 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(91, base_ring=CyclotomicField(12))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([8,7]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(11,91))

pari: order = charorder(g,chi)

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

## Basic properties

 Modulus: $$91$$ Conductor: $$91$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$12$$ 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: $$\Q(\zeta_{12})$$ Fixed field: 12.0.10331448031704891637.2

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$8$$ $$9$$ $$10$$ $$11$$ $$12$$
$$\chi_{91}(11,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-i$$ $$1$$ $$-1$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{91}(58,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$i$$ $$1$$ $$-1$$ $$i$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{91}(67,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$i$$ $$1$$ $$-1$$ $$i$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{91}(72,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-i$$ $$1$$ $$-1$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$