# Properties

 Label 232.p Modulus $232$ Conductor $232$ Order $14$ Real no Primitive yes Minimal yes Parity odd

# Related objects

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

sage: H = DirichletGroup(232, base_ring=CyclotomicField(14))

sage: M = H._module

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

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(83,232))

pari: order = charorder(g,chi)

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

## Basic properties

 Modulus: $$232$$ Conductor: $$232$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$14$$ 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: $$\Q(\zeta_{7})$$ Fixed field: 14.0.742003380228915810271232.1

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$3$$ $$5$$ $$7$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$19$$ $$21$$
$$\chi_{232}(83,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$1$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$
$$\chi_{232}(107,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$1$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$
$$\chi_{232}(123,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$1$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$
$$\chi_{232}(139,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$1$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$
$$\chi_{232}(219,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$1$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{13}{14}\right)$$
$$\chi_{232}(227,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$1$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$