# Properties

 Label 2240.ej Modulus $2240$ Conductor $224$ Order $24$ Real no Primitive no Minimal no Parity even

# Related objects

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

sage: H = DirichletGroup(2240, base_ring=CyclotomicField(24))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([12,9,0,4]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(311,2240))

pari: order = charorder(g,chi)

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

## Basic properties

 Modulus: $$2240$$ Conductor: $$224$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$24$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 224.be sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Related number fields

 Field of values: $$\Q(\zeta_{24})$$ Fixed field: 24.24.790224330201082600125157415256880139617697792.1

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$3$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$27$$ $$29$$ $$31$$
$$\chi_{2240}(311,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{2240}(551,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{2240}(871,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{2240}(1111,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{2240}(1431,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{2240}(1671,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{2240}(1991,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{2240}(2231,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{3}\right)$$