# Properties

 Label 1380.bm Modulus $1380$ Conductor $345$ Order $22$ Real no Primitive no Minimal yes Parity odd

# Learn more

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

sage: H = DirichletGroup(1380, base_ring=CyclotomicField(22))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,11,11,18]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(29,1380))

pari: order = charorder(g,chi)

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

## Basic properties

 Modulus: $$1380$$ Conductor: $$345$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$22$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 345.p 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: $$\Q(\zeta_{11})$$ Fixed field: 22.0.14844328957686912445797815584548193359375.1

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$
$$\chi_{1380}(29,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$
$$\chi_{1380}(209,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$
$$\chi_{1380}(269,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$
$$\chi_{1380}(449,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$
$$\chi_{1380}(509,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$
$$\chi_{1380}(629,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$
$$\chi_{1380}(749,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$
$$\chi_{1380}(809,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$
$$\chi_{1380}(869,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$
$$\chi_{1380}(929,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$