Properties

 Label 966.u Modulus $966$ Conductor $483$ Order $22$ Real no Primitive no Minimal yes Parity odd

Related objects

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

H = DirichletGroup(966, base_ring=CyclotomicField(22))

M = H._module

chi = DirichletCharacter(H, M([11,11,21]))

chi.galois_orbit()

[g,chi] = znchar(Mod(83,966))

order = charorder(g,chi)

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

Basic properties

 Modulus: $$966$$ Conductor: $$483$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$22$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 483.w 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: Number field defined by a degree 22 polynomial

Characters in Galois orbit

Character $$-1$$ $$1$$ $$5$$ $$11$$ $$13$$ $$17$$ $$19$$ $$25$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{966}(83,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{966}(125,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{966}(251,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{966}(293,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$
$$\chi_{966}(419,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$
$$\chi_{966}(503,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{966}(755,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$
$$\chi_{966}(797,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$
$$\chi_{966}(839,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{966}(881,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$