# Properties

 Label 966.y Modulus $966$ Conductor $161$ Order $33$ Real no Primitive no Minimal yes Parity even

# Learn more

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

H = DirichletGroup(966, base_ring=CyclotomicField(66))

M = H._module

chi = DirichletCharacter(H, M([0,44,6]))

chi.galois_orbit()

[g,chi] = znchar(Mod(25,966))

order = charorder(g,chi)

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

## Basic properties

 Modulus: $$966$$ Conductor: $$161$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$33$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 161.m sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Related number fields

 Field of values: $$\Q(\zeta_{33})$$ Fixed field: 33.33.277966181338944111003326058293667039541136678070715028736001.1

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$5$$ $$11$$ $$13$$ $$17$$ $$19$$ $$25$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{966}(25,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{966}(121,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$
$$\chi_{966}(151,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{966}(163,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{966}(193,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{966}(289,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{966}(331,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{966}(361,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$
$$\chi_{966}(403,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{966}(445,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$
$$\chi_{966}(487,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$
$$\chi_{966}(499,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$
$$\chi_{966}(541,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{966}(583,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$
$$\chi_{966}(625,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$
$$\chi_{966}(739,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{966}(823,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$
$$\chi_{966}(877,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{966}(949,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$
$$\chi_{966}(961,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$