# Properties

 Label 966.bc Modulus $966$ Conductor $483$ Order $66$ 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(66))

M = H._module

chi = DirichletCharacter(H, M([33,55,3]))

chi.galois_orbit()

[g,chi] = znchar(Mod(5,966))

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: $$66$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 483.ba 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: $$\Q(\zeta_{33})$$ Fixed field: Number field defined by a degree 66 polynomial

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$5$$ $$11$$ $$13$$ $$17$$ $$19$$ $$25$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{966}(5,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{6}{11}\right)$$
$$\chi_{966}(17,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{9}{11}\right)$$
$$\chi_{966}(89,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{966}(143,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{6}{11}\right)$$
$$\chi_{966}(227,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{966}(341,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{2}{11}\right)$$
$$\chi_{966}(383,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{3}{11}\right)$$
$$\chi_{966}(425,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{966}(467,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{4}{11}\right)$$
$$\chi_{966}(479,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{2}{11}\right)$$
$$\chi_{966}(521,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{3}{11}\right)$$
$$\chi_{966}(563,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{966}(605,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{4}{11}\right)$$
$$\chi_{966}(635,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{966}(677,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{966}(773,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{966}(803,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{966}(815,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{966}(845,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{9}{11}\right)$$
$$\chi_{966}(941,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{1}{11}\right)$$