# Properties

 Label 161.p Modulus $161$ Conductor $161$ Order $66$ Real no Primitive yes Minimal yes Parity odd

# Related objects

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

H = DirichletGroup(161, base_ring=CyclotomicField(66))

M = H._module

chi = DirichletCharacter(H, M([44,27]))

chi.galois_orbit()

[g,chi] = znchar(Mod(11,161))

order = charorder(g,chi)

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

## Basic properties

 Modulus: $$161$$ Conductor: $$161$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$66$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$8$$ $$9$$ $$10$$ $$11$$ $$12$$
$$\chi_{161}(11,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{17}{33}\right)$$
$$\chi_{161}(30,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{31}{33}\right)$$
$$\chi_{161}(37,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{25}{33}\right)$$
$$\chi_{161}(44,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{16}{33}\right)$$
$$\chi_{161}(51,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{19}{33}\right)$$
$$\chi_{161}(53,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{20}{33}\right)$$
$$\chi_{161}(60,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{14}{33}\right)$$
$$\chi_{161}(65,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{10}{33}\right)$$
$$\chi_{161}(67,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{5}{33}\right)$$
$$\chi_{161}(74,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{8}{33}\right)$$
$$\chi_{161}(79,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{13}{33}\right)$$
$$\chi_{161}(86,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{1}{33}\right)$$
$$\chi_{161}(88,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{32}{33}\right)$$
$$\chi_{161}(102,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{2}{33}\right)$$
$$\chi_{161}(107,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{4}{33}\right)$$
$$\chi_{161}(109,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{23}{33}\right)$$
$$\chi_{161}(130,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{26}{33}\right)$$
$$\chi_{161}(135,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{7}{33}\right)$$
$$\chi_{161}(149,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{28}{33}\right)$$
$$\chi_{161}(158,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{29}{33}\right)$$