# Properties

 Label 199.i Modulus $199$ Conductor $199$ Order $33$ Real no Primitive yes Minimal yes Parity even

# Related objects

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

sage: H = DirichletGroup(199, base_ring=CyclotomicField(66))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([46]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(5,199))

pari: order = charorder(g,chi)

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

## Basic properties

 Modulus: $$199$$ Conductor: $$199$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$33$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$
$$\chi_{199}(5,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{199}(8,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$
$$\chi_{199}(25,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{199}(28,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{199}(40,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$
$$\chi_{199}(52,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$
$$\chi_{199}(64,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{199}(90,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$
$$\chi_{199}(98,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$
$$\chi_{199}(111,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{199}(116,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$
$$\chi_{199}(117,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{199}(123,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$
$$\chi_{199}(132,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{199}(140,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{199}(144,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{199}(157,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$
$$\chi_{199}(172,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$
$$\chi_{199}(182,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{199}(187,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$