# Properties

 Label 483.bf Modulus $483$ Conductor $161$ Order $66$ Real no Primitive no Minimal yes Parity even

# Related objects

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

sage: H = DirichletGroup(483, base_ring=CyclotomicField(66))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,11,9]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(10,483))

pari: order = charorder(g,chi)

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

## Basic properties

 Modulus: $$483$$ Conductor: $$161$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$66$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 161.o 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: Number field defined by a degree 66 polynomial

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$8$$ $$10$$ $$11$$ $$13$$ $$16$$ $$17$$ $$19$$
$$\chi_{483}(10,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$
$$\chi_{483}(19,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$
$$\chi_{483}(40,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$
$$\chi_{483}(61,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$
$$\chi_{483}(103,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$
$$\chi_{483}(136,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$
$$\chi_{483}(145,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$
$$\chi_{483}(157,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$
$$\chi_{483}(166,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$
$$\chi_{483}(178,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$
$$\chi_{483}(199,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$
$$\chi_{483}(241,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$
$$\chi_{483}(250,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$
$$\chi_{483}(283,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$
$$\chi_{483}(304,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$
$$\chi_{483}(313,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$
$$\chi_{483}(355,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$
$$\chi_{483}(388,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$
$$\chi_{483}(451,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$
$$\chi_{483}(481,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$