# Properties

 Label 483.y Modulus $483$ Conductor $161$ Order $33$ 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([0,44,12]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(4,483))

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: $$33$$ 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 $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$8$$ $$10$$ $$11$$ $$13$$ $$16$$ $$17$$ $$19$$
$$\chi_{483}(4,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$
$$\chi_{483}(16,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$
$$\chi_{483}(25,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$
$$\chi_{483}(58,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$
$$\chi_{483}(100,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$
$$\chi_{483}(121,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$
$$\chi_{483}(142,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$
$$\chi_{483}(151,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$
$$\chi_{483}(163,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$
$$\chi_{483}(193,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$
$$\chi_{483}(256,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$
$$\chi_{483}(289,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$
$$\chi_{483}(331,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$
$$\chi_{483}(340,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$
$$\chi_{483}(361,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$
$$\chi_{483}(394,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$
$$\chi_{483}(403,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$
$$\chi_{483}(445,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$
$$\chi_{483}(466,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$
$$\chi_{483}(478,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$