# Properties

 Label 4235.co Modulus $4235$ Conductor $4235$ Order $66$ Real no Primitive yes Minimal yes Parity even

# Related objects

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

sage: H = DirichletGroup(4235, base_ring=CyclotomicField(66))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([33,55,27]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(54,4235))

pari: order = charorder(g,chi)

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

## Basic properties

 Modulus: $$4235$$ Conductor: $$4235$$ 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: 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$6$$ $$8$$ $$9$$ $$12$$ $$13$$ $$16$$ $$17$$
$$\chi_{4235}(54,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{25}{66}\right)$$
$$\chi_{4235}(164,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{53}{66}\right)$$
$$\chi_{4235}(439,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{13}{66}\right)$$
$$\chi_{4235}(549,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{41}{66}\right)$$
$$\chi_{4235}(824,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{1}{66}\right)$$
$$\chi_{4235}(934,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{29}{66}\right)$$
$$\chi_{4235}(1319,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{17}{66}\right)$$
$$\chi_{4235}(1594,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{43}{66}\right)$$
$$\chi_{4235}(1704,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{5}{66}\right)$$
$$\chi_{4235}(1979,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$
$$\chi_{4235}(2089,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{59}{66}\right)$$
$$\chi_{4235}(2364,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{19}{66}\right)$$
$$\chi_{4235}(2474,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{47}{66}\right)$$
$$\chi_{4235}(2749,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{7}{66}\right)$$
$$\chi_{4235}(2859,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{35}{66}\right)$$
$$\chi_{4235}(3134,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{61}{66}\right)$$
$$\chi_{4235}(3244,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{23}{66}\right)$$
$$\chi_{4235}(3519,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{49}{66}\right)$$
$$\chi_{4235}(3904,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{37}{66}\right)$$
$$\chi_{4235}(4014,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{65}{66}\right)$$