# Properties

 Label 4830.cw Modulus $4830$ Conductor $2415$ 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(4830, base_ring=CyclotomicField(66))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([33,33,11,42]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(59,4830))

pari: order = charorder(g,chi)

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

## Basic properties

 Modulus: $$4830$$ Conductor: $$2415$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$66$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 2415.de 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 $$-1$$ $$1$$ $$11$$ $$13$$ $$17$$ $$19$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$ $$47$$
$$\chi_{4830}(59,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{4830}(269,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{4830}(509,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{4830}(719,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{4830}(899,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{4830}(929,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{4830}(1139,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{4830}(1319,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{4830}(1559,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{4830}(2189,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{4830}(2579,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{4830}(2789,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{4830}(2819,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{4830}(2999,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{4830}(3029,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{4830}(3209,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{4830}(3629,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{4830}(3659,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{4830}(4079,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{4830}(4259,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{5}{6}\right)$$