from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2665, base_ring=CyclotomicField(120))
M = H._module
chi = DirichletCharacter(H, M([0,50,3]))
chi.galois_orbit()
[g,chi] = znchar(Mod(6,2665))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(2665\) | |
| Conductor: | \(533\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 533.cd | 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: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
First 31 of 32 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(14\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{2665}(6,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{5}{8}\right)\) |
| \(\chi_{2665}(11,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{37}{120}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{7}{8}\right)\) |
| \(\chi_{2665}(106,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{1}{8}\right)\) |
| \(\chi_{2665}(111,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{91}{120}\right)\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{3}{8}\right)\) |
| \(\chi_{2665}(176,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{7}{8}\right)\) |
| \(\chi_{2665}(591,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{91}{120}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{47}{120}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{5}{8}\right)\) |
| \(\chi_{2665}(691,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{47}{120}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{1}{8}\right)\) |
| \(\chi_{2665}(721,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{107}{120}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{1}{8}\right)\) |
| \(\chi_{2665}(726,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{3}{8}\right)\) |
| \(\chi_{2665}(791,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{7}{8}\right)\) |
| \(\chi_{2665}(891,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{3}{8}\right)\) |
| \(\chi_{2665}(956,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{43}{120}\right)\) | \(e\left(\frac{37}{120}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{3}{8}\right)\) |
| \(\chi_{2665}(1081,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{43}{120}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{1}{8}\right)\) |
| \(\chi_{2665}(1211,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{91}{120}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{1}{8}\right)\) |
| \(\chi_{2665}(1306,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{1}{8}\right)\) |
| \(\chi_{2665}(1346,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{7}{8}\right)\) |
| \(\chi_{2665}(1506,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{97}{120}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{3}{8}\right)\) |
| \(\chi_{2665}(1536,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{5}{8}\right)\) |
| \(\chi_{2665}(1571,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{3}{8}\right)\) |
| \(\chi_{2665}(1606,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{3}{8}\right)\) |
| \(\chi_{2665}(1666,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{5}{8}\right)\) |
| \(\chi_{2665}(1696,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{1}{8}\right)\) |
| \(\chi_{2665}(1826,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{97}{120}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{1}{8}\right)\) |
| \(\chi_{2665}(1961,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{47}{120}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{7}{8}\right)\) |
| \(\chi_{2665}(1996,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{97}{120}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{7}{8}\right)\) |
| \(\chi_{2665}(2056,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{107}{120}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{5}{8}\right)\) |
| \(\chi_{2665}(2061,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{7}{8}\right)\) |
| \(\chi_{2665}(2151,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{37}{120}\right)\) | \(e\left(\frac{43}{120}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{5}{8}\right)\) |
| \(\chi_{2665}(2221,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{107}{120}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{3}{8}\right)\) |
| \(\chi_{2665}(2281,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{5}{8}\right)\) |
| \(\chi_{2665}(2611,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{7}{8}\right)\) |