from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(78))
M = H._module
chi = DirichletCharacter(H, M([26,46]))
chi.galois_orbit()
[g,chi] = znchar(Mod(9,1183))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(1183\) | |
| Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | 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: | $\Q(\zeta_{39})$ |
| Fixed field: | 39.39.253721406991290895924770503111827676888647505643788160579278763946491805765758913183386148271215912203961.1 |
Characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{1183}(9,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{38}{39}\right)\) |
| \(\chi_{1183}(81,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{37}{39}\right)\) |
| \(\chi_{1183}(100,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{32}{39}\right)\) |
| \(\chi_{1183}(172,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{19}{39}\right)\) |
| \(\chi_{1183}(263,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{1}{39}\right)\) |
| \(\chi_{1183}(282,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{20}{39}\right)\) |
| \(\chi_{1183}(354,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{22}{39}\right)\) |
| \(\chi_{1183}(373,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{14}{39}\right)\) |
| \(\chi_{1183}(445,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{4}{39}\right)\) |
| \(\chi_{1183}(464,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{8}{39}\right)\) |
| \(\chi_{1183}(536,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{25}{39}\right)\) |
| \(\chi_{1183}(555,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{2}{39}\right)\) |
| \(\chi_{1183}(627,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{7}{39}\right)\) |
| \(\chi_{1183}(646,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{35}{39}\right)\) |
| \(\chi_{1183}(718,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{28}{39}\right)\) |
| \(\chi_{1183}(737,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{29}{39}\right)\) |
| \(\chi_{1183}(809,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{10}{39}\right)\) |
| \(\chi_{1183}(828,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{23}{39}\right)\) |
| \(\chi_{1183}(900,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{31}{39}\right)\) |
| \(\chi_{1183}(919,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{17}{39}\right)\) |
| \(\chi_{1183}(1010,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{11}{39}\right)\) |
| \(\chi_{1183}(1082,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{34}{39}\right)\) |
| \(\chi_{1183}(1101,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{5}{39}\right)\) |
| \(\chi_{1183}(1173,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{16}{39}\right)\) |