from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(376, base_ring=CyclotomicField(46))
M = H._module
chi = DirichletCharacter(H, M([0,23,1]))
chi.galois_orbit()
[g,chi] = znchar(Mod(5,376))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(376\) | |
| Conductor: | \(376\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(46\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | \(\Q(\zeta_{23})\) |
| Fixed field: | 46.0.1036270912454247829848884601705469565826954223470060599867947317935733537595789906053570110685184.1 |
Characters in Galois orbit
| Character | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{376}(5,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{21}{46}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{29}{46}\right)\) |
| \(\chi_{376}(13,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{43}{46}\right)\) |
| \(\chi_{376}(29,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{3}{46}\right)\) |
| \(\chi_{376}(45,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{15}{46}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{39}{46}\right)\) |
| \(\chi_{376}(69,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{17}{46}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{35}{46}\right)\) |
| \(\chi_{376}(77,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{21}{46}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{27}{46}\right)\) |
| \(\chi_{376}(85,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{35}{46}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{33}{46}\right)\) |
| \(\chi_{376}(109,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{11}{46}\right)\) |
| \(\chi_{376}(117,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{7}{46}\right)\) |
| \(\chi_{376}(125,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{17}{46}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{41}{46}\right)\) |
| \(\chi_{376}(133,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{7}{46}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{25}{46}\right)\) |
| \(\chi_{376}(181,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{31}{46}\right)\) |
| \(\chi_{376}(221,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{11}{46}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{15}{46}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{1}{46}\right)\) |
| \(\chi_{376}(229,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{21}{46}\right)\) |
| \(\chi_{376}(245,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{35}{46}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{45}{46}\right)\) |
| \(\chi_{376}(261,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{11}{46}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{13}{46}\right)\) |
| \(\chi_{376}(293,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{25}{46}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{9}{46}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{19}{46}\right)\) |
| \(\chi_{376}(301,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{46}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{25}{46}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{17}{46}\right)\) |
| \(\chi_{376}(317,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{3}{46}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{37}{46}\right)\) |
| \(\chi_{376}(325,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{7}{46}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{9}{46}\right)\) |
| \(\chi_{376}(349,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{15}{46}\right)\) |
| \(\chi_{376}(373,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{9}{46}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{5}{46}\right)\) |