from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8752, base_ring=CyclotomicField(546))
M = H._module
chi = DirichletCharacter(H, M([273,0,415]))
chi.galois_orbit()
[g,chi] = znchar(Mod(63,8752))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(8752\) | |
| Conductor: | \(2188\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(546\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 2188.bd | 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: | $\Q(\zeta_{273})$ |
| Fixed field: | Number field defined by a degree 546 polynomial (not computed) |
First 25 of 144 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{8752}(63,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{29}{546}\right)\) | \(e\left(\frac{215}{273}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{341}{546}\right)\) | \(e\left(\frac{421}{546}\right)\) | \(e\left(\frac{173}{546}\right)\) | \(e\left(\frac{14}{39}\right)\) |
| \(\chi_{8752}(95,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{47}{546}\right)\) | \(e\left(\frac{179}{273}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{515}{546}\right)\) | \(e\left(\frac{61}{546}\right)\) | \(e\left(\frac{431}{546}\right)\) | \(e\left(\frac{20}{39}\right)\) |
| \(\chi_{8752}(159,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{347}{546}\right)\) | \(e\left(\frac{125}{273}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{503}{546}\right)\) | \(e\left(\frac{67}{546}\right)\) | \(e\left(\frac{545}{546}\right)\) | \(e\left(\frac{29}{39}\right)\) |
| \(\chi_{8752}(175,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{73}{546}\right)\) | \(e\left(\frac{127}{273}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{463}{546}\right)\) | \(e\left(\frac{269}{546}\right)\) | \(e\left(\frac{379}{546}\right)\) | \(e\left(\frac{7}{39}\right)\) |
| \(\chi_{8752}(207,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{187}{546}\right)\) | \(e\left(\frac{172}{273}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{109}{546}\right)\) | \(e\left(\frac{173}{546}\right)\) | \(e\left(\frac{193}{546}\right)\) | \(e\left(\frac{19}{39}\right)\) |
| \(\chi_{8752}(223,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{397}{546}\right)\) | \(e\left(\frac{25}{273}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{319}{546}\right)\) | \(e\left(\frac{341}{546}\right)\) | \(e\left(\frac{109}{546}\right)\) | \(e\left(\frac{37}{39}\right)\) |
| \(\chi_{8752}(271,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{467}{546}\right)\) | \(e\left(\frac{158}{273}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{389}{546}\right)\) | \(e\left(\frac{397}{546}\right)\) | \(e\left(\frac{263}{546}\right)\) | \(e\left(\frac{17}{39}\right)\) |
| \(\chi_{8752}(431,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{223}{546}\right)\) | \(e\left(\frac{100}{273}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{457}{546}\right)\) | \(e\left(\frac{545}{546}\right)\) | \(e\left(\frac{163}{546}\right)\) | \(e\left(\frac{31}{39}\right)\) |
| \(\chi_{8752}(511,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{241}{546}\right)\) | \(e\left(\frac{64}{273}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{85}{546}\right)\) | \(e\left(\frac{185}{546}\right)\) | \(e\left(\frac{421}{546}\right)\) | \(e\left(\frac{37}{39}\right)\) |
| \(\chi_{8752}(543,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{85}{546}\right)\) | \(e\left(\frac{103}{273}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{397}{546}\right)\) | \(e\left(\frac{29}{546}\right)\) | \(e\left(\frac{187}{546}\right)\) | \(e\left(\frac{37}{39}\right)\) |
| \(\chi_{8752}(559,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{163}{546}\right)\) | \(e\left(\frac{220}{273}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{241}{546}\right)\) | \(e\left(\frac{107}{546}\right)\) | \(e\left(\frac{31}{546}\right)\) | \(e\left(\frac{37}{39}\right)\) |
| \(\chi_{8752}(639,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{389}{546}\right)\) | \(e\left(\frac{41}{273}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{545}{546}\right)\) | \(e\left(\frac{319}{546}\right)\) | \(e\left(\frac{419}{546}\right)\) | \(e\left(\frac{17}{39}\right)\) |
| \(\chi_{8752}(655,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{319}{546}\right)\) | \(e\left(\frac{181}{273}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{475}{546}\right)\) | \(e\left(\frac{263}{546}\right)\) | \(e\left(\frac{265}{546}\right)\) | \(e\left(\frac{37}{39}\right)\) |
| \(\chi_{8752}(671,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{541}{546}\right)\) | \(e\left(\frac{10}{273}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{73}{546}\right)\) | \(e\left(\frac{191}{546}\right)\) | \(e\left(\frac{535}{546}\right)\) | \(e\left(\frac{7}{39}\right)\) |
| \(\chi_{8752}(767,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{157}{546}\right)\) | \(e\left(\frac{232}{273}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{1}{546}\right)\) | \(e\left(\frac{227}{546}\right)\) | \(e\left(\frac{127}{546}\right)\) | \(e\left(\frac{22}{39}\right)\) |
| \(\chi_{8752}(911,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{101}{546}\right)\) | \(e\left(\frac{71}{273}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{491}{546}\right)\) | \(e\left(\frac{73}{546}\right)\) | \(e\left(\frac{113}{546}\right)\) | \(e\left(\frac{38}{39}\right)\) |
| \(\chi_{8752}(959,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{61}{546}\right)\) | \(e\left(\frac{151}{273}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{529}{546}\right)\) | \(e\left(\frac{509}{546}\right)\) | \(e\left(\frac{25}{546}\right)\) | \(e\left(\frac{16}{39}\right)\) |
| \(\chi_{8752}(975,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{421}{546}\right)\) | \(e\left(\frac{250}{273}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{187}{546}\right)\) | \(e\left(\frac{407}{546}\right)\) | \(e\left(\frac{271}{546}\right)\) | \(e\left(\frac{19}{39}\right)\) |
| \(\chi_{8752}(1151,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{25}{546}\right)\) | \(e\left(\frac{223}{273}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{181}{546}\right)\) | \(e\left(\frac{137}{546}\right)\) | \(e\left(\frac{55}{546}\right)\) | \(e\left(\frac{4}{39}\right)\) |
| \(\chi_{8752}(1247,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{431}{546}\right)\) | \(e\left(\frac{230}{273}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{41}{546}\right)\) | \(e\left(\frac{25}{546}\right)\) | \(e\left(\frac{293}{546}\right)\) | \(e\left(\frac{5}{39}\right)\) |
| \(\chi_{8752}(1295,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{59}{546}\right)\) | \(e\left(\frac{155}{273}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{449}{546}\right)\) | \(e\left(\frac{367}{546}\right)\) | \(e\left(\frac{239}{546}\right)\) | \(e\left(\frac{11}{39}\right)\) |
| \(\chi_{8752}(1375,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{545}{546}\right)\) | \(e\left(\frac{2}{273}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{233}{546}\right)\) | \(e\left(\frac{475}{546}\right)\) | \(e\left(\frac{107}{546}\right)\) | \(e\left(\frac{17}{39}\right)\) |
| \(\chi_{8752}(1391,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{479}{546}\right)\) | \(e\left(\frac{134}{273}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{323}{546}\right)\) | \(e\left(\frac{157}{546}\right)\) | \(e\left(\frac{71}{546}\right)\) | \(e\left(\frac{8}{39}\right)\) |
| \(\chi_{8752}(1439,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{209}{546}\right)\) | \(e\left(\frac{128}{273}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{443}{546}\right)\) | \(e\left(\frac{97}{546}\right)\) | \(e\left(\frac{23}{546}\right)\) | \(e\left(\frac{35}{39}\right)\) |
| \(\chi_{8752}(1519,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{475}{546}\right)\) | \(e\left(\frac{142}{273}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{163}{546}\right)\) | \(e\left(\frac{419}{546}\right)\) | \(e\left(\frac{499}{546}\right)\) | \(e\left(\frac{37}{39}\right)\) |