from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9126, base_ring=CyclotomicField(468))
M = H._module
chi = DirichletCharacter(H, M([130,27]))
chi.galois_orbit()
[g,chi] = znchar(Mod(5,9126))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(9126\) | |
| Conductor: | \(4563\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(468\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 4563.do | 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: | $\Q(\zeta_{468})$ |
| Fixed field: | Number field defined by a degree 468 polynomial (not computed) |
First 31 of 144 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{9126}(5,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{425}{468}\right)\) | \(e\left(\frac{289}{468}\right)\) | \(e\left(\frac{259}{468}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{191}{234}\right)\) | \(e\left(\frac{137}{234}\right)\) | \(e\left(\frac{359}{468}\right)\) | \(e\left(\frac{41}{78}\right)\) |
| \(\chi_{9126}(47,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{271}{468}\right)\) | \(e\left(\frac{203}{468}\right)\) | \(e\left(\frac{305}{468}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{37}{234}\right)\) | \(e\left(\frac{127}{234}\right)\) | \(e\left(\frac{121}{468}\right)\) | \(e\left(\frac{1}{78}\right)\) |
| \(\chi_{9126}(83,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{409}{468}\right)\) | \(e\left(\frac{353}{468}\right)\) | \(e\left(\frac{203}{468}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{175}{234}\right)\) | \(e\left(\frac{139}{234}\right)\) | \(e\left(\frac{79}{468}\right)\) | \(e\left(\frac{49}{78}\right)\) |
| \(\chi_{9126}(203,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{95}{468}\right)\) | \(e\left(\frac{439}{468}\right)\) | \(e\left(\frac{157}{468}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{95}{234}\right)\) | \(e\left(\frac{149}{234}\right)\) | \(e\left(\frac{317}{468}\right)\) | \(e\left(\frac{11}{78}\right)\) |
| \(\chi_{9126}(281,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{468}\right)\) | \(e\left(\frac{323}{468}\right)\) | \(e\left(\frac{317}{468}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{7}{234}\right)\) | \(e\left(\frac{43}{234}\right)\) | \(e\left(\frac{181}{468}\right)\) | \(e\left(\frac{55}{78}\right)\) |
| \(\chi_{9126}(317,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{361}{468}\right)\) | \(e\left(\frac{77}{468}\right)\) | \(e\left(\frac{35}{468}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{127}{234}\right)\) | \(e\left(\frac{145}{234}\right)\) | \(e\left(\frac{175}{468}\right)\) | \(e\left(\frac{73}{78}\right)\) |
| \(\chi_{9126}(473,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{329}{468}\right)\) | \(e\left(\frac{205}{468}\right)\) | \(e\left(\frac{391}{468}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{95}{234}\right)\) | \(e\left(\frac{149}{234}\right)\) | \(e\left(\frac{83}{468}\right)\) | \(e\left(\frac{11}{78}\right)\) |
| \(\chi_{9126}(515,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{211}{468}\right)\) | \(e\left(\frac{443}{468}\right)\) | \(e\left(\frac{329}{468}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{211}{234}\right)\) | \(e\left(\frac{193}{234}\right)\) | \(e\left(\frac{241}{468}\right)\) | \(e\left(\frac{31}{78}\right)\) |
| \(\chi_{9126}(551,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{313}{468}\right)\) | \(e\left(\frac{269}{468}\right)\) | \(e\left(\frac{335}{468}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{79}{234}\right)\) | \(e\left(\frac{151}{234}\right)\) | \(e\left(\frac{271}{468}\right)\) | \(e\left(\frac{19}{78}\right)\) |
| \(\chi_{9126}(671,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{35}{468}\right)\) | \(e\left(\frac{211}{468}\right)\) | \(e\left(\frac{181}{468}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{35}{234}\right)\) | \(e\left(\frac{215}{234}\right)\) | \(e\left(\frac{437}{468}\right)\) | \(e\left(\frac{41}{78}\right)\) |
| \(\chi_{9126}(707,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{281}{468}\right)\) | \(e\left(\frac{397}{468}\right)\) | \(e\left(\frac{223}{468}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{47}{234}\right)\) | \(e\left(\frac{155}{234}\right)\) | \(e\left(\frac{179}{468}\right)\) | \(e\left(\frac{35}{78}\right)\) |
| \(\chi_{9126}(749,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{415}{468}\right)\) | \(e\left(\frac{95}{468}\right)\) | \(e\left(\frac{341}{468}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{181}{234}\right)\) | \(e\left(\frac{109}{234}\right)\) | \(e\left(\frac{301}{468}\right)\) | \(e\left(\frac{7}{78}\right)\) |
| \(\chi_{9126}(785,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{265}{468}\right)\) | \(e\left(\frac{461}{468}\right)\) | \(e\left(\frac{167}{468}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{31}{234}\right)\) | \(e\left(\frac{157}{234}\right)\) | \(e\left(\frac{367}{468}\right)\) | \(e\left(\frac{43}{78}\right)\) |
| \(\chi_{9126}(905,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{239}{468}\right)\) | \(e\left(\frac{331}{468}\right)\) | \(e\left(\frac{193}{468}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{5}{234}\right)\) | \(e\left(\frac{131}{234}\right)\) | \(e\left(\frac{29}{468}\right)\) | \(e\left(\frac{17}{78}\right)\) |
| \(\chi_{9126}(941,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{233}{468}\right)\) | \(e\left(\frac{121}{468}\right)\) | \(e\left(\frac{55}{468}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{233}{234}\right)\) | \(e\left(\frac{161}{234}\right)\) | \(e\left(\frac{275}{468}\right)\) | \(e\left(\frac{59}{78}\right)\) |
| \(\chi_{9126}(983,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{151}{468}\right)\) | \(e\left(\frac{215}{468}\right)\) | \(e\left(\frac{353}{468}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{151}{234}\right)\) | \(e\left(\frac{25}{234}\right)\) | \(e\left(\frac{361}{468}\right)\) | \(e\left(\frac{61}{78}\right)\) |
| \(\chi_{9126}(1019,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{217}{468}\right)\) | \(e\left(\frac{185}{468}\right)\) | \(e\left(\frac{467}{468}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{217}{234}\right)\) | \(e\left(\frac{163}{234}\right)\) | \(e\left(\frac{463}{468}\right)\) | \(e\left(\frac{67}{78}\right)\) |
| \(\chi_{9126}(1139,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{443}{468}\right)\) | \(e\left(\frac{451}{468}\right)\) | \(e\left(\frac{205}{468}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{209}{234}\right)\) | \(e\left(\frac{47}{234}\right)\) | \(e\left(\frac{89}{468}\right)\) | \(e\left(\frac{71}{78}\right)\) |
| \(\chi_{9126}(1175,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{185}{468}\right)\) | \(e\left(\frac{313}{468}\right)\) | \(e\left(\frac{355}{468}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{185}{234}\right)\) | \(e\left(\frac{167}{234}\right)\) | \(e\left(\frac{371}{468}\right)\) | \(e\left(\frac{5}{78}\right)\) |
| \(\chi_{9126}(1217,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{355}{468}\right)\) | \(e\left(\frac{335}{468}\right)\) | \(e\left(\frac{365}{468}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{121}{234}\right)\) | \(e\left(\frac{175}{234}\right)\) | \(e\left(\frac{421}{468}\right)\) | \(e\left(\frac{37}{78}\right)\) |
| \(\chi_{9126}(1373,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{179}{468}\right)\) | \(e\left(\frac{103}{468}\right)\) | \(e\left(\frac{217}{468}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{179}{234}\right)\) | \(e\left(\frac{197}{234}\right)\) | \(e\left(\frac{149}{468}\right)\) | \(e\left(\frac{47}{78}\right)\) |
| \(\chi_{9126}(1409,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{137}{468}\right)\) | \(e\left(\frac{37}{468}\right)\) | \(e\left(\frac{187}{468}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{137}{234}\right)\) | \(e\left(\frac{173}{234}\right)\) | \(e\left(\frac{467}{468}\right)\) | \(e\left(\frac{29}{78}\right)\) |
| \(\chi_{9126}(1487,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{121}{468}\right)\) | \(e\left(\frac{101}{468}\right)\) | \(e\left(\frac{131}{468}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{121}{234}\right)\) | \(e\left(\frac{175}{234}\right)\) | \(e\left(\frac{187}{468}\right)\) | \(e\left(\frac{37}{78}\right)\) |
| \(\chi_{9126}(1607,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{383}{468}\right)\) | \(e\left(\frac{223}{468}\right)\) | \(e\left(\frac{229}{468}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{149}{234}\right)\) | \(e\left(\frac{113}{234}\right)\) | \(e\left(\frac{209}{468}\right)\) | \(e\left(\frac{23}{78}\right)\) |
| \(\chi_{9126}(1643,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{468}\right)\) | \(e\left(\frac{229}{468}\right)\) | \(e\left(\frac{19}{468}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{89}{234}\right)\) | \(e\left(\frac{179}{234}\right)\) | \(e\left(\frac{95}{468}\right)\) | \(e\left(\frac{53}{78}\right)\) |
| \(\chi_{9126}(1685,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{295}{468}\right)\) | \(e\left(\frac{107}{468}\right)\) | \(e\left(\frac{389}{468}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{61}{234}\right)\) | \(e\left(\frac{7}{234}\right)\) | \(e\left(\frac{73}{468}\right)\) | \(e\left(\frac{67}{78}\right)\) |
| \(\chi_{9126}(1721,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{468}\right)\) | \(e\left(\frac{293}{468}\right)\) | \(e\left(\frac{431}{468}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{73}{234}\right)\) | \(e\left(\frac{181}{234}\right)\) | \(e\left(\frac{283}{468}\right)\) | \(e\left(\frac{61}{78}\right)\) |
| \(\chi_{9126}(1841,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{119}{468}\right)\) | \(e\left(\frac{343}{468}\right)\) | \(e\left(\frac{241}{468}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{119}{234}\right)\) | \(e\left(\frac{29}{234}\right)\) | \(e\left(\frac{269}{468}\right)\) | \(e\left(\frac{77}{78}\right)\) |
| \(\chi_{9126}(1877,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{468}\right)\) | \(e\left(\frac{421}{468}\right)\) | \(e\left(\frac{319}{468}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{41}{234}\right)\) | \(e\left(\frac{185}{234}\right)\) | \(e\left(\frac{191}{468}\right)\) | \(e\left(\frac{77}{78}\right)\) |
| \(\chi_{9126}(1919,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{468}\right)\) | \(e\left(\frac{227}{468}\right)\) | \(e\left(\frac{401}{468}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{31}{234}\right)\) | \(e\left(\frac{157}{234}\right)\) | \(e\left(\frac{133}{468}\right)\) | \(e\left(\frac{43}{78}\right)\) |
| \(\chi_{9126}(1955,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{25}{468}\right)\) | \(e\left(\frac{17}{468}\right)\) | \(e\left(\frac{263}{468}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{25}{234}\right)\) | \(e\left(\frac{187}{234}\right)\) | \(e\left(\frac{379}{468}\right)\) | \(e\left(\frac{7}{78}\right)\) |