from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4563, base_ring=CyclotomicField(468))
M = H._module
chi = DirichletCharacter(H, M([130,27]))
chi.galois_orbit()
[g,chi] = znchar(Mod(5,4563))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(4563\) | |
| Conductor: | \(4563\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(468\) | 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: | $\Q(\zeta_{468})$ |
| Fixed field: | Number field defined by a degree 468 polynomial (not computed) |
First 31 of 144 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{4563}(5,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{157}{468}\right)\) | \(e\left(\frac{157}{234}\right)\) | \(e\left(\frac{425}{468}\right)\) | \(e\left(\frac{289}{468}\right)\) | \(e\left(\frac{1}{156}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{259}{468}\right)\) | \(e\left(\frac{223}{234}\right)\) | \(e\left(\frac{40}{117}\right)\) | \(e\left(\frac{23}{39}\right)\) |
| \(\chi_{4563}(47,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{371}{468}\right)\) | \(e\left(\frac{137}{234}\right)\) | \(e\left(\frac{271}{468}\right)\) | \(e\left(\frac{203}{468}\right)\) | \(e\left(\frac{59}{156}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{305}{468}\right)\) | \(e\left(\frac{53}{234}\right)\) | \(e\left(\frac{20}{117}\right)\) | \(e\left(\frac{31}{39}\right)\) |
| \(\chi_{4563}(83,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{161}{468}\right)\) | \(e\left(\frac{161}{234}\right)\) | \(e\left(\frac{409}{468}\right)\) | \(e\left(\frac{353}{468}\right)\) | \(e\left(\frac{5}{156}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{203}{468}\right)\) | \(e\left(\frac{23}{234}\right)\) | \(e\left(\frac{44}{117}\right)\) | \(e\left(\frac{37}{39}\right)\) |
| \(\chi_{4563}(86,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{468}\right)\) | \(e\left(\frac{31}{234}\right)\) | \(e\left(\frac{227}{468}\right)\) | \(e\left(\frac{379}{468}\right)\) | \(e\left(\frac{31}{156}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{385}{468}\right)\) | \(e\left(\frac{205}{234}\right)\) | \(e\left(\frac{31}{117}\right)\) | \(e\left(\frac{11}{39}\right)\) |
| \(\chi_{4563}(122,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{397}{468}\right)\) | \(e\left(\frac{163}{234}\right)\) | \(e\left(\frac{401}{468}\right)\) | \(e\left(\frac{385}{468}\right)\) | \(e\left(\frac{85}{156}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{175}{468}\right)\) | \(e\left(\frac{157}{234}\right)\) | \(e\left(\frac{46}{117}\right)\) | \(e\left(\frac{5}{39}\right)\) |
| \(\chi_{4563}(164,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{287}{468}\right)\) | \(e\left(\frac{53}{234}\right)\) | \(e\left(\frac{139}{468}\right)\) | \(e\left(\frac{263}{468}\right)\) | \(e\left(\frac{131}{156}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{77}{468}\right)\) | \(e\left(\frac{41}{234}\right)\) | \(e\left(\frac{53}{117}\right)\) | \(e\left(\frac{10}{39}\right)\) |
| \(\chi_{4563}(200,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{401}{468}\right)\) | \(e\left(\frac{167}{234}\right)\) | \(e\left(\frac{385}{468}\right)\) | \(e\left(\frac{449}{468}\right)\) | \(e\left(\frac{89}{156}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{119}{468}\right)\) | \(e\left(\frac{191}{234}\right)\) | \(e\left(\frac{50}{117}\right)\) | \(e\left(\frac{19}{39}\right)\) |
| \(\chi_{4563}(203,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{415}{468}\right)\) | \(e\left(\frac{181}{234}\right)\) | \(e\left(\frac{95}{468}\right)\) | \(e\left(\frac{439}{468}\right)\) | \(e\left(\frac{103}{156}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{157}{468}\right)\) | \(e\left(\frac{193}{234}\right)\) | \(e\left(\frac{64}{117}\right)\) | \(e\left(\frac{29}{39}\right)\) |
| \(\chi_{4563}(281,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{203}{468}\right)\) | \(e\left(\frac{203}{234}\right)\) | \(e\left(\frac{7}{468}\right)\) | \(e\left(\frac{323}{468}\right)\) | \(e\left(\frac{47}{156}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{317}{468}\right)\) | \(e\left(\frac{29}{234}\right)\) | \(e\left(\frac{86}{117}\right)\) | \(e\left(\frac{28}{39}\right)\) |
| \(\chi_{4563}(317,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{173}{468}\right)\) | \(e\left(\frac{173}{234}\right)\) | \(e\left(\frac{361}{468}\right)\) | \(e\left(\frac{77}{468}\right)\) | \(e\left(\frac{17}{156}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{35}{468}\right)\) | \(e\left(\frac{125}{234}\right)\) | \(e\left(\frac{56}{117}\right)\) | \(e\left(\frac{1}{39}\right)\) |
| \(\chi_{4563}(320,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{331}{468}\right)\) | \(e\left(\frac{97}{234}\right)\) | \(e\left(\frac{431}{468}\right)\) | \(e\left(\frac{31}{468}\right)\) | \(e\left(\frac{19}{156}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{397}{468}\right)\) | \(e\left(\frac{181}{234}\right)\) | \(e\left(\frac{97}{117}\right)\) | \(e\left(\frac{8}{39}\right)\) |
| \(\chi_{4563}(356,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{409}{468}\right)\) | \(e\left(\frac{175}{234}\right)\) | \(e\left(\frac{353}{468}\right)\) | \(e\left(\frac{109}{468}\right)\) | \(e\left(\frac{97}{156}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{7}{468}\right)\) | \(e\left(\frac{25}{234}\right)\) | \(e\left(\frac{58}{117}\right)\) | \(e\left(\frac{8}{39}\right)\) |
| \(\chi_{4563}(398,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{119}{468}\right)\) | \(e\left(\frac{119}{234}\right)\) | \(e\left(\frac{343}{468}\right)\) | \(e\left(\frac{383}{468}\right)\) | \(e\left(\frac{119}{156}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{89}{468}\right)\) | \(e\left(\frac{17}{234}\right)\) | \(e\left(\frac{2}{117}\right)\) | \(e\left(\frac{7}{39}\right)\) |
| \(\chi_{4563}(434,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{413}{468}\right)\) | \(e\left(\frac{179}{234}\right)\) | \(e\left(\frac{337}{468}\right)\) | \(e\left(\frac{173}{468}\right)\) | \(e\left(\frac{101}{156}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{419}{468}\right)\) | \(e\left(\frac{59}{234}\right)\) | \(e\left(\frac{62}{117}\right)\) | \(e\left(\frac{22}{39}\right)\) |
| \(\chi_{4563}(473,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{181}{468}\right)\) | \(e\left(\frac{181}{234}\right)\) | \(e\left(\frac{329}{468}\right)\) | \(e\left(\frac{205}{468}\right)\) | \(e\left(\frac{25}{156}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{391}{468}\right)\) | \(e\left(\frac{193}{234}\right)\) | \(e\left(\frac{64}{117}\right)\) | \(e\left(\frac{29}{39}\right)\) |
| \(\chi_{4563}(515,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{35}{468}\right)\) | \(e\left(\frac{35}{234}\right)\) | \(e\left(\frac{211}{468}\right)\) | \(e\left(\frac{443}{468}\right)\) | \(e\left(\frac{35}{156}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{329}{468}\right)\) | \(e\left(\frac{5}{234}\right)\) | \(e\left(\frac{35}{117}\right)\) | \(e\left(\frac{25}{39}\right)\) |
| \(\chi_{4563}(551,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{185}{468}\right)\) | \(e\left(\frac{185}{234}\right)\) | \(e\left(\frac{313}{468}\right)\) | \(e\left(\frac{269}{468}\right)\) | \(e\left(\frac{29}{156}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{335}{468}\right)\) | \(e\left(\frac{227}{234}\right)\) | \(e\left(\frac{68}{117}\right)\) | \(e\left(\frac{4}{39}\right)\) |
| \(\chi_{4563}(554,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{163}{468}\right)\) | \(e\left(\frac{163}{234}\right)\) | \(e\left(\frac{167}{468}\right)\) | \(e\left(\frac{151}{468}\right)\) | \(e\left(\frac{7}{156}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{409}{468}\right)\) | \(e\left(\frac{157}{234}\right)\) | \(e\left(\frac{46}{117}\right)\) | \(e\left(\frac{5}{39}\right)\) |
| \(\chi_{4563}(590,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{421}{468}\right)\) | \(e\left(\frac{187}{234}\right)\) | \(e\left(\frac{305}{468}\right)\) | \(e\left(\frac{301}{468}\right)\) | \(e\left(\frac{109}{156}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{307}{468}\right)\) | \(e\left(\frac{127}{234}\right)\) | \(e\left(\frac{70}{117}\right)\) | \(e\left(\frac{11}{39}\right)\) |
| \(\chi_{4563}(632,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{419}{468}\right)\) | \(e\left(\frac{185}{234}\right)\) | \(e\left(\frac{79}{468}\right)\) | \(e\left(\frac{35}{468}\right)\) | \(e\left(\frac{107}{156}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{101}{468}\right)\) | \(e\left(\frac{227}{234}\right)\) | \(e\left(\frac{68}{117}\right)\) | \(e\left(\frac{4}{39}\right)\) |
| \(\chi_{4563}(668,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{425}{468}\right)\) | \(e\left(\frac{191}{234}\right)\) | \(e\left(\frac{289}{468}\right)\) | \(e\left(\frac{365}{468}\right)\) | \(e\left(\frac{113}{156}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{251}{468}\right)\) | \(e\left(\frac{161}{234}\right)\) | \(e\left(\frac{74}{117}\right)\) | \(e\left(\frac{25}{39}\right)\) |
| \(\chi_{4563}(671,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{468}\right)\) | \(e\left(\frac{79}{234}\right)\) | \(e\left(\frac{35}{468}\right)\) | \(e\left(\frac{211}{468}\right)\) | \(e\left(\frac{79}{156}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{181}{468}\right)\) | \(e\left(\frac{145}{234}\right)\) | \(e\left(\frac{79}{117}\right)\) | \(e\left(\frac{23}{39}\right)\) |
| \(\chi_{4563}(707,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{193}{468}\right)\) | \(e\left(\frac{193}{234}\right)\) | \(e\left(\frac{281}{468}\right)\) | \(e\left(\frac{397}{468}\right)\) | \(e\left(\frac{37}{156}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{223}{468}\right)\) | \(e\left(\frac{61}{234}\right)\) | \(e\left(\frac{76}{117}\right)\) | \(e\left(\frac{32}{39}\right)\) |
| \(\chi_{4563}(749,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{335}{468}\right)\) | \(e\left(\frac{101}{234}\right)\) | \(e\left(\frac{415}{468}\right)\) | \(e\left(\frac{95}{468}\right)\) | \(e\left(\frac{23}{156}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{341}{468}\right)\) | \(e\left(\frac{215}{234}\right)\) | \(e\left(\frac{101}{117}\right)\) | \(e\left(\frac{22}{39}\right)\) |
| \(\chi_{4563}(785,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{197}{468}\right)\) | \(e\left(\frac{197}{234}\right)\) | \(e\left(\frac{265}{468}\right)\) | \(e\left(\frac{461}{468}\right)\) | \(e\left(\frac{41}{156}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{167}{468}\right)\) | \(e\left(\frac{95}{234}\right)\) | \(e\left(\frac{80}{117}\right)\) | \(e\left(\frac{7}{39}\right)\) |
| \(\chi_{4563}(788,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{463}{468}\right)\) | \(e\left(\frac{229}{234}\right)\) | \(e\left(\frac{371}{468}\right)\) | \(e\left(\frac{271}{468}\right)\) | \(e\left(\frac{151}{156}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{421}{468}\right)\) | \(e\left(\frac{133}{234}\right)\) | \(e\left(\frac{112}{117}\right)\) | \(e\left(\frac{2}{39}\right)\) |
| \(\chi_{4563}(824,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{433}{468}\right)\) | \(e\left(\frac{199}{234}\right)\) | \(e\left(\frac{257}{468}\right)\) | \(e\left(\frac{25}{468}\right)\) | \(e\left(\frac{121}{156}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{139}{468}\right)\) | \(e\left(\frac{229}{234}\right)\) | \(e\left(\frac{82}{117}\right)\) | \(e\left(\frac{14}{39}\right)\) |
| \(\chi_{4563}(866,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{251}{468}\right)\) | \(e\left(\frac{17}{234}\right)\) | \(e\left(\frac{283}{468}\right)\) | \(e\left(\frac{155}{468}\right)\) | \(e\left(\frac{95}{156}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{113}{468}\right)\) | \(e\left(\frac{203}{234}\right)\) | \(e\left(\frac{17}{117}\right)\) | \(e\left(\frac{1}{39}\right)\) |
| \(\chi_{4563}(902,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{437}{468}\right)\) | \(e\left(\frac{203}{234}\right)\) | \(e\left(\frac{241}{468}\right)\) | \(e\left(\frac{89}{468}\right)\) | \(e\left(\frac{125}{156}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{83}{468}\right)\) | \(e\left(\frac{29}{234}\right)\) | \(e\left(\frac{86}{117}\right)\) | \(e\left(\frac{28}{39}\right)\) |
| \(\chi_{4563}(905,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{379}{468}\right)\) | \(e\left(\frac{145}{234}\right)\) | \(e\left(\frac{239}{468}\right)\) | \(e\left(\frac{331}{468}\right)\) | \(e\left(\frac{67}{156}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{193}{468}\right)\) | \(e\left(\frac{121}{234}\right)\) | \(e\left(\frac{28}{117}\right)\) | \(e\left(\frac{20}{39}\right)\) |
| \(\chi_{4563}(941,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{205}{468}\right)\) | \(e\left(\frac{205}{234}\right)\) | \(e\left(\frac{233}{468}\right)\) | \(e\left(\frac{121}{468}\right)\) | \(e\left(\frac{49}{156}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{55}{468}\right)\) | \(e\left(\frac{163}{234}\right)\) | \(e\left(\frac{88}{117}\right)\) | \(e\left(\frac{35}{39}\right)\) |