from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8043, base_ring=CyclotomicField(1146))
M = H._module
chi = DirichletCharacter(H, M([573,191,468]))
chi.galois_orbit()
[g,chi] = znchar(Mod(17,8043))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(8043\) | |
| Conductor: | \(8043\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1146\) | 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: | $\Q(\zeta_{573})$ |
| Fixed field: | Number field defined by a degree 1146 polynomial (not computed) |
First 31 of 380 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{8043}(17,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{637}{1146}\right)\) | \(e\left(\frac{64}{573}\right)\) | \(e\left(\frac{425}{573}\right)\) | \(e\left(\frac{255}{382}\right)\) | \(e\left(\frac{341}{1146}\right)\) | \(e\left(\frac{713}{1146}\right)\) | \(e\left(\frac{109}{382}\right)\) | \(e\left(\frac{128}{573}\right)\) | \(e\left(\frac{214}{573}\right)\) | \(e\left(\frac{1057}{1146}\right)\) |
| \(\chi_{8043}(38,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{505}{1146}\right)\) | \(e\left(\frac{505}{573}\right)\) | \(e\left(\frac{14}{573}\right)\) | \(e\left(\frac{123}{382}\right)\) | \(e\left(\frac{533}{1146}\right)\) | \(e\left(\frac{281}{1146}\right)\) | \(e\left(\frac{111}{382}\right)\) | \(e\left(\frac{437}{573}\right)\) | \(e\left(\frac{274}{573}\right)\) | \(e\left(\frac{775}{1146}\right)\) |
| \(\chi_{8043}(68,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1031}{1146}\right)\) | \(e\left(\frac{458}{573}\right)\) | \(e\left(\frac{445}{573}\right)\) | \(e\left(\frac{267}{382}\right)\) | \(e\left(\frac{775}{1146}\right)\) | \(e\left(\frac{787}{1146}\right)\) | \(e\left(\frac{213}{382}\right)\) | \(e\left(\frac{343}{573}\right)\) | \(e\left(\frac{278}{573}\right)\) | \(e\left(\frac{527}{1146}\right)\) |
| \(\chi_{8043}(101,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{277}{1146}\right)\) | \(e\left(\frac{277}{573}\right)\) | \(e\left(\frac{398}{573}\right)\) | \(e\left(\frac{277}{382}\right)\) | \(e\left(\frac{1073}{1146}\right)\) | \(e\left(\frac{785}{1146}\right)\) | \(e\left(\frac{45}{382}\right)\) | \(e\left(\frac{554}{573}\right)\) | \(e\left(\frac{13}{573}\right)\) | \(e\left(\frac{913}{1146}\right)\) |
| \(\chi_{8043}(110,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{827}{1146}\right)\) | \(e\left(\frac{254}{573}\right)\) | \(e\left(\frac{487}{573}\right)\) | \(e\left(\frac{63}{382}\right)\) | \(e\left(\frac{655}{1146}\right)\) | \(e\left(\frac{1057}{1146}\right)\) | \(e\left(\frac{355}{382}\right)\) | \(e\left(\frac{508}{573}\right)\) | \(e\left(\frac{527}{573}\right)\) | \(e\left(\frac{1133}{1146}\right)\) |
| \(\chi_{8043}(143,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{193}{1146}\right)\) | \(e\left(\frac{193}{573}\right)\) | \(e\left(\frac{449}{573}\right)\) | \(e\left(\frac{193}{382}\right)\) | \(e\left(\frac{1091}{1146}\right)\) | \(e\left(\frac{1031}{1146}\right)\) | \(e\left(\frac{81}{382}\right)\) | \(e\left(\frac{386}{573}\right)\) | \(e\left(\frac{520}{573}\right)\) | \(e\left(\frac{421}{1146}\right)\) |
| \(\chi_{8043}(152,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{899}{1146}\right)\) | \(e\left(\frac{326}{573}\right)\) | \(e\left(\frac{34}{573}\right)\) | \(e\left(\frac{135}{382}\right)\) | \(e\left(\frac{967}{1146}\right)\) | \(e\left(\frac{355}{1146}\right)\) | \(e\left(\frac{215}{382}\right)\) | \(e\left(\frac{79}{573}\right)\) | \(e\left(\frac{338}{573}\right)\) | \(e\left(\frac{245}{1146}\right)\) |
| \(\chi_{8043}(173,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1079}{1146}\right)\) | \(e\left(\frac{506}{573}\right)\) | \(e\left(\frac{334}{573}\right)\) | \(e\left(\frac{315}{382}\right)\) | \(e\left(\frac{601}{1146}\right)\) | \(e\left(\frac{319}{1146}\right)\) | \(e\left(\frac{247}{382}\right)\) | \(e\left(\frac{439}{573}\right)\) | \(e\left(\frac{152}{573}\right)\) | \(e\left(\frac{317}{1146}\right)\) |
| \(\chi_{8043}(185,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1105}{1146}\right)\) | \(e\left(\frac{532}{573}\right)\) | \(e\left(\frac{59}{573}\right)\) | \(e\left(\frac{341}{382}\right)\) | \(e\left(\frac{77}{1146}\right)\) | \(e\left(\frac{161}{1146}\right)\) | \(e\left(\frac{345}{382}\right)\) | \(e\left(\frac{491}{573}\right)\) | \(e\left(\frac{418}{573}\right)\) | \(e\left(\frac{1015}{1146}\right)\) |
| \(\chi_{8043}(206,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{757}{1146}\right)\) | \(e\left(\frac{184}{573}\right)\) | \(e\left(\frac{434}{573}\right)\) | \(e\left(\frac{375}{382}\right)\) | \(e\left(\frac{479}{1146}\right)\) | \(e\left(\frac{689}{1146}\right)\) | \(e\left(\frac{3}{382}\right)\) | \(e\left(\frac{368}{573}\right)\) | \(e\left(\frac{472}{573}\right)\) | \(e\left(\frac{1105}{1146}\right)\) |
| \(\chi_{8043}(227,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1081}{1146}\right)\) | \(e\left(\frac{508}{573}\right)\) | \(e\left(\frac{401}{573}\right)\) | \(e\left(\frac{317}{382}\right)\) | \(e\left(\frac{737}{1146}\right)\) | \(e\left(\frac{395}{1146}\right)\) | \(e\left(\frac{137}{382}\right)\) | \(e\left(\frac{443}{573}\right)\) | \(e\left(\frac{481}{573}\right)\) | \(e\left(\frac{547}{1146}\right)\) |
| \(\chi_{8043}(248,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{85}{1146}\right)\) | \(e\left(\frac{85}{573}\right)\) | \(e\left(\frac{269}{573}\right)\) | \(e\left(\frac{85}{382}\right)\) | \(e\left(\frac{623}{1146}\right)\) | \(e\left(\frac{365}{1146}\right)\) | \(e\left(\frac{291}{382}\right)\) | \(e\left(\frac{170}{573}\right)\) | \(e\left(\frac{517}{573}\right)\) | \(e\left(\frac{607}{1146}\right)\) |
| \(\chi_{8043}(278,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1073}{1146}\right)\) | \(e\left(\frac{500}{573}\right)\) | \(e\left(\frac{133}{573}\right)\) | \(e\left(\frac{309}{382}\right)\) | \(e\left(\frac{193}{1146}\right)\) | \(e\left(\frac{91}{1146}\right)\) | \(e\left(\frac{195}{382}\right)\) | \(e\left(\frac{427}{573}\right)\) | \(e\left(\frac{311}{573}\right)\) | \(e\left(\frac{773}{1146}\right)\) |
| \(\chi_{8043}(353,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{175}{1146}\right)\) | \(e\left(\frac{175}{573}\right)\) | \(e\left(\frac{419}{573}\right)\) | \(e\left(\frac{175}{382}\right)\) | \(e\left(\frac{1013}{1146}\right)\) | \(e\left(\frac{347}{1146}\right)\) | \(e\left(\frac{307}{382}\right)\) | \(e\left(\frac{350}{573}\right)\) | \(e\left(\frac{424}{573}\right)\) | \(e\left(\frac{643}{1146}\right)\) |
| \(\chi_{8043}(395,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{925}{1146}\right)\) | \(e\left(\frac{352}{573}\right)\) | \(e\left(\frac{332}{573}\right)\) | \(e\left(\frac{161}{382}\right)\) | \(e\left(\frac{443}{1146}\right)\) | \(e\left(\frac{197}{1146}\right)\) | \(e\left(\frac{313}{382}\right)\) | \(e\left(\frac{131}{573}\right)\) | \(e\left(\frac{31}{573}\right)\) | \(e\left(\frac{943}{1146}\right)\) |
| \(\chi_{8043}(404,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{671}{1146}\right)\) | \(e\left(\frac{98}{573}\right)\) | \(e\left(\frac{418}{573}\right)\) | \(e\left(\frac{289}{382}\right)\) | \(e\left(\frac{361}{1146}\right)\) | \(e\left(\frac{859}{1146}\right)\) | \(e\left(\frac{149}{382}\right)\) | \(e\left(\frac{196}{573}\right)\) | \(e\left(\frac{77}{573}\right)\) | \(e\left(\frac{383}{1146}\right)\) |
| \(\chi_{8043}(425,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{677}{1146}\right)\) | \(e\left(\frac{104}{573}\right)\) | \(e\left(\frac{46}{573}\right)\) | \(e\left(\frac{295}{382}\right)\) | \(e\left(\frac{769}{1146}\right)\) | \(e\left(\frac{1087}{1146}\right)\) | \(e\left(\frac{201}{382}\right)\) | \(e\left(\frac{208}{573}\right)\) | \(e\left(\frac{491}{573}\right)\) | \(e\left(\frac{1073}{1146}\right)\) |
| \(\chi_{8043}(437,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{835}{1146}\right)\) | \(e\left(\frac{262}{573}\right)\) | \(e\left(\frac{182}{573}\right)\) | \(e\left(\frac{71}{382}\right)\) | \(e\left(\frac{53}{1146}\right)\) | \(e\left(\frac{215}{1146}\right)\) | \(e\left(\frac{297}{382}\right)\) | \(e\left(\frac{524}{573}\right)\) | \(e\left(\frac{124}{573}\right)\) | \(e\left(\frac{907}{1146}\right)\) |
| \(\chi_{8043}(446,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{629}{1146}\right)\) | \(e\left(\frac{56}{573}\right)\) | \(e\left(\frac{157}{573}\right)\) | \(e\left(\frac{247}{382}\right)\) | \(e\left(\frac{943}{1146}\right)\) | \(e\left(\frac{409}{1146}\right)\) | \(e\left(\frac{167}{382}\right)\) | \(e\left(\frac{112}{573}\right)\) | \(e\left(\frac{44}{573}\right)\) | \(e\left(\frac{137}{1146}\right)\) |
| \(\chi_{8043}(458,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{571}{1146}\right)\) | \(e\left(\frac{571}{573}\right)\) | \(e\left(\frac{506}{573}\right)\) | \(e\left(\frac{189}{382}\right)\) | \(e\left(\frac{437}{1146}\right)\) | \(e\left(\frac{497}{1146}\right)\) | \(e\left(\frac{301}{382}\right)\) | \(e\left(\frac{569}{573}\right)\) | \(e\left(\frac{244}{573}\right)\) | \(e\left(\frac{343}{1146}\right)\) |
| \(\chi_{8043}(467,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{683}{1146}\right)\) | \(e\left(\frac{110}{573}\right)\) | \(e\left(\frac{247}{573}\right)\) | \(e\left(\frac{301}{382}\right)\) | \(e\left(\frac{31}{1146}\right)\) | \(e\left(\frac{169}{1146}\right)\) | \(e\left(\frac{253}{382}\right)\) | \(e\left(\frac{220}{573}\right)\) | \(e\left(\frac{332}{573}\right)\) | \(e\left(\frac{617}{1146}\right)\) |
| \(\chi_{8043}(479,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{943}{1146}\right)\) | \(e\left(\frac{370}{573}\right)\) | \(e\left(\frac{362}{573}\right)\) | \(e\left(\frac{179}{382}\right)\) | \(e\left(\frac{521}{1146}\right)\) | \(e\left(\frac{881}{1146}\right)\) | \(e\left(\frac{87}{382}\right)\) | \(e\left(\frac{167}{573}\right)\) | \(e\left(\frac{127}{573}\right)\) | \(e\left(\frac{721}{1146}\right)\) |
| \(\chi_{8043}(509,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{635}{1146}\right)\) | \(e\left(\frac{62}{573}\right)\) | \(e\left(\frac{358}{573}\right)\) | \(e\left(\frac{253}{382}\right)\) | \(e\left(\frac{205}{1146}\right)\) | \(e\left(\frac{637}{1146}\right)\) | \(e\left(\frac{219}{382}\right)\) | \(e\left(\frac{124}{573}\right)\) | \(e\left(\frac{458}{573}\right)\) | \(e\left(\frac{827}{1146}\right)\) |
| \(\chi_{8043}(521,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{109}{1146}\right)\) | \(e\left(\frac{109}{573}\right)\) | \(e\left(\frac{500}{573}\right)\) | \(e\left(\frac{109}{382}\right)\) | \(e\left(\frac{1109}{1146}\right)\) | \(e\left(\frac{131}{1146}\right)\) | \(e\left(\frac{117}{382}\right)\) | \(e\left(\frac{218}{573}\right)\) | \(e\left(\frac{454}{573}\right)\) | \(e\left(\frac{1075}{1146}\right)\) |
| \(\chi_{8043}(530,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{1146}\right)\) | \(e\left(\frac{47}{573}\right)\) | \(e\left(\frac{142}{573}\right)\) | \(e\left(\frac{47}{382}\right)\) | \(e\left(\frac{331}{1146}\right)\) | \(e\left(\frac{67}{1146}\right)\) | \(e\left(\frac{89}{382}\right)\) | \(e\left(\frac{94}{573}\right)\) | \(e\left(\frac{569}{573}\right)\) | \(e\left(\frac{821}{1146}\right)\) |
| \(\chi_{8043}(551,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{689}{1146}\right)\) | \(e\left(\frac{116}{573}\right)\) | \(e\left(\frac{448}{573}\right)\) | \(e\left(\frac{307}{382}\right)\) | \(e\left(\frac{439}{1146}\right)\) | \(e\left(\frac{397}{1146}\right)\) | \(e\left(\frac{305}{382}\right)\) | \(e\left(\frac{232}{573}\right)\) | \(e\left(\frac{173}{573}\right)\) | \(e\left(\frac{161}{1146}\right)\) |
| \(\chi_{8043}(572,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{587}{1146}\right)\) | \(e\left(\frac{14}{573}\right)\) | \(e\left(\frac{469}{573}\right)\) | \(e\left(\frac{205}{382}\right)\) | \(e\left(\frac{379}{1146}\right)\) | \(e\left(\frac{1105}{1146}\right)\) | \(e\left(\frac{185}{382}\right)\) | \(e\left(\frac{28}{573}\right)\) | \(e\left(\frac{11}{573}\right)\) | \(e\left(\frac{1037}{1146}\right)\) |
| \(\chi_{8043}(584,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{493}{1146}\right)\) | \(e\left(\frac{493}{573}\right)\) | \(e\left(\frac{185}{573}\right)\) | \(e\left(\frac{111}{382}\right)\) | \(e\left(\frac{863}{1146}\right)\) | \(e\left(\frac{971}{1146}\right)\) | \(e\left(\frac{7}{382}\right)\) | \(e\left(\frac{413}{573}\right)\) | \(e\left(\frac{19}{573}\right)\) | \(e\left(\frac{541}{1146}\right)\) |
| \(\chi_{8043}(626,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{745}{1146}\right)\) | \(e\left(\frac{172}{573}\right)\) | \(e\left(\frac{32}{573}\right)\) | \(e\left(\frac{363}{382}\right)\) | \(e\left(\frac{809}{1146}\right)\) | \(e\left(\frac{233}{1146}\right)\) | \(e\left(\frac{281}{382}\right)\) | \(e\left(\frac{344}{573}\right)\) | \(e\left(\frac{217}{573}\right)\) | \(e\left(\frac{871}{1146}\right)\) |
| \(\chi_{8043}(635,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{641}{1146}\right)\) | \(e\left(\frac{68}{573}\right)\) | \(e\left(\frac{559}{573}\right)\) | \(e\left(\frac{259}{382}\right)\) | \(e\left(\frac{613}{1146}\right)\) | \(e\left(\frac{865}{1146}\right)\) | \(e\left(\frac{271}{382}\right)\) | \(e\left(\frac{136}{573}\right)\) | \(e\left(\frac{299}{573}\right)\) | \(e\left(\frac{371}{1146}\right)\) |
| \(\chi_{8043}(677,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{1146}\right)\) | \(e\left(\frac{53}{573}\right)\) | \(e\left(\frac{343}{573}\right)\) | \(e\left(\frac{53}{382}\right)\) | \(e\left(\frac{739}{1146}\right)\) | \(e\left(\frac{295}{1146}\right)\) | \(e\left(\frac{141}{382}\right)\) | \(e\left(\frac{106}{573}\right)\) | \(e\left(\frac{410}{573}\right)\) | \(e\left(\frac{365}{1146}\right)\) |