from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8043, base_ring=CyclotomicField(1146))
M = H._module
chi = DirichletCharacter(H, M([573,382,402]))
chi.galois_orbit()
[g,chi] = znchar(Mod(2,8043))
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: | odd | 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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{8043}(2,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{197}{1146}\right)\) | \(e\left(\frac{197}{573}\right)\) | \(e\left(\frac{593}{1146}\right)\) | \(e\left(\frac{197}{382}\right)\) | \(e\left(\frac{395}{573}\right)\) | \(e\left(\frac{37}{1146}\right)\) | \(e\left(\frac{26}{191}\right)\) | \(e\left(\frac{394}{573}\right)\) | \(e\left(\frac{637}{1146}\right)\) | \(e\left(\frac{154}{573}\right)\) |
| \(\chi_{8043}(23,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{527}{1146}\right)\) | \(e\left(\frac{527}{573}\right)\) | \(e\left(\frac{929}{1146}\right)\) | \(e\left(\frac{145}{382}\right)\) | \(e\left(\frac{155}{573}\right)\) | \(e\left(\frac{1117}{1146}\right)\) | \(e\left(\frac{119}{191}\right)\) | \(e\left(\frac{481}{573}\right)\) | \(e\left(\frac{337}{1146}\right)\) | \(e\left(\frac{220}{573}\right)\) |
| \(\chi_{8043}(32,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{985}{1146}\right)\) | \(e\left(\frac{412}{573}\right)\) | \(e\left(\frac{673}{1146}\right)\) | \(e\left(\frac{221}{382}\right)\) | \(e\left(\frac{256}{573}\right)\) | \(e\left(\frac{185}{1146}\right)\) | \(e\left(\frac{130}{191}\right)\) | \(e\left(\frac{251}{573}\right)\) | \(e\left(\frac{893}{1146}\right)\) | \(e\left(\frac{197}{573}\right)\) |
| \(\chi_{8043}(65,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{749}{1146}\right)\) | \(e\left(\frac{176}{573}\right)\) | \(e\left(\frac{905}{1146}\right)\) | \(e\left(\frac{367}{382}\right)\) | \(e\left(\frac{254}{573}\right)\) | \(e\left(\frac{385}{1146}\right)\) | \(e\left(\frac{126}{191}\right)\) | \(e\left(\frac{352}{573}\right)\) | \(e\left(\frac{31}{1146}\right)\) | \(e\left(\frac{379}{573}\right)\) |
| \(\chi_{8043}(86,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{293}{1146}\right)\) | \(e\left(\frac{293}{573}\right)\) | \(e\left(\frac{149}{1146}\right)\) | \(e\left(\frac{293}{382}\right)\) | \(e\left(\frac{221}{573}\right)\) | \(e\left(\frac{247}{1146}\right)\) | \(e\left(\frac{60}{191}\right)\) | \(e\left(\frac{13}{573}\right)\) | \(e\left(\frac{133}{1146}\right)\) | \(e\left(\frac{517}{573}\right)\) |
| \(\chi_{8043}(116,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{775}{1146}\right)\) | \(e\left(\frac{202}{573}\right)\) | \(e\left(\frac{355}{1146}\right)\) | \(e\left(\frac{11}{382}\right)\) | \(e\left(\frac{565}{573}\right)\) | \(e\left(\frac{227}{1146}\right)\) | \(e\left(\frac{175}{191}\right)\) | \(e\left(\frac{404}{573}\right)\) | \(e\left(\frac{563}{1146}\right)\) | \(e\left(\frac{155}{573}\right)\) |
| \(\chi_{8043}(128,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{233}{1146}\right)\) | \(e\left(\frac{233}{573}\right)\) | \(e\left(\frac{713}{1146}\right)\) | \(e\left(\frac{233}{382}\right)\) | \(e\left(\frac{473}{573}\right)\) | \(e\left(\frac{259}{1146}\right)\) | \(e\left(\frac{182}{191}\right)\) | \(e\left(\frac{466}{573}\right)\) | \(e\left(\frac{1021}{1146}\right)\) | \(e\left(\frac{505}{573}\right)\) |
| \(\chi_{8043}(137,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{385}{1146}\right)\) | \(e\left(\frac{385}{573}\right)\) | \(e\left(\frac{583}{1146}\right)\) | \(e\left(\frac{3}{382}\right)\) | \(e\left(\frac{484}{573}\right)\) | \(e\left(\frac{305}{1146}\right)\) | \(e\left(\frac{13}{191}\right)\) | \(e\left(\frac{197}{573}\right)\) | \(e\left(\frac{605}{1146}\right)\) | \(e\left(\frac{77}{573}\right)\) |
| \(\chi_{8043}(149,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{269}{1146}\right)\) | \(e\left(\frac{269}{573}\right)\) | \(e\left(\frac{833}{1146}\right)\) | \(e\left(\frac{269}{382}\right)\) | \(e\left(\frac{551}{573}\right)\) | \(e\left(\frac{481}{1146}\right)\) | \(e\left(\frac{147}{191}\right)\) | \(e\left(\frac{538}{573}\right)\) | \(e\left(\frac{259}{1146}\right)\) | \(e\left(\frac{283}{573}\right)\) |
| \(\chi_{8043}(200,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{631}{1146}\right)\) | \(e\left(\frac{58}{573}\right)\) | \(e\left(\frac{1021}{1146}\right)\) | \(e\left(\frac{249}{382}\right)\) | \(e\left(\frac{253}{573}\right)\) | \(e\left(\frac{485}{1146}\right)\) | \(e\left(\frac{124}{191}\right)\) | \(e\left(\frac{116}{573}\right)\) | \(e\left(\frac{173}{1146}\right)\) | \(e\left(\frac{470}{573}\right)\) |
| \(\chi_{8043}(242,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{271}{1146}\right)\) | \(e\left(\frac{271}{573}\right)\) | \(e\left(\frac{967}{1146}\right)\) | \(e\left(\frac{271}{382}\right)\) | \(e\left(\frac{46}{573}\right)\) | \(e\left(\frac{557}{1146}\right)\) | \(e\left(\frac{92}{191}\right)\) | \(e\left(\frac{542}{573}\right)\) | \(e\left(\frac{917}{1146}\right)\) | \(e\left(\frac{398}{573}\right)\) |
| \(\chi_{8043}(263,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{187}{1146}\right)\) | \(e\left(\frac{187}{573}\right)\) | \(e\left(\frac{1069}{1146}\right)\) | \(e\left(\frac{187}{382}\right)\) | \(e\left(\frac{55}{573}\right)\) | \(e\left(\frac{803}{1146}\right)\) | \(e\left(\frac{110}{191}\right)\) | \(e\left(\frac{374}{573}\right)\) | \(e\left(\frac{785}{1146}\right)\) | \(e\left(\frac{152}{573}\right)\) |
| \(\chi_{8043}(284,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1099}{1146}\right)\) | \(e\left(\frac{526}{573}\right)\) | \(e\left(\frac{289}{1146}\right)\) | \(e\left(\frac{335}{382}\right)\) | \(e\left(\frac{121}{573}\right)\) | \(e\left(\frac{1079}{1146}\right)\) | \(e\left(\frac{51}{191}\right)\) | \(e\left(\frac{479}{573}\right)\) | \(e\left(\frac{581}{1146}\right)\) | \(e\left(\frac{449}{573}\right)\) |
| \(\chi_{8043}(305,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1075}{1146}\right)\) | \(e\left(\frac{502}{573}\right)\) | \(e\left(\frac{973}{1146}\right)\) | \(e\left(\frac{311}{382}\right)\) | \(e\left(\frac{451}{573}\right)\) | \(e\left(\frac{167}{1146}\right)\) | \(e\left(\frac{138}{191}\right)\) | \(e\left(\frac{431}{573}\right)\) | \(e\left(\frac{707}{1146}\right)\) | \(e\left(\frac{215}{573}\right)\) |
| \(\chi_{8043}(317,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{383}{1146}\right)\) | \(e\left(\frac{383}{573}\right)\) | \(e\left(\frac{449}{1146}\right)\) | \(e\left(\frac{1}{382}\right)\) | \(e\left(\frac{416}{573}\right)\) | \(e\left(\frac{229}{1146}\right)\) | \(e\left(\frac{68}{191}\right)\) | \(e\left(\frac{193}{573}\right)\) | \(e\left(\frac{1093}{1146}\right)\) | \(e\left(\frac{535}{573}\right)\) |
| \(\chi_{8043}(338,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{509}{1146}\right)\) | \(e\left(\frac{509}{573}\right)\) | \(e\left(\frac{869}{1146}\right)\) | \(e\left(\frac{127}{382}\right)\) | \(e\left(\frac{116}{573}\right)\) | \(e\left(\frac{433}{1146}\right)\) | \(e\left(\frac{41}{191}\right)\) | \(e\left(\frac{445}{573}\right)\) | \(e\left(\frac{145}{1146}\right)\) | \(e\left(\frac{331}{573}\right)\) |
| \(\chi_{8043}(368,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{169}{1146}\right)\) | \(e\left(\frac{169}{573}\right)\) | \(e\left(\frac{1009}{1146}\right)\) | \(e\left(\frac{169}{382}\right)\) | \(e\left(\frac{16}{573}\right)\) | \(e\left(\frac{119}{1146}\right)\) | \(e\left(\frac{32}{191}\right)\) | \(e\left(\frac{338}{573}\right)\) | \(e\left(\frac{593}{1146}\right)\) | \(e\left(\frac{263}{573}\right)\) |
| \(\chi_{8043}(389,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{919}{1146}\right)\) | \(e\left(\frac{346}{573}\right)\) | \(e\left(\frac{835}{1146}\right)\) | \(e\left(\frac{155}{382}\right)\) | \(e\left(\frac{304}{573}\right)\) | \(e\left(\frac{1115}{1146}\right)\) | \(e\left(\frac{35}{191}\right)\) | \(e\left(\frac{119}{573}\right)\) | \(e\left(\frac{953}{1146}\right)\) | \(e\left(\frac{413}{573}\right)\) |
| \(\chi_{8043}(401,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{113}{1146}\right)\) | \(e\left(\frac{113}{573}\right)\) | \(e\left(\frac{695}{1146}\right)\) | \(e\left(\frac{113}{382}\right)\) | \(e\left(\frac{404}{573}\right)\) | \(e\left(\frac{283}{1146}\right)\) | \(e\left(\frac{44}{191}\right)\) | \(e\left(\frac{226}{573}\right)\) | \(e\left(\frac{505}{1146}\right)\) | \(e\left(\frac{481}{573}\right)\) |
| \(\chi_{8043}(410,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{829}{1146}\right)\) | \(e\left(\frac{256}{573}\right)\) | \(e\left(\frac{535}{1146}\right)\) | \(e\left(\frac{65}{382}\right)\) | \(e\left(\frac{109}{573}\right)\) | \(e\left(\frac{1133}{1146}\right)\) | \(e\left(\frac{27}{191}\right)\) | \(e\left(\frac{512}{573}\right)\) | \(e\left(\frac{1139}{1146}\right)\) | \(e\left(\frac{395}{573}\right)\) |
| \(\chi_{8043}(431,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{937}{1146}\right)\) | \(e\left(\frac{364}{573}\right)\) | \(e\left(\frac{895}{1146}\right)\) | \(e\left(\frac{173}{382}\right)\) | \(e\left(\frac{343}{573}\right)\) | \(e\left(\frac{653}{1146}\right)\) | \(e\left(\frac{113}{191}\right)\) | \(e\left(\frac{155}{573}\right)\) | \(e\left(\frac{1145}{1146}\right)\) | \(e\left(\frac{302}{573}\right)\) |
| \(\chi_{8043}(452,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{103}{1146}\right)\) | \(e\left(\frac{103}{573}\right)\) | \(e\left(\frac{25}{1146}\right)\) | \(e\left(\frac{103}{382}\right)\) | \(e\left(\frac{64}{573}\right)\) | \(e\left(\frac{1049}{1146}\right)\) | \(e\left(\frac{128}{191}\right)\) | \(e\left(\frac{206}{573}\right)\) | \(e\left(\frac{653}{1146}\right)\) | \(e\left(\frac{479}{573}\right)\) |
| \(\chi_{8043}(464,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{23}{1146}\right)\) | \(e\left(\frac{23}{573}\right)\) | \(e\left(\frac{395}{1146}\right)\) | \(e\left(\frac{23}{382}\right)\) | \(e\left(\frac{209}{573}\right)\) | \(e\left(\frac{301}{1146}\right)\) | \(e\left(\frac{36}{191}\right)\) | \(e\left(\frac{46}{573}\right)\) | \(e\left(\frac{691}{1146}\right)\) | \(e\left(\frac{463}{573}\right)\) |
| \(\chi_{8043}(485,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{983}{1146}\right)\) | \(e\left(\frac{410}{573}\right)\) | \(e\left(\frac{539}{1146}\right)\) | \(e\left(\frac{219}{382}\right)\) | \(e\left(\frac{188}{573}\right)\) | \(e\left(\frac{109}{1146}\right)\) | \(e\left(\frac{185}{191}\right)\) | \(e\left(\frac{247}{573}\right)\) | \(e\left(\frac{235}{1146}\right)\) | \(e\left(\frac{82}{573}\right)\) |
| \(\chi_{8043}(527,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{131}{1146}\right)\) | \(e\left(\frac{131}{573}\right)\) | \(e\left(\frac{755}{1146}\right)\) | \(e\left(\frac{131}{382}\right)\) | \(e\left(\frac{443}{573}\right)\) | \(e\left(\frac{967}{1146}\right)\) | \(e\left(\frac{122}{191}\right)\) | \(e\left(\frac{262}{573}\right)\) | \(e\left(\frac{697}{1146}\right)\) | \(e\left(\frac{370}{573}\right)\) |
| \(\chi_{8043}(536,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{553}{1146}\right)\) | \(e\left(\frac{553}{573}\right)\) | \(e\left(\frac{379}{1146}\right)\) | \(e\left(\frac{171}{382}\right)\) | \(e\left(\frac{466}{573}\right)\) | \(e\left(\frac{959}{1146}\right)\) | \(e\left(\frac{168}{191}\right)\) | \(e\left(\frac{533}{573}\right)\) | \(e\left(\frac{869}{1146}\right)\) | \(e\left(\frac{569}{573}\right)\) |
| \(\chi_{8043}(548,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{779}{1146}\right)\) | \(e\left(\frac{206}{573}\right)\) | \(e\left(\frac{623}{1146}\right)\) | \(e\left(\frac{15}{382}\right)\) | \(e\left(\frac{128}{573}\right)\) | \(e\left(\frac{379}{1146}\right)\) | \(e\left(\frac{65}{191}\right)\) | \(e\left(\frac{412}{573}\right)\) | \(e\left(\frac{733}{1146}\right)\) | \(e\left(\frac{385}{573}\right)\) |
| \(\chi_{8043}(557,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{727}{1146}\right)\) | \(e\left(\frac{154}{573}\right)\) | \(e\left(\frac{577}{1146}\right)\) | \(e\left(\frac{345}{382}\right)\) | \(e\left(\frac{79}{573}\right)\) | \(e\left(\frac{695}{1146}\right)\) | \(e\left(\frac{158}{191}\right)\) | \(e\left(\frac{308}{573}\right)\) | \(e\left(\frac{815}{1146}\right)\) | \(e\left(\frac{260}{573}\right)\) |
| \(\chi_{8043}(569,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{413}{1146}\right)\) | \(e\left(\frac{413}{573}\right)\) | \(e\left(\frac{167}{1146}\right)\) | \(e\left(\frac{31}{382}\right)\) | \(e\left(\frac{290}{573}\right)\) | \(e\left(\frac{223}{1146}\right)\) | \(e\left(\frac{7}{191}\right)\) | \(e\left(\frac{253}{573}\right)\) | \(e\left(\frac{649}{1146}\right)\) | \(e\left(\frac{541}{573}\right)\) |
| \(\chi_{8043}(578,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{325}{1146}\right)\) | \(e\left(\frac{325}{573}\right)\) | \(e\left(\frac{1}{1146}\right)\) | \(e\left(\frac{325}{382}\right)\) | \(e\left(\frac{163}{573}\right)\) | \(e\left(\frac{317}{1146}\right)\) | \(e\left(\frac{135}{191}\right)\) | \(e\left(\frac{77}{573}\right)\) | \(e\left(\frac{347}{1146}\right)\) | \(e\left(\frac{65}{573}\right)\) |
| \(\chi_{8043}(590,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{443}{1146}\right)\) | \(e\left(\frac{443}{573}\right)\) | \(e\left(\frac{1031}{1146}\right)\) | \(e\left(\frac{61}{382}\right)\) | \(e\left(\frac{164}{573}\right)\) | \(e\left(\frac{217}{1146}\right)\) | \(e\left(\frac{137}{191}\right)\) | \(e\left(\frac{313}{573}\right)\) | \(e\left(\frac{205}{1146}\right)\) | \(e\left(\frac{547}{573}\right)\) |