from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8281, base_ring=CyclotomicField(546))
M = H._module
chi = DirichletCharacter(H, M([234,140]))
chi.galois_orbit()
[g,chi] = znchar(Mod(29,8281))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(8281\) | |
| Conductor: | \(8281\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(273\) | 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: | $\Q(\zeta_{273})$ |
| Fixed field: | Number field defined by a degree 273 polynomial (not computed) |
First 31 of 144 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{8281}(29,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{109}{273}\right)\) | \(e\left(\frac{61}{273}\right)\) | \(e\left(\frac{218}{273}\right)\) | \(e\left(\frac{67}{91}\right)\) | \(e\left(\frac{170}{273}\right)\) | \(e\left(\frac{18}{91}\right)\) | \(e\left(\frac{122}{273}\right)\) | \(e\left(\frac{37}{273}\right)\) | \(e\left(\frac{151}{273}\right)\) | \(e\left(\frac{2}{91}\right)\) |
| \(\chi_{8281}(113,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{212}{273}\right)\) | \(e\left(\frac{41}{273}\right)\) | \(e\left(\frac{151}{273}\right)\) | \(e\left(\frac{51}{91}\right)\) | \(e\left(\frac{253}{273}\right)\) | \(e\left(\frac{30}{91}\right)\) | \(e\left(\frac{82}{273}\right)\) | \(e\left(\frac{92}{273}\right)\) | \(e\left(\frac{191}{273}\right)\) | \(e\left(\frac{64}{91}\right)\) |
| \(\chi_{8281}(120,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{199}{273}\right)\) | \(e\left(\frac{184}{273}\right)\) | \(e\left(\frac{125}{273}\right)\) | \(e\left(\frac{38}{91}\right)\) | \(e\left(\frac{110}{273}\right)\) | \(e\left(\frac{17}{91}\right)\) | \(e\left(\frac{95}{273}\right)\) | \(e\left(\frac{40}{273}\right)\) | \(e\left(\frac{178}{273}\right)\) | \(e\left(\frac{12}{91}\right)\) |
| \(\chi_{8281}(204,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{8}{273}\right)\) | \(e\left(\frac{17}{273}\right)\) | \(e\left(\frac{16}{273}\right)\) | \(e\left(\frac{50}{91}\right)\) | \(e\left(\frac{25}{273}\right)\) | \(e\left(\frac{8}{91}\right)\) | \(e\left(\frac{34}{273}\right)\) | \(e\left(\frac{158}{273}\right)\) | \(e\left(\frac{239}{273}\right)\) | \(e\left(\frac{11}{91}\right)\) |
| \(\chi_{8281}(211,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{16}{273}\right)\) | \(e\left(\frac{34}{273}\right)\) | \(e\left(\frac{32}{273}\right)\) | \(e\left(\frac{9}{91}\right)\) | \(e\left(\frac{50}{273}\right)\) | \(e\left(\frac{16}{91}\right)\) | \(e\left(\frac{68}{273}\right)\) | \(e\left(\frac{43}{273}\right)\) | \(e\left(\frac{205}{273}\right)\) | \(e\left(\frac{22}{91}\right)\) |
| \(\chi_{8281}(302,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{106}{273}\right)\) | \(e\left(\frac{157}{273}\right)\) | \(e\left(\frac{212}{273}\right)\) | \(e\left(\frac{71}{91}\right)\) | \(e\left(\frac{263}{273}\right)\) | \(e\left(\frac{15}{91}\right)\) | \(e\left(\frac{41}{273}\right)\) | \(e\left(\frac{46}{273}\right)\) | \(e\left(\frac{232}{273}\right)\) | \(e\left(\frac{32}{91}\right)\) |
| \(\chi_{8281}(386,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{146}{273}\right)\) | \(e\left(\frac{242}{273}\right)\) | \(e\left(\frac{19}{273}\right)\) | \(e\left(\frac{48}{91}\right)\) | \(e\left(\frac{115}{273}\right)\) | \(e\left(\frac{55}{91}\right)\) | \(e\left(\frac{211}{273}\right)\) | \(e\left(\frac{17}{273}\right)\) | \(e\left(\frac{62}{273}\right)\) | \(e\left(\frac{87}{91}\right)\) |
| \(\chi_{8281}(477,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{215}{273}\right)\) | \(e\left(\frac{218}{273}\right)\) | \(e\left(\frac{157}{273}\right)\) | \(e\left(\frac{47}{91}\right)\) | \(e\left(\frac{160}{273}\right)\) | \(e\left(\frac{33}{91}\right)\) | \(e\left(\frac{163}{273}\right)\) | \(e\left(\frac{83}{273}\right)\) | \(e\left(\frac{110}{273}\right)\) | \(e\left(\frac{34}{91}\right)\) |
| \(\chi_{8281}(568,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{273}\right)\) | \(e\left(\frac{194}{273}\right)\) | \(e\left(\frac{22}{273}\right)\) | \(e\left(\frac{46}{91}\right)\) | \(e\left(\frac{205}{273}\right)\) | \(e\left(\frac{11}{91}\right)\) | \(e\left(\frac{115}{273}\right)\) | \(e\left(\frac{149}{273}\right)\) | \(e\left(\frac{158}{273}\right)\) | \(e\left(\frac{72}{91}\right)\) |
| \(\chi_{8281}(575,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{103}{273}\right)\) | \(e\left(\frac{253}{273}\right)\) | \(e\left(\frac{206}{273}\right)\) | \(e\left(\frac{75}{91}\right)\) | \(e\left(\frac{83}{273}\right)\) | \(e\left(\frac{12}{91}\right)\) | \(e\left(\frac{233}{273}\right)\) | \(e\left(\frac{55}{273}\right)\) | \(e\left(\frac{40}{273}\right)\) | \(e\left(\frac{62}{91}\right)\) |
| \(\chi_{8281}(659,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{80}{273}\right)\) | \(e\left(\frac{170}{273}\right)\) | \(e\left(\frac{160}{273}\right)\) | \(e\left(\frac{45}{91}\right)\) | \(e\left(\frac{250}{273}\right)\) | \(e\left(\frac{80}{91}\right)\) | \(e\left(\frac{67}{273}\right)\) | \(e\left(\frac{215}{273}\right)\) | \(e\left(\frac{206}{273}\right)\) | \(e\left(\frac{19}{91}\right)\) |
| \(\chi_{8281}(666,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{193}{273}\right)\) | \(e\left(\frac{103}{273}\right)\) | \(e\left(\frac{113}{273}\right)\) | \(e\left(\frac{46}{91}\right)\) | \(e\left(\frac{23}{273}\right)\) | \(e\left(\frac{11}{91}\right)\) | \(e\left(\frac{206}{273}\right)\) | \(e\left(\frac{58}{273}\right)\) | \(e\left(\frac{67}{273}\right)\) | \(e\left(\frac{72}{91}\right)\) |
| \(\chi_{8281}(750,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{149}{273}\right)\) | \(e\left(\frac{146}{273}\right)\) | \(e\left(\frac{25}{273}\right)\) | \(e\left(\frac{44}{91}\right)\) | \(e\left(\frac{22}{273}\right)\) | \(e\left(\frac{58}{91}\right)\) | \(e\left(\frac{19}{273}\right)\) | \(e\left(\frac{8}{273}\right)\) | \(e\left(\frac{254}{273}\right)\) | \(e\left(\frac{57}{91}\right)\) |
| \(\chi_{8281}(757,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{10}{273}\right)\) | \(e\left(\frac{226}{273}\right)\) | \(e\left(\frac{20}{273}\right)\) | \(e\left(\frac{17}{91}\right)\) | \(e\left(\frac{236}{273}\right)\) | \(e\left(\frac{10}{91}\right)\) | \(e\left(\frac{179}{273}\right)\) | \(e\left(\frac{61}{273}\right)\) | \(e\left(\frac{94}{273}\right)\) | \(e\left(\frac{82}{91}\right)\) |
| \(\chi_{8281}(841,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{218}{273}\right)\) | \(e\left(\frac{122}{273}\right)\) | \(e\left(\frac{163}{273}\right)\) | \(e\left(\frac{43}{91}\right)\) | \(e\left(\frac{67}{273}\right)\) | \(e\left(\frac{36}{91}\right)\) | \(e\left(\frac{244}{273}\right)\) | \(e\left(\frac{74}{273}\right)\) | \(e\left(\frac{29}{273}\right)\) | \(e\left(\frac{4}{91}\right)\) |
| \(\chi_{8281}(848,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{100}{273}\right)\) | \(e\left(\frac{76}{273}\right)\) | \(e\left(\frac{200}{273}\right)\) | \(e\left(\frac{79}{91}\right)\) | \(e\left(\frac{176}{273}\right)\) | \(e\left(\frac{9}{91}\right)\) | \(e\left(\frac{152}{273}\right)\) | \(e\left(\frac{64}{273}\right)\) | \(e\left(\frac{121}{273}\right)\) | \(e\left(\frac{1}{91}\right)\) |
| \(\chi_{8281}(939,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{190}{273}\right)\) | \(e\left(\frac{199}{273}\right)\) | \(e\left(\frac{107}{273}\right)\) | \(e\left(\frac{50}{91}\right)\) | \(e\left(\frac{116}{273}\right)\) | \(e\left(\frac{8}{91}\right)\) | \(e\left(\frac{125}{273}\right)\) | \(e\left(\frac{67}{273}\right)\) | \(e\left(\frac{148}{273}\right)\) | \(e\left(\frac{11}{91}\right)\) |
| \(\chi_{8281}(1023,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{83}{273}\right)\) | \(e\left(\frac{74}{273}\right)\) | \(e\left(\frac{166}{273}\right)\) | \(e\left(\frac{41}{91}\right)\) | \(e\left(\frac{157}{273}\right)\) | \(e\left(\frac{83}{91}\right)\) | \(e\left(\frac{148}{273}\right)\) | \(e\left(\frac{206}{273}\right)\) | \(e\left(\frac{125}{273}\right)\) | \(e\left(\frac{80}{91}\right)\) |
| \(\chi_{8281}(1114,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{152}{273}\right)\) | \(e\left(\frac{50}{273}\right)\) | \(e\left(\frac{31}{273}\right)\) | \(e\left(\frac{40}{91}\right)\) | \(e\left(\frac{202}{273}\right)\) | \(e\left(\frac{61}{91}\right)\) | \(e\left(\frac{100}{273}\right)\) | \(e\left(\frac{272}{273}\right)\) | \(e\left(\frac{173}{273}\right)\) | \(e\left(\frac{27}{91}\right)\) |
| \(\chi_{8281}(1121,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{97}{273}\right)\) | \(e\left(\frac{172}{273}\right)\) | \(e\left(\frac{194}{273}\right)\) | \(e\left(\frac{83}{91}\right)\) | \(e\left(\frac{269}{273}\right)\) | \(e\left(\frac{6}{91}\right)\) | \(e\left(\frac{71}{273}\right)\) | \(e\left(\frac{73}{273}\right)\) | \(e\left(\frac{202}{273}\right)\) | \(e\left(\frac{31}{91}\right)\) |
| \(\chi_{8281}(1212,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{187}{273}\right)\) | \(e\left(\frac{22}{273}\right)\) | \(e\left(\frac{101}{273}\right)\) | \(e\left(\frac{54}{91}\right)\) | \(e\left(\frac{209}{273}\right)\) | \(e\left(\frac{5}{91}\right)\) | \(e\left(\frac{44}{273}\right)\) | \(e\left(\frac{76}{273}\right)\) | \(e\left(\frac{229}{273}\right)\) | \(e\left(\frac{41}{91}\right)\) |
| \(\chi_{8281}(1296,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{273}\right)\) | \(e\left(\frac{2}{273}\right)\) | \(e\left(\frac{34}{273}\right)\) | \(e\left(\frac{38}{91}\right)\) | \(e\left(\frac{19}{273}\right)\) | \(e\left(\frac{17}{91}\right)\) | \(e\left(\frac{4}{273}\right)\) | \(e\left(\frac{131}{273}\right)\) | \(e\left(\frac{269}{273}\right)\) | \(e\left(\frac{12}{91}\right)\) |
| \(\chi_{8281}(1303,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{273}\right)\) | \(e\left(\frac{145}{273}\right)\) | \(e\left(\frac{8}{273}\right)\) | \(e\left(\frac{25}{91}\right)\) | \(e\left(\frac{149}{273}\right)\) | \(e\left(\frac{4}{91}\right)\) | \(e\left(\frac{17}{273}\right)\) | \(e\left(\frac{79}{273}\right)\) | \(e\left(\frac{256}{273}\right)\) | \(e\left(\frac{51}{91}\right)\) |
| \(\chi_{8281}(1387,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{86}{273}\right)\) | \(e\left(\frac{251}{273}\right)\) | \(e\left(\frac{172}{273}\right)\) | \(e\left(\frac{37}{91}\right)\) | \(e\left(\frac{64}{273}\right)\) | \(e\left(\frac{86}{91}\right)\) | \(e\left(\frac{229}{273}\right)\) | \(e\left(\frac{197}{273}\right)\) | \(e\left(\frac{44}{273}\right)\) | \(e\left(\frac{50}{91}\right)\) |
| \(\chi_{8281}(1394,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{94}{273}\right)\) | \(e\left(\frac{268}{273}\right)\) | \(e\left(\frac{188}{273}\right)\) | \(e\left(\frac{87}{91}\right)\) | \(e\left(\frac{89}{273}\right)\) | \(e\left(\frac{3}{91}\right)\) | \(e\left(\frac{263}{273}\right)\) | \(e\left(\frac{82}{273}\right)\) | \(e\left(\frac{10}{273}\right)\) | \(e\left(\frac{61}{91}\right)\) |
| \(\chi_{8281}(1478,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{155}{273}\right)\) | \(e\left(\frac{227}{273}\right)\) | \(e\left(\frac{37}{273}\right)\) | \(e\left(\frac{36}{91}\right)\) | \(e\left(\frac{109}{273}\right)\) | \(e\left(\frac{64}{91}\right)\) | \(e\left(\frac{181}{273}\right)\) | \(e\left(\frac{263}{273}\right)\) | \(e\left(\frac{92}{273}\right)\) | \(e\left(\frac{88}{91}\right)\) |
| \(\chi_{8281}(1485,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{184}{273}\right)\) | \(e\left(\frac{118}{273}\right)\) | \(e\left(\frac{95}{273}\right)\) | \(e\left(\frac{58}{91}\right)\) | \(e\left(\frac{29}{273}\right)\) | \(e\left(\frac{2}{91}\right)\) | \(e\left(\frac{236}{273}\right)\) | \(e\left(\frac{85}{273}\right)\) | \(e\left(\frac{37}{273}\right)\) | \(e\left(\frac{71}{91}\right)\) |
| \(\chi_{8281}(1576,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{273}\right)\) | \(e\left(\frac{241}{273}\right)\) | \(e\left(\frac{2}{273}\right)\) | \(e\left(\frac{29}{91}\right)\) | \(e\left(\frac{242}{273}\right)\) | \(e\left(\frac{1}{91}\right)\) | \(e\left(\frac{209}{273}\right)\) | \(e\left(\frac{88}{273}\right)\) | \(e\left(\frac{64}{273}\right)\) | \(e\left(\frac{81}{91}\right)\) |
| \(\chi_{8281}(1660,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{20}{273}\right)\) | \(e\left(\frac{179}{273}\right)\) | \(e\left(\frac{40}{273}\right)\) | \(e\left(\frac{34}{91}\right)\) | \(e\left(\frac{199}{273}\right)\) | \(e\left(\frac{20}{91}\right)\) | \(e\left(\frac{85}{273}\right)\) | \(e\left(\frac{122}{273}\right)\) | \(e\left(\frac{188}{273}\right)\) | \(e\left(\frac{73}{91}\right)\) |
| \(\chi_{8281}(1751,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{273}\right)\) | \(e\left(\frac{155}{273}\right)\) | \(e\left(\frac{178}{273}\right)\) | \(e\left(\frac{33}{91}\right)\) | \(e\left(\frac{244}{273}\right)\) | \(e\left(\frac{89}{91}\right)\) | \(e\left(\frac{37}{273}\right)\) | \(e\left(\frac{188}{273}\right)\) | \(e\left(\frac{236}{273}\right)\) | \(e\left(\frac{20}{91}\right)\) |
| \(\chi_{8281}(1758,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{181}{273}\right)\) | \(e\left(\frac{214}{273}\right)\) | \(e\left(\frac{89}{273}\right)\) | \(e\left(\frac{62}{91}\right)\) | \(e\left(\frac{122}{273}\right)\) | \(e\left(\frac{90}{91}\right)\) | \(e\left(\frac{155}{273}\right)\) | \(e\left(\frac{94}{273}\right)\) | \(e\left(\frac{118}{273}\right)\) | \(e\left(\frac{10}{91}\right)\) |