from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8281, base_ring=CyclotomicField(1092))
M = H._module
chi = DirichletCharacter(H, M([962,889]))
chi.galois_orbit()
[g,chi] = znchar(Mod(24,8281))
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: | \(1092\) | 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: | $\Q(\zeta_{1092})$ |
| Fixed field: | Number field defined by a degree 1092 polynomial (not computed) |
First 31 of 288 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{8281}(24,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{785}{1092}\right)\) | \(e\left(\frac{151}{182}\right)\) | \(e\left(\frac{239}{546}\right)\) | \(e\left(\frac{955}{1092}\right)\) | \(e\left(\frac{599}{1092}\right)\) | \(e\left(\frac{57}{364}\right)\) | \(e\left(\frac{60}{91}\right)\) | \(e\left(\frac{54}{91}\right)\) | \(e\left(\frac{33}{364}\right)\) | \(e\left(\frac{73}{273}\right)\) |
| \(\chi_{8281}(33,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{913}{1092}\right)\) | \(e\left(\frac{75}{182}\right)\) | \(e\left(\frac{367}{546}\right)\) | \(e\left(\frac{443}{1092}\right)\) | \(e\left(\frac{271}{1092}\right)\) | \(e\left(\frac{185}{364}\right)\) | \(e\left(\frac{75}{91}\right)\) | \(e\left(\frac{22}{91}\right)\) | \(e\left(\frac{337}{364}\right)\) | \(e\left(\frac{23}{273}\right)\) |
| \(\chi_{8281}(110,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{583}{1092}\right)\) | \(e\left(\frac{15}{182}\right)\) | \(e\left(\frac{37}{546}\right)\) | \(e\left(\frac{125}{1092}\right)\) | \(e\left(\frac{673}{1092}\right)\) | \(e\left(\frac{219}{364}\right)\) | \(e\left(\frac{15}{91}\right)\) | \(e\left(\frac{59}{91}\right)\) | \(e\left(\frac{31}{364}\right)\) | \(e\left(\frac{41}{273}\right)\) |
| \(\chi_{8281}(115,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{401}{1092}\right)\) | \(e\left(\frac{15}{182}\right)\) | \(e\left(\frac{401}{546}\right)\) | \(e\left(\frac{307}{1092}\right)\) | \(e\left(\frac{491}{1092}\right)\) | \(e\left(\frac{37}{364}\right)\) | \(e\left(\frac{15}{91}\right)\) | \(e\left(\frac{59}{91}\right)\) | \(e\left(\frac{213}{364}\right)\) | \(e\left(\frac{223}{273}\right)\) |
| \(\chi_{8281}(124,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{733}{1092}\right)\) | \(e\left(\frac{125}{182}\right)\) | \(e\left(\frac{187}{546}\right)\) | \(e\left(\frac{71}{1092}\right)\) | \(e\left(\frac{391}{1092}\right)\) | \(e\left(\frac{5}{364}\right)\) | \(e\left(\frac{34}{91}\right)\) | \(e\left(\frac{67}{91}\right)\) | \(e\left(\frac{137}{364}\right)\) | \(e\left(\frac{8}{273}\right)\) |
| \(\chi_{8281}(171,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{995}{1092}\right)\) | \(e\left(\frac{123}{182}\right)\) | \(e\left(\frac{449}{546}\right)\) | \(e\left(\frac{661}{1092}\right)\) | \(e\left(\frac{641}{1092}\right)\) | \(e\left(\frac{267}{364}\right)\) | \(e\left(\frac{32}{91}\right)\) | \(e\left(\frac{47}{91}\right)\) | \(e\left(\frac{327}{364}\right)\) | \(e\left(\frac{136}{273}\right)\) |
| \(\chi_{8281}(201,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1075}{1092}\right)\) | \(e\left(\frac{121}{182}\right)\) | \(e\left(\frac{529}{546}\right)\) | \(e\left(\frac{341}{1092}\right)\) | \(e\left(\frac{709}{1092}\right)\) | \(e\left(\frac{347}{364}\right)\) | \(e\left(\frac{30}{91}\right)\) | \(e\left(\frac{27}{91}\right)\) | \(e\left(\frac{335}{364}\right)\) | \(e\left(\frac{173}{273}\right)\) |
| \(\chi_{8281}(206,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{1092}\right)\) | \(e\left(\frac{61}{182}\right)\) | \(e\left(\frac{17}{546}\right)\) | \(e\left(\frac{751}{1092}\right)\) | \(e\left(\frac{383}{1092}\right)\) | \(e\left(\frac{17}{364}\right)\) | \(e\left(\frac{61}{91}\right)\) | \(e\left(\frac{64}{91}\right)\) | \(e\left(\frac{29}{364}\right)\) | \(e\left(\frac{100}{273}\right)\) |
| \(\chi_{8281}(262,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{443}{1092}\right)\) | \(e\left(\frac{155}{182}\right)\) | \(e\left(\frac{443}{546}\right)\) | \(e\left(\frac{685}{1092}\right)\) | \(e\left(\frac{281}{1092}\right)\) | \(e\left(\frac{79}{364}\right)\) | \(e\left(\frac{64}{91}\right)\) | \(e\left(\frac{3}{91}\right)\) | \(e\left(\frac{199}{364}\right)\) | \(e\left(\frac{181}{273}\right)\) |
| \(\chi_{8281}(292,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{475}{1092}\right)\) | \(e\left(\frac{45}{182}\right)\) | \(e\left(\frac{475}{546}\right)\) | \(e\left(\frac{557}{1092}\right)\) | \(e\left(\frac{745}{1092}\right)\) | \(e\left(\frac{111}{364}\right)\) | \(e\left(\frac{45}{91}\right)\) | \(e\left(\frac{86}{91}\right)\) | \(e\left(\frac{275}{364}\right)\) | \(e\left(\frac{32}{273}\right)\) |
| \(\chi_{8281}(297,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{725}{1092}\right)\) | \(e\left(\frac{107}{182}\right)\) | \(e\left(\frac{179}{546}\right)\) | \(e\left(\frac{103}{1092}\right)\) | \(e\left(\frac{275}{1092}\right)\) | \(e\left(\frac{361}{364}\right)\) | \(e\left(\frac{16}{91}\right)\) | \(e\left(\frac{69}{91}\right)\) | \(e\left(\frac{209}{364}\right)\) | \(e\left(\frac{250}{273}\right)\) |
| \(\chi_{8281}(306,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{373}{1092}\right)\) | \(e\left(\frac{43}{182}\right)\) | \(e\left(\frac{373}{546}\right)\) | \(e\left(\frac{419}{1092}\right)\) | \(e\left(\frac{631}{1092}\right)\) | \(e\left(\frac{9}{364}\right)\) | \(e\left(\frac{43}{91}\right)\) | \(e\left(\frac{66}{91}\right)\) | \(e\left(\frac{101}{364}\right)\) | \(e\left(\frac{251}{273}\right)\) |
| \(\chi_{8281}(353,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{983}{1092}\right)\) | \(e\left(\frac{5}{182}\right)\) | \(e\left(\frac{437}{546}\right)\) | \(e\left(\frac{709}{1092}\right)\) | \(e\left(\frac{1013}{1092}\right)\) | \(e\left(\frac{255}{364}\right)\) | \(e\left(\frac{5}{91}\right)\) | \(e\left(\frac{50}{91}\right)\) | \(e\left(\frac{71}{364}\right)\) | \(e\left(\frac{226}{273}\right)\) |
| \(\chi_{8281}(383,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{967}{1092}\right)\) | \(e\left(\frac{151}{182}\right)\) | \(e\left(\frac{421}{546}\right)\) | \(e\left(\frac{773}{1092}\right)\) | \(e\left(\frac{781}{1092}\right)\) | \(e\left(\frac{239}{364}\right)\) | \(e\left(\frac{60}{91}\right)\) | \(e\left(\frac{54}{91}\right)\) | \(e\left(\frac{215}{364}\right)\) | \(e\left(\frac{164}{273}\right)\) |
| \(\chi_{8281}(388,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{341}{1092}\right)\) | \(e\left(\frac{153}{182}\right)\) | \(e\left(\frac{341}{546}\right)\) | \(e\left(\frac{547}{1092}\right)\) | \(e\left(\frac{167}{1092}\right)\) | \(e\left(\frac{341}{364}\right)\) | \(e\left(\frac{62}{91}\right)\) | \(e\left(\frac{74}{91}\right)\) | \(e\left(\frac{25}{364}\right)\) | \(e\left(\frac{127}{273}\right)\) |
| \(\chi_{8281}(397,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{193}{1092}\right)\) | \(e\left(\frac{93}{182}\right)\) | \(e\left(\frac{193}{546}\right)\) | \(e\left(\frac{47}{1092}\right)\) | \(e\left(\frac{751}{1092}\right)\) | \(e\left(\frac{193}{364}\right)\) | \(e\left(\frac{2}{91}\right)\) | \(e\left(\frac{20}{91}\right)\) | \(e\left(\frac{265}{364}\right)\) | \(e\left(\frac{236}{273}\right)\) |
| \(\chi_{8281}(444,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{431}{1092}\right)\) | \(e\left(\frac{37}{182}\right)\) | \(e\left(\frac{431}{546}\right)\) | \(e\left(\frac{733}{1092}\right)\) | \(e\left(\frac{653}{1092}\right)\) | \(e\left(\frac{67}{364}\right)\) | \(e\left(\frac{37}{91}\right)\) | \(e\left(\frac{6}{91}\right)\) | \(e\left(\frac{307}{364}\right)\) | \(e\left(\frac{271}{273}\right)\) |
| \(\chi_{8281}(474,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{367}{1092}\right)\) | \(e\left(\frac{75}{182}\right)\) | \(e\left(\frac{367}{546}\right)\) | \(e\left(\frac{989}{1092}\right)\) | \(e\left(\frac{817}{1092}\right)\) | \(e\left(\frac{3}{364}\right)\) | \(e\left(\frac{75}{91}\right)\) | \(e\left(\frac{22}{91}\right)\) | \(e\left(\frac{155}{364}\right)\) | \(e\left(\frac{23}{273}\right)\) |
| \(\chi_{8281}(479,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1049}{1092}\right)\) | \(e\left(\frac{17}{182}\right)\) | \(e\left(\frac{503}{546}\right)\) | \(e\left(\frac{991}{1092}\right)\) | \(e\left(\frac{59}{1092}\right)\) | \(e\left(\frac{321}{364}\right)\) | \(e\left(\frac{17}{91}\right)\) | \(e\left(\frac{79}{91}\right)\) | \(e\left(\frac{205}{364}\right)\) | \(e\left(\frac{4}{273}\right)\) |
| \(\chi_{8281}(535,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{971}{1092}\right)\) | \(e\left(\frac{69}{182}\right)\) | \(e\left(\frac{425}{546}\right)\) | \(e\left(\frac{757}{1092}\right)\) | \(e\left(\frac{293}{1092}\right)\) | \(e\left(\frac{243}{364}\right)\) | \(e\left(\frac{69}{91}\right)\) | \(e\left(\frac{53}{91}\right)\) | \(e\left(\frac{179}{364}\right)\) | \(e\left(\frac{43}{273}\right)\) |
| \(\chi_{8281}(565,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{859}{1092}\right)\) | \(e\left(\frac{181}{182}\right)\) | \(e\left(\frac{313}{546}\right)\) | \(e\left(\frac{113}{1092}\right)\) | \(e\left(\frac{853}{1092}\right)\) | \(e\left(\frac{131}{364}\right)\) | \(e\left(\frac{90}{91}\right)\) | \(e\left(\frac{81}{91}\right)\) | \(e\left(\frac{95}{364}\right)\) | \(e\left(\frac{155}{273}\right)\) |
| \(\chi_{8281}(579,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{925}{1092}\right)\) | \(e\left(\frac{11}{182}\right)\) | \(e\left(\frac{379}{546}\right)\) | \(e\left(\frac{395}{1092}\right)\) | \(e\left(\frac{991}{1092}\right)\) | \(e\left(\frac{197}{364}\right)\) | \(e\left(\frac{11}{91}\right)\) | \(e\left(\frac{19}{91}\right)\) | \(e\left(\frac{229}{364}\right)\) | \(e\left(\frac{206}{273}\right)\) |
| \(\chi_{8281}(626,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{419}{1092}\right)\) | \(e\left(\frac{101}{182}\right)\) | \(e\left(\frac{419}{546}\right)\) | \(e\left(\frac{781}{1092}\right)\) | \(e\left(\frac{1025}{1092}\right)\) | \(e\left(\frac{55}{364}\right)\) | \(e\left(\frac{10}{91}\right)\) | \(e\left(\frac{9}{91}\right)\) | \(e\left(\frac{51}{364}\right)\) | \(e\left(\frac{88}{273}\right)\) |
| \(\chi_{8281}(661,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{281}{1092}\right)\) | \(e\left(\frac{109}{182}\right)\) | \(e\left(\frac{281}{546}\right)\) | \(e\left(\frac{787}{1092}\right)\) | \(e\left(\frac{935}{1092}\right)\) | \(e\left(\frac{281}{364}\right)\) | \(e\left(\frac{18}{91}\right)\) | \(e\left(\frac{89}{91}\right)\) | \(e\left(\frac{201}{364}\right)\) | \(e\left(\frac{31}{273}\right)\) |
| \(\chi_{8281}(670,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{745}{1092}\right)\) | \(e\left(\frac{61}{182}\right)\) | \(e\left(\frac{199}{546}\right)\) | \(e\left(\frac{23}{1092}\right)\) | \(e\left(\frac{19}{1092}\right)\) | \(e\left(\frac{17}{364}\right)\) | \(e\left(\frac{61}{91}\right)\) | \(e\left(\frac{64}{91}\right)\) | \(e\left(\frac{29}{364}\right)\) | \(e\left(\frac{191}{273}\right)\) |
| \(\chi_{8281}(747,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{751}{1092}\right)\) | \(e\left(\frac{29}{182}\right)\) | \(e\left(\frac{205}{546}\right)\) | \(e\left(\frac{545}{1092}\right)\) | \(e\left(\frac{925}{1092}\right)\) | \(e\left(\frac{23}{364}\right)\) | \(e\left(\frac{29}{91}\right)\) | \(e\left(\frac{17}{91}\right)\) | \(e\left(\frac{339}{364}\right)\) | \(e\left(\frac{146}{273}\right)\) |
| \(\chi_{8281}(752,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{989}{1092}\right)\) | \(e\left(\frac{155}{182}\right)\) | \(e\left(\frac{443}{546}\right)\) | \(e\left(\frac{139}{1092}\right)\) | \(e\left(\frac{827}{1092}\right)\) | \(e\left(\frac{261}{364}\right)\) | \(e\left(\frac{64}{91}\right)\) | \(e\left(\frac{3}{91}\right)\) | \(e\left(\frac{17}{364}\right)\) | \(e\left(\frac{181}{273}\right)\) |
| \(\chi_{8281}(761,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{565}{1092}\right)\) | \(e\left(\frac{111}{182}\right)\) | \(e\left(\frac{19}{546}\right)\) | \(e\left(\frac{743}{1092}\right)\) | \(e\left(\frac{139}{1092}\right)\) | \(e\left(\frac{201}{364}\right)\) | \(e\left(\frac{20}{91}\right)\) | \(e\left(\frac{18}{91}\right)\) | \(e\left(\frac{193}{364}\right)\) | \(e\left(\frac{176}{273}\right)\) |
| \(\chi_{8281}(808,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{407}{1092}\right)\) | \(e\left(\frac{165}{182}\right)\) | \(e\left(\frac{407}{546}\right)\) | \(e\left(\frac{829}{1092}\right)\) | \(e\left(\frac{305}{1092}\right)\) | \(e\left(\frac{43}{364}\right)\) | \(e\left(\frac{74}{91}\right)\) | \(e\left(\frac{12}{91}\right)\) | \(e\left(\frac{159}{364}\right)\) | \(e\left(\frac{178}{273}\right)\) |
| \(\chi_{8281}(838,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{151}{1092}\right)\) | \(e\left(\frac{135}{182}\right)\) | \(e\left(\frac{151}{546}\right)\) | \(e\left(\frac{761}{1092}\right)\) | \(e\left(\frac{961}{1092}\right)\) | \(e\left(\frac{151}{364}\right)\) | \(e\left(\frac{44}{91}\right)\) | \(e\left(\frac{76}{91}\right)\) | \(e\left(\frac{279}{364}\right)\) | \(e\left(\frac{5}{273}\right)\) |
| \(\chi_{8281}(843,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{605}{1092}\right)\) | \(e\left(\frac{19}{182}\right)\) | \(e\left(\frac{59}{546}\right)\) | \(e\left(\frac{583}{1092}\right)\) | \(e\left(\frac{719}{1092}\right)\) | \(e\left(\frac{241}{364}\right)\) | \(e\left(\frac{19}{91}\right)\) | \(e\left(\frac{8}{91}\right)\) | \(e\left(\frac{197}{364}\right)\) | \(e\left(\frac{58}{273}\right)\) |