from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1081, base_ring=CyclotomicField(506))
M = H._module
chi = DirichletCharacter(H, M([23,11]))
chi.galois_orbit()
[g,chi] = znchar(Mod(5,1081))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(1081\) | |
| Conductor: | \(1081\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(506\) | 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: | $\Q(\zeta_{253})$ |
| Fixed field: | Number field defined by a degree 506 polynomial (not computed) |
First 31 of 220 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{1081}(5,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{122}{253}\right)\) | \(e\left(\frac{41}{253}\right)\) | \(e\left(\frac{244}{253}\right)\) | \(e\left(\frac{17}{253}\right)\) | \(e\left(\frac{163}{253}\right)\) | \(e\left(\frac{283}{506}\right)\) | \(e\left(\frac{113}{253}\right)\) | \(e\left(\frac{82}{253}\right)\) | \(e\left(\frac{139}{253}\right)\) | \(e\left(\frac{142}{253}\right)\) |
| \(\chi_{1081}(10,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{179}{253}\right)\) | \(e\left(\frac{112}{253}\right)\) | \(e\left(\frac{105}{253}\right)\) | \(e\left(\frac{139}{253}\right)\) | \(e\left(\frac{38}{253}\right)\) | \(e\left(\frac{409}{506}\right)\) | \(e\left(\frac{31}{253}\right)\) | \(e\left(\frac{224}{253}\right)\) | \(e\left(\frac{65}{253}\right)\) | \(e\left(\frac{30}{253}\right)\) |
| \(\chi_{1081}(11,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{141}{253}\right)\) | \(e\left(\frac{149}{253}\right)\) | \(e\left(\frac{29}{253}\right)\) | \(e\left(\frac{142}{253}\right)\) | \(e\left(\frac{37}{253}\right)\) | \(e\left(\frac{325}{506}\right)\) | \(e\left(\frac{170}{253}\right)\) | \(e\left(\frac{45}{253}\right)\) | \(e\left(\frac{30}{253}\right)\) | \(e\left(\frac{189}{253}\right)\) |
| \(\chi_{1081}(15,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{193}{253}\right)\) | \(e\left(\frac{125}{253}\right)\) | \(e\left(\frac{133}{253}\right)\) | \(e\left(\frac{58}{253}\right)\) | \(e\left(\frac{65}{253}\right)\) | \(e\left(\frac{147}{506}\right)\) | \(e\left(\frac{73}{253}\right)\) | \(e\left(\frac{250}{253}\right)\) | \(e\left(\frac{251}{253}\right)\) | \(e\left(\frac{38}{253}\right)\) |
| \(\chi_{1081}(19,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{246}{253}\right)\) | \(e\left(\frac{120}{253}\right)\) | \(e\left(\frac{239}{253}\right)\) | \(e\left(\frac{167}{253}\right)\) | \(e\left(\frac{113}{253}\right)\) | \(e\left(\frac{131}{506}\right)\) | \(e\left(\frac{232}{253}\right)\) | \(e\left(\frac{240}{253}\right)\) | \(e\left(\frac{160}{253}\right)\) | \(e\left(\frac{249}{253}\right)\) |
| \(\chi_{1081}(20,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{236}{253}\right)\) | \(e\left(\frac{183}{253}\right)\) | \(e\left(\frac{219}{253}\right)\) | \(e\left(\frac{8}{253}\right)\) | \(e\left(\frac{166}{253}\right)\) | \(e\left(\frac{29}{506}\right)\) | \(e\left(\frac{202}{253}\right)\) | \(e\left(\frac{113}{253}\right)\) | \(e\left(\frac{244}{253}\right)\) | \(e\left(\frac{171}{253}\right)\) |
| \(\chi_{1081}(30,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{250}{253}\right)\) | \(e\left(\frac{196}{253}\right)\) | \(e\left(\frac{247}{253}\right)\) | \(e\left(\frac{180}{253}\right)\) | \(e\left(\frac{193}{253}\right)\) | \(e\left(\frac{273}{506}\right)\) | \(e\left(\frac{244}{253}\right)\) | \(e\left(\frac{139}{253}\right)\) | \(e\left(\frac{177}{253}\right)\) | \(e\left(\frac{179}{253}\right)\) |
| \(\chi_{1081}(33,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{212}{253}\right)\) | \(e\left(\frac{233}{253}\right)\) | \(e\left(\frac{171}{253}\right)\) | \(e\left(\frac{183}{253}\right)\) | \(e\left(\frac{192}{253}\right)\) | \(e\left(\frac{189}{506}\right)\) | \(e\left(\frac{130}{253}\right)\) | \(e\left(\frac{213}{253}\right)\) | \(e\left(\frac{142}{253}\right)\) | \(e\left(\frac{85}{253}\right)\) |
| \(\chi_{1081}(38,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{50}{253}\right)\) | \(e\left(\frac{191}{253}\right)\) | \(e\left(\frac{100}{253}\right)\) | \(e\left(\frac{36}{253}\right)\) | \(e\left(\frac{241}{253}\right)\) | \(e\left(\frac{257}{506}\right)\) | \(e\left(\frac{150}{253}\right)\) | \(e\left(\frac{129}{253}\right)\) | \(e\left(\frac{86}{253}\right)\) | \(e\left(\frac{137}{253}\right)\) |
| \(\chi_{1081}(40,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{40}{253}\right)\) | \(e\left(\frac{1}{253}\right)\) | \(e\left(\frac{80}{253}\right)\) | \(e\left(\frac{130}{253}\right)\) | \(e\left(\frac{41}{253}\right)\) | \(e\left(\frac{155}{506}\right)\) | \(e\left(\frac{120}{253}\right)\) | \(e\left(\frac{2}{253}\right)\) | \(e\left(\frac{170}{253}\right)\) | \(e\left(\frac{59}{253}\right)\) |
| \(\chi_{1081}(43,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{137}{253}\right)\) | \(e\left(\frac{73}{253}\right)\) | \(e\left(\frac{21}{253}\right)\) | \(e\left(\frac{129}{253}\right)\) | \(e\left(\frac{210}{253}\right)\) | \(e\left(\frac{183}{506}\right)\) | \(e\left(\frac{158}{253}\right)\) | \(e\left(\frac{146}{253}\right)\) | \(e\left(\frac{13}{253}\right)\) | \(e\left(\frac{6}{253}\right)\) |
| \(\chi_{1081}(44,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{253}\right)\) | \(e\left(\frac{38}{253}\right)\) | \(e\left(\frac{4}{253}\right)\) | \(e\left(\frac{133}{253}\right)\) | \(e\left(\frac{40}{253}\right)\) | \(e\left(\frac{71}{506}\right)\) | \(e\left(\frac{6}{253}\right)\) | \(e\left(\frac{76}{253}\right)\) | \(e\left(\frac{135}{253}\right)\) | \(e\left(\frac{218}{253}\right)\) |
| \(\chi_{1081}(57,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{64}{253}\right)\) | \(e\left(\frac{204}{253}\right)\) | \(e\left(\frac{128}{253}\right)\) | \(e\left(\frac{208}{253}\right)\) | \(e\left(\frac{15}{253}\right)\) | \(e\left(\frac{501}{506}\right)\) | \(e\left(\frac{192}{253}\right)\) | \(e\left(\frac{155}{253}\right)\) | \(e\left(\frac{19}{253}\right)\) | \(e\left(\frac{145}{253}\right)\) |
| \(\chi_{1081}(60,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{54}{253}\right)\) | \(e\left(\frac{14}{253}\right)\) | \(e\left(\frac{108}{253}\right)\) | \(e\left(\frac{49}{253}\right)\) | \(e\left(\frac{68}{253}\right)\) | \(e\left(\frac{399}{506}\right)\) | \(e\left(\frac{162}{253}\right)\) | \(e\left(\frac{28}{253}\right)\) | \(e\left(\frac{103}{253}\right)\) | \(e\left(\frac{67}{253}\right)\) |
| \(\chi_{1081}(66,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{16}{253}\right)\) | \(e\left(\frac{51}{253}\right)\) | \(e\left(\frac{32}{253}\right)\) | \(e\left(\frac{52}{253}\right)\) | \(e\left(\frac{67}{253}\right)\) | \(e\left(\frac{315}{506}\right)\) | \(e\left(\frac{48}{253}\right)\) | \(e\left(\frac{102}{253}\right)\) | \(e\left(\frac{68}{253}\right)\) | \(e\left(\frac{226}{253}\right)\) |
| \(\chi_{1081}(67,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{167}{253}\right)\) | \(e\left(\frac{137}{253}\right)\) | \(e\left(\frac{81}{253}\right)\) | \(e\left(\frac{100}{253}\right)\) | \(e\left(\frac{51}{253}\right)\) | \(e\left(\frac{489}{506}\right)\) | \(e\left(\frac{248}{253}\right)\) | \(e\left(\frac{21}{253}\right)\) | \(e\left(\frac{14}{253}\right)\) | \(e\left(\frac{240}{253}\right)\) |
| \(\chi_{1081}(76,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{107}{253}\right)\) | \(e\left(\frac{9}{253}\right)\) | \(e\left(\frac{214}{253}\right)\) | \(e\left(\frac{158}{253}\right)\) | \(e\left(\frac{116}{253}\right)\) | \(e\left(\frac{383}{506}\right)\) | \(e\left(\frac{68}{253}\right)\) | \(e\left(\frac{18}{253}\right)\) | \(e\left(\frac{12}{253}\right)\) | \(e\left(\frac{25}{253}\right)\) |
| \(\chi_{1081}(80,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{97}{253}\right)\) | \(e\left(\frac{72}{253}\right)\) | \(e\left(\frac{194}{253}\right)\) | \(e\left(\frac{252}{253}\right)\) | \(e\left(\frac{169}{253}\right)\) | \(e\left(\frac{281}{506}\right)\) | \(e\left(\frac{38}{253}\right)\) | \(e\left(\frac{144}{253}\right)\) | \(e\left(\frac{96}{253}\right)\) | \(e\left(\frac{200}{253}\right)\) |
| \(\chi_{1081}(86,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{194}{253}\right)\) | \(e\left(\frac{144}{253}\right)\) | \(e\left(\frac{135}{253}\right)\) | \(e\left(\frac{251}{253}\right)\) | \(e\left(\frac{85}{253}\right)\) | \(e\left(\frac{309}{506}\right)\) | \(e\left(\frac{76}{253}\right)\) | \(e\left(\frac{35}{253}\right)\) | \(e\left(\frac{192}{253}\right)\) | \(e\left(\frac{147}{253}\right)\) |
| \(\chi_{1081}(88,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{59}{253}\right)\) | \(e\left(\frac{109}{253}\right)\) | \(e\left(\frac{118}{253}\right)\) | \(e\left(\frac{2}{253}\right)\) | \(e\left(\frac{168}{253}\right)\) | \(e\left(\frac{197}{506}\right)\) | \(e\left(\frac{177}{253}\right)\) | \(e\left(\frac{218}{253}\right)\) | \(e\left(\frac{61}{253}\right)\) | \(e\left(\frac{106}{253}\right)\) |
| \(\chi_{1081}(90,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{68}{253}\right)\) | \(e\left(\frac{27}{253}\right)\) | \(e\left(\frac{136}{253}\right)\) | \(e\left(\frac{221}{253}\right)\) | \(e\left(\frac{95}{253}\right)\) | \(e\left(\frac{137}{506}\right)\) | \(e\left(\frac{204}{253}\right)\) | \(e\left(\frac{54}{253}\right)\) | \(e\left(\frac{36}{253}\right)\) | \(e\left(\frac{75}{253}\right)\) |
| \(\chi_{1081}(99,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{30}{253}\right)\) | \(e\left(\frac{64}{253}\right)\) | \(e\left(\frac{60}{253}\right)\) | \(e\left(\frac{224}{253}\right)\) | \(e\left(\frac{94}{253}\right)\) | \(e\left(\frac{53}{506}\right)\) | \(e\left(\frac{90}{253}\right)\) | \(e\left(\frac{128}{253}\right)\) | \(e\left(\frac{1}{253}\right)\) | \(e\left(\frac{234}{253}\right)\) |
| \(\chi_{1081}(107,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{215}{253}\right)\) | \(e\left(\frac{37}{253}\right)\) | \(e\left(\frac{177}{253}\right)\) | \(e\left(\frac{3}{253}\right)\) | \(e\left(\frac{252}{253}\right)\) | \(e\left(\frac{169}{506}\right)\) | \(e\left(\frac{139}{253}\right)\) | \(e\left(\frac{74}{253}\right)\) | \(e\left(\frac{218}{253}\right)\) | \(e\left(\frac{159}{253}\right)\) |
| \(\chi_{1081}(109,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{216}{253}\right)\) | \(e\left(\frac{56}{253}\right)\) | \(e\left(\frac{179}{253}\right)\) | \(e\left(\frac{196}{253}\right)\) | \(e\left(\frac{19}{253}\right)\) | \(e\left(\frac{331}{506}\right)\) | \(e\left(\frac{142}{253}\right)\) | \(e\left(\frac{112}{253}\right)\) | \(e\left(\frac{159}{253}\right)\) | \(e\left(\frac{15}{253}\right)\) |
| \(\chi_{1081}(113,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{200}{253}\right)\) | \(e\left(\frac{5}{253}\right)\) | \(e\left(\frac{147}{253}\right)\) | \(e\left(\frac{144}{253}\right)\) | \(e\left(\frac{205}{253}\right)\) | \(e\left(\frac{269}{506}\right)\) | \(e\left(\frac{94}{253}\right)\) | \(e\left(\frac{10}{253}\right)\) | \(e\left(\frac{91}{253}\right)\) | \(e\left(\frac{42}{253}\right)\) |
| \(\chi_{1081}(120,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{111}{253}\right)\) | \(e\left(\frac{85}{253}\right)\) | \(e\left(\frac{222}{253}\right)\) | \(e\left(\frac{171}{253}\right)\) | \(e\left(\frac{196}{253}\right)\) | \(e\left(\frac{19}{506}\right)\) | \(e\left(\frac{80}{253}\right)\) | \(e\left(\frac{170}{253}\right)\) | \(e\left(\frac{29}{253}\right)\) | \(e\left(\frac{208}{253}\right)\) |
| \(\chi_{1081}(125,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{113}{253}\right)\) | \(e\left(\frac{123}{253}\right)\) | \(e\left(\frac{226}{253}\right)\) | \(e\left(\frac{51}{253}\right)\) | \(e\left(\frac{236}{253}\right)\) | \(e\left(\frac{343}{506}\right)\) | \(e\left(\frac{86}{253}\right)\) | \(e\left(\frac{246}{253}\right)\) | \(e\left(\frac{164}{253}\right)\) | \(e\left(\frac{173}{253}\right)\) |
| \(\chi_{1081}(129,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{208}{253}\right)\) | \(e\left(\frac{157}{253}\right)\) | \(e\left(\frac{163}{253}\right)\) | \(e\left(\frac{170}{253}\right)\) | \(e\left(\frac{112}{253}\right)\) | \(e\left(\frac{47}{506}\right)\) | \(e\left(\frac{118}{253}\right)\) | \(e\left(\frac{61}{253}\right)\) | \(e\left(\frac{125}{253}\right)\) | \(e\left(\frac{155}{253}\right)\) |
| \(\chi_{1081}(132,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{253}\right)\) | \(e\left(\frac{122}{253}\right)\) | \(e\left(\frac{146}{253}\right)\) | \(e\left(\frac{174}{253}\right)\) | \(e\left(\frac{195}{253}\right)\) | \(e\left(\frac{441}{506}\right)\) | \(e\left(\frac{219}{253}\right)\) | \(e\left(\frac{244}{253}\right)\) | \(e\left(\frac{247}{253}\right)\) | \(e\left(\frac{114}{253}\right)\) |
| \(\chi_{1081}(134,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{224}{253}\right)\) | \(e\left(\frac{208}{253}\right)\) | \(e\left(\frac{195}{253}\right)\) | \(e\left(\frac{222}{253}\right)\) | \(e\left(\frac{179}{253}\right)\) | \(e\left(\frac{109}{506}\right)\) | \(e\left(\frac{166}{253}\right)\) | \(e\left(\frac{163}{253}\right)\) | \(e\left(\frac{193}{253}\right)\) | \(e\left(\frac{128}{253}\right)\) |
| \(\chi_{1081}(135,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{82}{253}\right)\) | \(e\left(\frac{40}{253}\right)\) | \(e\left(\frac{164}{253}\right)\) | \(e\left(\frac{140}{253}\right)\) | \(e\left(\frac{122}{253}\right)\) | \(e\left(\frac{381}{506}\right)\) | \(e\left(\frac{246}{253}\right)\) | \(e\left(\frac{80}{253}\right)\) | \(e\left(\frac{222}{253}\right)\) | \(e\left(\frac{83}{253}\right)\) |