from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5445, base_ring=CyclotomicField(660))
M = H._module
chi = DirichletCharacter(H, M([110,165,6]))
chi.galois_orbit()
[g,chi] = znchar(Mod(2,5445))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(5445\) | |
| Conductor: | \(5445\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(660\) | 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: | $\Q(\zeta_{660})$ |
| Fixed field: | Number field defined by a degree 660 polynomial (not computed) |
First 31 of 160 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{5445}(2,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{281}{660}\right)\) | \(e\left(\frac{281}{330}\right)\) | \(e\left(\frac{647}{660}\right)\) | \(e\left(\frac{61}{220}\right)\) | \(e\left(\frac{1}{660}\right)\) | \(e\left(\frac{67}{165}\right)\) | \(e\left(\frac{116}{165}\right)\) | \(e\left(\frac{43}{220}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{29}{132}\right)\) |
| \(\chi_{5445}(68,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{31}{660}\right)\) | \(e\left(\frac{31}{330}\right)\) | \(e\left(\frac{217}{660}\right)\) | \(e\left(\frac{31}{220}\right)\) | \(e\left(\frac{491}{660}\right)\) | \(e\left(\frac{62}{165}\right)\) | \(e\left(\frac{31}{165}\right)\) | \(e\left(\frac{213}{220}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{115}{132}\right)\) |
| \(\chi_{5445}(83,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{119}{660}\right)\) | \(e\left(\frac{119}{330}\right)\) | \(e\left(\frac{173}{660}\right)\) | \(e\left(\frac{119}{220}\right)\) | \(e\left(\frac{139}{660}\right)\) | \(e\left(\frac{73}{165}\right)\) | \(e\left(\frac{119}{165}\right)\) | \(e\left(\frac{37}{220}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{71}{132}\right)\) |
| \(\chi_{5445}(128,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{647}{660}\right)\) | \(e\left(\frac{317}{330}\right)\) | \(e\left(\frac{569}{660}\right)\) | \(e\left(\frac{207}{220}\right)\) | \(e\left(\frac{7}{660}\right)\) | \(e\left(\frac{139}{165}\right)\) | \(e\left(\frac{152}{165}\right)\) | \(e\left(\frac{81}{220}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{71}{132}\right)\) |
| \(\chi_{5445}(167,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{481}{660}\right)\) | \(e\left(\frac{151}{330}\right)\) | \(e\left(\frac{67}{660}\right)\) | \(e\left(\frac{41}{220}\right)\) | \(e\left(\frac{401}{660}\right)\) | \(e\left(\frac{137}{165}\right)\) | \(e\left(\frac{151}{165}\right)\) | \(e\left(\frac{83}{220}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{13}{132}\right)\) |
| \(\chi_{5445}(173,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{563}{660}\right)\) | \(e\left(\frac{233}{330}\right)\) | \(e\left(\frac{641}{660}\right)\) | \(e\left(\frac{123}{220}\right)\) | \(e\left(\frac{103}{660}\right)\) | \(e\left(\frac{136}{165}\right)\) | \(e\left(\frac{68}{165}\right)\) | \(e\left(\frac{29}{220}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{83}{132}\right)\) |
| \(\chi_{5445}(182,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{269}{660}\right)\) | \(e\left(\frac{269}{330}\right)\) | \(e\left(\frac{563}{660}\right)\) | \(e\left(\frac{49}{220}\right)\) | \(e\left(\frac{109}{660}\right)\) | \(e\left(\frac{43}{165}\right)\) | \(e\left(\frac{104}{165}\right)\) | \(e\left(\frac{67}{220}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{125}{132}\right)\) |
| \(\chi_{5445}(227,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{257}{660}\right)\) | \(e\left(\frac{257}{330}\right)\) | \(e\left(\frac{479}{660}\right)\) | \(e\left(\frac{37}{220}\right)\) | \(e\left(\frac{217}{660}\right)\) | \(e\left(\frac{19}{165}\right)\) | \(e\left(\frac{92}{165}\right)\) | \(e\left(\frac{91}{220}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{89}{132}\right)\) |
| \(\chi_{5445}(248,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{259}{660}\right)\) | \(e\left(\frac{259}{330}\right)\) | \(e\left(\frac{493}{660}\right)\) | \(e\left(\frac{39}{220}\right)\) | \(e\left(\frac{419}{660}\right)\) | \(e\left(\frac{23}{165}\right)\) | \(e\left(\frac{94}{165}\right)\) | \(e\left(\frac{197}{220}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{7}{132}\right)\) |
| \(\chi_{5445}(272,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{593}{660}\right)\) | \(e\left(\frac{263}{330}\right)\) | \(e\left(\frac{191}{660}\right)\) | \(e\left(\frac{153}{220}\right)\) | \(e\left(\frac{493}{660}\right)\) | \(e\left(\frac{31}{165}\right)\) | \(e\left(\frac{98}{165}\right)\) | \(e\left(\frac{79}{220}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{41}{132}\right)\) |
| \(\chi_{5445}(293,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{547}{660}\right)\) | \(e\left(\frac{217}{330}\right)\) | \(e\left(\frac{529}{660}\right)\) | \(e\left(\frac{107}{220}\right)\) | \(e\left(\frac{467}{660}\right)\) | \(e\left(\frac{104}{165}\right)\) | \(e\left(\frac{52}{165}\right)\) | \(e\left(\frac{61}{220}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{79}{132}\right)\) |
| \(\chi_{5445}(338,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{283}{660}\right)\) | \(e\left(\frac{283}{330}\right)\) | \(e\left(\frac{1}{660}\right)\) | \(e\left(\frac{63}{220}\right)\) | \(e\left(\frac{203}{660}\right)\) | \(e\left(\frac{71}{165}\right)\) | \(e\left(\frac{118}{165}\right)\) | \(e\left(\frac{149}{220}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{79}{132}\right)\) |
| \(\chi_{5445}(347,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{409}{660}\right)\) | \(e\left(\frac{79}{330}\right)\) | \(e\left(\frac{223}{660}\right)\) | \(e\left(\frac{189}{220}\right)\) | \(e\left(\frac{389}{660}\right)\) | \(e\left(\frac{158}{165}\right)\) | \(e\left(\frac{79}{165}\right)\) | \(e\left(\frac{7}{220}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{61}{132}\right)\) |
| \(\chi_{5445}(392,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{157}{660}\right)\) | \(e\left(\frac{157}{330}\right)\) | \(e\left(\frac{439}{660}\right)\) | \(e\left(\frac{157}{220}\right)\) | \(e\left(\frac{17}{660}\right)\) | \(e\left(\frac{149}{165}\right)\) | \(e\left(\frac{157}{165}\right)\) | \(e\left(\frac{71}{220}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{97}{132}\right)\) |
| \(\chi_{5445}(398,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{431}{660}\right)\) | \(e\left(\frac{101}{330}\right)\) | \(e\left(\frac{377}{660}\right)\) | \(e\left(\frac{211}{220}\right)\) | \(e\left(\frac{631}{660}\right)\) | \(e\left(\frac{37}{165}\right)\) | \(e\left(\frac{101}{165}\right)\) | \(e\left(\frac{73}{220}\right)\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{83}{132}\right)\) |
| \(\chi_{5445}(437,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{313}{660}\right)\) | \(e\left(\frac{313}{330}\right)\) | \(e\left(\frac{211}{660}\right)\) | \(e\left(\frac{93}{220}\right)\) | \(e\left(\frac{593}{660}\right)\) | \(e\left(\frac{131}{165}\right)\) | \(e\left(\frac{148}{165}\right)\) | \(e\left(\frac{199}{220}\right)\) | \(e\left(\frac{52}{55}\right)\) | \(e\left(\frac{37}{132}\right)\) |
| \(\chi_{5445}(497,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{221}{660}\right)\) | \(e\left(\frac{221}{330}\right)\) | \(e\left(\frac{227}{660}\right)\) | \(e\left(\frac{1}{220}\right)\) | \(e\left(\frac{541}{660}\right)\) | \(e\left(\frac{112}{165}\right)\) | \(e\left(\frac{56}{165}\right)\) | \(e\left(\frac{163}{220}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{113}{132}\right)\) |
| \(\chi_{5445}(563,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{631}{660}\right)\) | \(e\left(\frac{301}{330}\right)\) | \(e\left(\frac{457}{660}\right)\) | \(e\left(\frac{191}{220}\right)\) | \(e\left(\frac{371}{660}\right)\) | \(e\left(\frac{107}{165}\right)\) | \(e\left(\frac{136}{165}\right)\) | \(e\left(\frac{113}{220}\right)\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{67}{132}\right)\) |
| \(\chi_{5445}(623,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{347}{660}\right)\) | \(e\left(\frac{17}{330}\right)\) | \(e\left(\frac{449}{660}\right)\) | \(e\left(\frac{127}{220}\right)\) | \(e\left(\frac{67}{660}\right)\) | \(e\left(\frac{34}{165}\right)\) | \(e\left(\frac{17}{165}\right)\) | \(e\left(\frac{21}{220}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{95}{132}\right)\) |
| \(\chi_{5445}(662,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{421}{660}\right)\) | \(e\left(\frac{91}{330}\right)\) | \(e\left(\frac{307}{660}\right)\) | \(e\left(\frac{201}{220}\right)\) | \(e\left(\frac{281}{660}\right)\) | \(e\left(\frac{17}{165}\right)\) | \(e\left(\frac{91}{165}\right)\) | \(e\left(\frac{203}{220}\right)\) | \(e\left(\frac{29}{55}\right)\) | \(e\left(\frac{97}{132}\right)\) |
| \(\chi_{5445}(668,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{383}{660}\right)\) | \(e\left(\frac{53}{330}\right)\) | \(e\left(\frac{41}{660}\right)\) | \(e\left(\frac{163}{220}\right)\) | \(e\left(\frac{403}{660}\right)\) | \(e\left(\frac{106}{165}\right)\) | \(e\left(\frac{53}{165}\right)\) | \(e\left(\frac{169}{220}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{71}{132}\right)\) |
| \(\chi_{5445}(677,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{29}{660}\right)\) | \(e\left(\frac{29}{330}\right)\) | \(e\left(\frac{203}{660}\right)\) | \(e\left(\frac{29}{220}\right)\) | \(e\left(\frac{289}{660}\right)\) | \(e\left(\frac{58}{165}\right)\) | \(e\left(\frac{29}{165}\right)\) | \(e\left(\frac{107}{220}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{65}{132}\right)\) |
| \(\chi_{5445}(722,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{617}{660}\right)\) | \(e\left(\frac{287}{330}\right)\) | \(e\left(\frac{359}{660}\right)\) | \(e\left(\frac{177}{220}\right)\) | \(e\left(\frac{277}{660}\right)\) | \(e\left(\frac{79}{165}\right)\) | \(e\left(\frac{122}{165}\right)\) | \(e\left(\frac{31}{220}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{113}{132}\right)\) |
| \(\chi_{5445}(743,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{19}{660}\right)\) | \(e\left(\frac{19}{330}\right)\) | \(e\left(\frac{133}{660}\right)\) | \(e\left(\frac{19}{220}\right)\) | \(e\left(\frac{599}{660}\right)\) | \(e\left(\frac{38}{165}\right)\) | \(e\left(\frac{19}{165}\right)\) | \(e\left(\frac{17}{220}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{79}{132}\right)\) |
| \(\chi_{5445}(767,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{413}{660}\right)\) | \(e\left(\frac{83}{330}\right)\) | \(e\left(\frac{251}{660}\right)\) | \(e\left(\frac{193}{220}\right)\) | \(e\left(\frac{133}{660}\right)\) | \(e\left(\frac{1}{165}\right)\) | \(e\left(\frac{83}{165}\right)\) | \(e\left(\frac{219}{220}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{29}{132}\right)\) |
| \(\chi_{5445}(788,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{247}{660}\right)\) | \(e\left(\frac{247}{330}\right)\) | \(e\left(\frac{409}{660}\right)\) | \(e\left(\frac{27}{220}\right)\) | \(e\left(\frac{527}{660}\right)\) | \(e\left(\frac{164}{165}\right)\) | \(e\left(\frac{82}{165}\right)\) | \(e\left(\frac{1}{220}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{103}{132}\right)\) |
| \(\chi_{5445}(833,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{103}{660}\right)\) | \(e\left(\frac{103}{330}\right)\) | \(e\left(\frac{61}{660}\right)\) | \(e\left(\frac{103}{220}\right)\) | \(e\left(\frac{503}{660}\right)\) | \(e\left(\frac{41}{165}\right)\) | \(e\left(\frac{103}{165}\right)\) | \(e\left(\frac{69}{220}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{67}{132}\right)\) |
| \(\chi_{5445}(842,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{169}{660}\right)\) | \(e\left(\frac{169}{330}\right)\) | \(e\left(\frac{523}{660}\right)\) | \(e\left(\frac{169}{220}\right)\) | \(e\left(\frac{569}{660}\right)\) | \(e\left(\frac{8}{165}\right)\) | \(e\left(\frac{4}{165}\right)\) | \(e\left(\frac{47}{220}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{1}{132}\right)\) |
| \(\chi_{5445}(893,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{371}{660}\right)\) | \(e\left(\frac{41}{330}\right)\) | \(e\left(\frac{617}{660}\right)\) | \(e\left(\frac{151}{220}\right)\) | \(e\left(\frac{511}{660}\right)\) | \(e\left(\frac{82}{165}\right)\) | \(e\left(\frac{41}{165}\right)\) | \(e\left(\frac{193}{220}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{35}{132}\right)\) |
| \(\chi_{5445}(932,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{133}{660}\right)\) | \(e\left(\frac{133}{330}\right)\) | \(e\left(\frac{271}{660}\right)\) | \(e\left(\frac{133}{220}\right)\) | \(e\left(\frac{233}{660}\right)\) | \(e\left(\frac{101}{165}\right)\) | \(e\left(\frac{133}{165}\right)\) | \(e\left(\frac{119}{220}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{25}{132}\right)\) |
| \(\chi_{5445}(992,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{161}{660}\right)\) | \(e\left(\frac{161}{330}\right)\) | \(e\left(\frac{467}{660}\right)\) | \(e\left(\frac{161}{220}\right)\) | \(e\left(\frac{421}{660}\right)\) | \(e\left(\frac{157}{165}\right)\) | \(e\left(\frac{161}{165}\right)\) | \(e\left(\frac{63}{220}\right)\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{65}{132}\right)\) |