from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5445, base_ring=CyclotomicField(660))
M = H._module
chi = DirichletCharacter(H, M([220,495,108]))
chi.galois_orbit()
[g,chi] = znchar(Mod(58,5445))
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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{5445}(58,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{163}{660}\right)\) | \(e\left(\frac{163}{330}\right)\) | \(e\left(\frac{151}{660}\right)\) | \(e\left(\frac{163}{220}\right)\) | \(e\left(\frac{293}{660}\right)\) | \(e\left(\frac{157}{330}\right)\) | \(e\left(\frac{163}{165}\right)\) | \(e\left(\frac{169}{220}\right)\) | \(e\left(\frac{9}{110}\right)\) | \(e\left(\frac{49}{132}\right)\) |
| \(\chi_{5445}(97,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{161}{660}\right)\) | \(e\left(\frac{161}{330}\right)\) | \(e\left(\frac{137}{660}\right)\) | \(e\left(\frac{161}{220}\right)\) | \(e\left(\frac{91}{660}\right)\) | \(e\left(\frac{149}{330}\right)\) | \(e\left(\frac{161}{165}\right)\) | \(e\left(\frac{63}{220}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{131}{132}\right)\) |
| \(\chi_{5445}(103,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{127}{660}\right)\) | \(e\left(\frac{127}{330}\right)\) | \(e\left(\frac{559}{660}\right)\) | \(e\left(\frac{127}{220}\right)\) | \(e\left(\frac{617}{660}\right)\) | \(e\left(\frac{13}{330}\right)\) | \(e\left(\frac{127}{165}\right)\) | \(e\left(\frac{21}{220}\right)\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{73}{132}\right)\) |
| \(\chi_{5445}(157,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{133}{660}\right)\) | \(e\left(\frac{133}{330}\right)\) | \(e\left(\frac{601}{660}\right)\) | \(e\left(\frac{133}{220}\right)\) | \(e\left(\frac{563}{660}\right)\) | \(e\left(\frac{37}{330}\right)\) | \(e\left(\frac{133}{165}\right)\) | \(e\left(\frac{119}{220}\right)\) | \(e\left(\frac{89}{110}\right)\) | \(e\left(\frac{91}{132}\right)\) |
| \(\chi_{5445}(223,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{443}{660}\right)\) | \(e\left(\frac{113}{330}\right)\) | \(e\left(\frac{131}{660}\right)\) | \(e\left(\frac{3}{220}\right)\) | \(e\left(\frac{193}{660}\right)\) | \(e\left(\frac{287}{330}\right)\) | \(e\left(\frac{113}{165}\right)\) | \(e\left(\frac{49}{220}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{53}{132}\right)\) |
| \(\chi_{5445}(247,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{169}{660}\right)\) | \(e\left(\frac{169}{330}\right)\) | \(e\left(\frac{193}{660}\right)\) | \(e\left(\frac{169}{220}\right)\) | \(e\left(\frac{239}{660}\right)\) | \(e\left(\frac{181}{330}\right)\) | \(e\left(\frac{4}{165}\right)\) | \(e\left(\frac{47}{220}\right)\) | \(e\left(\frac{37}{110}\right)\) | \(e\left(\frac{67}{132}\right)\) |
| \(\chi_{5445}(268,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{227}{660}\right)\) | \(e\left(\frac{227}{330}\right)\) | \(e\left(\frac{599}{660}\right)\) | \(e\left(\frac{7}{220}\right)\) | \(e\left(\frac{157}{660}\right)\) | \(e\left(\frac{83}{330}\right)\) | \(e\left(\frac{62}{165}\right)\) | \(e\left(\frac{41}{220}\right)\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{65}{132}\right)\) |
| \(\chi_{5445}(313,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{179}{660}\right)\) | \(e\left(\frac{179}{330}\right)\) | \(e\left(\frac{263}{660}\right)\) | \(e\left(\frac{179}{220}\right)\) | \(e\left(\frac{589}{660}\right)\) | \(e\left(\frac{221}{330}\right)\) | \(e\left(\frac{14}{165}\right)\) | \(e\left(\frac{137}{220}\right)\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{53}{132}\right)\) |
| \(\chi_{5445}(322,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{413}{660}\right)\) | \(e\left(\frac{83}{330}\right)\) | \(e\left(\frac{581}{660}\right)\) | \(e\left(\frac{193}{220}\right)\) | \(e\left(\frac{463}{660}\right)\) | \(e\left(\frac{167}{330}\right)\) | \(e\left(\frac{83}{165}\right)\) | \(e\left(\frac{219}{220}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{95}{132}\right)\) |
| \(\chi_{5445}(328,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{211}{660}\right)\) | \(e\left(\frac{211}{330}\right)\) | \(e\left(\frac{487}{660}\right)\) | \(e\left(\frac{211}{220}\right)\) | \(e\left(\frac{521}{660}\right)\) | \(e\left(\frac{19}{330}\right)\) | \(e\left(\frac{46}{165}\right)\) | \(e\left(\frac{73}{220}\right)\) | \(e\left(\frac{13}{110}\right)\) | \(e\left(\frac{61}{132}\right)\) |
| \(\chi_{5445}(367,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{617}{660}\right)\) | \(e\left(\frac{287}{330}\right)\) | \(e\left(\frac{29}{660}\right)\) | \(e\left(\frac{177}{220}\right)\) | \(e\left(\frac{607}{660}\right)\) | \(e\left(\frac{323}{330}\right)\) | \(e\left(\frac{122}{165}\right)\) | \(e\left(\frac{31}{220}\right)\) | \(e\left(\frac{1}{110}\right)\) | \(e\left(\frac{47}{132}\right)\) |
| \(\chi_{5445}(412,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{29}{660}\right)\) | \(e\left(\frac{29}{330}\right)\) | \(e\left(\frac{533}{660}\right)\) | \(e\left(\frac{29}{220}\right)\) | \(e\left(\frac{619}{660}\right)\) | \(e\left(\frac{281}{330}\right)\) | \(e\left(\frac{29}{165}\right)\) | \(e\left(\frac{107}{220}\right)\) | \(e\left(\frac{7}{110}\right)\) | \(e\left(\frac{131}{132}\right)\) |
| \(\chi_{5445}(427,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{421}{660}\right)\) | \(e\left(\frac{91}{330}\right)\) | \(e\left(\frac{637}{660}\right)\) | \(e\left(\frac{201}{220}\right)\) | \(e\left(\frac{611}{660}\right)\) | \(e\left(\frac{199}{330}\right)\) | \(e\left(\frac{91}{165}\right)\) | \(e\left(\frac{203}{220}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{31}{132}\right)\) |
| \(\chi_{5445}(553,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{343}{660}\right)\) | \(e\left(\frac{13}{330}\right)\) | \(e\left(\frac{91}{660}\right)\) | \(e\left(\frac{123}{220}\right)\) | \(e\left(\frac{653}{660}\right)\) | \(e\left(\frac{217}{330}\right)\) | \(e\left(\frac{13}{165}\right)\) | \(e\left(\frac{29}{220}\right)\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{61}{132}\right)\) |
| \(\chi_{5445}(592,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{221}{660}\right)\) | \(e\left(\frac{221}{330}\right)\) | \(e\left(\frac{557}{660}\right)\) | \(e\left(\frac{1}{220}\right)\) | \(e\left(\frac{211}{660}\right)\) | \(e\left(\frac{59}{330}\right)\) | \(e\left(\frac{56}{165}\right)\) | \(e\left(\frac{163}{220}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{47}{132}\right)\) |
| \(\chi_{5445}(598,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{427}{660}\right)\) | \(e\left(\frac{97}{330}\right)\) | \(e\left(\frac{19}{660}\right)\) | \(e\left(\frac{207}{220}\right)\) | \(e\left(\frac{557}{660}\right)\) | \(e\left(\frac{223}{330}\right)\) | \(e\left(\frac{97}{165}\right)\) | \(e\left(\frac{81}{220}\right)\) | \(e\left(\frac{31}{110}\right)\) | \(e\left(\frac{49}{132}\right)\) |
| \(\chi_{5445}(643,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{559}{660}\right)\) | \(e\left(\frac{229}{330}\right)\) | \(e\left(\frac{283}{660}\right)\) | \(e\left(\frac{119}{220}\right)\) | \(e\left(\frac{29}{660}\right)\) | \(e\left(\frac{91}{330}\right)\) | \(e\left(\frac{64}{165}\right)\) | \(e\left(\frac{37}{220}\right)\) | \(e\left(\frac{97}{110}\right)\) | \(e\left(\frac{49}{132}\right)\) |
| \(\chi_{5445}(652,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{313}{660}\right)\) | \(e\left(\frac{313}{330}\right)\) | \(e\left(\frac{541}{660}\right)\) | \(e\left(\frac{93}{220}\right)\) | \(e\left(\frac{263}{660}\right)\) | \(e\left(\frac{97}{330}\right)\) | \(e\left(\frac{148}{165}\right)\) | \(e\left(\frac{199}{220}\right)\) | \(e\left(\frac{49}{110}\right)\) | \(e\left(\frac{103}{132}\right)\) |
| \(\chi_{5445}(697,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{157}{660}\right)\) | \(e\left(\frac{157}{330}\right)\) | \(e\left(\frac{109}{660}\right)\) | \(e\left(\frac{157}{220}\right)\) | \(e\left(\frac{347}{660}\right)\) | \(e\left(\frac{133}{330}\right)\) | \(e\left(\frac{157}{165}\right)\) | \(e\left(\frac{71}{220}\right)\) | \(e\left(\frac{91}{110}\right)\) | \(e\left(\frac{31}{132}\right)\) |
| \(\chi_{5445}(718,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{623}{660}\right)\) | \(e\left(\frac{293}{330}\right)\) | \(e\left(\frac{71}{660}\right)\) | \(e\left(\frac{183}{220}\right)\) | \(e\left(\frac{553}{660}\right)\) | \(e\left(\frac{17}{330}\right)\) | \(e\left(\frac{128}{165}\right)\) | \(e\left(\frac{129}{220}\right)\) | \(e\left(\frac{29}{110}\right)\) | \(e\left(\frac{65}{132}\right)\) |
| \(\chi_{5445}(742,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{409}{660}\right)\) | \(e\left(\frac{79}{330}\right)\) | \(e\left(\frac{553}{660}\right)\) | \(e\left(\frac{189}{220}\right)\) | \(e\left(\frac{59}{660}\right)\) | \(e\left(\frac{151}{330}\right)\) | \(e\left(\frac{79}{165}\right)\) | \(e\left(\frac{7}{220}\right)\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{127}{132}\right)\) |
| \(\chi_{5445}(763,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{527}{660}\right)\) | \(e\left(\frac{197}{330}\right)\) | \(e\left(\frac{59}{660}\right)\) | \(e\left(\frac{87}{220}\right)\) | \(e\left(\frac{97}{660}\right)\) | \(e\left(\frac{293}{330}\right)\) | \(e\left(\frac{32}{165}\right)\) | \(e\left(\frac{101}{220}\right)\) | \(e\left(\frac{21}{110}\right)\) | \(e\left(\frac{41}{132}\right)\) |
| \(\chi_{5445}(808,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{419}{660}\right)\) | \(e\left(\frac{89}{330}\right)\) | \(e\left(\frac{623}{660}\right)\) | \(e\left(\frac{199}{220}\right)\) | \(e\left(\frac{409}{660}\right)\) | \(e\left(\frac{191}{330}\right)\) | \(e\left(\frac{89}{165}\right)\) | \(e\left(\frac{97}{220}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{113}{132}\right)\) |
| \(\chi_{5445}(817,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{593}{660}\right)\) | \(e\left(\frac{263}{330}\right)\) | \(e\left(\frac{521}{660}\right)\) | \(e\left(\frac{153}{220}\right)\) | \(e\left(\frac{163}{660}\right)\) | \(e\left(\frac{227}{330}\right)\) | \(e\left(\frac{98}{165}\right)\) | \(e\left(\frac{79}{220}\right)\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{107}{132}\right)\) |
| \(\chi_{5445}(823,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{271}{660}\right)\) | \(e\left(\frac{271}{330}\right)\) | \(e\left(\frac{247}{660}\right)\) | \(e\left(\frac{51}{220}\right)\) | \(e\left(\frac{641}{660}\right)\) | \(e\left(\frac{259}{330}\right)\) | \(e\left(\frac{106}{165}\right)\) | \(e\left(\frac{173}{220}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{109}{132}\right)\) |
| \(\chi_{5445}(862,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{257}{660}\right)\) | \(e\left(\frac{257}{330}\right)\) | \(e\left(\frac{149}{660}\right)\) | \(e\left(\frac{37}{220}\right)\) | \(e\left(\frac{547}{660}\right)\) | \(e\left(\frac{203}{330}\right)\) | \(e\left(\frac{92}{165}\right)\) | \(e\left(\frac{91}{220}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{23}{132}\right)\) |
| \(\chi_{5445}(907,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{269}{660}\right)\) | \(e\left(\frac{269}{330}\right)\) | \(e\left(\frac{233}{660}\right)\) | \(e\left(\frac{49}{220}\right)\) | \(e\left(\frac{439}{660}\right)\) | \(e\left(\frac{251}{330}\right)\) | \(e\left(\frac{104}{165}\right)\) | \(e\left(\frac{67}{220}\right)\) | \(e\left(\frac{27}{110}\right)\) | \(e\left(\frac{59}{132}\right)\) |
| \(\chi_{5445}(922,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{481}{660}\right)\) | \(e\left(\frac{151}{330}\right)\) | \(e\left(\frac{397}{660}\right)\) | \(e\left(\frac{41}{220}\right)\) | \(e\left(\frac{71}{660}\right)\) | \(e\left(\frac{109}{330}\right)\) | \(e\left(\frac{151}{165}\right)\) | \(e\left(\frac{83}{220}\right)\) | \(e\left(\frac{63}{110}\right)\) | \(e\left(\frac{79}{132}\right)\) |
| \(\chi_{5445}(988,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{71}{660}\right)\) | \(e\left(\frac{71}{330}\right)\) | \(e\left(\frac{167}{660}\right)\) | \(e\left(\frac{71}{220}\right)\) | \(e\left(\frac{241}{660}\right)\) | \(e\left(\frac{119}{330}\right)\) | \(e\left(\frac{71}{165}\right)\) | \(e\left(\frac{133}{220}\right)\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{125}{132}\right)\) |
| \(\chi_{5445}(1048,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{523}{660}\right)\) | \(e\left(\frac{193}{330}\right)\) | \(e\left(\frac{31}{660}\right)\) | \(e\left(\frac{83}{220}\right)\) | \(e\left(\frac{353}{660}\right)\) | \(e\left(\frac{277}{330}\right)\) | \(e\left(\frac{28}{165}\right)\) | \(e\left(\frac{109}{220}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{73}{132}\right)\) |
| \(\chi_{5445}(1087,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{281}{660}\right)\) | \(e\left(\frac{281}{330}\right)\) | \(e\left(\frac{317}{660}\right)\) | \(e\left(\frac{61}{220}\right)\) | \(e\left(\frac{331}{660}\right)\) | \(e\left(\frac{299}{330}\right)\) | \(e\left(\frac{116}{165}\right)\) | \(e\left(\frac{43}{220}\right)\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{95}{132}\right)\) |