from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16335, base_ring=CyclotomicField(660))
M = H._module
chi = DirichletCharacter(H, M([110,495,18]))
chi.galois_orbit()
[g,chi] = znchar(Mod(8,16335))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(16335\) | |
| Conductor: | \(5445\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(660\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 5445.dp | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| 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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{16335}(8,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{623}{660}\right)\) | \(e\left(\frac{293}{330}\right)\) | \(e\left(\frac{401}{660}\right)\) | \(e\left(\frac{183}{220}\right)\) | \(e\left(\frac{223}{660}\right)\) | \(e\left(\frac{91}{165}\right)\) | \(e\left(\frac{128}{165}\right)\) | \(e\left(\frac{129}{220}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{131}{132}\right)\) |
| \(\chi_{16335}(17,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{349}{660}\right)\) | \(e\left(\frac{19}{330}\right)\) | \(e\left(\frac{463}{660}\right)\) | \(e\left(\frac{129}{220}\right)\) | \(e\left(\frac{269}{660}\right)\) | \(e\left(\frac{38}{165}\right)\) | \(e\left(\frac{19}{165}\right)\) | \(e\left(\frac{127}{220}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{13}{132}\right)\) |
| \(\chi_{16335}(62,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{137}{660}\right)\) | \(e\left(\frac{137}{330}\right)\) | \(e\left(\frac{299}{660}\right)\) | \(e\left(\frac{137}{220}\right)\) | \(e\left(\frac{637}{660}\right)\) | \(e\left(\frac{109}{165}\right)\) | \(e\left(\frac{137}{165}\right)\) | \(e\left(\frac{111}{220}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{125}{132}\right)\) |
| \(\chi_{16335}(332,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{461}{660}\right)\) | \(e\left(\frac{131}{330}\right)\) | \(e\left(\frac{587}{660}\right)\) | \(e\left(\frac{21}{220}\right)\) | \(e\left(\frac{361}{660}\right)\) | \(e\left(\frac{97}{165}\right)\) | \(e\left(\frac{131}{165}\right)\) | \(e\left(\frac{123}{220}\right)\) | \(e\left(\frac{49}{55}\right)\) | \(e\left(\frac{41}{132}\right)\) |
| \(\chi_{16335}(413,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{179}{660}\right)\) | \(e\left(\frac{179}{330}\right)\) | \(e\left(\frac{593}{660}\right)\) | \(e\left(\frac{179}{220}\right)\) | \(e\left(\frac{259}{660}\right)\) | \(e\left(\frac{28}{165}\right)\) | \(e\left(\frac{14}{165}\right)\) | \(e\left(\frac{137}{220}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{119}{132}\right)\) |
| \(\chi_{16335}(503,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{223}{660}\right)\) | \(e\left(\frac{223}{330}\right)\) | \(e\left(\frac{241}{660}\right)\) | \(e\left(\frac{3}{220}\right)\) | \(e\left(\frac{83}{660}\right)\) | \(e\left(\frac{116}{165}\right)\) | \(e\left(\frac{58}{165}\right)\) | \(e\left(\frac{49}{220}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{31}{132}\right)\) |
| \(\chi_{16335}(557,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{277}{660}\right)\) | \(e\left(\frac{277}{330}\right)\) | \(e\left(\frac{619}{660}\right)\) | \(e\left(\frac{57}{220}\right)\) | \(e\left(\frac{257}{660}\right)\) | \(e\left(\frac{59}{165}\right)\) | \(e\left(\frac{112}{165}\right)\) | \(e\left(\frac{51}{220}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{61}{132}\right)\) |
| \(\chi_{16335}(827,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{181}{660}\right)\) | \(e\left(\frac{181}{330}\right)\) | \(e\left(\frac{607}{660}\right)\) | \(e\left(\frac{181}{220}\right)\) | \(e\left(\frac{461}{660}\right)\) | \(e\left(\frac{32}{165}\right)\) | \(e\left(\frac{16}{165}\right)\) | \(e\left(\frac{23}{220}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{37}{132}\right)\) |
| \(\chi_{16335}(908,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{379}{660}\right)\) | \(e\left(\frac{49}{330}\right)\) | \(e\left(\frac{13}{660}\right)\) | \(e\left(\frac{159}{220}\right)\) | \(e\left(\frac{659}{660}\right)\) | \(e\left(\frac{98}{165}\right)\) | \(e\left(\frac{49}{165}\right)\) | \(e\left(\frac{177}{220}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{103}{132}\right)\) |
| \(\chi_{16335}(953,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{587}{660}\right)\) | \(e\left(\frac{257}{330}\right)\) | \(e\left(\frac{149}{660}\right)\) | \(e\left(\frac{147}{220}\right)\) | \(e\left(\frac{547}{660}\right)\) | \(e\left(\frac{19}{165}\right)\) | \(e\left(\frac{92}{165}\right)\) | \(e\left(\frac{201}{220}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{23}{132}\right)\) |
| \(\chi_{16335}(1007,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{89}{660}\right)\) | \(e\left(\frac{89}{330}\right)\) | \(e\left(\frac{623}{660}\right)\) | \(e\left(\frac{89}{220}\right)\) | \(e\left(\frac{409}{660}\right)\) | \(e\left(\frac{13}{165}\right)\) | \(e\left(\frac{89}{165}\right)\) | \(e\left(\frac{207}{220}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{113}{132}\right)\) |
| \(\chi_{16335}(1097,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{73}{660}\right)\) | \(e\left(\frac{73}{330}\right)\) | \(e\left(\frac{511}{660}\right)\) | \(e\left(\frac{73}{220}\right)\) | \(e\left(\frac{113}{660}\right)\) | \(e\left(\frac{146}{165}\right)\) | \(e\left(\frac{73}{165}\right)\) | \(e\left(\frac{19}{220}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{109}{132}\right)\) |
| \(\chi_{16335}(1223,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{551}{660}\right)\) | \(e\left(\frac{221}{330}\right)\) | \(e\left(\frac{557}{660}\right)\) | \(e\left(\frac{111}{220}\right)\) | \(e\left(\frac{211}{660}\right)\) | \(e\left(\frac{112}{165}\right)\) | \(e\left(\frac{56}{165}\right)\) | \(e\left(\frac{53}{220}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{47}{132}\right)\) |
| \(\chi_{16335}(1448,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{67}{660}\right)\) | \(e\left(\frac{67}{330}\right)\) | \(e\left(\frac{469}{660}\right)\) | \(e\left(\frac{67}{220}\right)\) | \(e\left(\frac{167}{660}\right)\) | \(e\left(\frac{134}{165}\right)\) | \(e\left(\frac{67}{165}\right)\) | \(e\left(\frac{141}{220}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{91}{132}\right)\) |
| \(\chi_{16335}(1493,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{83}{660}\right)\) | \(e\left(\frac{83}{330}\right)\) | \(e\left(\frac{581}{660}\right)\) | \(e\left(\frac{83}{220}\right)\) | \(e\left(\frac{463}{660}\right)\) | \(e\left(\frac{1}{165}\right)\) | \(e\left(\frac{83}{165}\right)\) | \(e\left(\frac{109}{220}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{95}{132}\right)\) |
| \(\chi_{16335}(1502,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{289}{660}\right)\) | \(e\left(\frac{289}{330}\right)\) | \(e\left(\frac{43}{660}\right)\) | \(e\left(\frac{69}{220}\right)\) | \(e\left(\frac{149}{660}\right)\) | \(e\left(\frac{83}{165}\right)\) | \(e\left(\frac{124}{165}\right)\) | \(e\left(\frac{27}{220}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{97}{132}\right)\) |
| \(\chi_{16335}(1547,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{557}{660}\right)\) | \(e\left(\frac{227}{330}\right)\) | \(e\left(\frac{599}{660}\right)\) | \(e\left(\frac{117}{220}\right)\) | \(e\left(\frac{157}{660}\right)\) | \(e\left(\frac{124}{165}\right)\) | \(e\left(\frac{62}{165}\right)\) | \(e\left(\frac{151}{220}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{65}{132}\right)\) |
| \(\chi_{16335}(1718,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{271}{660}\right)\) | \(e\left(\frac{271}{330}\right)\) | \(e\left(\frac{577}{660}\right)\) | \(e\left(\frac{51}{220}\right)\) | \(e\left(\frac{311}{660}\right)\) | \(e\left(\frac{47}{165}\right)\) | \(e\left(\frac{106}{165}\right)\) | \(e\left(\frac{173}{220}\right)\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{43}{132}\right)\) |
| \(\chi_{16335}(1817,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{281}{660}\right)\) | \(e\left(\frac{281}{330}\right)\) | \(e\left(\frac{647}{660}\right)\) | \(e\left(\frac{61}{220}\right)\) | \(e\left(\frac{1}{660}\right)\) | \(e\left(\frac{67}{165}\right)\) | \(e\left(\frac{116}{165}\right)\) | \(e\left(\frac{43}{220}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{29}{132}\right)\) |
| \(\chi_{16335}(1898,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{119}{660}\right)\) | \(e\left(\frac{119}{330}\right)\) | \(e\left(\frac{173}{660}\right)\) | \(e\left(\frac{119}{220}\right)\) | \(e\left(\frac{139}{660}\right)\) | \(e\left(\frac{73}{165}\right)\) | \(e\left(\frac{119}{165}\right)\) | \(e\left(\frac{37}{220}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{71}{132}\right)\) |
| \(\chi_{16335}(1988,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{343}{660}\right)\) | \(e\left(\frac{13}{330}\right)\) | \(e\left(\frac{421}{660}\right)\) | \(e\left(\frac{123}{220}\right)\) | \(e\left(\frac{323}{660}\right)\) | \(e\left(\frac{26}{165}\right)\) | \(e\left(\frac{13}{165}\right)\) | \(e\left(\frac{29}{220}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{127}{132}\right)\) |
| \(\chi_{16335}(2042,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{37}{660}\right)\) | \(e\left(\frac{37}{330}\right)\) | \(e\left(\frac{259}{660}\right)\) | \(e\left(\frac{37}{220}\right)\) | \(e\left(\frac{437}{660}\right)\) | \(e\left(\frac{74}{165}\right)\) | \(e\left(\frac{37}{165}\right)\) | \(e\left(\frac{91}{220}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{1}{132}\right)\) |
| \(\chi_{16335}(2087,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{593}{660}\right)\) | \(e\left(\frac{263}{330}\right)\) | \(e\left(\frac{191}{660}\right)\) | \(e\left(\frac{153}{220}\right)\) | \(e\left(\frac{493}{660}\right)\) | \(e\left(\frac{31}{165}\right)\) | \(e\left(\frac{98}{165}\right)\) | \(e\left(\frac{79}{220}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{41}{132}\right)\) |
| \(\chi_{16335}(2312,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{660}\right)\) | \(e\left(\frac{1}{330}\right)\) | \(e\left(\frac{7}{660}\right)\) | \(e\left(\frac{1}{220}\right)\) | \(e\left(\frac{101}{660}\right)\) | \(e\left(\frac{2}{165}\right)\) | \(e\left(\frac{1}{165}\right)\) | \(e\left(\frac{163}{220}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{25}{132}\right)\) |
| \(\chi_{16335}(2438,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{347}{660}\right)\) | \(e\left(\frac{17}{330}\right)\) | \(e\left(\frac{449}{660}\right)\) | \(e\left(\frac{127}{220}\right)\) | \(e\left(\frac{67}{660}\right)\) | \(e\left(\frac{34}{165}\right)\) | \(e\left(\frac{17}{165}\right)\) | \(e\left(\frac{21}{220}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{95}{132}\right)\) |
| \(\chi_{16335}(2492,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{29}{660}\right)\) | \(e\left(\frac{29}{330}\right)\) | \(e\left(\frac{203}{660}\right)\) | \(e\left(\frac{29}{220}\right)\) | \(e\left(\frac{289}{660}\right)\) | \(e\left(\frac{58}{165}\right)\) | \(e\left(\frac{29}{165}\right)\) | \(e\left(\frac{107}{220}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{65}{132}\right)\) |
| \(\chi_{16335}(2582,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{193}{660}\right)\) | \(e\left(\frac{193}{330}\right)\) | \(e\left(\frac{31}{660}\right)\) | \(e\left(\frac{193}{220}\right)\) | \(e\left(\frac{353}{660}\right)\) | \(e\left(\frac{56}{165}\right)\) | \(e\left(\frac{28}{165}\right)\) | \(e\left(\frac{219}{220}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{73}{132}\right)\) |
| \(\chi_{16335}(2708,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{371}{660}\right)\) | \(e\left(\frac{41}{330}\right)\) | \(e\left(\frac{617}{660}\right)\) | \(e\left(\frac{151}{220}\right)\) | \(e\left(\frac{511}{660}\right)\) | \(e\left(\frac{82}{165}\right)\) | \(e\left(\frac{41}{165}\right)\) | \(e\left(\frac{193}{220}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{35}{132}\right)\) |
| \(\chi_{16335}(2933,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{487}{660}\right)\) | \(e\left(\frac{157}{330}\right)\) | \(e\left(\frac{109}{660}\right)\) | \(e\left(\frac{47}{220}\right)\) | \(e\left(\frac{347}{660}\right)\) | \(e\left(\frac{149}{165}\right)\) | \(e\left(\frac{157}{165}\right)\) | \(e\left(\frac{181}{220}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{31}{132}\right)\) |
| \(\chi_{16335}(2978,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{203}{660}\right)\) | \(e\left(\frac{203}{330}\right)\) | \(e\left(\frac{101}{660}\right)\) | \(e\left(\frac{203}{220}\right)\) | \(e\left(\frac{43}{660}\right)\) | \(e\left(\frac{76}{165}\right)\) | \(e\left(\frac{38}{165}\right)\) | \(e\left(\frac{89}{220}\right)\) | \(e\left(\frac{52}{55}\right)\) | \(e\left(\frac{59}{132}\right)\) |
| \(\chi_{16335}(2987,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{229}{660}\right)\) | \(e\left(\frac{229}{330}\right)\) | \(e\left(\frac{283}{660}\right)\) | \(e\left(\frac{9}{220}\right)\) | \(e\left(\frac{29}{660}\right)\) | \(e\left(\frac{128}{165}\right)\) | \(e\left(\frac{64}{165}\right)\) | \(e\left(\frac{147}{220}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{49}{132}\right)\) |