from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3267, base_ring=CyclotomicField(330))
M = H._module
chi = DirichletCharacter(H, M([55,9]))
chi.galois_orbit()
[g,chi] = znchar(Mod(8,3267))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(3267\) | |
| Conductor: | \(1089\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 1089.bd | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
First 31 of 80 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{3267}(8,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{32}{165}\right)\) | \(e\left(\frac{64}{165}\right)\) | \(e\left(\frac{281}{330}\right)\) | \(e\left(\frac{283}{330}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{29}{330}\right)\) | \(e\left(\frac{17}{330}\right)\) | \(e\left(\frac{128}{165}\right)\) | \(e\left(\frac{46}{55}\right)\) |
| \(\chi_{3267}(17,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{46}{165}\right)\) | \(e\left(\frac{92}{165}\right)\) | \(e\left(\frac{43}{330}\right)\) | \(e\left(\frac{149}{330}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{217}{330}\right)\) | \(e\left(\frac{241}{330}\right)\) | \(e\left(\frac{19}{165}\right)\) | \(e\left(\frac{18}{55}\right)\) |
| \(\chi_{3267}(35,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{149}{165}\right)\) | \(e\left(\frac{133}{165}\right)\) | \(e\left(\frac{107}{330}\right)\) | \(e\left(\frac{271}{330}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{233}{330}\right)\) | \(e\left(\frac{239}{330}\right)\) | \(e\left(\frac{101}{165}\right)\) | \(e\left(\frac{32}{55}\right)\) |
| \(\chi_{3267}(62,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{158}{165}\right)\) | \(e\left(\frac{151}{165}\right)\) | \(e\left(\frac{119}{330}\right)\) | \(e\left(\frac{67}{330}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{71}{330}\right)\) | \(e\left(\frac{53}{330}\right)\) | \(e\left(\frac{137}{165}\right)\) | \(e\left(\frac{14}{55}\right)\) |
| \(\chi_{3267}(116,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{56}{165}\right)\) | \(e\left(\frac{112}{165}\right)\) | \(e\left(\frac{203}{330}\right)\) | \(e\left(\frac{289}{330}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{257}{330}\right)\) | \(e\left(\frac{71}{330}\right)\) | \(e\left(\frac{59}{165}\right)\) | \(e\left(\frac{53}{55}\right)\) |
| \(\chi_{3267}(206,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{157}{165}\right)\) | \(e\left(\frac{149}{165}\right)\) | \(e\left(\frac{301}{330}\right)\) | \(e\left(\frac{53}{330}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{199}{330}\right)\) | \(e\left(\frac{37}{330}\right)\) | \(e\left(\frac{133}{165}\right)\) | \(e\left(\frac{16}{55}\right)\) |
| \(\chi_{3267}(260,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{165}\right)\) | \(e\left(\frac{146}{165}\right)\) | \(e\left(\frac{79}{330}\right)\) | \(e\left(\frac{197}{330}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{61}{330}\right)\) | \(e\left(\frac{13}{330}\right)\) | \(e\left(\frac{127}{165}\right)\) | \(e\left(\frac{19}{55}\right)\) |
| \(\chi_{3267}(305,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{137}{165}\right)\) | \(e\left(\frac{109}{165}\right)\) | \(e\left(\frac{311}{330}\right)\) | \(e\left(\frac{103}{330}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{119}{330}\right)\) | \(e\left(\frac{47}{330}\right)\) | \(e\left(\frac{53}{165}\right)\) | \(e\left(\frac{1}{55}\right)\) |
| \(\chi_{3267}(314,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{76}{165}\right)\) | \(e\left(\frac{152}{165}\right)\) | \(e\left(\frac{193}{330}\right)\) | \(e\left(\frac{239}{330}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{7}{330}\right)\) | \(e\left(\frac{61}{330}\right)\) | \(e\left(\frac{139}{165}\right)\) | \(e\left(\frac{13}{55}\right)\) |
| \(\chi_{3267}(332,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{74}{165}\right)\) | \(e\left(\frac{148}{165}\right)\) | \(e\left(\frac{227}{330}\right)\) | \(e\left(\frac{211}{330}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{263}{330}\right)\) | \(e\left(\frac{29}{330}\right)\) | \(e\left(\frac{131}{165}\right)\) | \(e\left(\frac{17}{55}\right)\) |
| \(\chi_{3267}(359,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{113}{165}\right)\) | \(e\left(\frac{61}{165}\right)\) | \(e\left(\frac{59}{330}\right)\) | \(e\left(\frac{97}{330}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{221}{330}\right)\) | \(e\left(\frac{323}{330}\right)\) | \(e\left(\frac{122}{165}\right)\) | \(e\left(\frac{49}{55}\right)\) |
| \(\chi_{3267}(413,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{86}{165}\right)\) | \(e\left(\frac{7}{165}\right)\) | \(e\left(\frac{23}{330}\right)\) | \(e\left(\frac{49}{330}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{47}{330}\right)\) | \(e\left(\frac{221}{330}\right)\) | \(e\left(\frac{14}{165}\right)\) | \(e\left(\frac{48}{55}\right)\) |
| \(\chi_{3267}(503,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{97}{165}\right)\) | \(e\left(\frac{29}{165}\right)\) | \(e\left(\frac{1}{330}\right)\) | \(e\left(\frac{203}{330}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{289}{330}\right)\) | \(e\left(\frac{67}{330}\right)\) | \(e\left(\frac{58}{165}\right)\) | \(e\left(\frac{26}{55}\right)\) |
| \(\chi_{3267}(530,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{165}\right)\) | \(e\left(\frac{158}{165}\right)\) | \(e\left(\frac{307}{330}\right)\) | \(e\left(\frac{281}{330}\right)\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{283}{330}\right)\) | \(e\left(\frac{109}{330}\right)\) | \(e\left(\frac{151}{165}\right)\) | \(e\left(\frac{7}{55}\right)\) |
| \(\chi_{3267}(557,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{28}{165}\right)\) | \(e\left(\frac{56}{165}\right)\) | \(e\left(\frac{19}{330}\right)\) | \(e\left(\frac{227}{330}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{211}{330}\right)\) | \(e\left(\frac{283}{330}\right)\) | \(e\left(\frac{112}{165}\right)\) | \(e\left(\frac{54}{55}\right)\) |
| \(\chi_{3267}(611,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{106}{165}\right)\) | \(e\left(\frac{47}{165}\right)\) | \(e\left(\frac{13}{330}\right)\) | \(e\left(\frac{329}{330}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{127}{330}\right)\) | \(e\left(\frac{211}{330}\right)\) | \(e\left(\frac{94}{165}\right)\) | \(e\left(\frac{8}{55}\right)\) |
| \(\chi_{3267}(629,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{164}{165}\right)\) | \(e\left(\frac{163}{165}\right)\) | \(e\left(\frac{17}{330}\right)\) | \(e\left(\frac{151}{330}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{293}{330}\right)\) | \(e\left(\frac{149}{330}\right)\) | \(e\left(\frac{161}{165}\right)\) | \(e\left(\frac{2}{55}\right)\) |
| \(\chi_{3267}(656,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{68}{165}\right)\) | \(e\left(\frac{136}{165}\right)\) | \(e\left(\frac{329}{330}\right)\) | \(e\left(\frac{127}{330}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{41}{330}\right)\) | \(e\left(\frac{263}{330}\right)\) | \(e\left(\frac{107}{165}\right)\) | \(e\left(\frac{29}{55}\right)\) |
| \(\chi_{3267}(710,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{116}{165}\right)\) | \(e\left(\frac{67}{165}\right)\) | \(e\left(\frac{173}{330}\right)\) | \(e\left(\frac{139}{330}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{167}{330}\right)\) | \(e\left(\frac{41}{330}\right)\) | \(e\left(\frac{134}{165}\right)\) | \(e\left(\frac{43}{55}\right)\) |
| \(\chi_{3267}(800,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{165}\right)\) | \(e\left(\frac{74}{165}\right)\) | \(e\left(\frac{31}{330}\right)\) | \(e\left(\frac{23}{330}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{49}{330}\right)\) | \(e\left(\frac{97}{330}\right)\) | \(e\left(\frac{148}{165}\right)\) | \(e\left(\frac{36}{55}\right)\) |
| \(\chi_{3267}(827,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{165}\right)\) | \(e\left(\frac{8}{165}\right)\) | \(e\left(\frac{97}{330}\right)\) | \(e\left(\frac{221}{330}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{313}{330}\right)\) | \(e\left(\frac{229}{330}\right)\) | \(e\left(\frac{16}{165}\right)\) | \(e\left(\frac{47}{55}\right)\) |
| \(\chi_{3267}(854,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{148}{165}\right)\) | \(e\left(\frac{131}{165}\right)\) | \(e\left(\frac{289}{330}\right)\) | \(e\left(\frac{257}{330}\right)\) | \(e\left(\frac{38}{55}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{31}{330}\right)\) | \(e\left(\frac{223}{330}\right)\) | \(e\left(\frac{97}{165}\right)\) | \(e\left(\frac{34}{55}\right)\) |
| \(\chi_{3267}(899,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{165}\right)\) | \(e\left(\frac{34}{165}\right)\) | \(e\left(\frac{41}{330}\right)\) | \(e\left(\frac{73}{330}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{299}{330}\right)\) | \(e\left(\frac{107}{330}\right)\) | \(e\left(\frac{68}{165}\right)\) | \(e\left(\frac{21}{55}\right)\) |
| \(\chi_{3267}(908,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{136}{165}\right)\) | \(e\left(\frac{107}{165}\right)\) | \(e\left(\frac{163}{330}\right)\) | \(e\left(\frac{89}{330}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{247}{330}\right)\) | \(e\left(\frac{31}{330}\right)\) | \(e\left(\frac{49}{165}\right)\) | \(e\left(\frac{3}{55}\right)\) |
| \(\chi_{3267}(926,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{165}\right)\) | \(e\left(\frac{13}{165}\right)\) | \(e\left(\frac{137}{330}\right)\) | \(e\left(\frac{91}{330}\right)\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{323}{330}\right)\) | \(e\left(\frac{269}{330}\right)\) | \(e\left(\frac{26}{165}\right)\) | \(e\left(\frac{42}{55}\right)\) |
| \(\chi_{3267}(953,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{165}\right)\) | \(e\left(\frac{46}{165}\right)\) | \(e\left(\frac{269}{330}\right)\) | \(e\left(\frac{157}{330}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{191}{330}\right)\) | \(e\left(\frac{203}{330}\right)\) | \(e\left(\frac{92}{165}\right)\) | \(e\left(\frac{9}{55}\right)\) |
| \(\chi_{3267}(1007,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{146}{165}\right)\) | \(e\left(\frac{127}{165}\right)\) | \(e\left(\frac{323}{330}\right)\) | \(e\left(\frac{229}{330}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{287}{330}\right)\) | \(e\left(\frac{191}{330}\right)\) | \(e\left(\frac{89}{165}\right)\) | \(e\left(\frac{38}{55}\right)\) |
| \(\chi_{3267}(1097,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{142}{165}\right)\) | \(e\left(\frac{119}{165}\right)\) | \(e\left(\frac{61}{330}\right)\) | \(e\left(\frac{173}{330}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{139}{330}\right)\) | \(e\left(\frac{127}{330}\right)\) | \(e\left(\frac{73}{165}\right)\) | \(e\left(\frac{46}{55}\right)\) |
| \(\chi_{3267}(1124,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{94}{165}\right)\) | \(e\left(\frac{23}{165}\right)\) | \(e\left(\frac{217}{330}\right)\) | \(e\left(\frac{161}{330}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{13}{330}\right)\) | \(e\left(\frac{19}{330}\right)\) | \(e\left(\frac{46}{165}\right)\) | \(e\left(\frac{32}{55}\right)\) |
| \(\chi_{3267}(1151,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{103}{165}\right)\) | \(e\left(\frac{41}{165}\right)\) | \(e\left(\frac{229}{330}\right)\) | \(e\left(\frac{287}{330}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{181}{330}\right)\) | \(e\left(\frac{163}{330}\right)\) | \(e\left(\frac{82}{165}\right)\) | \(e\left(\frac{14}{55}\right)\) |
| \(\chi_{3267}(1196,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{122}{165}\right)\) | \(e\left(\frac{79}{165}\right)\) | \(e\left(\frac{71}{330}\right)\) | \(e\left(\frac{223}{330}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{59}{330}\right)\) | \(e\left(\frac{137}{330}\right)\) | \(e\left(\frac{158}{165}\right)\) | \(e\left(\frac{31}{55}\right)\) |