from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3381, base_ring=CyclotomicField(462))
M = H._module
chi = DirichletCharacter(H, M([0,11,378]))
chi.galois_orbit()
[g,chi] = znchar(Mod(52,3381))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(3381\) | |
| Conductor: | \(1127\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(462\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 1127.bf | 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: | $\Q(\zeta_{231})$ |
| Fixed field: | Number field defined by a degree 462 polynomial (not computed) |
First 31 of 120 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{3381}(52,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{59}{231}\right)\) | \(e\left(\frac{118}{231}\right)\) | \(e\left(\frac{235}{462}\right)\) | \(e\left(\frac{59}{77}\right)\) | \(e\left(\frac{353}{462}\right)\) | \(e\left(\frac{73}{231}\right)\) | \(e\left(\frac{37}{154}\right)\) | \(e\left(\frac{5}{231}\right)\) | \(e\left(\frac{149}{462}\right)\) | \(e\left(\frac{7}{66}\right)\) |
| \(\chi_{3381}(73,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{62}{231}\right)\) | \(e\left(\frac{124}{231}\right)\) | \(e\left(\frac{337}{462}\right)\) | \(e\left(\frac{62}{77}\right)\) | \(e\left(\frac{461}{462}\right)\) | \(e\left(\frac{202}{231}\right)\) | \(e\left(\frac{95}{154}\right)\) | \(e\left(\frac{17}{231}\right)\) | \(e\left(\frac{137}{462}\right)\) | \(e\left(\frac{37}{66}\right)\) |
| \(\chi_{3381}(82,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{151}{231}\right)\) | \(e\left(\frac{71}{231}\right)\) | \(e\left(\frac{437}{462}\right)\) | \(e\left(\frac{74}{77}\right)\) | \(e\left(\frac{277}{462}\right)\) | \(e\left(\frac{179}{231}\right)\) | \(e\left(\frac{19}{154}\right)\) | \(e\left(\frac{142}{231}\right)\) | \(e\left(\frac{397}{462}\right)\) | \(e\left(\frac{47}{66}\right)\) |
| \(\chi_{3381}(94,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{86}{231}\right)\) | \(e\left(\frac{172}{231}\right)\) | \(e\left(\frac{229}{462}\right)\) | \(e\left(\frac{9}{77}\right)\) | \(e\left(\frac{401}{462}\right)\) | \(e\left(\frac{79}{231}\right)\) | \(e\left(\frac{97}{154}\right)\) | \(e\left(\frac{113}{231}\right)\) | \(e\left(\frac{41}{462}\right)\) | \(e\left(\frac{13}{66}\right)\) |
| \(\chi_{3381}(124,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{100}{231}\right)\) | \(e\left(\frac{200}{231}\right)\) | \(e\left(\frac{89}{462}\right)\) | \(e\left(\frac{23}{77}\right)\) | \(e\left(\frac{289}{462}\right)\) | \(e\left(\frac{65}{231}\right)\) | \(e\left(\frac{111}{154}\right)\) | \(e\left(\frac{169}{231}\right)\) | \(e\left(\frac{139}{462}\right)\) | \(e\left(\frac{65}{66}\right)\) |
| \(\chi_{3381}(187,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{160}{231}\right)\) | \(e\left(\frac{89}{231}\right)\) | \(e\left(\frac{281}{462}\right)\) | \(e\left(\frac{6}{77}\right)\) | \(e\left(\frac{139}{462}\right)\) | \(e\left(\frac{104}{231}\right)\) | \(e\left(\frac{39}{154}\right)\) | \(e\left(\frac{178}{231}\right)\) | \(e\left(\frac{361}{462}\right)\) | \(e\left(\frac{5}{66}\right)\) |
| \(\chi_{3381}(220,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{41}{231}\right)\) | \(e\left(\frac{82}{231}\right)\) | \(e\left(\frac{85}{462}\right)\) | \(e\left(\frac{41}{77}\right)\) | \(e\left(\frac{167}{462}\right)\) | \(e\left(\frac{223}{231}\right)\) | \(e\left(\frac{151}{154}\right)\) | \(e\left(\frac{164}{231}\right)\) | \(e\left(\frac{221}{462}\right)\) | \(e\left(\frac{25}{66}\right)\) |
| \(\chi_{3381}(262,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{89}{231}\right)\) | \(e\left(\frac{178}{231}\right)\) | \(e\left(\frac{331}{462}\right)\) | \(e\left(\frac{12}{77}\right)\) | \(e\left(\frac{47}{462}\right)\) | \(e\left(\frac{208}{231}\right)\) | \(e\left(\frac{1}{154}\right)\) | \(e\left(\frac{125}{231}\right)\) | \(e\left(\frac{29}{462}\right)\) | \(e\left(\frac{43}{66}\right)\) |
| \(\chi_{3381}(271,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{142}{231}\right)\) | \(e\left(\frac{53}{231}\right)\) | \(e\left(\frac{131}{462}\right)\) | \(e\left(\frac{65}{77}\right)\) | \(e\left(\frac{415}{462}\right)\) | \(e\left(\frac{23}{231}\right)\) | \(e\left(\frac{153}{154}\right)\) | \(e\left(\frac{106}{231}\right)\) | \(e\left(\frac{433}{462}\right)\) | \(e\left(\frac{23}{66}\right)\) |
| \(\chi_{3381}(292,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{190}{231}\right)\) | \(e\left(\frac{149}{231}\right)\) | \(e\left(\frac{377}{462}\right)\) | \(e\left(\frac{36}{77}\right)\) | \(e\left(\frac{295}{462}\right)\) | \(e\left(\frac{8}{231}\right)\) | \(e\left(\frac{3}{154}\right)\) | \(e\left(\frac{67}{231}\right)\) | \(e\left(\frac{241}{462}\right)\) | \(e\left(\frac{41}{66}\right)\) |
| \(\chi_{3381}(334,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{13}{231}\right)\) | \(e\left(\frac{26}{231}\right)\) | \(e\left(\frac{365}{462}\right)\) | \(e\left(\frac{13}{77}\right)\) | \(e\left(\frac{391}{462}\right)\) | \(e\left(\frac{20}{231}\right)\) | \(e\left(\frac{123}{154}\right)\) | \(e\left(\frac{52}{231}\right)\) | \(e\left(\frac{25}{462}\right)\) | \(e\left(\frac{53}{66}\right)\) |
| \(\chi_{3381}(376,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{214}{231}\right)\) | \(e\left(\frac{197}{231}\right)\) | \(e\left(\frac{269}{462}\right)\) | \(e\left(\frac{60}{77}\right)\) | \(e\left(\frac{235}{462}\right)\) | \(e\left(\frac{116}{231}\right)\) | \(e\left(\frac{5}{154}\right)\) | \(e\left(\frac{163}{231}\right)\) | \(e\left(\frac{145}{462}\right)\) | \(e\left(\frac{17}{66}\right)\) |
| \(\chi_{3381}(397,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{136}{231}\right)\) | \(e\left(\frac{41}{231}\right)\) | \(e\left(\frac{389}{462}\right)\) | \(e\left(\frac{59}{77}\right)\) | \(e\left(\frac{199}{462}\right)\) | \(e\left(\frac{227}{231}\right)\) | \(e\left(\frac{37}{154}\right)\) | \(e\left(\frac{82}{231}\right)\) | \(e\left(\frac{457}{462}\right)\) | \(e\left(\frac{29}{66}\right)\) |
| \(\chi_{3381}(409,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{131}{231}\right)\) | \(e\left(\frac{31}{231}\right)\) | \(e\left(\frac{373}{462}\right)\) | \(e\left(\frac{54}{77}\right)\) | \(e\left(\frac{173}{462}\right)\) | \(e\left(\frac{166}{231}\right)\) | \(e\left(\frac{43}{154}\right)\) | \(e\left(\frac{62}{231}\right)\) | \(e\left(\frac{323}{462}\right)\) | \(e\left(\frac{1}{66}\right)\) |
| \(\chi_{3381}(418,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{205}{231}\right)\) | \(e\left(\frac{179}{231}\right)\) | \(e\left(\frac{425}{462}\right)\) | \(e\left(\frac{51}{77}\right)\) | \(e\left(\frac{373}{462}\right)\) | \(e\left(\frac{191}{231}\right)\) | \(e\left(\frac{139}{154}\right)\) | \(e\left(\frac{127}{231}\right)\) | \(e\left(\frac{181}{462}\right)\) | \(e\left(\frac{59}{66}\right)\) |
| \(\chi_{3381}(430,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{113}{231}\right)\) | \(e\left(\frac{226}{231}\right)\) | \(e\left(\frac{223}{462}\right)\) | \(e\left(\frac{36}{77}\right)\) | \(e\left(\frac{449}{462}\right)\) | \(e\left(\frac{85}{231}\right)\) | \(e\left(\frac{3}{154}\right)\) | \(e\left(\frac{221}{231}\right)\) | \(e\left(\frac{395}{462}\right)\) | \(e\left(\frac{19}{66}\right)\) |
| \(\chi_{3381}(439,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{64}{231}\right)\) | \(e\left(\frac{128}{231}\right)\) | \(e\left(\frac{251}{462}\right)\) | \(e\left(\frac{64}{77}\right)\) | \(e\left(\frac{379}{462}\right)\) | \(e\left(\frac{134}{231}\right)\) | \(e\left(\frac{31}{154}\right)\) | \(e\left(\frac{25}{231}\right)\) | \(e\left(\frac{283}{462}\right)\) | \(e\left(\frac{35}{66}\right)\) |
| \(\chi_{3381}(514,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{104}{231}\right)\) | \(e\left(\frac{208}{231}\right)\) | \(e\left(\frac{379}{462}\right)\) | \(e\left(\frac{27}{77}\right)\) | \(e\left(\frac{125}{462}\right)\) | \(e\left(\frac{160}{231}\right)\) | \(e\left(\frac{137}{154}\right)\) | \(e\left(\frac{185}{231}\right)\) | \(e\left(\frac{431}{462}\right)\) | \(e\left(\frac{61}{66}\right)\) |
| \(\chi_{3381}(535,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{191}{231}\right)\) | \(e\left(\frac{151}{231}\right)\) | \(e\left(\frac{103}{462}\right)\) | \(e\left(\frac{37}{77}\right)\) | \(e\left(\frac{23}{462}\right)\) | \(e\left(\frac{205}{231}\right)\) | \(e\left(\frac{125}{154}\right)\) | \(e\left(\frac{71}{231}\right)\) | \(e\left(\frac{83}{462}\right)\) | \(e\left(\frac{7}{66}\right)\) |
| \(\chi_{3381}(556,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{194}{231}\right)\) | \(e\left(\frac{157}{231}\right)\) | \(e\left(\frac{205}{462}\right)\) | \(e\left(\frac{40}{77}\right)\) | \(e\left(\frac{131}{462}\right)\) | \(e\left(\frac{103}{231}\right)\) | \(e\left(\frac{29}{154}\right)\) | \(e\left(\frac{83}{231}\right)\) | \(e\left(\frac{71}{462}\right)\) | \(e\left(\frac{37}{66}\right)\) |
| \(\chi_{3381}(565,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{184}{231}\right)\) | \(e\left(\frac{137}{231}\right)\) | \(e\left(\frac{173}{462}\right)\) | \(e\left(\frac{30}{77}\right)\) | \(e\left(\frac{79}{462}\right)\) | \(e\left(\frac{212}{231}\right)\) | \(e\left(\frac{41}{154}\right)\) | \(e\left(\frac{43}{231}\right)\) | \(e\left(\frac{265}{462}\right)\) | \(e\left(\frac{47}{66}\right)\) |
| \(\chi_{3381}(577,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{218}{231}\right)\) | \(e\left(\frac{205}{231}\right)\) | \(e\left(\frac{97}{462}\right)\) | \(e\left(\frac{64}{77}\right)\) | \(e\left(\frac{71}{462}\right)\) | \(e\left(\frac{211}{231}\right)\) | \(e\left(\frac{31}{154}\right)\) | \(e\left(\frac{179}{231}\right)\) | \(e\left(\frac{437}{462}\right)\) | \(e\left(\frac{13}{66}\right)\) |
| \(\chi_{3381}(670,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{193}{231}\right)\) | \(e\left(\frac{155}{231}\right)\) | \(e\left(\frac{17}{462}\right)\) | \(e\left(\frac{39}{77}\right)\) | \(e\left(\frac{403}{462}\right)\) | \(e\left(\frac{137}{231}\right)\) | \(e\left(\frac{61}{154}\right)\) | \(e\left(\frac{79}{231}\right)\) | \(e\left(\frac{229}{462}\right)\) | \(e\left(\frac{5}{66}\right)\) |
| \(\chi_{3381}(703,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{173}{231}\right)\) | \(e\left(\frac{115}{231}\right)\) | \(e\left(\frac{415}{462}\right)\) | \(e\left(\frac{19}{77}\right)\) | \(e\left(\frac{299}{462}\right)\) | \(e\left(\frac{124}{231}\right)\) | \(e\left(\frac{85}{154}\right)\) | \(e\left(\frac{230}{231}\right)\) | \(e\left(\frac{155}{462}\right)\) | \(e\left(\frac{25}{66}\right)\) |
| \(\chi_{3381}(745,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{221}{231}\right)\) | \(e\left(\frac{211}{231}\right)\) | \(e\left(\frac{199}{462}\right)\) | \(e\left(\frac{67}{77}\right)\) | \(e\left(\frac{179}{462}\right)\) | \(e\left(\frac{109}{231}\right)\) | \(e\left(\frac{89}{154}\right)\) | \(e\left(\frac{191}{231}\right)\) | \(e\left(\frac{425}{462}\right)\) | \(e\left(\frac{43}{66}\right)\) |
| \(\chi_{3381}(775,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{223}{231}\right)\) | \(e\left(\frac{215}{231}\right)\) | \(e\left(\frac{113}{462}\right)\) | \(e\left(\frac{69}{77}\right)\) | \(e\left(\frac{97}{462}\right)\) | \(e\left(\frac{41}{231}\right)\) | \(e\left(\frac{25}{154}\right)\) | \(e\left(\frac{199}{231}\right)\) | \(e\left(\frac{109}{462}\right)\) | \(e\left(\frac{41}{66}\right)\) |
| \(\chi_{3381}(808,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{83}{231}\right)\) | \(e\left(\frac{166}{231}\right)\) | \(e\left(\frac{127}{462}\right)\) | \(e\left(\frac{6}{77}\right)\) | \(e\left(\frac{293}{462}\right)\) | \(e\left(\frac{181}{231}\right)\) | \(e\left(\frac{39}{154}\right)\) | \(e\left(\frac{101}{231}\right)\) | \(e\left(\frac{53}{462}\right)\) | \(e\left(\frac{49}{66}\right)\) |
| \(\chi_{3381}(817,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{46}{231}\right)\) | \(e\left(\frac{92}{231}\right)\) | \(e\left(\frac{101}{462}\right)\) | \(e\left(\frac{46}{77}\right)\) | \(e\left(\frac{193}{462}\right)\) | \(e\left(\frac{53}{231}\right)\) | \(e\left(\frac{145}{154}\right)\) | \(e\left(\frac{184}{231}\right)\) | \(e\left(\frac{355}{462}\right)\) | \(e\left(\frac{53}{66}\right)\) |
| \(\chi_{3381}(859,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{16}{231}\right)\) | \(e\left(\frac{32}{231}\right)\) | \(e\left(\frac{5}{462}\right)\) | \(e\left(\frac{16}{77}\right)\) | \(e\left(\frac{37}{462}\right)\) | \(e\left(\frac{149}{231}\right)\) | \(e\left(\frac{27}{154}\right)\) | \(e\left(\frac{64}{231}\right)\) | \(e\left(\frac{13}{462}\right)\) | \(e\left(\frac{17}{66}\right)\) |
| \(\chi_{3381}(880,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{169}{231}\right)\) | \(e\left(\frac{107}{231}\right)\) | \(e\left(\frac{125}{462}\right)\) | \(e\left(\frac{15}{77}\right)\) | \(e\left(\frac{1}{462}\right)\) | \(e\left(\frac{29}{231}\right)\) | \(e\left(\frac{59}{154}\right)\) | \(e\left(\frac{214}{231}\right)\) | \(e\left(\frac{325}{462}\right)\) | \(e\left(\frac{29}{66}\right)\) |
| \(\chi_{3381}(892,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{32}{231}\right)\) | \(e\left(\frac{64}{231}\right)\) | \(e\left(\frac{241}{462}\right)\) | \(e\left(\frac{32}{77}\right)\) | \(e\left(\frac{305}{462}\right)\) | \(e\left(\frac{67}{231}\right)\) | \(e\left(\frac{131}{154}\right)\) | \(e\left(\frac{128}{231}\right)\) | \(e\left(\frac{257}{462}\right)\) | \(e\left(\frac{1}{66}\right)\) |