from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2541, base_ring=CyclotomicField(330))
M = H._module
chi = DirichletCharacter(H, M([0,275,249]))
chi.galois_orbit()
[g,chi] = znchar(Mod(19,2541))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(2541\) | |
| Conductor: | \(847\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 847.be | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| 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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{2541}(19,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{139}{330}\right)\) | \(e\left(\frac{139}{165}\right)\) | \(e\left(\frac{1}{330}\right)\) | \(e\left(\frac{29}{110}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{113}{165}\right)\) | \(e\left(\frac{133}{165}\right)\) | \(e\left(\frac{131}{165}\right)\) | \(e\left(\frac{93}{110}\right)\) |
| \(\chi_{2541}(52,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{330}\right)\) | \(e\left(\frac{89}{165}\right)\) | \(e\left(\frac{41}{330}\right)\) | \(e\left(\frac{89}{110}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{13}{165}\right)\) | \(e\left(\frac{8}{165}\right)\) | \(e\left(\frac{91}{165}\right)\) | \(e\left(\frac{73}{110}\right)\) |
| \(\chi_{2541}(61,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{217}{330}\right)\) | \(e\left(\frac{52}{165}\right)\) | \(e\left(\frac{163}{330}\right)\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{104}{165}\right)\) | \(e\left(\frac{64}{165}\right)\) | \(e\left(\frac{68}{165}\right)\) | \(e\left(\frac{89}{110}\right)\) |
| \(\chi_{2541}(73,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{221}{330}\right)\) | \(e\left(\frac{56}{165}\right)\) | \(e\left(\frac{239}{330}\right)\) | \(e\left(\frac{1}{110}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{112}{165}\right)\) | \(e\left(\frac{107}{165}\right)\) | \(e\left(\frac{124}{165}\right)\) | \(e\left(\frac{7}{110}\right)\) |
| \(\chi_{2541}(145,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{163}{330}\right)\) | \(e\left(\frac{163}{165}\right)\) | \(e\left(\frac{127}{330}\right)\) | \(e\left(\frac{53}{110}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{161}{165}\right)\) | \(e\left(\frac{61}{165}\right)\) | \(e\left(\frac{137}{165}\right)\) | \(e\left(\frac{41}{110}\right)\) |
| \(\chi_{2541}(178,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{293}{330}\right)\) | \(e\left(\frac{128}{165}\right)\) | \(e\left(\frac{287}{330}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{91}{165}\right)\) | \(e\left(\frac{56}{165}\right)\) | \(e\left(\frac{142}{165}\right)\) | \(e\left(\frac{71}{110}\right)\) |
| \(\chi_{2541}(250,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{229}{330}\right)\) | \(e\left(\frac{64}{165}\right)\) | \(e\left(\frac{61}{330}\right)\) | \(e\left(\frac{9}{110}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{128}{165}\right)\) | \(e\left(\frac{28}{165}\right)\) | \(e\left(\frac{71}{165}\right)\) | \(e\left(\frac{63}{110}\right)\) |
| \(\chi_{2541}(271,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{271}{330}\right)\) | \(e\left(\frac{106}{165}\right)\) | \(e\left(\frac{199}{330}\right)\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{47}{165}\right)\) | \(e\left(\frac{67}{165}\right)\) | \(e\left(\frac{164}{165}\right)\) | \(e\left(\frac{27}{110}\right)\) |
| \(\chi_{2541}(283,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{179}{330}\right)\) | \(e\left(\frac{14}{165}\right)\) | \(e\left(\frac{101}{330}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{28}{165}\right)\) | \(e\left(\frac{68}{165}\right)\) | \(e\left(\frac{31}{165}\right)\) | \(e\left(\frac{43}{110}\right)\) |
| \(\chi_{2541}(292,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{330}\right)\) | \(e\left(\frac{7}{165}\right)\) | \(e\left(\frac{133}{330}\right)\) | \(e\left(\frac{7}{110}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{14}{165}\right)\) | \(e\left(\frac{34}{165}\right)\) | \(e\left(\frac{98}{165}\right)\) | \(e\left(\frac{49}{110}\right)\) |
| \(\chi_{2541}(304,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{330}\right)\) | \(e\left(\frac{41}{165}\right)\) | \(e\left(\frac{119}{330}\right)\) | \(e\left(\frac{41}{110}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{82}{165}\right)\) | \(e\left(\frac{152}{165}\right)\) | \(e\left(\frac{79}{165}\right)\) | \(e\left(\frac{67}{110}\right)\) |
| \(\chi_{2541}(325,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{197}{330}\right)\) | \(e\left(\frac{32}{165}\right)\) | \(e\left(\frac{113}{330}\right)\) | \(e\left(\frac{87}{110}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{64}{165}\right)\) | \(e\left(\frac{14}{165}\right)\) | \(e\left(\frac{118}{165}\right)\) | \(e\left(\frac{59}{110}\right)\) |
| \(\chi_{2541}(376,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{193}{330}\right)\) | \(e\left(\frac{28}{165}\right)\) | \(e\left(\frac{37}{330}\right)\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{56}{165}\right)\) | \(e\left(\frac{136}{165}\right)\) | \(e\left(\frac{62}{165}\right)\) | \(e\left(\frac{31}{110}\right)\) |
| \(\chi_{2541}(409,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{323}{330}\right)\) | \(e\left(\frac{158}{165}\right)\) | \(e\left(\frac{197}{330}\right)\) | \(e\left(\frac{103}{110}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{38}{55}\right)\) | \(e\left(\frac{151}{165}\right)\) | \(e\left(\frac{131}{165}\right)\) | \(e\left(\frac{67}{165}\right)\) | \(e\left(\frac{61}{110}\right)\) |
| \(\chi_{2541}(502,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{91}{330}\right)\) | \(e\left(\frac{91}{165}\right)\) | \(e\left(\frac{79}{330}\right)\) | \(e\left(\frac{91}{110}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{17}{165}\right)\) | \(e\left(\frac{112}{165}\right)\) | \(e\left(\frac{119}{165}\right)\) | \(e\left(\frac{87}{110}\right)\) |
| \(\chi_{2541}(514,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{269}{330}\right)\) | \(e\left(\frac{104}{165}\right)\) | \(e\left(\frac{161}{330}\right)\) | \(e\left(\frac{49}{110}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{43}{165}\right)\) | \(e\left(\frac{128}{165}\right)\) | \(e\left(\frac{136}{165}\right)\) | \(e\left(\frac{13}{110}\right)\) |
| \(\chi_{2541}(523,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{127}{330}\right)\) | \(e\left(\frac{127}{165}\right)\) | \(e\left(\frac{103}{330}\right)\) | \(e\left(\frac{17}{110}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{89}{165}\right)\) | \(e\left(\frac{4}{165}\right)\) | \(e\left(\frac{128}{165}\right)\) | \(e\left(\frac{9}{110}\right)\) |
| \(\chi_{2541}(535,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{191}{330}\right)\) | \(e\left(\frac{26}{165}\right)\) | \(e\left(\frac{329}{330}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{52}{165}\right)\) | \(e\left(\frac{32}{165}\right)\) | \(e\left(\frac{34}{165}\right)\) | \(e\left(\frac{17}{110}\right)\) |
| \(\chi_{2541}(556,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{317}{330}\right)\) | \(e\left(\frac{152}{165}\right)\) | \(e\left(\frac{83}{330}\right)\) | \(e\left(\frac{97}{110}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{139}{165}\right)\) | \(e\left(\frac{149}{165}\right)\) | \(e\left(\frac{148}{165}\right)\) | \(e\left(\frac{19}{110}\right)\) |
| \(\chi_{2541}(607,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{223}{330}\right)\) | \(e\left(\frac{58}{165}\right)\) | \(e\left(\frac{277}{330}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{116}{165}\right)\) | \(e\left(\frac{46}{165}\right)\) | \(e\left(\frac{152}{165}\right)\) | \(e\left(\frac{21}{110}\right)\) |
| \(\chi_{2541}(640,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{330}\right)\) | \(e\left(\frac{23}{165}\right)\) | \(e\left(\frac{107}{330}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{46}{165}\right)\) | \(e\left(\frac{41}{165}\right)\) | \(e\left(\frac{157}{165}\right)\) | \(e\left(\frac{51}{110}\right)\) |
| \(\chi_{2541}(712,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{330}\right)\) | \(e\left(\frac{79}{165}\right)\) | \(e\left(\frac{181}{330}\right)\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{158}{165}\right)\) | \(e\left(\frac{148}{165}\right)\) | \(e\left(\frac{116}{165}\right)\) | \(e\left(\frac{3}{110}\right)\) |
| \(\chi_{2541}(733,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{241}{330}\right)\) | \(e\left(\frac{76}{165}\right)\) | \(e\left(\frac{289}{330}\right)\) | \(e\left(\frac{21}{110}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{152}{165}\right)\) | \(e\left(\frac{157}{165}\right)\) | \(e\left(\frac{74}{165}\right)\) | \(e\left(\frac{37}{110}\right)\) |
| \(\chi_{2541}(745,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{330}\right)\) | \(e\left(\frac{29}{165}\right)\) | \(e\left(\frac{221}{330}\right)\) | \(e\left(\frac{29}{110}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{58}{165}\right)\) | \(e\left(\frac{23}{165}\right)\) | \(e\left(\frac{76}{165}\right)\) | \(e\left(\frac{93}{110}\right)\) |
| \(\chi_{2541}(754,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{247}{330}\right)\) | \(e\left(\frac{82}{165}\right)\) | \(e\left(\frac{73}{330}\right)\) | \(e\left(\frac{27}{110}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{164}{165}\right)\) | \(e\left(\frac{139}{165}\right)\) | \(e\left(\frac{158}{165}\right)\) | \(e\left(\frac{79}{110}\right)\) |
| \(\chi_{2541}(787,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{107}{330}\right)\) | \(e\left(\frac{107}{165}\right)\) | \(e\left(\frac{53}{330}\right)\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{49}{165}\right)\) | \(e\left(\frac{119}{165}\right)\) | \(e\left(\frac{13}{165}\right)\) | \(e\left(\frac{89}{110}\right)\) |
| \(\chi_{2541}(871,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{330}\right)\) | \(e\left(\frac{53}{165}\right)\) | \(e\left(\frac{17}{330}\right)\) | \(e\left(\frac{53}{110}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{106}{165}\right)\) | \(e\left(\frac{116}{165}\right)\) | \(e\left(\frac{82}{165}\right)\) | \(e\left(\frac{41}{110}\right)\) |
| \(\chi_{2541}(943,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{169}{330}\right)\) | \(e\left(\frac{4}{165}\right)\) | \(e\left(\frac{241}{330}\right)\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{49}{55}\right)\) | \(e\left(\frac{8}{165}\right)\) | \(e\left(\frac{43}{165}\right)\) | \(e\left(\frac{56}{165}\right)\) | \(e\left(\frac{83}{110}\right)\) |
| \(\chi_{2541}(964,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{330}\right)\) | \(e\left(\frac{61}{165}\right)\) | \(e\left(\frac{169}{330}\right)\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{122}{165}\right)\) | \(e\left(\frac{37}{165}\right)\) | \(e\left(\frac{29}{165}\right)\) | \(e\left(\frac{97}{110}\right)\) |
| \(\chi_{2541}(976,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{119}{330}\right)\) | \(e\left(\frac{119}{165}\right)\) | \(e\left(\frac{281}{330}\right)\) | \(e\left(\frac{9}{110}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{73}{165}\right)\) | \(e\left(\frac{83}{165}\right)\) | \(e\left(\frac{16}{165}\right)\) | \(e\left(\frac{63}{110}\right)\) |
| \(\chi_{2541}(985,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{330}\right)\) | \(e\left(\frac{37}{165}\right)\) | \(e\left(\frac{43}{330}\right)\) | \(e\left(\frac{37}{110}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{74}{165}\right)\) | \(e\left(\frac{109}{165}\right)\) | \(e\left(\frac{23}{165}\right)\) | \(e\left(\frac{39}{110}\right)\) |