from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5445, base_ring=CyclotomicField(330))
M = H._module
chi = DirichletCharacter(H, M([275,0,69]))
chi.galois_orbit()
[g,chi] = znchar(Mod(41,5445))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(5445\) | |
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: | 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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{5445}(41,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{165}\right)\) | \(e\left(\frac{14}{165}\right)\) | \(e\left(\frac{263}{330}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{259}{330}\right)\) | \(e\left(\frac{277}{330}\right)\) | \(e\left(\frac{28}{165}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{53}{66}\right)\) |
\(\chi_{5445}(101,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{59}{165}\right)\) | \(e\left(\frac{118}{165}\right)\) | \(e\left(\frac{1}{330}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{203}{330}\right)\) | \(e\left(\frac{119}{330}\right)\) | \(e\left(\frac{71}{165}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{13}{66}\right)\) |
\(\chi_{5445}(266,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{109}{165}\right)\) | \(e\left(\frac{53}{165}\right)\) | \(e\left(\frac{41}{330}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{73}{330}\right)\) | \(e\left(\frac{259}{330}\right)\) | \(e\left(\frac{106}{165}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{5}{66}\right)\) |
\(\chi_{5445}(281,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{146}{165}\right)\) | \(e\left(\frac{127}{165}\right)\) | \(e\left(\frac{229}{330}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{287}{330}\right)\) | \(e\left(\frac{191}{330}\right)\) | \(e\left(\frac{89}{165}\right)\) | \(e\left(\frac{38}{55}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{7}{66}\right)\) |
\(\chi_{5445}(326,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{8}{165}\right)\) | \(e\left(\frac{16}{165}\right)\) | \(e\left(\frac{277}{330}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{131}{330}\right)\) | \(e\left(\frac{293}{330}\right)\) | \(e\left(\frac{32}{165}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{21}{110}\right)\) | \(e\left(\frac{37}{66}\right)\) |
\(\chi_{5445}(371,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{32}{165}\right)\) | \(e\left(\frac{64}{165}\right)\) | \(e\left(\frac{283}{330}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{29}{330}\right)\) | \(e\left(\frac{17}{330}\right)\) | \(e\left(\frac{128}{165}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{29}{110}\right)\) | \(e\left(\frac{49}{66}\right)\) |
\(\chi_{5445}(446,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{16}{165}\right)\) | \(e\left(\frac{32}{165}\right)\) | \(e\left(\frac{59}{330}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{97}{330}\right)\) | \(e\left(\frac{91}{330}\right)\) | \(e\left(\frac{64}{165}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{97}{110}\right)\) | \(e\left(\frac{41}{66}\right)\) |
\(\chi_{5445}(491,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{148}{165}\right)\) | \(e\left(\frac{131}{165}\right)\) | \(e\left(\frac{257}{330}\right)\) | \(e\left(\frac{38}{55}\right)\) | \(e\left(\frac{31}{330}\right)\) | \(e\left(\frac{223}{330}\right)\) | \(e\left(\frac{97}{165}\right)\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{31}{110}\right)\) | \(e\left(\frac{41}{66}\right)\) |
\(\chi_{5445}(536,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{127}{165}\right)\) | \(e\left(\frac{89}{165}\right)\) | \(e\left(\frac{293}{330}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{79}{330}\right)\) | \(e\left(\frac{217}{330}\right)\) | \(e\left(\frac{13}{165}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{47}{66}\right)\) |
\(\chi_{5445}(761,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{94}{165}\right)\) | \(e\left(\frac{23}{165}\right)\) | \(e\left(\frac{161}{330}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{13}{330}\right)\) | \(e\left(\frac{19}{330}\right)\) | \(e\left(\frac{46}{165}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{13}{110}\right)\) | \(e\left(\frac{47}{66}\right)\) |
\(\chi_{5445}(776,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{86}{165}\right)\) | \(e\left(\frac{7}{165}\right)\) | \(e\left(\frac{49}{330}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{47}{330}\right)\) | \(e\left(\frac{221}{330}\right)\) | \(e\left(\frac{14}{165}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{43}{66}\right)\) |
\(\chi_{5445}(821,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{98}{165}\right)\) | \(e\left(\frac{31}{165}\right)\) | \(e\left(\frac{217}{330}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{161}{330}\right)\) | \(e\left(\frac{83}{330}\right)\) | \(e\left(\frac{62}{165}\right)\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{49}{66}\right)\) |
\(\chi_{5445}(866,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{152}{165}\right)\) | \(e\left(\frac{139}{165}\right)\) | \(e\left(\frac{313}{330}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{179}{330}\right)\) | \(e\left(\frac{287}{330}\right)\) | \(e\left(\frac{113}{165}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{43}{66}\right)\) |
\(\chi_{5445}(986,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{165}\right)\) | \(e\left(\frac{146}{165}\right)\) | \(e\left(\frac{197}{330}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{61}{330}\right)\) | \(e\left(\frac{13}{330}\right)\) | \(e\left(\frac{127}{165}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{53}{66}\right)\) |
\(\chi_{5445}(1031,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{82}{165}\right)\) | \(e\left(\frac{164}{165}\right)\) | \(e\left(\frac{323}{330}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{229}{330}\right)\) | \(e\left(\frac{157}{330}\right)\) | \(e\left(\frac{163}{165}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{9}{110}\right)\) | \(e\left(\frac{41}{66}\right)\) |
\(\chi_{5445}(1091,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{165}\right)\) | \(e\left(\frac{58}{165}\right)\) | \(e\left(\frac{241}{330}\right)\) | \(e\left(\frac{29}{55}\right)\) | \(e\left(\frac{83}{330}\right)\) | \(e\left(\frac{299}{330}\right)\) | \(e\left(\frac{116}{165}\right)\) | \(e\left(\frac{52}{55}\right)\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{31}{66}\right)\) |
\(\chi_{5445}(1256,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{165}\right)\) | \(e\left(\frac{158}{165}\right)\) | \(e\left(\frac{281}{330}\right)\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{283}{330}\right)\) | \(e\left(\frac{109}{330}\right)\) | \(e\left(\frac{151}{165}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{63}{110}\right)\) | \(e\left(\frac{23}{66}\right)\) |
\(\chi_{5445}(1271,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{26}{165}\right)\) | \(e\left(\frac{52}{165}\right)\) | \(e\left(\frac{199}{330}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{137}{330}\right)\) | \(e\left(\frac{251}{330}\right)\) | \(e\left(\frac{104}{165}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{27}{110}\right)\) | \(e\left(\frac{13}{66}\right)\) |
\(\chi_{5445}(1316,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{165}\right)\) | \(e\left(\frac{46}{165}\right)\) | \(e\left(\frac{157}{330}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{191}{330}\right)\) | \(e\left(\frac{203}{330}\right)\) | \(e\left(\frac{92}{165}\right)\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{61}{66}\right)\) |
\(\chi_{5445}(1361,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{107}{165}\right)\) | \(e\left(\frac{49}{165}\right)\) | \(e\left(\frac{13}{330}\right)\) | \(e\left(\frac{52}{55}\right)\) | \(e\left(\frac{329}{330}\right)\) | \(e\left(\frac{227}{330}\right)\) | \(e\left(\frac{98}{165}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{37}{66}\right)\) |
\(\chi_{5445}(1436,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{165}\right)\) | \(e\left(\frac{122}{165}\right)\) | \(e\left(\frac{29}{330}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{277}{330}\right)\) | \(e\left(\frac{151}{330}\right)\) | \(e\left(\frac{79}{165}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{47}{66}\right)\) |
\(\chi_{5445}(1481,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{163}{165}\right)\) | \(e\left(\frac{161}{165}\right)\) | \(e\left(\frac{137}{330}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{91}{330}\right)\) | \(e\left(\frac{133}{330}\right)\) | \(e\left(\frac{157}{165}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{91}{110}\right)\) | \(e\left(\frac{65}{66}\right)\) |
\(\chi_{5445}(1526,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{165}\right)\) | \(e\left(\frac{74}{165}\right)\) | \(e\left(\frac{23}{330}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{49}{330}\right)\) | \(e\left(\frac{97}{330}\right)\) | \(e\left(\frac{148}{165}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{49}{110}\right)\) | \(e\left(\frac{35}{66}\right)\) |
\(\chi_{5445}(1586,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{14}{165}\right)\) | \(e\left(\frac{28}{165}\right)\) | \(e\left(\frac{31}{330}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{23}{330}\right)\) | \(e\left(\frac{59}{330}\right)\) | \(e\left(\frac{56}{165}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{7}{66}\right)\) |
\(\chi_{5445}(1751,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{64}{165}\right)\) | \(e\left(\frac{128}{165}\right)\) | \(e\left(\frac{71}{330}\right)\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{223}{330}\right)\) | \(e\left(\frac{199}{330}\right)\) | \(e\left(\frac{91}{165}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{65}{66}\right)\) |
\(\chi_{5445}(1766,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{131}{165}\right)\) | \(e\left(\frac{97}{165}\right)\) | \(e\left(\frac{19}{330}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{227}{330}\right)\) | \(e\left(\frac{281}{330}\right)\) | \(e\left(\frac{29}{165}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{7}{110}\right)\) | \(e\left(\frac{49}{66}\right)\) |
\(\chi_{5445}(1811,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{113}{165}\right)\) | \(e\left(\frac{61}{165}\right)\) | \(e\left(\frac{97}{330}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{221}{330}\right)\) | \(e\left(\frac{323}{330}\right)\) | \(e\left(\frac{122}{165}\right)\) | \(e\left(\frac{49}{55}\right)\) | \(e\left(\frac{1}{110}\right)\) | \(e\left(\frac{7}{66}\right)\) |
\(\chi_{5445}(1856,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{62}{165}\right)\) | \(e\left(\frac{124}{165}\right)\) | \(e\left(\frac{43}{330}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{149}{330}\right)\) | \(e\left(\frac{167}{330}\right)\) | \(e\left(\frac{83}{165}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{31}{66}\right)\) |
\(\chi_{5445}(1931,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{165}\right)\) | \(e\left(\frac{2}{165}\right)\) | \(e\left(\frac{179}{330}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{37}{330}\right)\) | \(e\left(\frac{181}{330}\right)\) | \(e\left(\frac{4}{165}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{37}{110}\right)\) | \(e\left(\frac{17}{66}\right)\) |
\(\chi_{5445}(2021,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{157}{165}\right)\) | \(e\left(\frac{149}{165}\right)\) | \(e\left(\frac{53}{330}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{199}{330}\right)\) | \(e\left(\frac{37}{330}\right)\) | \(e\left(\frac{133}{165}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{89}{110}\right)\) | \(e\left(\frac{29}{66}\right)\) |
\(\chi_{5445}(2081,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{164}{165}\right)\) | \(e\left(\frac{163}{165}\right)\) | \(e\left(\frac{151}{330}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{293}{330}\right)\) | \(e\left(\frac{149}{330}\right)\) | \(e\left(\frac{161}{165}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{49}{66}\right)\) |