from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5577, base_ring=CyclotomicField(390))
M = H._module
chi = DirichletCharacter(H, M([195,351,365]))
chi.galois_orbit()
[g,chi] = znchar(Mod(17,5577))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(5577\) | |
| Conductor: | \(5577\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(390\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | 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: | $\Q(\zeta_{195})$ |
| Fixed field: | Number field defined by a degree 390 polynomial (not computed) |
First 31 of 96 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(14\) | \(16\) | \(17\) | \(19\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{5577}(17,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{131}{390}\right)\) | \(e\left(\frac{131}{195}\right)\) | \(e\left(\frac{34}{65}\right)\) | \(e\left(\frac{86}{195}\right)\) | \(e\left(\frac{1}{130}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{101}{130}\right)\) | \(e\left(\frac{67}{195}\right)\) | \(e\left(\frac{47}{195}\right)\) | \(e\left(\frac{8}{15}\right)\) |
| \(\chi_{5577}(62,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{133}{390}\right)\) | \(e\left(\frac{133}{195}\right)\) | \(e\left(\frac{37}{65}\right)\) | \(e\left(\frac{193}{195}\right)\) | \(e\left(\frac{3}{130}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{43}{130}\right)\) | \(e\left(\frac{71}{195}\right)\) | \(e\left(\frac{76}{195}\right)\) | \(e\left(\frac{4}{15}\right)\) |
| \(\chi_{5577}(95,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{263}{390}\right)\) | \(e\left(\frac{68}{195}\right)\) | \(e\left(\frac{37}{65}\right)\) | \(e\left(\frac{128}{195}\right)\) | \(e\left(\frac{3}{130}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{43}{130}\right)\) | \(e\left(\frac{136}{195}\right)\) | \(e\left(\frac{11}{195}\right)\) | \(e\left(\frac{14}{15}\right)\) |
| \(\chi_{5577}(101,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{390}\right)\) | \(e\left(\frac{19}{195}\right)\) | \(e\left(\frac{61}{65}\right)\) | \(e\left(\frac{139}{195}\right)\) | \(e\left(\frac{19}{130}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{99}{130}\right)\) | \(e\left(\frac{38}{195}\right)\) | \(e\left(\frac{178}{195}\right)\) | \(e\left(\frac{7}{15}\right)\) |
| \(\chi_{5577}(134,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{329}{390}\right)\) | \(e\left(\frac{134}{195}\right)\) | \(e\left(\frac{6}{65}\right)\) | \(e\left(\frac{149}{195}\right)\) | \(e\left(\frac{69}{130}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{79}{130}\right)\) | \(e\left(\frac{73}{195}\right)\) | \(e\left(\frac{188}{195}\right)\) | \(e\left(\frac{2}{15}\right)\) |
| \(\chi_{5577}(140,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{217}{390}\right)\) | \(e\left(\frac{22}{195}\right)\) | \(e\left(\frac{33}{65}\right)\) | \(e\left(\frac{7}{195}\right)\) | \(e\left(\frac{87}{130}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{77}{130}\right)\) | \(e\left(\frac{44}{195}\right)\) | \(e\left(\frac{124}{195}\right)\) | \(e\left(\frac{1}{15}\right)\) |
| \(\chi_{5577}(173,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{317}{390}\right)\) | \(e\left(\frac{122}{195}\right)\) | \(e\left(\frac{53}{65}\right)\) | \(e\left(\frac{92}{195}\right)\) | \(e\left(\frac{57}{130}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{37}{130}\right)\) | \(e\left(\frac{49}{195}\right)\) | \(e\left(\frac{14}{195}\right)\) | \(e\left(\frac{11}{15}\right)\) |
| \(\chi_{5577}(413,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{121}{390}\right)\) | \(e\left(\frac{121}{195}\right)\) | \(e\left(\frac{19}{65}\right)\) | \(e\left(\frac{136}{195}\right)\) | \(e\left(\frac{121}{130}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{1}{130}\right)\) | \(e\left(\frac{47}{195}\right)\) | \(e\left(\frac{97}{195}\right)\) | \(e\left(\frac{13}{15}\right)\) |
| \(\chi_{5577}(446,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{311}{390}\right)\) | \(e\left(\frac{116}{195}\right)\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{161}{195}\right)\) | \(e\left(\frac{51}{130}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{81}{130}\right)\) | \(e\left(\frac{37}{195}\right)\) | \(e\left(\frac{122}{195}\right)\) | \(e\left(\frac{8}{15}\right)\) |
| \(\chi_{5577}(491,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{283}{390}\right)\) | \(e\left(\frac{88}{195}\right)\) | \(e\left(\frac{2}{65}\right)\) | \(e\left(\frac{28}{195}\right)\) | \(e\left(\frac{23}{130}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{113}{130}\right)\) | \(e\left(\frac{176}{195}\right)\) | \(e\left(\frac{106}{195}\right)\) | \(e\left(\frac{4}{15}\right)\) |
| \(\chi_{5577}(524,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{390}\right)\) | \(e\left(\frac{53}{195}\right)\) | \(e\left(\frac{47}{65}\right)\) | \(e\left(\frac{8}{195}\right)\) | \(e\left(\frac{53}{130}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{23}{130}\right)\) | \(e\left(\frac{106}{195}\right)\) | \(e\left(\frac{86}{195}\right)\) | \(e\left(\frac{14}{15}\right)\) |
| \(\chi_{5577}(563,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{119}{390}\right)\) | \(e\left(\frac{119}{195}\right)\) | \(e\left(\frac{16}{65}\right)\) | \(e\left(\frac{29}{195}\right)\) | \(e\left(\frac{119}{130}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{59}{130}\right)\) | \(e\left(\frac{43}{195}\right)\) | \(e\left(\frac{68}{195}\right)\) | \(e\left(\frac{2}{15}\right)\) |
| \(\chi_{5577}(569,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{367}{390}\right)\) | \(e\left(\frac{172}{195}\right)\) | \(e\left(\frac{63}{65}\right)\) | \(e\left(\frac{37}{195}\right)\) | \(e\left(\frac{107}{130}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{17}{130}\right)\) | \(e\left(\frac{149}{195}\right)\) | \(e\left(\frac{154}{195}\right)\) | \(e\left(\frac{1}{15}\right)\) |
| \(\chi_{5577}(602,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{107}{390}\right)\) | \(e\left(\frac{107}{195}\right)\) | \(e\left(\frac{63}{65}\right)\) | \(e\left(\frac{167}{195}\right)\) | \(e\left(\frac{107}{130}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{17}{130}\right)\) | \(e\left(\frac{19}{195}\right)\) | \(e\left(\frac{89}{195}\right)\) | \(e\left(\frac{11}{15}\right)\) |
| \(\chi_{5577}(842,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{271}{390}\right)\) | \(e\left(\frac{76}{195}\right)\) | \(e\left(\frac{49}{65}\right)\) | \(e\left(\frac{166}{195}\right)\) | \(e\left(\frac{11}{130}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{71}{130}\right)\) | \(e\left(\frac{152}{195}\right)\) | \(e\left(\frac{127}{195}\right)\) | \(e\left(\frac{13}{15}\right)\) |
| \(\chi_{5577}(875,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{101}{390}\right)\) | \(e\left(\frac{101}{195}\right)\) | \(e\left(\frac{54}{65}\right)\) | \(e\left(\frac{41}{195}\right)\) | \(e\left(\frac{101}{130}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{61}{130}\right)\) | \(e\left(\frac{7}{195}\right)\) | \(e\left(\frac{2}{195}\right)\) | \(e\left(\frac{8}{15}\right)\) |
| \(\chi_{5577}(920,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{390}\right)\) | \(e\left(\frac{43}{195}\right)\) | \(e\left(\frac{32}{65}\right)\) | \(e\left(\frac{58}{195}\right)\) | \(e\left(\frac{43}{130}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{53}{130}\right)\) | \(e\left(\frac{86}{195}\right)\) | \(e\left(\frac{136}{195}\right)\) | \(e\left(\frac{4}{15}\right)\) |
| \(\chi_{5577}(953,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{233}{390}\right)\) | \(e\left(\frac{38}{195}\right)\) | \(e\left(\frac{57}{65}\right)\) | \(e\left(\frac{83}{195}\right)\) | \(e\left(\frac{103}{130}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{3}{130}\right)\) | \(e\left(\frac{76}{195}\right)\) | \(e\left(\frac{161}{195}\right)\) | \(e\left(\frac{14}{15}\right)\) |
| \(\chi_{5577}(959,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{319}{390}\right)\) | \(e\left(\frac{124}{195}\right)\) | \(e\left(\frac{56}{65}\right)\) | \(e\left(\frac{4}{195}\right)\) | \(e\left(\frac{59}{130}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{109}{130}\right)\) | \(e\left(\frac{53}{195}\right)\) | \(e\left(\frac{43}{195}\right)\) | \(e\left(\frac{7}{15}\right)\) |
| \(\chi_{5577}(998,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{127}{390}\right)\) | \(e\left(\frac{127}{195}\right)\) | \(e\left(\frac{28}{65}\right)\) | \(e\left(\frac{67}{195}\right)\) | \(e\left(\frac{127}{130}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{87}{130}\right)\) | \(e\left(\frac{59}{195}\right)\) | \(e\left(\frac{184}{195}\right)\) | \(e\left(\frac{1}{15}\right)\) |
| \(\chi_{5577}(1031,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{287}{390}\right)\) | \(e\left(\frac{92}{195}\right)\) | \(e\left(\frac{8}{65}\right)\) | \(e\left(\frac{47}{195}\right)\) | \(e\left(\frac{27}{130}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{127}{130}\right)\) | \(e\left(\frac{184}{195}\right)\) | \(e\left(\frac{164}{195}\right)\) | \(e\left(\frac{11}{15}\right)\) |
| \(\chi_{5577}(1271,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{390}\right)\) | \(e\left(\frac{31}{195}\right)\) | \(e\left(\frac{14}{65}\right)\) | \(e\left(\frac{1}{195}\right)\) | \(e\left(\frac{31}{130}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{11}{130}\right)\) | \(e\left(\frac{62}{195}\right)\) | \(e\left(\frac{157}{195}\right)\) | \(e\left(\frac{13}{15}\right)\) |
| \(\chi_{5577}(1304,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{281}{390}\right)\) | \(e\left(\frac{86}{195}\right)\) | \(e\left(\frac{64}{65}\right)\) | \(e\left(\frac{116}{195}\right)\) | \(e\left(\frac{21}{130}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{41}{130}\right)\) | \(e\left(\frac{172}{195}\right)\) | \(e\left(\frac{77}{195}\right)\) | \(e\left(\frac{8}{15}\right)\) |
| \(\chi_{5577}(1349,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{193}{390}\right)\) | \(e\left(\frac{193}{195}\right)\) | \(e\left(\frac{62}{65}\right)\) | \(e\left(\frac{88}{195}\right)\) | \(e\left(\frac{63}{130}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{123}{130}\right)\) | \(e\left(\frac{191}{195}\right)\) | \(e\left(\frac{166}{195}\right)\) | \(e\left(\frac{4}{15}\right)\) |
| \(\chi_{5577}(1382,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{390}\right)\) | \(e\left(\frac{23}{195}\right)\) | \(e\left(\frac{2}{65}\right)\) | \(e\left(\frac{158}{195}\right)\) | \(e\left(\frac{23}{130}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{113}{130}\right)\) | \(e\left(\frac{46}{195}\right)\) | \(e\left(\frac{41}{195}\right)\) | \(e\left(\frac{14}{15}\right)\) |
| \(\chi_{5577}(1388,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{390}\right)\) | \(e\left(\frac{79}{195}\right)\) | \(e\left(\frac{21}{65}\right)\) | \(e\left(\frac{34}{195}\right)\) | \(e\left(\frac{79}{130}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{49}{130}\right)\) | \(e\left(\frac{158}{195}\right)\) | \(e\left(\frac{73}{195}\right)\) | \(e\left(\frac{7}{15}\right)\) |
| \(\chi_{5577}(1421,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{390}\right)\) | \(e\left(\frac{89}{195}\right)\) | \(e\left(\frac{36}{65}\right)\) | \(e\left(\frac{179}{195}\right)\) | \(e\left(\frac{89}{130}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{19}{130}\right)\) | \(e\left(\frac{178}{195}\right)\) | \(e\left(\frac{23}{195}\right)\) | \(e\left(\frac{2}{15}\right)\) |
| \(\chi_{5577}(1427,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{277}{390}\right)\) | \(e\left(\frac{82}{195}\right)\) | \(e\left(\frac{58}{65}\right)\) | \(e\left(\frac{97}{195}\right)\) | \(e\left(\frac{17}{130}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{27}{130}\right)\) | \(e\left(\frac{164}{195}\right)\) | \(e\left(\frac{19}{195}\right)\) | \(e\left(\frac{1}{15}\right)\) |
| \(\chi_{5577}(1460,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{77}{390}\right)\) | \(e\left(\frac{77}{195}\right)\) | \(e\left(\frac{18}{65}\right)\) | \(e\left(\frac{122}{195}\right)\) | \(e\left(\frac{77}{130}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{107}{130}\right)\) | \(e\left(\frac{154}{195}\right)\) | \(e\left(\frac{44}{195}\right)\) | \(e\left(\frac{11}{15}\right)\) |
| \(\chi_{5577}(1700,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{181}{390}\right)\) | \(e\left(\frac{181}{195}\right)\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{31}{195}\right)\) | \(e\left(\frac{51}{130}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{81}{130}\right)\) | \(e\left(\frac{167}{195}\right)\) | \(e\left(\frac{187}{195}\right)\) | \(e\left(\frac{13}{15}\right)\) |
| \(\chi_{5577}(1733,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{390}\right)\) | \(e\left(\frac{71}{195}\right)\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{191}{195}\right)\) | \(e\left(\frac{71}{130}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{21}{130}\right)\) | \(e\left(\frac{142}{195}\right)\) | \(e\left(\frac{152}{195}\right)\) | \(e\left(\frac{8}{15}\right)\) |