from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5577, base_ring=CyclotomicField(390))
M = H._module
chi = DirichletCharacter(H, M([195,273,100]))
chi.galois_orbit()
[g,chi] = znchar(Mod(29,5577))
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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(14\) | \(16\) | \(17\) | \(19\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{5577}(29,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{195}\right)\) | \(e\left(\frac{178}{195}\right)\) | \(e\left(\frac{79}{130}\right)\) | \(e\left(\frac{131}{390}\right)\) | \(e\left(\frac{24}{65}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{103}{130}\right)\) | \(e\left(\frac{161}{195}\right)\) | \(e\left(\frac{46}{195}\right)\) | \(e\left(\frac{23}{30}\right)\) |
| \(\chi_{5577}(35,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{67}{195}\right)\) | \(e\left(\frac{134}{195}\right)\) | \(e\left(\frac{77}{130}\right)\) | \(e\left(\frac{103}{390}\right)\) | \(e\left(\frac{2}{65}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{79}{130}\right)\) | \(e\left(\frac{73}{195}\right)\) | \(e\left(\frac{188}{195}\right)\) | \(e\left(\frac{19}{30}\right)\) |
| \(\chi_{5577}(68,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{107}{195}\right)\) | \(e\left(\frac{19}{195}\right)\) | \(e\left(\frac{57}{130}\right)\) | \(e\left(\frac{83}{390}\right)\) | \(e\left(\frac{42}{65}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{99}{130}\right)\) | \(e\left(\frac{38}{195}\right)\) | \(e\left(\frac{178}{195}\right)\) | \(e\left(\frac{29}{30}\right)\) |
| \(\chi_{5577}(74,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{151}{195}\right)\) | \(e\left(\frac{107}{195}\right)\) | \(e\left(\frac{61}{130}\right)\) | \(e\left(\frac{139}{390}\right)\) | \(e\left(\frac{21}{65}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{17}{130}\right)\) | \(e\left(\frac{19}{195}\right)\) | \(e\left(\frac{89}{195}\right)\) | \(e\left(\frac{7}{30}\right)\) |
| \(\chi_{5577}(107,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{86}{195}\right)\) | \(e\left(\frac{172}{195}\right)\) | \(e\left(\frac{61}{130}\right)\) | \(e\left(\frac{269}{390}\right)\) | \(e\left(\frac{21}{65}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{17}{130}\right)\) | \(e\left(\frac{149}{195}\right)\) | \(e\left(\frac{154}{195}\right)\) | \(e\left(\frac{17}{30}\right)\) |
| \(\chi_{5577}(347,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{193}{195}\right)\) | \(e\left(\frac{191}{195}\right)\) | \(e\left(\frac{53}{130}\right)\) | \(e\left(\frac{157}{390}\right)\) | \(e\left(\frac{63}{65}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{51}{130}\right)\) | \(e\left(\frac{187}{195}\right)\) | \(e\left(\frac{137}{195}\right)\) | \(e\left(\frac{1}{30}\right)\) |
| \(\chi_{5577}(380,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{173}{195}\right)\) | \(e\left(\frac{151}{195}\right)\) | \(e\left(\frac{63}{130}\right)\) | \(e\left(\frac{167}{390}\right)\) | \(e\left(\frac{43}{65}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{41}{130}\right)\) | \(e\left(\frac{107}{195}\right)\) | \(e\left(\frac{142}{195}\right)\) | \(e\left(\frac{11}{30}\right)\) |
| \(\chi_{5577}(425,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{49}{195}\right)\) | \(e\left(\frac{98}{195}\right)\) | \(e\left(\frac{99}{130}\right)\) | \(e\left(\frac{151}{390}\right)\) | \(e\left(\frac{49}{65}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{83}{130}\right)\) | \(e\left(\frac{1}{195}\right)\) | \(e\left(\frac{56}{195}\right)\) | \(e\left(\frac{13}{30}\right)\) |
| \(\chi_{5577}(458,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{14}{195}\right)\) | \(e\left(\frac{28}{195}\right)\) | \(e\left(\frac{19}{130}\right)\) | \(e\left(\frac{71}{390}\right)\) | \(e\left(\frac{14}{65}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{33}{130}\right)\) | \(e\left(\frac{56}{195}\right)\) | \(e\left(\frac{16}{195}\right)\) | \(e\left(\frac{23}{30}\right)\) |
| \(\chi_{5577}(464,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{172}{195}\right)\) | \(e\left(\frac{149}{195}\right)\) | \(e\left(\frac{57}{130}\right)\) | \(e\left(\frac{343}{390}\right)\) | \(e\left(\frac{42}{65}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{99}{130}\right)\) | \(e\left(\frac{103}{195}\right)\) | \(e\left(\frac{113}{195}\right)\) | \(e\left(\frac{19}{30}\right)\) |
| \(\chi_{5577}(497,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{32}{195}\right)\) | \(e\left(\frac{64}{195}\right)\) | \(e\left(\frac{127}{130}\right)\) | \(e\left(\frac{23}{390}\right)\) | \(e\left(\frac{32}{65}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{29}{130}\right)\) | \(e\left(\frac{128}{195}\right)\) | \(e\left(\frac{148}{195}\right)\) | \(e\left(\frac{29}{30}\right)\) |
| \(\chi_{5577}(503,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{195}\right)\) | \(e\left(\frac{122}{195}\right)\) | \(e\left(\frac{41}{130}\right)\) | \(e\left(\frac{379}{390}\right)\) | \(e\left(\frac{61}{65}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{37}{130}\right)\) | \(e\left(\frac{49}{195}\right)\) | \(e\left(\frac{14}{195}\right)\) | \(e\left(\frac{7}{30}\right)\) |
| \(\chi_{5577}(536,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{195}\right)\) | \(e\left(\frac{22}{195}\right)\) | \(e\left(\frac{1}{130}\right)\) | \(e\left(\frac{209}{390}\right)\) | \(e\left(\frac{11}{65}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{77}{130}\right)\) | \(e\left(\frac{44}{195}\right)\) | \(e\left(\frac{124}{195}\right)\) | \(e\left(\frac{17}{30}\right)\) |
| \(\chi_{5577}(776,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{103}{195}\right)\) | \(e\left(\frac{11}{195}\right)\) | \(e\left(\frac{33}{130}\right)\) | \(e\left(\frac{7}{390}\right)\) | \(e\left(\frac{38}{65}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{71}{130}\right)\) | \(e\left(\frac{22}{195}\right)\) | \(e\left(\frac{62}{195}\right)\) | \(e\left(\frac{1}{30}\right)\) |
| \(\chi_{5577}(809,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{98}{195}\right)\) | \(e\left(\frac{1}{195}\right)\) | \(e\left(\frac{3}{130}\right)\) | \(e\left(\frac{107}{390}\right)\) | \(e\left(\frac{33}{65}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{101}{130}\right)\) | \(e\left(\frac{2}{195}\right)\) | \(e\left(\frac{112}{195}\right)\) | \(e\left(\frac{11}{30}\right)\) |
| \(\chi_{5577}(854,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{154}{195}\right)\) | \(e\left(\frac{113}{195}\right)\) | \(e\left(\frac{79}{130}\right)\) | \(e\left(\frac{1}{390}\right)\) | \(e\left(\frac{24}{65}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{103}{130}\right)\) | \(e\left(\frac{31}{195}\right)\) | \(e\left(\frac{176}{195}\right)\) | \(e\left(\frac{13}{30}\right)\) |
| \(\chi_{5577}(887,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{134}{195}\right)\) | \(e\left(\frac{73}{195}\right)\) | \(e\left(\frac{89}{130}\right)\) | \(e\left(\frac{11}{390}\right)\) | \(e\left(\frac{4}{65}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{93}{130}\right)\) | \(e\left(\frac{146}{195}\right)\) | \(e\left(\frac{181}{195}\right)\) | \(e\left(\frac{23}{30}\right)\) |
| \(\chi_{5577}(893,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{82}{195}\right)\) | \(e\left(\frac{164}{195}\right)\) | \(e\left(\frac{37}{130}\right)\) | \(e\left(\frac{193}{390}\right)\) | \(e\left(\frac{17}{65}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{119}{130}\right)\) | \(e\left(\frac{133}{195}\right)\) | \(e\left(\frac{38}{195}\right)\) | \(e\left(\frac{19}{30}\right)\) |
| \(\chi_{5577}(926,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{152}{195}\right)\) | \(e\left(\frac{109}{195}\right)\) | \(e\left(\frac{67}{130}\right)\) | \(e\left(\frac{353}{390}\right)\) | \(e\left(\frac{22}{65}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{89}{130}\right)\) | \(e\left(\frac{23}{195}\right)\) | \(e\left(\frac{118}{195}\right)\) | \(e\left(\frac{29}{30}\right)\) |
| \(\chi_{5577}(932,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{166}{195}\right)\) | \(e\left(\frac{137}{195}\right)\) | \(e\left(\frac{21}{130}\right)\) | \(e\left(\frac{229}{390}\right)\) | \(e\left(\frac{36}{65}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{57}{130}\right)\) | \(e\left(\frac{79}{195}\right)\) | \(e\left(\frac{134}{195}\right)\) | \(e\left(\frac{7}{30}\right)\) |
| \(\chi_{5577}(965,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{131}{195}\right)\) | \(e\left(\frac{67}{195}\right)\) | \(e\left(\frac{71}{130}\right)\) | \(e\left(\frac{149}{390}\right)\) | \(e\left(\frac{1}{65}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{7}{130}\right)\) | \(e\left(\frac{134}{195}\right)\) | \(e\left(\frac{94}{195}\right)\) | \(e\left(\frac{17}{30}\right)\) |
| \(\chi_{5577}(1238,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{195}\right)\) | \(e\left(\frac{46}{195}\right)\) | \(e\left(\frac{73}{130}\right)\) | \(e\left(\frac{47}{390}\right)\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{31}{130}\right)\) | \(e\left(\frac{92}{195}\right)\) | \(e\left(\frac{82}{195}\right)\) | \(e\left(\frac{11}{30}\right)\) |
| \(\chi_{5577}(1283,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{64}{195}\right)\) | \(e\left(\frac{128}{195}\right)\) | \(e\left(\frac{59}{130}\right)\) | \(e\left(\frac{241}{390}\right)\) | \(e\left(\frac{64}{65}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{123}{130}\right)\) | \(e\left(\frac{61}{195}\right)\) | \(e\left(\frac{101}{195}\right)\) | \(e\left(\frac{13}{30}\right)\) |
| \(\chi_{5577}(1316,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{59}{195}\right)\) | \(e\left(\frac{118}{195}\right)\) | \(e\left(\frac{29}{130}\right)\) | \(e\left(\frac{341}{390}\right)\) | \(e\left(\frac{59}{65}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{23}{130}\right)\) | \(e\left(\frac{41}{195}\right)\) | \(e\left(\frac{151}{195}\right)\) | \(e\left(\frac{23}{30}\right)\) |
| \(\chi_{5577}(1322,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{187}{195}\right)\) | \(e\left(\frac{179}{195}\right)\) | \(e\left(\frac{17}{130}\right)\) | \(e\left(\frac{43}{390}\right)\) | \(e\left(\frac{57}{65}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{9}{130}\right)\) | \(e\left(\frac{163}{195}\right)\) | \(e\left(\frac{158}{195}\right)\) | \(e\left(\frac{19}{30}\right)\) |
| \(\chi_{5577}(1355,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{77}{195}\right)\) | \(e\left(\frac{154}{195}\right)\) | \(e\left(\frac{7}{130}\right)\) | \(e\left(\frac{293}{390}\right)\) | \(e\left(\frac{12}{65}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{19}{130}\right)\) | \(e\left(\frac{113}{195}\right)\) | \(e\left(\frac{88}{195}\right)\) | \(e\left(\frac{29}{30}\right)\) |
| \(\chi_{5577}(1361,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{76}{195}\right)\) | \(e\left(\frac{152}{195}\right)\) | \(e\left(\frac{1}{130}\right)\) | \(e\left(\frac{79}{390}\right)\) | \(e\left(\frac{11}{65}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{77}{130}\right)\) | \(e\left(\frac{109}{195}\right)\) | \(e\left(\frac{59}{195}\right)\) | \(e\left(\frac{7}{30}\right)\) |
| \(\chi_{5577}(1394,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{56}{195}\right)\) | \(e\left(\frac{112}{195}\right)\) | \(e\left(\frac{11}{130}\right)\) | \(e\left(\frac{89}{390}\right)\) | \(e\left(\frac{56}{65}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{67}{130}\right)\) | \(e\left(\frac{29}{195}\right)\) | \(e\left(\frac{64}{195}\right)\) | \(e\left(\frac{17}{30}\right)\) |
| \(\chi_{5577}(1634,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{118}{195}\right)\) | \(e\left(\frac{41}{195}\right)\) | \(e\left(\frac{123}{130}\right)\) | \(e\left(\frac{97}{390}\right)\) | \(e\left(\frac{53}{65}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{111}{130}\right)\) | \(e\left(\frac{82}{195}\right)\) | \(e\left(\frac{107}{195}\right)\) | \(e\left(\frac{1}{30}\right)\) |
| \(\chi_{5577}(1745,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{179}{195}\right)\) | \(e\left(\frac{163}{195}\right)\) | \(e\left(\frac{99}{130}\right)\) | \(e\left(\frac{281}{390}\right)\) | \(e\left(\frac{49}{65}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{83}{130}\right)\) | \(e\left(\frac{131}{195}\right)\) | \(e\left(\frac{121}{195}\right)\) | \(e\left(\frac{23}{30}\right)\) |
| \(\chi_{5577}(1751,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{97}{195}\right)\) | \(e\left(\frac{194}{195}\right)\) | \(e\left(\frac{127}{130}\right)\) | \(e\left(\frac{283}{390}\right)\) | \(e\left(\frac{32}{65}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{29}{130}\right)\) | \(e\left(\frac{193}{195}\right)\) | \(e\left(\frac{83}{195}\right)\) | \(e\left(\frac{19}{30}\right)\) |