from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2058, base_ring=CyclotomicField(294))
M = H._module
chi = DirichletCharacter(H, M([147,29]))
chi.galois_orbit()
[g,chi] = znchar(Mod(5,2058))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(2058\) | |
| Conductor: | \(1029\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(294\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 1029.x | 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: | $\Q(\zeta_{147})$ |
| Fixed field: | Number field defined by a degree 294 polynomial (not computed) |
First 31 of 84 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{2058}(5,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{147}\right)\) | \(e\left(\frac{5}{294}\right)\) | \(e\left(\frac{11}{98}\right)\) | \(e\left(\frac{142}{147}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{199}{294}\right)\) | \(e\left(\frac{106}{147}\right)\) | \(e\left(\frac{97}{98}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{44}{147}\right)\) |
| \(\chi_{2058}(17,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{142}{147}\right)\) | \(e\left(\frac{55}{294}\right)\) | \(e\left(\frac{23}{98}\right)\) | \(e\left(\frac{92}{147}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{131}{294}\right)\) | \(e\left(\frac{137}{147}\right)\) | \(e\left(\frac{87}{98}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{43}{147}\right)\) |
| \(\chi_{2058}(47,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{104}{147}\right)\) | \(e\left(\frac{179}{294}\right)\) | \(e\left(\frac{41}{98}\right)\) | \(e\left(\frac{115}{147}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{127}{294}\right)\) | \(e\left(\frac{61}{147}\right)\) | \(e\left(\frac{23}{98}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{17}{147}\right)\) |
| \(\chi_{2058}(59,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{115}{147}\right)\) | \(e\left(\frac{205}{294}\right)\) | \(e\left(\frac{59}{98}\right)\) | \(e\left(\frac{89}{147}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{221}{294}\right)\) | \(e\left(\frac{83}{147}\right)\) | \(e\left(\frac{57}{98}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{40}{147}\right)\) |
| \(\chi_{2058}(89,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{50}{147}\right)\) | \(e\left(\frac{185}{294}\right)\) | \(e\left(\frac{15}{98}\right)\) | \(e\left(\frac{109}{147}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{13}{294}\right)\) | \(e\left(\frac{100}{147}\right)\) | \(e\left(\frac{61}{98}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{11}{147}\right)\) |
| \(\chi_{2058}(101,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{25}{147}\right)\) | \(e\left(\frac{19}{294}\right)\) | \(e\left(\frac{81}{98}\right)\) | \(e\left(\frac{128}{147}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{227}{294}\right)\) | \(e\left(\frac{50}{147}\right)\) | \(e\left(\frac{55}{98}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{79}{147}\right)\) |
| \(\chi_{2058}(131,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{38}{147}\right)\) | \(e\left(\frac{23}{294}\right)\) | \(e\left(\frac{31}{98}\right)\) | \(e\left(\frac{124}{147}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{151}{294}\right)\) | \(e\left(\frac{76}{147}\right)\) | \(e\left(\frac{15}{98}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{26}{147}\right)\) |
| \(\chi_{2058}(143,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{147}\right)\) | \(e\left(\frac{85}{294}\right)\) | \(e\left(\frac{89}{98}\right)\) | \(e\left(\frac{62}{147}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{149}{294}\right)\) | \(e\left(\frac{38}{147}\right)\) | \(e\left(\frac{81}{98}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{13}{147}\right)\) |
| \(\chi_{2058}(173,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{68}{147}\right)\) | \(e\left(\frac{281}{294}\right)\) | \(e\left(\frac{89}{98}\right)\) | \(e\left(\frac{13}{147}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{247}{294}\right)\) | \(e\left(\frac{136}{147}\right)\) | \(e\left(\frac{81}{98}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{62}{147}\right)\) |
| \(\chi_{2058}(185,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{97}{147}\right)\) | \(e\left(\frac{109}{294}\right)\) | \(e\left(\frac{83}{98}\right)\) | \(e\left(\frac{38}{147}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{281}{294}\right)\) | \(e\left(\frac{47}{147}\right)\) | \(e\left(\frac{37}{98}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{136}{147}\right)\) |
| \(\chi_{2058}(257,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{107}{147}\right)\) | \(e\left(\frac{293}{294}\right)\) | \(e\left(\frac{37}{98}\right)\) | \(e\left(\frac{1}{147}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{19}{294}\right)\) | \(e\left(\frac{67}{147}\right)\) | \(e\left(\frac{59}{98}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{50}{147}\right)\) |
| \(\chi_{2058}(269,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{64}{147}\right)\) | \(e\left(\frac{31}{294}\right)\) | \(e\left(\frac{29}{98}\right)\) | \(e\left(\frac{116}{147}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{293}{294}\right)\) | \(e\left(\frac{128}{147}\right)\) | \(e\left(\frac{33}{98}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{67}{147}\right)\) |
| \(\chi_{2058}(299,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{116}{147}\right)\) | \(e\left(\frac{47}{294}\right)\) | \(e\left(\frac{25}{98}\right)\) | \(e\left(\frac{100}{147}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{283}{294}\right)\) | \(e\left(\frac{85}{147}\right)\) | \(e\left(\frac{69}{98}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{2}{147}\right)\) |
| \(\chi_{2058}(311,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{100}{147}\right)\) | \(e\left(\frac{223}{294}\right)\) | \(e\left(\frac{79}{98}\right)\) | \(e\left(\frac{71}{147}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{173}{294}\right)\) | \(e\left(\frac{53}{147}\right)\) | \(e\left(\frac{73}{98}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{22}{147}\right)\) |
| \(\chi_{2058}(341,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{20}{147}\right)\) | \(e\left(\frac{221}{294}\right)\) | \(e\left(\frac{55}{98}\right)\) | \(e\left(\frac{73}{147}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{211}{294}\right)\) | \(e\left(\frac{40}{147}\right)\) | \(e\left(\frac{93}{98}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{122}{147}\right)\) |
| \(\chi_{2058}(353,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{147}\right)\) | \(e\left(\frac{79}{294}\right)\) | \(e\left(\frac{17}{98}\right)\) | \(e\left(\frac{68}{147}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{263}{294}\right)\) | \(e\left(\frac{146}{147}\right)\) | \(e\left(\frac{43}{98}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{19}{147}\right)\) |
| \(\chi_{2058}(383,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{113}{147}\right)\) | \(e\left(\frac{227}{294}\right)\) | \(e\left(\frac{29}{98}\right)\) | \(e\left(\frac{67}{147}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{97}{294}\right)\) | \(e\left(\frac{79}{147}\right)\) | \(e\left(\frac{33}{98}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{116}{147}\right)\) |
| \(\chi_{2058}(395,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{130}{147}\right)\) | \(e\left(\frac{187}{294}\right)\) | \(e\left(\frac{39}{98}\right)\) | \(e\left(\frac{107}{147}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{269}{294}\right)\) | \(e\left(\frac{113}{147}\right)\) | \(e\left(\frac{41}{98}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{58}{147}\right)\) |
| \(\chi_{2058}(425,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{101}{147}\right)\) | \(e\left(\frac{65}{294}\right)\) | \(e\left(\frac{45}{98}\right)\) | \(e\left(\frac{82}{147}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{235}{294}\right)\) | \(e\left(\frac{55}{147}\right)\) | \(e\left(\frac{85}{98}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{131}{147}\right)\) |
| \(\chi_{2058}(437,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{124}{147}\right)\) | \(e\left(\frac{253}{294}\right)\) | \(e\left(\frac{47}{98}\right)\) | \(e\left(\frac{41}{147}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{191}{294}\right)\) | \(e\left(\frac{101}{147}\right)\) | \(e\left(\frac{67}{98}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{139}{147}\right)\) |
| \(\chi_{2058}(467,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{131}{147}\right)\) | \(e\left(\frac{29}{294}\right)\) | \(e\left(\frac{5}{98}\right)\) | \(e\left(\frac{118}{147}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{37}{294}\right)\) | \(e\left(\frac{115}{147}\right)\) | \(e\left(\frac{53}{98}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{20}{147}\right)\) |
| \(\chi_{2058}(479,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{55}{147}\right)\) | \(e\left(\frac{277}{294}\right)\) | \(e\left(\frac{41}{98}\right)\) | \(e\left(\frac{17}{147}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{29}{294}\right)\) | \(e\left(\frac{110}{147}\right)\) | \(e\left(\frac{23}{98}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{115}{147}\right)\) |
| \(\chi_{2058}(551,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{147}\right)\) | \(e\left(\frac{41}{294}\right)\) | \(e\left(\frac{51}{98}\right)\) | \(e\left(\frac{106}{147}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{103}{294}\right)\) | \(e\left(\frac{46}{147}\right)\) | \(e\left(\frac{31}{98}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{8}{147}\right)\) |
| \(\chi_{2058}(563,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{22}{147}\right)\) | \(e\left(\frac{199}{294}\right)\) | \(e\left(\frac{85}{98}\right)\) | \(e\left(\frac{95}{147}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{41}{294}\right)\) | \(e\left(\frac{44}{147}\right)\) | \(e\left(\frac{19}{98}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{46}{147}\right)\) |
| \(\chi_{2058}(593,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{32}{147}\right)\) | \(e\left(\frac{89}{294}\right)\) | \(e\left(\frac{39}{98}\right)\) | \(e\left(\frac{58}{147}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{73}{294}\right)\) | \(e\left(\frac{64}{147}\right)\) | \(e\left(\frac{41}{98}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{107}{147}\right)\) |
| \(\chi_{2058}(605,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{58}{147}\right)\) | \(e\left(\frac{97}{294}\right)\) | \(e\left(\frac{37}{98}\right)\) | \(e\left(\frac{50}{147}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{215}{294}\right)\) | \(e\left(\frac{116}{147}\right)\) | \(e\left(\frac{59}{98}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{1}{147}\right)\) |
| \(\chi_{2058}(635,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{83}{147}\right)\) | \(e\left(\frac{263}{294}\right)\) | \(e\left(\frac{69}{98}\right)\) | \(e\left(\frac{31}{147}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{294}\right)\) | \(e\left(\frac{19}{147}\right)\) | \(e\left(\frac{65}{98}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{80}{147}\right)\) |
| \(\chi_{2058}(647,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{147}\right)\) | \(e\left(\frac{247}{294}\right)\) | \(e\left(\frac{73}{98}\right)\) | \(e\left(\frac{47}{147}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{294}\right)\) | \(e\left(\frac{62}{147}\right)\) | \(e\left(\frac{29}{98}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{145}{147}\right)\) |
| \(\chi_{2058}(677,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{147}\right)\) | \(e\left(\frac{269}{294}\right)\) | \(e\left(\frac{43}{98}\right)\) | \(e\left(\frac{25}{147}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{181}{294}\right)\) | \(e\left(\frac{58}{147}\right)\) | \(e\left(\frac{5}{98}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{74}{147}\right)\) |
| \(\chi_{2058}(689,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{88}{147}\right)\) | \(e\left(\frac{61}{294}\right)\) | \(e\left(\frac{95}{98}\right)\) | \(e\left(\frac{86}{147}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{17}{294}\right)\) | \(e\left(\frac{29}{147}\right)\) | \(e\left(\frac{27}{98}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{37}{147}\right)\) |
| \(\chi_{2058}(719,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{147}\right)\) | \(e\left(\frac{107}{294}\right)\) | \(e\left(\frac{59}{98}\right)\) | \(e\left(\frac{40}{147}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{25}{294}\right)\) | \(e\left(\frac{34}{147}\right)\) | \(e\left(\frac{57}{98}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{89}{147}\right)\) |