from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(258))
M = H._module
chi = DirichletCharacter(H, M([220]))
chi.galois_orbit()
[g,chi] = znchar(Mod(6,1849))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(1849\) | |
| Conductor: | \(1849\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(129\) | 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: | $\Q(\zeta_{129})$ |
| Fixed field: | Number field defined by a degree 129 polynomial (not computed) |
First 31 of 84 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{1849}(6,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{14}{43}\right)\) | \(e\left(\frac{110}{129}\right)\) | \(e\left(\frac{28}{43}\right)\) | \(e\left(\frac{74}{129}\right)\) | \(e\left(\frac{23}{129}\right)\) | \(e\left(\frac{118}{129}\right)\) | \(e\left(\frac{42}{43}\right)\) | \(e\left(\frac{91}{129}\right)\) | \(e\left(\frac{116}{129}\right)\) | \(e\left(\frac{11}{43}\right)\) |
| \(\chi_{1849}(36,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{28}{43}\right)\) | \(e\left(\frac{91}{129}\right)\) | \(e\left(\frac{13}{43}\right)\) | \(e\left(\frac{19}{129}\right)\) | \(e\left(\frac{46}{129}\right)\) | \(e\left(\frac{107}{129}\right)\) | \(e\left(\frac{41}{43}\right)\) | \(e\left(\frac{53}{129}\right)\) | \(e\left(\frac{103}{129}\right)\) | \(e\left(\frac{22}{43}\right)\) |
| \(\chi_{1849}(49,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{24}{43}\right)\) | \(e\left(\frac{35}{129}\right)\) | \(e\left(\frac{5}{43}\right)\) | \(e\left(\frac{47}{129}\right)\) | \(e\left(\frac{107}{129}\right)\) | \(e\left(\frac{61}{129}\right)\) | \(e\left(\frac{29}{43}\right)\) | \(e\left(\frac{70}{129}\right)\) | \(e\left(\frac{119}{129}\right)\) | \(e\left(\frac{25}{43}\right)\) |
| \(\chi_{1849}(79,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{43}\right)\) | \(e\left(\frac{100}{129}\right)\) | \(e\left(\frac{2}{43}\right)\) | \(e\left(\frac{79}{129}\right)\) | \(e\left(\frac{103}{129}\right)\) | \(e\left(\frac{119}{129}\right)\) | \(e\left(\frac{3}{43}\right)\) | \(e\left(\frac{71}{129}\right)\) | \(e\left(\frac{82}{129}\right)\) | \(e\left(\frac{10}{43}\right)\) |
| \(\chi_{1849}(92,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{34}{43}\right)\) | \(e\left(\frac{89}{129}\right)\) | \(e\left(\frac{25}{43}\right)\) | \(e\left(\frac{20}{129}\right)\) | \(e\left(\frac{62}{129}\right)\) | \(e\left(\frac{4}{129}\right)\) | \(e\left(\frac{16}{43}\right)\) | \(e\left(\frac{49}{129}\right)\) | \(e\left(\frac{122}{129}\right)\) | \(e\left(\frac{39}{43}\right)\) |
| \(\chi_{1849}(122,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{43}\right)\) | \(e\left(\frac{109}{129}\right)\) | \(e\left(\frac{34}{43}\right)\) | \(e\left(\frac{10}{129}\right)\) | \(e\left(\frac{31}{129}\right)\) | \(e\left(\frac{2}{129}\right)\) | \(e\left(\frac{8}{43}\right)\) | \(e\left(\frac{89}{129}\right)\) | \(e\left(\frac{61}{129}\right)\) | \(e\left(\frac{41}{43}\right)\) |
| \(\chi_{1849}(135,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{43}\right)\) | \(e\left(\frac{14}{129}\right)\) | \(e\left(\frac{2}{43}\right)\) | \(e\left(\frac{122}{129}\right)\) | \(e\left(\frac{17}{129}\right)\) | \(e\left(\frac{76}{129}\right)\) | \(e\left(\frac{3}{43}\right)\) | \(e\left(\frac{28}{129}\right)\) | \(e\left(\frac{125}{129}\right)\) | \(e\left(\frac{10}{43}\right)\) |
| \(\chi_{1849}(165,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{33}{43}\right)\) | \(e\left(\frac{118}{129}\right)\) | \(e\left(\frac{23}{43}\right)\) | \(e\left(\frac{70}{129}\right)\) | \(e\left(\frac{88}{129}\right)\) | \(e\left(\frac{14}{129}\right)\) | \(e\left(\frac{13}{43}\right)\) | \(e\left(\frac{107}{129}\right)\) | \(e\left(\frac{40}{129}\right)\) | \(e\left(\frac{29}{43}\right)\) |
| \(\chi_{1849}(178,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{43}\right)\) | \(e\left(\frac{68}{129}\right)\) | \(e\left(\frac{22}{43}\right)\) | \(e\left(\frac{95}{129}\right)\) | \(e\left(\frac{101}{129}\right)\) | \(e\left(\frac{19}{129}\right)\) | \(e\left(\frac{33}{43}\right)\) | \(e\left(\frac{7}{129}\right)\) | \(e\left(\frac{128}{129}\right)\) | \(e\left(\frac{24}{43}\right)\) |
| \(\chi_{1849}(208,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{6}{43}\right)\) | \(e\left(\frac{127}{129}\right)\) | \(e\left(\frac{12}{43}\right)\) | \(e\left(\frac{1}{129}\right)\) | \(e\left(\frac{16}{129}\right)\) | \(e\left(\frac{26}{129}\right)\) | \(e\left(\frac{18}{43}\right)\) | \(e\left(\frac{125}{129}\right)\) | \(e\left(\frac{19}{129}\right)\) | \(e\left(\frac{17}{43}\right)\) |
| \(\chi_{1849}(221,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{21}{43}\right)\) | \(e\left(\frac{122}{129}\right)\) | \(e\left(\frac{42}{43}\right)\) | \(e\left(\frac{68}{129}\right)\) | \(e\left(\frac{56}{129}\right)\) | \(e\left(\frac{91}{129}\right)\) | \(e\left(\frac{20}{43}\right)\) | \(e\left(\frac{115}{129}\right)\) | \(e\left(\frac{2}{129}\right)\) | \(e\left(\frac{38}{43}\right)\) |
| \(\chi_{1849}(251,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{22}{43}\right)\) | \(e\left(\frac{7}{129}\right)\) | \(e\left(\frac{1}{43}\right)\) | \(e\left(\frac{61}{129}\right)\) | \(e\left(\frac{73}{129}\right)\) | \(e\left(\frac{38}{129}\right)\) | \(e\left(\frac{23}{43}\right)\) | \(e\left(\frac{14}{129}\right)\) | \(e\left(\frac{127}{129}\right)\) | \(e\left(\frac{5}{43}\right)\) |
| \(\chi_{1849}(264,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{43}\right)\) | \(e\left(\frac{47}{129}\right)\) | \(e\left(\frac{19}{43}\right)\) | \(e\left(\frac{41}{129}\right)\) | \(e\left(\frac{11}{129}\right)\) | \(e\left(\frac{34}{129}\right)\) | \(e\left(\frac{7}{43}\right)\) | \(e\left(\frac{94}{129}\right)\) | \(e\left(\frac{5}{129}\right)\) | \(e\left(\frac{9}{43}\right)\) |
| \(\chi_{1849}(294,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{38}{43}\right)\) | \(e\left(\frac{16}{129}\right)\) | \(e\left(\frac{33}{43}\right)\) | \(e\left(\frac{121}{129}\right)\) | \(e\left(\frac{1}{129}\right)\) | \(e\left(\frac{50}{129}\right)\) | \(e\left(\frac{28}{43}\right)\) | \(e\left(\frac{32}{129}\right)\) | \(e\left(\frac{106}{129}\right)\) | \(e\left(\frac{36}{43}\right)\) |
| \(\chi_{1849}(307,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{43}\right)\) | \(e\left(\frac{101}{129}\right)\) | \(e\left(\frac{39}{43}\right)\) | \(e\left(\frac{14}{129}\right)\) | \(e\left(\frac{95}{129}\right)\) | \(e\left(\frac{106}{129}\right)\) | \(e\left(\frac{37}{43}\right)\) | \(e\left(\frac{73}{129}\right)\) | \(e\left(\frac{8}{129}\right)\) | \(e\left(\frac{23}{43}\right)\) |
| \(\chi_{1849}(337,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{43}\right)\) | \(e\left(\frac{25}{129}\right)\) | \(e\left(\frac{22}{43}\right)\) | \(e\left(\frac{52}{129}\right)\) | \(e\left(\frac{58}{129}\right)\) | \(e\left(\frac{62}{129}\right)\) | \(e\left(\frac{33}{43}\right)\) | \(e\left(\frac{50}{129}\right)\) | \(e\left(\frac{85}{129}\right)\) | \(e\left(\frac{24}{43}\right)\) |
| \(\chi_{1849}(350,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{8}{43}\right)\) | \(e\left(\frac{26}{129}\right)\) | \(e\left(\frac{16}{43}\right)\) | \(e\left(\frac{116}{129}\right)\) | \(e\left(\frac{50}{129}\right)\) | \(e\left(\frac{49}{129}\right)\) | \(e\left(\frac{24}{43}\right)\) | \(e\left(\frac{52}{129}\right)\) | \(e\left(\frac{11}{129}\right)\) | \(e\left(\frac{37}{43}\right)\) |
| \(\chi_{1849}(380,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{27}{43}\right)\) | \(e\left(\frac{34}{129}\right)\) | \(e\left(\frac{11}{43}\right)\) | \(e\left(\frac{112}{129}\right)\) | \(e\left(\frac{115}{129}\right)\) | \(e\left(\frac{74}{129}\right)\) | \(e\left(\frac{38}{43}\right)\) | \(e\left(\frac{68}{129}\right)\) | \(e\left(\frac{64}{129}\right)\) | \(e\left(\frac{12}{43}\right)\) |
| \(\chi_{1849}(393,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{18}{43}\right)\) | \(e\left(\frac{80}{129}\right)\) | \(e\left(\frac{36}{43}\right)\) | \(e\left(\frac{89}{129}\right)\) | \(e\left(\frac{5}{129}\right)\) | \(e\left(\frac{121}{129}\right)\) | \(e\left(\frac{11}{43}\right)\) | \(e\left(\frac{31}{129}\right)\) | \(e\left(\frac{14}{129}\right)\) | \(e\left(\frac{8}{43}\right)\) |
| \(\chi_{1849}(436,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{28}{43}\right)\) | \(e\left(\frac{5}{129}\right)\) | \(e\left(\frac{13}{43}\right)\) | \(e\left(\frac{62}{129}\right)\) | \(e\left(\frac{89}{129}\right)\) | \(e\left(\frac{64}{129}\right)\) | \(e\left(\frac{41}{43}\right)\) | \(e\left(\frac{10}{129}\right)\) | \(e\left(\frac{17}{129}\right)\) | \(e\left(\frac{22}{43}\right)\) |
| \(\chi_{1849}(466,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{16}{43}\right)\) | \(e\left(\frac{52}{129}\right)\) | \(e\left(\frac{32}{43}\right)\) | \(e\left(\frac{103}{129}\right)\) | \(e\left(\frac{100}{129}\right)\) | \(e\left(\frac{98}{129}\right)\) | \(e\left(\frac{5}{43}\right)\) | \(e\left(\frac{104}{129}\right)\) | \(e\left(\frac{22}{129}\right)\) | \(e\left(\frac{31}{43}\right)\) |
| \(\chi_{1849}(479,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{38}{43}\right)\) | \(e\left(\frac{59}{129}\right)\) | \(e\left(\frac{33}{43}\right)\) | \(e\left(\frac{35}{129}\right)\) | \(e\left(\frac{44}{129}\right)\) | \(e\left(\frac{7}{129}\right)\) | \(e\left(\frac{28}{43}\right)\) | \(e\left(\frac{118}{129}\right)\) | \(e\left(\frac{20}{129}\right)\) | \(e\left(\frac{36}{43}\right)\) |
| \(\chi_{1849}(509,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{32}{43}\right)\) | \(e\left(\frac{61}{129}\right)\) | \(e\left(\frac{21}{43}\right)\) | \(e\left(\frac{34}{129}\right)\) | \(e\left(\frac{28}{129}\right)\) | \(e\left(\frac{110}{129}\right)\) | \(e\left(\frac{10}{43}\right)\) | \(e\left(\frac{122}{129}\right)\) | \(e\left(\frac{1}{129}\right)\) | \(e\left(\frac{19}{43}\right)\) |
| \(\chi_{1849}(522,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{43}\right)\) | \(e\left(\frac{113}{129}\right)\) | \(e\left(\frac{10}{43}\right)\) | \(e\left(\frac{8}{129}\right)\) | \(e\left(\frac{128}{129}\right)\) | \(e\left(\frac{79}{129}\right)\) | \(e\left(\frac{15}{43}\right)\) | \(e\left(\frac{97}{129}\right)\) | \(e\left(\frac{23}{129}\right)\) | \(e\left(\frac{7}{43}\right)\) |
| \(\chi_{1849}(552,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{43}\right)\) | \(e\left(\frac{70}{129}\right)\) | \(e\left(\frac{10}{43}\right)\) | \(e\left(\frac{94}{129}\right)\) | \(e\left(\frac{85}{129}\right)\) | \(e\left(\frac{122}{129}\right)\) | \(e\left(\frac{15}{43}\right)\) | \(e\left(\frac{11}{129}\right)\) | \(e\left(\frac{109}{129}\right)\) | \(e\left(\frac{7}{43}\right)\) |
| \(\chi_{1849}(565,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{15}{43}\right)\) | \(e\left(\frac{38}{129}\right)\) | \(e\left(\frac{30}{43}\right)\) | \(e\left(\frac{110}{129}\right)\) | \(e\left(\frac{83}{129}\right)\) | \(e\left(\frac{22}{129}\right)\) | \(e\left(\frac{2}{43}\right)\) | \(e\left(\frac{76}{129}\right)\) | \(e\left(\frac{26}{129}\right)\) | \(e\left(\frac{21}{43}\right)\) |
| \(\chi_{1849}(595,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{21}{43}\right)\) | \(e\left(\frac{79}{129}\right)\) | \(e\left(\frac{42}{43}\right)\) | \(e\left(\frac{25}{129}\right)\) | \(e\left(\frac{13}{129}\right)\) | \(e\left(\frac{5}{129}\right)\) | \(e\left(\frac{20}{43}\right)\) | \(e\left(\frac{29}{129}\right)\) | \(e\left(\frac{88}{129}\right)\) | \(e\left(\frac{38}{43}\right)\) |
| \(\chi_{1849}(608,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{25}{43}\right)\) | \(e\left(\frac{92}{129}\right)\) | \(e\left(\frac{7}{43}\right)\) | \(e\left(\frac{83}{129}\right)\) | \(e\left(\frac{38}{129}\right)\) | \(e\left(\frac{94}{129}\right)\) | \(e\left(\frac{32}{43}\right)\) | \(e\left(\frac{55}{129}\right)\) | \(e\left(\frac{29}{129}\right)\) | \(e\left(\frac{35}{43}\right)\) |
| \(\chi_{1849}(638,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{43}\right)\) | \(e\left(\frac{88}{129}\right)\) | \(e\left(\frac{31}{43}\right)\) | \(e\left(\frac{85}{129}\right)\) | \(e\left(\frac{70}{129}\right)\) | \(e\left(\frac{17}{129}\right)\) | \(e\left(\frac{25}{43}\right)\) | \(e\left(\frac{47}{129}\right)\) | \(e\left(\frac{67}{129}\right)\) | \(e\left(\frac{26}{43}\right)\) |
| \(\chi_{1849}(651,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{35}{43}\right)\) | \(e\left(\frac{17}{129}\right)\) | \(e\left(\frac{27}{43}\right)\) | \(e\left(\frac{56}{129}\right)\) | \(e\left(\frac{122}{129}\right)\) | \(e\left(\frac{37}{129}\right)\) | \(e\left(\frac{19}{43}\right)\) | \(e\left(\frac{34}{129}\right)\) | \(e\left(\frac{32}{129}\right)\) | \(e\left(\frac{6}{43}\right)\) |
| \(\chi_{1849}(681,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{10}{43}\right)\) | \(e\left(\frac{97}{129}\right)\) | \(e\left(\frac{20}{43}\right)\) | \(e\left(\frac{16}{129}\right)\) | \(e\left(\frac{127}{129}\right)\) | \(e\left(\frac{29}{129}\right)\) | \(e\left(\frac{30}{43}\right)\) | \(e\left(\frac{65}{129}\right)\) | \(e\left(\frac{46}{129}\right)\) | \(e\left(\frac{14}{43}\right)\) |