from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3017, base_ring=CyclotomicField(1290))
M = H._module
chi = DirichletCharacter(H, M([430,921]))
chi.galois_orbit()
[g,chi] = znchar(Mod(37,3017))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(3017\) | |
| Conductor: | \(3017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1290\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | $\Q(\zeta_{645})$ |
| Fixed field: | Number field defined by a degree 1290 polynomial (not computed) |
First 31 of 336 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{3017}(37,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{95}{129}\right)\) | \(e\left(\frac{31}{129}\right)\) | \(e\left(\frac{61}{129}\right)\) | \(e\left(\frac{541}{645}\right)\) | \(e\left(\frac{42}{43}\right)\) | \(e\left(\frac{9}{43}\right)\) | \(e\left(\frac{62}{129}\right)\) | \(e\left(\frac{371}{645}\right)\) | \(e\left(\frac{494}{645}\right)\) | \(e\left(\frac{92}{129}\right)\) |
| \(\chi_{3017}(39,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{4}{129}\right)\) | \(e\left(\frac{95}{129}\right)\) | \(e\left(\frac{8}{129}\right)\) | \(e\left(\frac{551}{645}\right)\) | \(e\left(\frac{33}{43}\right)\) | \(e\left(\frac{4}{43}\right)\) | \(e\left(\frac{61}{129}\right)\) | \(e\left(\frac{571}{645}\right)\) | \(e\left(\frac{124}{645}\right)\) | \(e\left(\frac{103}{129}\right)\) |
| \(\chi_{3017}(51,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{101}{129}\right)\) | \(e\left(\frac{109}{129}\right)\) | \(e\left(\frac{73}{129}\right)\) | \(e\left(\frac{13}{645}\right)\) | \(e\left(\frac{27}{43}\right)\) | \(e\left(\frac{15}{43}\right)\) | \(e\left(\frac{89}{129}\right)\) | \(e\left(\frac{518}{645}\right)\) | \(e\left(\frac{422}{645}\right)\) | \(e\left(\frac{53}{129}\right)\) |
| \(\chi_{3017}(65,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{11}{129}\right)\) | \(e\left(\frac{100}{129}\right)\) | \(e\left(\frac{22}{129}\right)\) | \(e\left(\frac{322}{645}\right)\) | \(e\left(\frac{37}{43}\right)\) | \(e\left(\frac{11}{43}\right)\) | \(e\left(\frac{71}{129}\right)\) | \(e\left(\frac{377}{645}\right)\) | \(e\left(\frac{83}{645}\right)\) | \(e\left(\frac{122}{129}\right)\) |
| \(\chi_{3017}(67,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{52}{129}\right)\) | \(e\left(\frac{74}{129}\right)\) | \(e\left(\frac{104}{129}\right)\) | \(e\left(\frac{584}{645}\right)\) | \(e\left(\frac{42}{43}\right)\) | \(e\left(\frac{9}{43}\right)\) | \(e\left(\frac{19}{129}\right)\) | \(e\left(\frac{199}{645}\right)\) | \(e\left(\frac{451}{645}\right)\) | \(e\left(\frac{49}{129}\right)\) |
| \(\chi_{3017}(74,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{124}{129}\right)\) | \(e\left(\frac{107}{129}\right)\) | \(e\left(\frac{119}{129}\right)\) | \(e\left(\frac{311}{645}\right)\) | \(e\left(\frac{34}{43}\right)\) | \(e\left(\frac{38}{43}\right)\) | \(e\left(\frac{85}{129}\right)\) | \(e\left(\frac{286}{645}\right)\) | \(e\left(\frac{619}{645}\right)\) | \(e\left(\frac{97}{129}\right)\) |
| \(\chi_{3017}(79,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{41}{129}\right)\) | \(e\left(\frac{103}{129}\right)\) | \(e\left(\frac{82}{129}\right)\) | \(e\left(\frac{4}{645}\right)\) | \(e\left(\frac{5}{43}\right)\) | \(e\left(\frac{41}{43}\right)\) | \(e\left(\frac{77}{129}\right)\) | \(e\left(\frac{209}{645}\right)\) | \(e\left(\frac{626}{645}\right)\) | \(e\left(\frac{56}{129}\right)\) |
| \(\chi_{3017}(86,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{89}{129}\right)\) | \(e\left(\frac{82}{129}\right)\) | \(e\left(\frac{49}{129}\right)\) | \(e\left(\frac{424}{645}\right)\) | \(e\left(\frac{14}{43}\right)\) | \(e\left(\frac{3}{43}\right)\) | \(e\left(\frac{35}{129}\right)\) | \(e\left(\frac{224}{645}\right)\) | \(e\left(\frac{566}{645}\right)\) | \(e\left(\frac{2}{129}\right)\) |
| \(\chi_{3017}(93,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{14}{129}\right)\) | \(e\left(\frac{10}{129}\right)\) | \(e\left(\frac{28}{129}\right)\) | \(e\left(\frac{187}{645}\right)\) | \(e\left(\frac{8}{43}\right)\) | \(e\left(\frac{14}{43}\right)\) | \(e\left(\frac{20}{129}\right)\) | \(e\left(\frac{257}{645}\right)\) | \(e\left(\frac{563}{645}\right)\) | \(e\left(\frac{38}{129}\right)\) |
| \(\chi_{3017}(102,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{129}\right)\) | \(e\left(\frac{56}{129}\right)\) | \(e\left(\frac{2}{129}\right)\) | \(e\left(\frac{428}{645}\right)\) | \(e\left(\frac{19}{43}\right)\) | \(e\left(\frac{1}{43}\right)\) | \(e\left(\frac{112}{129}\right)\) | \(e\left(\frac{433}{645}\right)\) | \(e\left(\frac{547}{645}\right)\) | \(e\left(\frac{58}{129}\right)\) |
| \(\chi_{3017}(130,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{40}{129}\right)\) | \(e\left(\frac{47}{129}\right)\) | \(e\left(\frac{80}{129}\right)\) | \(e\left(\frac{92}{645}\right)\) | \(e\left(\frac{29}{43}\right)\) | \(e\left(\frac{40}{43}\right)\) | \(e\left(\frac{94}{129}\right)\) | \(e\left(\frac{292}{645}\right)\) | \(e\left(\frac{208}{645}\right)\) | \(e\left(\frac{127}{129}\right)\) |
| \(\chi_{3017}(137,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{22}{129}\right)\) | \(e\left(\frac{71}{129}\right)\) | \(e\left(\frac{44}{129}\right)\) | \(e\left(\frac{386}{645}\right)\) | \(e\left(\frac{31}{43}\right)\) | \(e\left(\frac{22}{43}\right)\) | \(e\left(\frac{13}{129}\right)\) | \(e\left(\frac{496}{645}\right)\) | \(e\left(\frac{424}{645}\right)\) | \(e\left(\frac{115}{129}\right)\) |
| \(\chi_{3017}(142,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{50}{129}\right)\) | \(e\left(\frac{91}{129}\right)\) | \(e\left(\frac{100}{129}\right)\) | \(e\left(\frac{631}{645}\right)\) | \(e\left(\frac{4}{43}\right)\) | \(e\left(\frac{7}{43}\right)\) | \(e\left(\frac{53}{129}\right)\) | \(e\left(\frac{236}{645}\right)\) | \(e\left(\frac{389}{645}\right)\) | \(e\left(\frac{62}{129}\right)\) |
| \(\chi_{3017}(156,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{62}{129}\right)\) | \(e\left(\frac{118}{129}\right)\) | \(e\left(\frac{124}{129}\right)\) | \(e\left(\frac{91}{645}\right)\) | \(e\left(\frac{17}{43}\right)\) | \(e\left(\frac{19}{43}\right)\) | \(e\left(\frac{107}{129}\right)\) | \(e\left(\frac{401}{645}\right)\) | \(e\left(\frac{374}{645}\right)\) | \(e\left(\frac{113}{129}\right)\) |
| \(\chi_{3017}(158,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{70}{129}\right)\) | \(e\left(\frac{50}{129}\right)\) | \(e\left(\frac{11}{129}\right)\) | \(e\left(\frac{419}{645}\right)\) | \(e\left(\frac{40}{43}\right)\) | \(e\left(\frac{27}{43}\right)\) | \(e\left(\frac{100}{129}\right)\) | \(e\left(\frac{124}{645}\right)\) | \(e\left(\frac{106}{645}\right)\) | \(e\left(\frac{61}{129}\right)\) |
| \(\chi_{3017}(170,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{8}{129}\right)\) | \(e\left(\frac{61}{129}\right)\) | \(e\left(\frac{16}{129}\right)\) | \(e\left(\frac{199}{645}\right)\) | \(e\left(\frac{23}{43}\right)\) | \(e\left(\frac{8}{43}\right)\) | \(e\left(\frac{122}{129}\right)\) | \(e\left(\frac{239}{645}\right)\) | \(e\left(\frac{506}{645}\right)\) | \(e\left(\frac{77}{129}\right)\) |
| \(\chi_{3017}(172,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{118}{129}\right)\) | \(e\left(\frac{29}{129}\right)\) | \(e\left(\frac{107}{129}\right)\) | \(e\left(\frac{194}{645}\right)\) | \(e\left(\frac{6}{43}\right)\) | \(e\left(\frac{32}{43}\right)\) | \(e\left(\frac{58}{129}\right)\) | \(e\left(\frac{139}{645}\right)\) | \(e\left(\frac{46}{645}\right)\) | \(e\left(\frac{7}{129}\right)\) |
| \(\chi_{3017}(191,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{17}{129}\right)\) | \(e\left(\frac{49}{129}\right)\) | \(e\left(\frac{34}{129}\right)\) | \(e\left(\frac{181}{645}\right)\) | \(e\left(\frac{22}{43}\right)\) | \(e\left(\frac{17}{43}\right)\) | \(e\left(\frac{98}{129}\right)\) | \(e\left(\frac{266}{645}\right)\) | \(e\left(\frac{269}{645}\right)\) | \(e\left(\frac{83}{129}\right)\) |
| \(\chi_{3017}(193,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{34}{129}\right)\) | \(e\left(\frac{98}{129}\right)\) | \(e\left(\frac{68}{129}\right)\) | \(e\left(\frac{491}{645}\right)\) | \(e\left(\frac{1}{43}\right)\) | \(e\left(\frac{34}{43}\right)\) | \(e\left(\frac{67}{129}\right)\) | \(e\left(\frac{16}{645}\right)\) | \(e\left(\frac{409}{645}\right)\) | \(e\left(\frac{37}{129}\right)\) |
| \(\chi_{3017}(219,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{80}{129}\right)\) | \(e\left(\frac{94}{129}\right)\) | \(e\left(\frac{31}{129}\right)\) | \(e\left(\frac{313}{645}\right)\) | \(e\left(\frac{15}{43}\right)\) | \(e\left(\frac{37}{43}\right)\) | \(e\left(\frac{59}{129}\right)\) | \(e\left(\frac{68}{645}\right)\) | \(e\left(\frac{287}{645}\right)\) | \(e\left(\frac{125}{129}\right)\) |
| \(\chi_{3017}(226,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{113}{129}\right)\) | \(e\left(\frac{7}{129}\right)\) | \(e\left(\frac{97}{129}\right)\) | \(e\left(\frac{118}{645}\right)\) | \(e\left(\frac{40}{43}\right)\) | \(e\left(\frac{27}{43}\right)\) | \(e\left(\frac{14}{129}\right)\) | \(e\left(\frac{38}{645}\right)\) | \(e\left(\frac{407}{645}\right)\) | \(e\left(\frac{104}{129}\right)\) |
| \(\chi_{3017}(233,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{77}{129}\right)\) | \(e\left(\frac{55}{129}\right)\) | \(e\left(\frac{25}{129}\right)\) | \(e\left(\frac{319}{645}\right)\) | \(e\left(\frac{1}{43}\right)\) | \(e\left(\frac{34}{43}\right)\) | \(e\left(\frac{110}{129}\right)\) | \(e\left(\frac{59}{645}\right)\) | \(e\left(\frac{581}{645}\right)\) | \(e\left(\frac{80}{129}\right)\) |
| \(\chi_{3017}(235,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{61}{129}\right)\) | \(e\left(\frac{62}{129}\right)\) | \(e\left(\frac{122}{129}\right)\) | \(e\left(\frac{566}{645}\right)\) | \(e\left(\frac{41}{43}\right)\) | \(e\left(\frac{18}{43}\right)\) | \(e\left(\frac{124}{129}\right)\) | \(e\left(\frac{226}{645}\right)\) | \(e\left(\frac{214}{645}\right)\) | \(e\left(\frac{55}{129}\right)\) |
| \(\chi_{3017}(247,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{17}{129}\right)\) | \(e\left(\frac{49}{129}\right)\) | \(e\left(\frac{34}{129}\right)\) | \(e\left(\frac{568}{645}\right)\) | \(e\left(\frac{22}{43}\right)\) | \(e\left(\frac{17}{43}\right)\) | \(e\left(\frac{98}{129}\right)\) | \(e\left(\frac{8}{645}\right)\) | \(e\left(\frac{527}{645}\right)\) | \(e\left(\frac{83}{129}\right)\) |
| \(\chi_{3017}(249,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{109}{129}\right)\) | \(e\left(\frac{41}{129}\right)\) | \(e\left(\frac{89}{129}\right)\) | \(e\left(\frac{599}{645}\right)\) | \(e\left(\frac{7}{43}\right)\) | \(e\left(\frac{23}{43}\right)\) | \(e\left(\frac{82}{129}\right)\) | \(e\left(\frac{499}{645}\right)\) | \(e\left(\frac{541}{645}\right)\) | \(e\left(\frac{1}{129}\right)\) |
| \(\chi_{3017}(254,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{62}{129}\right)\) | \(e\left(\frac{118}{129}\right)\) | \(e\left(\frac{124}{129}\right)\) | \(e\left(\frac{607}{645}\right)\) | \(e\left(\frac{17}{43}\right)\) | \(e\left(\frac{19}{43}\right)\) | \(e\left(\frac{107}{129}\right)\) | \(e\left(\frac{272}{645}\right)\) | \(e\left(\frac{503}{645}\right)\) | \(e\left(\frac{113}{129}\right)\) |
| \(\chi_{3017}(268,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{110}{129}\right)\) | \(e\left(\frac{97}{129}\right)\) | \(e\left(\frac{91}{129}\right)\) | \(e\left(\frac{124}{645}\right)\) | \(e\left(\frac{26}{43}\right)\) | \(e\left(\frac{24}{43}\right)\) | \(e\left(\frac{65}{129}\right)\) | \(e\left(\frac{29}{645}\right)\) | \(e\left(\frac{56}{645}\right)\) | \(e\left(\frac{59}{129}\right)\) |
| \(\chi_{3017}(284,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{79}{129}\right)\) | \(e\left(\frac{38}{129}\right)\) | \(e\left(\frac{29}{129}\right)\) | \(e\left(\frac{401}{645}\right)\) | \(e\left(\frac{39}{43}\right)\) | \(e\left(\frac{36}{43}\right)\) | \(e\left(\frac{76}{129}\right)\) | \(e\left(\frac{151}{645}\right)\) | \(e\left(\frac{514}{645}\right)\) | \(e\left(\frac{67}{129}\right)\) |
| \(\chi_{3017}(296,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{53}{129}\right)\) | \(e\left(\frac{1}{129}\right)\) | \(e\left(\frac{106}{129}\right)\) | \(e\left(\frac{496}{645}\right)\) | \(e\left(\frac{18}{43}\right)\) | \(e\left(\frac{10}{43}\right)\) | \(e\left(\frac{2}{129}\right)\) | \(e\left(\frac{116}{645}\right)\) | \(e\left(\frac{224}{645}\right)\) | \(e\left(\frac{107}{129}\right)\) |
| \(\chi_{3017}(310,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{50}{129}\right)\) | \(e\left(\frac{91}{129}\right)\) | \(e\left(\frac{100}{129}\right)\) | \(e\left(\frac{373}{645}\right)\) | \(e\left(\frac{4}{43}\right)\) | \(e\left(\frac{7}{43}\right)\) | \(e\left(\frac{53}{129}\right)\) | \(e\left(\frac{623}{645}\right)\) | \(e\left(\frac{2}{645}\right)\) | \(e\left(\frac{62}{129}\right)\) |
| \(\chi_{3017}(312,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{91}{129}\right)\) | \(e\left(\frac{65}{129}\right)\) | \(e\left(\frac{53}{129}\right)\) | \(e\left(\frac{506}{645}\right)\) | \(e\left(\frac{9}{43}\right)\) | \(e\left(\frac{5}{43}\right)\) | \(e\left(\frac{1}{129}\right)\) | \(e\left(\frac{316}{645}\right)\) | \(e\left(\frac{499}{645}\right)\) | \(e\left(\frac{118}{129}\right)\) |