from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2183, base_ring=CyclotomicField(522))
M = H._module
chi = DirichletCharacter(H, M([377,450]))
chi.galois_orbit()
[g,chi] = znchar(Mod(3,2183))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(2183\) | |
| Conductor: | \(2183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(522\) | 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: | $\Q(\zeta_{261})$ |
| Fixed field: | Number field defined by a degree 522 polynomial (not computed) |
First 31 of 168 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{2183}(3,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{305}{522}\right)\) | \(e\left(\frac{230}{261}\right)\) | \(e\left(\frac{44}{261}\right)\) | \(e\left(\frac{409}{522}\right)\) | \(e\left(\frac{27}{58}\right)\) | \(e\left(\frac{164}{261}\right)\) | \(e\left(\frac{131}{174}\right)\) | \(e\left(\frac{199}{261}\right)\) | \(e\left(\frac{32}{87}\right)\) | \(e\left(\frac{19}{87}\right)\) |
| \(\chi_{2183}(4,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{522}\right)\) | \(e\left(\frac{44}{261}\right)\) | \(e\left(\frac{47}{261}\right)\) | \(e\left(\frac{253}{522}\right)\) | \(e\left(\frac{15}{58}\right)\) | \(e\left(\frac{104}{261}\right)\) | \(e\left(\frac{47}{174}\right)\) | \(e\left(\frac{88}{261}\right)\) | \(e\left(\frac{50}{87}\right)\) | \(e\left(\frac{46}{87}\right)\) |
| \(\chi_{2183}(21,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{409}{522}\right)\) | \(e\left(\frac{133}{261}\right)\) | \(e\left(\frac{148}{261}\right)\) | \(e\left(\frac{47}{522}\right)\) | \(e\left(\frac{17}{58}\right)\) | \(e\left(\frac{172}{261}\right)\) | \(e\left(\frac{61}{174}\right)\) | \(e\left(\frac{5}{261}\right)\) | \(e\left(\frac{76}{87}\right)\) | \(e\left(\frac{56}{87}\right)\) |
| \(\chi_{2183}(25,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{253}{522}\right)\) | \(e\left(\frac{148}{261}\right)\) | \(e\left(\frac{253}{261}\right)\) | \(e\left(\frac{329}{522}\right)\) | \(e\left(\frac{3}{58}\right)\) | \(e\left(\frac{160}{261}\right)\) | \(e\left(\frac{79}{174}\right)\) | \(e\left(\frac{35}{261}\right)\) | \(e\left(\frac{10}{87}\right)\) | \(e\left(\frac{44}{87}\right)\) |
| \(\chi_{2183}(28,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{151}{522}\right)\) | \(e\left(\frac{208}{261}\right)\) | \(e\left(\frac{151}{261}\right)\) | \(e\left(\frac{413}{522}\right)\) | \(e\left(\frac{5}{58}\right)\) | \(e\left(\frac{112}{261}\right)\) | \(e\left(\frac{151}{174}\right)\) | \(e\left(\frac{155}{261}\right)\) | \(e\left(\frac{7}{87}\right)\) | \(e\left(\frac{83}{87}\right)\) |
| \(\chi_{2183}(41,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{155}{522}\right)\) | \(e\left(\frac{134}{261}\right)\) | \(e\left(\frac{155}{261}\right)\) | \(e\left(\frac{379}{522}\right)\) | \(e\left(\frac{47}{58}\right)\) | \(e\left(\frac{32}{261}\right)\) | \(e\left(\frac{155}{174}\right)\) | \(e\left(\frac{7}{261}\right)\) | \(e\left(\frac{2}{87}\right)\) | \(e\left(\frac{61}{87}\right)\) |
| \(\chi_{2183}(62,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{522}\right)\) | \(e\left(\frac{85}{261}\right)\) | \(e\left(\frac{73}{261}\right)\) | \(e\left(\frac{293}{522}\right)\) | \(e\left(\frac{27}{58}\right)\) | \(e\left(\frac{106}{261}\right)\) | \(e\left(\frac{73}{174}\right)\) | \(e\left(\frac{170}{261}\right)\) | \(e\left(\frac{61}{87}\right)\) | \(e\left(\frac{77}{87}\right)\) |
| \(\chi_{2183}(78,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{371}{522}\right)\) | \(e\left(\frac{53}{261}\right)\) | \(e\left(\frac{110}{261}\right)\) | \(e\left(\frac{109}{522}\right)\) | \(e\left(\frac{53}{58}\right)\) | \(e\left(\frac{149}{261}\right)\) | \(e\left(\frac{23}{174}\right)\) | \(e\left(\frac{106}{261}\right)\) | \(e\left(\frac{80}{87}\right)\) | \(e\left(\frac{4}{87}\right)\) |
| \(\chi_{2183}(95,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{193}{522}\right)\) | \(e\left(\frac{214}{261}\right)\) | \(e\left(\frac{193}{261}\right)\) | \(e\left(\frac{317}{522}\right)\) | \(e\left(\frac{11}{58}\right)\) | \(e\left(\frac{55}{261}\right)\) | \(e\left(\frac{19}{174}\right)\) | \(e\left(\frac{167}{261}\right)\) | \(e\left(\frac{85}{87}\right)\) | \(e\left(\frac{26}{87}\right)\) |
| \(\chi_{2183}(104,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{113}{522}\right)\) | \(e\left(\frac{128}{261}\right)\) | \(e\left(\frac{113}{261}\right)\) | \(e\left(\frac{475}{522}\right)\) | \(e\left(\frac{41}{58}\right)\) | \(e\left(\frac{89}{261}\right)\) | \(e\left(\frac{113}{174}\right)\) | \(e\left(\frac{256}{261}\right)\) | \(e\left(\frac{11}{87}\right)\) | \(e\left(\frac{31}{87}\right)\) |
| \(\chi_{2183}(139,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{522}\right)\) | \(e\left(\frac{46}{261}\right)\) | \(e\left(\frac{61}{261}\right)\) | \(e\left(\frac{395}{522}\right)\) | \(e\left(\frac{17}{58}\right)\) | \(e\left(\frac{85}{261}\right)\) | \(e\left(\frac{61}{174}\right)\) | \(e\left(\frac{92}{261}\right)\) | \(e\left(\frac{76}{87}\right)\) | \(e\left(\frac{56}{87}\right)\) |
| \(\chi_{2183}(169,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{85}{522}\right)\) | \(e\left(\frac{124}{261}\right)\) | \(e\left(\frac{85}{261}\right)\) | \(e\left(\frac{191}{522}\right)\) | \(e\left(\frac{37}{58}\right)\) | \(e\left(\frac{127}{261}\right)\) | \(e\left(\frac{85}{174}\right)\) | \(e\left(\frac{248}{261}\right)\) | \(e\left(\frac{46}{87}\right)\) | \(e\left(\frac{11}{87}\right)\) |
| \(\chi_{2183}(189,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{497}{522}\right)\) | \(e\left(\frac{71}{261}\right)\) | \(e\left(\frac{236}{261}\right)\) | \(e\left(\frac{343}{522}\right)\) | \(e\left(\frac{13}{58}\right)\) | \(e\left(\frac{239}{261}\right)\) | \(e\left(\frac{149}{174}\right)\) | \(e\left(\frac{142}{261}\right)\) | \(e\left(\frac{53}{87}\right)\) | \(e\left(\frac{7}{87}\right)\) |
| \(\chi_{2183}(206,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{49}{522}\right)\) | \(e\left(\frac{7}{261}\right)\) | \(e\left(\frac{49}{261}\right)\) | \(e\left(\frac{497}{522}\right)\) | \(e\left(\frac{7}{58}\right)\) | \(e\left(\frac{64}{261}\right)\) | \(e\left(\frac{49}{174}\right)\) | \(e\left(\frac{14}{261}\right)\) | \(e\left(\frac{4}{87}\right)\) | \(e\left(\frac{35}{87}\right)\) |
| \(\chi_{2183}(213,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{367}{522}\right)\) | \(e\left(\frac{127}{261}\right)\) | \(e\left(\frac{106}{261}\right)\) | \(e\left(\frac{143}{522}\right)\) | \(e\left(\frac{11}{58}\right)\) | \(e\left(\frac{229}{261}\right)\) | \(e\left(\frac{19}{174}\right)\) | \(e\left(\frac{254}{261}\right)\) | \(e\left(\frac{85}{87}\right)\) | \(e\left(\frac{26}{87}\right)\) |
| \(\chi_{2183}(225,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{341}{522}\right)\) | \(e\left(\frac{86}{261}\right)\) | \(e\left(\frac{80}{261}\right)\) | \(e\left(\frac{103}{522}\right)\) | \(e\left(\frac{57}{58}\right)\) | \(e\left(\frac{227}{261}\right)\) | \(e\left(\frac{167}{174}\right)\) | \(e\left(\frac{172}{261}\right)\) | \(e\left(\frac{74}{87}\right)\) | \(e\left(\frac{82}{87}\right)\) |
| \(\chi_{2183}(226,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{353}{522}\right)\) | \(e\left(\frac{125}{261}\right)\) | \(e\left(\frac{92}{261}\right)\) | \(e\left(\frac{1}{522}\right)\) | \(e\left(\frac{9}{58}\right)\) | \(e\left(\frac{248}{261}\right)\) | \(e\left(\frac{5}{174}\right)\) | \(e\left(\frac{250}{261}\right)\) | \(e\left(\frac{59}{87}\right)\) | \(e\left(\frac{16}{87}\right)\) |
| \(\chi_{2183}(243,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{481}{522}\right)\) | \(e\left(\frac{106}{261}\right)\) | \(e\left(\frac{220}{261}\right)\) | \(e\left(\frac{479}{522}\right)\) | \(e\left(\frac{19}{58}\right)\) | \(e\left(\frac{37}{261}\right)\) | \(e\left(\frac{133}{174}\right)\) | \(e\left(\frac{212}{261}\right)\) | \(e\left(\frac{73}{87}\right)\) | \(e\left(\frac{8}{87}\right)\) |
| \(\chi_{2183}(252,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{239}{522}\right)\) | \(e\left(\frac{146}{261}\right)\) | \(e\left(\frac{239}{261}\right)\) | \(e\left(\frac{187}{522}\right)\) | \(e\left(\frac{1}{58}\right)\) | \(e\left(\frac{179}{261}\right)\) | \(e\left(\frac{65}{174}\right)\) | \(e\left(\frac{31}{261}\right)\) | \(e\left(\frac{71}{87}\right)\) | \(e\left(\frac{34}{87}\right)\) |
| \(\chi_{2183}(262,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{269}{522}\right)\) | \(e\left(\frac{113}{261}\right)\) | \(e\left(\frac{8}{261}\right)\) | \(e\left(\frac{193}{522}\right)\) | \(e\left(\frac{55}{58}\right)\) | \(e\left(\frac{101}{261}\right)\) | \(e\left(\frac{95}{174}\right)\) | \(e\left(\frac{226}{261}\right)\) | \(e\left(\frac{77}{87}\right)\) | \(e\left(\frac{43}{87}\right)\) |
| \(\chi_{2183}(263,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{335}{522}\right)\) | \(e\left(\frac{197}{261}\right)\) | \(e\left(\frac{74}{261}\right)\) | \(e\left(\frac{415}{522}\right)\) | \(e\left(\frac{23}{58}\right)\) | \(e\left(\frac{86}{261}\right)\) | \(e\left(\frac{161}{174}\right)\) | \(e\left(\frac{133}{261}\right)\) | \(e\left(\frac{38}{87}\right)\) | \(e\left(\frac{28}{87}\right)\) |
| \(\chi_{2183}(284,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{109}{522}\right)\) | \(e\left(\frac{202}{261}\right)\) | \(e\left(\frac{109}{261}\right)\) | \(e\left(\frac{509}{522}\right)\) | \(e\left(\frac{57}{58}\right)\) | \(e\left(\frac{169}{261}\right)\) | \(e\left(\frac{109}{174}\right)\) | \(e\left(\frac{143}{261}\right)\) | \(e\left(\frac{16}{87}\right)\) | \(e\left(\frac{53}{87}\right)\) |
| \(\chi_{2183}(287,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{259}{522}\right)\) | \(e\left(\frac{37}{261}\right)\) | \(e\left(\frac{259}{261}\right)\) | \(e\left(\frac{17}{522}\right)\) | \(e\left(\frac{37}{58}\right)\) | \(e\left(\frac{40}{261}\right)\) | \(e\left(\frac{85}{174}\right)\) | \(e\left(\frac{74}{261}\right)\) | \(e\left(\frac{46}{87}\right)\) | \(e\left(\frac{11}{87}\right)\) |
| \(\chi_{2183}(289,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{401}{522}\right)\) | \(e\left(\frac{20}{261}\right)\) | \(e\left(\frac{140}{261}\right)\) | \(e\left(\frac{115}{522}\right)\) | \(e\left(\frac{49}{58}\right)\) | \(e\left(\frac{71}{261}\right)\) | \(e\left(\frac{53}{174}\right)\) | \(e\left(\frac{40}{261}\right)\) | \(e\left(\frac{86}{87}\right)\) | \(e\left(\frac{13}{87}\right)\) |
| \(\chi_{2183}(299,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{395}{522}\right)\) | \(e\left(\frac{131}{261}\right)\) | \(e\left(\frac{134}{261}\right)\) | \(e\left(\frac{427}{522}\right)\) | \(e\left(\frac{15}{58}\right)\) | \(e\left(\frac{191}{261}\right)\) | \(e\left(\frac{47}{174}\right)\) | \(e\left(\frac{1}{261}\right)\) | \(e\left(\frac{50}{87}\right)\) | \(e\left(\frac{46}{87}\right)\) |
| \(\chi_{2183}(300,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{83}{522}\right)\) | \(e\left(\frac{161}{261}\right)\) | \(e\left(\frac{83}{261}\right)\) | \(e\left(\frac{469}{522}\right)\) | \(e\left(\frac{45}{58}\right)\) | \(e\left(\frac{167}{261}\right)\) | \(e\left(\frac{83}{174}\right)\) | \(e\left(\frac{61}{261}\right)\) | \(e\left(\frac{5}{87}\right)\) | \(e\left(\frac{22}{87}\right)\) |
| \(\chi_{2183}(317,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{522}\right)\) | \(e\left(\frac{79}{261}\right)\) | \(e\left(\frac{31}{261}\right)\) | \(e\left(\frac{389}{522}\right)\) | \(e\left(\frac{21}{58}\right)\) | \(e\left(\frac{163}{261}\right)\) | \(e\left(\frac{31}{174}\right)\) | \(e\left(\frac{158}{261}\right)\) | \(e\left(\frac{70}{87}\right)\) | \(e\left(\frac{47}{87}\right)\) |
| \(\chi_{2183}(321,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{522}\right)\) | \(e\left(\frac{229}{261}\right)\) | \(e\left(\frac{37}{261}\right)\) | \(e\left(\frac{77}{522}\right)\) | \(e\left(\frac{55}{58}\right)\) | \(e\left(\frac{43}{261}\right)\) | \(e\left(\frac{37}{174}\right)\) | \(e\left(\frac{197}{261}\right)\) | \(e\left(\frac{19}{87}\right)\) | \(e\left(\frac{14}{87}\right)\) |
| \(\chi_{2183}(324,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{223}{522}\right)\) | \(e\left(\frac{181}{261}\right)\) | \(e\left(\frac{223}{261}\right)\) | \(e\left(\frac{323}{522}\right)\) | \(e\left(\frac{7}{58}\right)\) | \(e\left(\frac{238}{261}\right)\) | \(e\left(\frac{49}{174}\right)\) | \(e\left(\frac{101}{261}\right)\) | \(e\left(\frac{4}{87}\right)\) | \(e\left(\frac{35}{87}\right)\) |
| \(\chi_{2183}(336,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{503}{522}\right)\) | \(e\left(\frac{221}{261}\right)\) | \(e\left(\frac{242}{261}\right)\) | \(e\left(\frac{31}{522}\right)\) | \(e\left(\frac{47}{58}\right)\) | \(e\left(\frac{119}{261}\right)\) | \(e\left(\frac{155}{174}\right)\) | \(e\left(\frac{181}{261}\right)\) | \(e\left(\frac{2}{87}\right)\) | \(e\left(\frac{61}{87}\right)\) |
| \(\chi_{2183}(358,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{163}{522}\right)\) | \(e\left(\frac{247}{261}\right)\) | \(e\left(\frac{163}{261}\right)\) | \(e\left(\frac{311}{522}\right)\) | \(e\left(\frac{15}{58}\right)\) | \(e\left(\frac{133}{261}\right)\) | \(e\left(\frac{163}{174}\right)\) | \(e\left(\frac{233}{261}\right)\) | \(e\left(\frac{79}{87}\right)\) | \(e\left(\frac{17}{87}\right)\) |