from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3283, base_ring=CyclotomicField(462))
M = H._module
chi = DirichletCharacter(H, M([110,14]))
chi.galois_orbit()
[g,chi] = znchar(Mod(4,3283))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(3283\) | |
| Conductor: | \(3283\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(231\) | 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: | $\Q(\zeta_{231})$ |
| Fixed field: | Number field defined by a degree 231 polynomial (not computed) |
First 31 of 120 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{3283}(4,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{77}\right)\) | \(e\left(\frac{97}{231}\right)\) | \(e\left(\frac{34}{77}\right)\) | \(e\left(\frac{83}{231}\right)\) | \(e\left(\frac{148}{231}\right)\) | \(e\left(\frac{51}{77}\right)\) | \(e\left(\frac{194}{231}\right)\) | \(e\left(\frac{134}{231}\right)\) | \(e\left(\frac{24}{77}\right)\) | \(e\left(\frac{199}{231}\right)\) |
| \(\chi_{3283}(16,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{34}{77}\right)\) | \(e\left(\frac{194}{231}\right)\) | \(e\left(\frac{68}{77}\right)\) | \(e\left(\frac{166}{231}\right)\) | \(e\left(\frac{65}{231}\right)\) | \(e\left(\frac{25}{77}\right)\) | \(e\left(\frac{157}{231}\right)\) | \(e\left(\frac{37}{231}\right)\) | \(e\left(\frac{48}{77}\right)\) | \(e\left(\frac{167}{231}\right)\) |
| \(\chi_{3283}(23,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{77}\right)\) | \(e\left(\frac{104}{231}\right)\) | \(e\left(\frac{69}{77}\right)\) | \(e\left(\frac{139}{231}\right)\) | \(e\left(\frac{92}{231}\right)\) | \(e\left(\frac{65}{77}\right)\) | \(e\left(\frac{208}{231}\right)\) | \(e\left(\frac{127}{231}\right)\) | \(e\left(\frac{17}{77}\right)\) | \(e\left(\frac{80}{231}\right)\) |
| \(\chi_{3283}(60,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{77}\right)\) | \(e\left(\frac{10}{231}\right)\) | \(e\left(\frac{17}{77}\right)\) | \(e\left(\frac{80}{231}\right)\) | \(e\left(\frac{151}{231}\right)\) | \(e\left(\frac{64}{77}\right)\) | \(e\left(\frac{20}{231}\right)\) | \(e\left(\frac{221}{231}\right)\) | \(e\left(\frac{12}{77}\right)\) | \(e\left(\frac{61}{231}\right)\) |
| \(\chi_{3283}(65,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{69}{77}\right)\) | \(e\left(\frac{131}{231}\right)\) | \(e\left(\frac{61}{77}\right)\) | \(e\left(\frac{124}{231}\right)\) | \(e\left(\frac{107}{231}\right)\) | \(e\left(\frac{53}{77}\right)\) | \(e\left(\frac{31}{231}\right)\) | \(e\left(\frac{100}{231}\right)\) | \(e\left(\frac{34}{77}\right)\) | \(e\left(\frac{83}{231}\right)\) |
| \(\chi_{3283}(86,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{74}{77}\right)\) | \(e\left(\frac{155}{231}\right)\) | \(e\left(\frac{71}{77}\right)\) | \(e\left(\frac{85}{231}\right)\) | \(e\left(\frac{146}{231}\right)\) | \(e\left(\frac{68}{77}\right)\) | \(e\left(\frac{79}{231}\right)\) | \(e\left(\frac{76}{231}\right)\) | \(e\left(\frac{32}{77}\right)\) | \(e\left(\frac{137}{231}\right)\) |
| \(\chi_{3283}(88,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{76}{77}\right)\) | \(e\left(\frac{103}{231}\right)\) | \(e\left(\frac{75}{77}\right)\) | \(e\left(\frac{131}{231}\right)\) | \(e\left(\frac{100}{231}\right)\) | \(e\left(\frac{74}{77}\right)\) | \(e\left(\frac{206}{231}\right)\) | \(e\left(\frac{128}{231}\right)\) | \(e\left(\frac{62}{77}\right)\) | \(e\left(\frac{97}{231}\right)\) |
| \(\chi_{3283}(102,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{59}{77}\right)\) | \(e\left(\frac{160}{231}\right)\) | \(e\left(\frac{41}{77}\right)\) | \(e\left(\frac{125}{231}\right)\) | \(e\left(\frac{106}{231}\right)\) | \(e\left(\frac{23}{77}\right)\) | \(e\left(\frac{89}{231}\right)\) | \(e\left(\frac{71}{231}\right)\) | \(e\left(\frac{38}{77}\right)\) | \(e\left(\frac{52}{231}\right)\) |
| \(\chi_{3283}(121,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{24}{77}\right)\) | \(e\left(\frac{146}{231}\right)\) | \(e\left(\frac{48}{77}\right)\) | \(e\left(\frac{13}{231}\right)\) | \(e\left(\frac{218}{231}\right)\) | \(e\left(\frac{72}{77}\right)\) | \(e\left(\frac{61}{231}\right)\) | \(e\left(\frac{85}{231}\right)\) | \(e\left(\frac{52}{77}\right)\) | \(e\left(\frac{59}{231}\right)\) |
| \(\chi_{3283}(123,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{77}\right)\) | \(e\left(\frac{172}{231}\right)\) | \(e\left(\frac{46}{77}\right)\) | \(e\left(\frac{221}{231}\right)\) | \(e\left(\frac{10}{231}\right)\) | \(e\left(\frac{69}{77}\right)\) | \(e\left(\frac{113}{231}\right)\) | \(e\left(\frac{59}{231}\right)\) | \(e\left(\frac{37}{77}\right)\) | \(e\left(\frac{79}{231}\right)\) |
| \(\chi_{3283}(240,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{64}{77}\right)\) | \(e\left(\frac{107}{231}\right)\) | \(e\left(\frac{51}{77}\right)\) | \(e\left(\frac{163}{231}\right)\) | \(e\left(\frac{68}{231}\right)\) | \(e\left(\frac{38}{77}\right)\) | \(e\left(\frac{214}{231}\right)\) | \(e\left(\frac{124}{231}\right)\) | \(e\left(\frac{36}{77}\right)\) | \(e\left(\frac{29}{231}\right)\) |
| \(\chi_{3283}(256,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{68}{77}\right)\) | \(e\left(\frac{157}{231}\right)\) | \(e\left(\frac{59}{77}\right)\) | \(e\left(\frac{101}{231}\right)\) | \(e\left(\frac{130}{231}\right)\) | \(e\left(\frac{50}{77}\right)\) | \(e\left(\frac{83}{231}\right)\) | \(e\left(\frac{74}{231}\right)\) | \(e\left(\frac{19}{77}\right)\) | \(e\left(\frac{103}{231}\right)\) |
| \(\chi_{3283}(317,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{77}\right)\) | \(e\left(\frac{20}{231}\right)\) | \(e\left(\frac{34}{77}\right)\) | \(e\left(\frac{160}{231}\right)\) | \(e\left(\frac{71}{231}\right)\) | \(e\left(\frac{51}{77}\right)\) | \(e\left(\frac{40}{231}\right)\) | \(e\left(\frac{211}{231}\right)\) | \(e\left(\frac{24}{77}\right)\) | \(e\left(\frac{122}{231}\right)\) |
| \(\chi_{3283}(345,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{26}{77}\right)\) | \(e\left(\frac{17}{231}\right)\) | \(e\left(\frac{52}{77}\right)\) | \(e\left(\frac{136}{231}\right)\) | \(e\left(\frac{95}{231}\right)\) | \(e\left(\frac{1}{77}\right)\) | \(e\left(\frac{34}{231}\right)\) | \(e\left(\frac{214}{231}\right)\) | \(e\left(\frac{5}{77}\right)\) | \(e\left(\frac{173}{231}\right)\) |
| \(\chi_{3283}(352,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{16}{77}\right)\) | \(e\left(\frac{200}{231}\right)\) | \(e\left(\frac{32}{77}\right)\) | \(e\left(\frac{214}{231}\right)\) | \(e\left(\frac{17}{231}\right)\) | \(e\left(\frac{48}{77}\right)\) | \(e\left(\frac{169}{231}\right)\) | \(e\left(\frac{31}{231}\right)\) | \(e\left(\frac{9}{77}\right)\) | \(e\left(\frac{65}{231}\right)\) |
| \(\chi_{3283}(368,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{30}{77}\right)\) | \(e\left(\frac{67}{231}\right)\) | \(e\left(\frac{60}{77}\right)\) | \(e\left(\frac{74}{231}\right)\) | \(e\left(\frac{157}{231}\right)\) | \(e\left(\frac{13}{77}\right)\) | \(e\left(\frac{134}{231}\right)\) | \(e\left(\frac{164}{231}\right)\) | \(e\left(\frac{65}{77}\right)\) | \(e\left(\frac{16}{231}\right)\) |
| \(\chi_{3283}(382,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{62}{77}\right)\) | \(e\left(\frac{82}{231}\right)\) | \(e\left(\frac{47}{77}\right)\) | \(e\left(\frac{194}{231}\right)\) | \(e\left(\frac{37}{231}\right)\) | \(e\left(\frac{32}{77}\right)\) | \(e\left(\frac{164}{231}\right)\) | \(e\left(\frac{149}{231}\right)\) | \(e\left(\frac{6}{77}\right)\) | \(e\left(\frac{223}{231}\right)\) |
| \(\chi_{3283}(408,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{76}{77}\right)\) | \(e\left(\frac{26}{231}\right)\) | \(e\left(\frac{75}{77}\right)\) | \(e\left(\frac{208}{231}\right)\) | \(e\left(\frac{23}{231}\right)\) | \(e\left(\frac{74}{77}\right)\) | \(e\left(\frac{52}{231}\right)\) | \(e\left(\frac{205}{231}\right)\) | \(e\left(\frac{62}{77}\right)\) | \(e\left(\frac{20}{231}\right)\) |
| \(\chi_{3283}(438,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{64}{77}\right)\) | \(e\left(\frac{184}{231}\right)\) | \(e\left(\frac{51}{77}\right)\) | \(e\left(\frac{86}{231}\right)\) | \(e\left(\frac{145}{231}\right)\) | \(e\left(\frac{38}{77}\right)\) | \(e\left(\frac{137}{231}\right)\) | \(e\left(\frac{47}{231}\right)\) | \(e\left(\frac{36}{77}\right)\) | \(e\left(\frac{106}{231}\right)\) |
| \(\chi_{3283}(473,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{39}{77}\right)\) | \(e\left(\frac{64}{231}\right)\) | \(e\left(\frac{1}{77}\right)\) | \(e\left(\frac{50}{231}\right)\) | \(e\left(\frac{181}{231}\right)\) | \(e\left(\frac{40}{77}\right)\) | \(e\left(\frac{128}{231}\right)\) | \(e\left(\frac{167}{231}\right)\) | \(e\left(\frac{46}{77}\right)\) | \(e\left(\frac{67}{231}\right)\) |
| \(\chi_{3283}(485,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{77}\right)\) | \(e\left(\frac{128}{231}\right)\) | \(e\left(\frac{2}{77}\right)\) | \(e\left(\frac{100}{231}\right)\) | \(e\left(\frac{131}{231}\right)\) | \(e\left(\frac{3}{77}\right)\) | \(e\left(\frac{25}{231}\right)\) | \(e\left(\frac{103}{231}\right)\) | \(e\left(\frac{15}{77}\right)\) | \(e\left(\frac{134}{231}\right)\) |
| \(\chi_{3283}(492,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{40}{77}\right)\) | \(e\left(\frac{38}{231}\right)\) | \(e\left(\frac{3}{77}\right)\) | \(e\left(\frac{73}{231}\right)\) | \(e\left(\frac{158}{231}\right)\) | \(e\left(\frac{43}{77}\right)\) | \(e\left(\frac{76}{231}\right)\) | \(e\left(\frac{193}{231}\right)\) | \(e\left(\frac{61}{77}\right)\) | \(e\left(\frac{47}{231}\right)\) |
| \(\chi_{3283}(529,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{69}{77}\right)\) | \(e\left(\frac{208}{231}\right)\) | \(e\left(\frac{61}{77}\right)\) | \(e\left(\frac{47}{231}\right)\) | \(e\left(\frac{184}{231}\right)\) | \(e\left(\frac{53}{77}\right)\) | \(e\left(\frac{185}{231}\right)\) | \(e\left(\frac{23}{231}\right)\) | \(e\left(\frac{34}{77}\right)\) | \(e\left(\frac{160}{231}\right)\) |
| \(\chi_{3283}(534,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{36}{77}\right)\) | \(e\left(\frac{65}{231}\right)\) | \(e\left(\frac{72}{77}\right)\) | \(e\left(\frac{58}{231}\right)\) | \(e\left(\frac{173}{231}\right)\) | \(e\left(\frac{31}{77}\right)\) | \(e\left(\frac{130}{231}\right)\) | \(e\left(\frac{166}{231}\right)\) | \(e\left(\frac{1}{77}\right)\) | \(e\left(\frac{50}{231}\right)\) |
| \(\chi_{3283}(555,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{77}\right)\) | \(e\left(\frac{89}{231}\right)\) | \(e\left(\frac{5}{77}\right)\) | \(e\left(\frac{19}{231}\right)\) | \(e\left(\frac{212}{231}\right)\) | \(e\left(\frac{46}{77}\right)\) | \(e\left(\frac{178}{231}\right)\) | \(e\left(\frac{142}{231}\right)\) | \(e\left(\frac{76}{77}\right)\) | \(e\left(\frac{104}{231}\right)\) |
| \(\chi_{3283}(571,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{77}\right)\) | \(e\left(\frac{127}{231}\right)\) | \(e\left(\frac{8}{77}\right)\) | \(e\left(\frac{92}{231}\right)\) | \(e\left(\frac{139}{231}\right)\) | \(e\left(\frac{12}{77}\right)\) | \(e\left(\frac{23}{231}\right)\) | \(e\left(\frac{104}{231}\right)\) | \(e\left(\frac{60}{77}\right)\) | \(e\left(\frac{151}{231}\right)\) |
| \(\chi_{3283}(590,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{68}{77}\right)\) | \(e\left(\frac{80}{231}\right)\) | \(e\left(\frac{59}{77}\right)\) | \(e\left(\frac{178}{231}\right)\) | \(e\left(\frac{53}{231}\right)\) | \(e\left(\frac{50}{77}\right)\) | \(e\left(\frac{160}{231}\right)\) | \(e\left(\frac{151}{231}\right)\) | \(e\left(\frac{19}{77}\right)\) | \(e\left(\frac{26}{231}\right)\) |
| \(\chi_{3283}(592,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{45}{77}\right)\) | \(e\left(\frac{139}{231}\right)\) | \(e\left(\frac{13}{77}\right)\) | \(e\left(\frac{188}{231}\right)\) | \(e\left(\frac{43}{231}\right)\) | \(e\left(\frac{58}{77}\right)\) | \(e\left(\frac{47}{231}\right)\) | \(e\left(\frac{92}{231}\right)\) | \(e\left(\frac{59}{77}\right)\) | \(e\left(\frac{178}{231}\right)\) |
| \(\chi_{3283}(709,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{77}\right)\) | \(e\left(\frac{41}{231}\right)\) | \(e\left(\frac{62}{77}\right)\) | \(e\left(\frac{97}{231}\right)\) | \(e\left(\frac{134}{231}\right)\) | \(e\left(\frac{16}{77}\right)\) | \(e\left(\frac{82}{231}\right)\) | \(e\left(\frac{190}{231}\right)\) | \(e\left(\frac{3}{77}\right)\) | \(e\left(\frac{227}{231}\right)\) |
| \(\chi_{3283}(725,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{77}\right)\) | \(e\left(\frac{124}{231}\right)\) | \(e\left(\frac{26}{77}\right)\) | \(e\left(\frac{68}{231}\right)\) | \(e\left(\frac{163}{231}\right)\) | \(e\left(\frac{39}{77}\right)\) | \(e\left(\frac{17}{231}\right)\) | \(e\left(\frac{107}{231}\right)\) | \(e\left(\frac{41}{77}\right)\) | \(e\left(\frac{202}{231}\right)\) |
| \(\chi_{3283}(786,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{77}\right)\) | \(e\left(\frac{185}{231}\right)\) | \(e\left(\frac{45}{77}\right)\) | \(e\left(\frac{94}{231}\right)\) | \(e\left(\frac{137}{231}\right)\) | \(e\left(\frac{29}{77}\right)\) | \(e\left(\frac{139}{231}\right)\) | \(e\left(\frac{46}{231}\right)\) | \(e\left(\frac{68}{77}\right)\) | \(e\left(\frac{89}{231}\right)\) |