from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2432, base_ring=CyclotomicField(288))
M = H._module
chi = DirichletCharacter(H, M([144,99,64]))
chi.galois_orbit()
[g,chi] = znchar(Mod(35,2432))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(2432\) | |
| Conductor: | \(2432\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(288\) | 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: | $\Q(\zeta_{288})$ |
| Fixed field: | Number field defined by a degree 288 polynomial (not computed) |
First 31 of 96 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{2432}(35,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{121}{288}\right)\) | \(e\left(\frac{259}{288}\right)\) | \(e\left(\frac{13}{48}\right)\) | \(e\left(\frac{121}{144}\right)\) | \(e\left(\frac{37}{96}\right)\) | \(e\left(\frac{77}{288}\right)\) | \(e\left(\frac{23}{72}\right)\) | \(e\left(\frac{61}{72}\right)\) | \(e\left(\frac{199}{288}\right)\) | \(e\left(\frac{109}{144}\right)\) |
| \(\chi_{2432}(43,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{223}{288}\right)\) | \(e\left(\frac{37}{288}\right)\) | \(e\left(\frac{43}{48}\right)\) | \(e\left(\frac{79}{144}\right)\) | \(e\left(\frac{19}{96}\right)\) | \(e\left(\frac{11}{288}\right)\) | \(e\left(\frac{65}{72}\right)\) | \(e\left(\frac{19}{72}\right)\) | \(e\left(\frac{193}{288}\right)\) | \(e\left(\frac{139}{144}\right)\) |
| \(\chi_{2432}(99,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{137}{288}\right)\) | \(e\left(\frac{179}{288}\right)\) | \(e\left(\frac{29}{48}\right)\) | \(e\left(\frac{137}{144}\right)\) | \(e\left(\frac{53}{96}\right)\) | \(e\left(\frac{61}{288}\right)\) | \(e\left(\frac{7}{72}\right)\) | \(e\left(\frac{53}{72}\right)\) | \(e\left(\frac{23}{288}\right)\) | \(e\left(\frac{77}{144}\right)\) |
| \(\chi_{2432}(123,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{107}{288}\right)\) | \(e\left(\frac{41}{288}\right)\) | \(e\left(\frac{23}{48}\right)\) | \(e\left(\frac{107}{144}\right)\) | \(e\left(\frac{47}{96}\right)\) | \(e\left(\frac{199}{288}\right)\) | \(e\left(\frac{37}{72}\right)\) | \(e\left(\frac{23}{72}\right)\) | \(e\left(\frac{245}{288}\right)\) | \(e\left(\frac{119}{144}\right)\) |
| \(\chi_{2432}(131,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{288}\right)\) | \(e\left(\frac{283}{288}\right)\) | \(e\left(\frac{37}{48}\right)\) | \(e\left(\frac{1}{144}\right)\) | \(e\left(\frac{13}{96}\right)\) | \(e\left(\frac{53}{288}\right)\) | \(e\left(\frac{71}{72}\right)\) | \(e\left(\frac{13}{72}\right)\) | \(e\left(\frac{223}{288}\right)\) | \(e\left(\frac{133}{144}\right)\) |
| \(\chi_{2432}(139,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{167}{288}\right)\) | \(e\left(\frac{29}{288}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(e\left(\frac{23}{144}\right)\) | \(e\left(\frac{59}{96}\right)\) | \(e\left(\frac{211}{288}\right)\) | \(e\left(\frac{49}{72}\right)\) | \(e\left(\frac{11}{72}\right)\) | \(e\left(\frac{89}{288}\right)\) | \(e\left(\frac{35}{144}\right)\) |
| \(\chi_{2432}(187,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{283}{288}\right)\) | \(e\left(\frac{25}{288}\right)\) | \(e\left(\frac{7}{48}\right)\) | \(e\left(\frac{139}{144}\right)\) | \(e\left(\frac{31}{96}\right)\) | \(e\left(\frac{23}{288}\right)\) | \(e\left(\frac{5}{72}\right)\) | \(e\left(\frac{7}{72}\right)\) | \(e\left(\frac{37}{288}\right)\) | \(e\left(\frac{55}{144}\right)\) |
| \(\chi_{2432}(195,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{241}{288}\right)\) | \(e\left(\frac{235}{288}\right)\) | \(e\left(\frac{37}{48}\right)\) | \(e\left(\frac{97}{144}\right)\) | \(e\left(\frac{61}{96}\right)\) | \(e\left(\frac{101}{288}\right)\) | \(e\left(\frac{47}{72}\right)\) | \(e\left(\frac{37}{72}\right)\) | \(e\left(\frac{175}{288}\right)\) | \(e\left(\frac{85}{144}\right)\) |
| \(\chi_{2432}(251,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{11}{288}\right)\) | \(e\left(\frac{233}{288}\right)\) | \(e\left(\frac{23}{48}\right)\) | \(e\left(\frac{11}{144}\right)\) | \(e\left(\frac{47}{96}\right)\) | \(e\left(\frac{7}{288}\right)\) | \(e\left(\frac{61}{72}\right)\) | \(e\left(\frac{71}{72}\right)\) | \(e\left(\frac{149}{288}\right)\) | \(e\left(\frac{23}{144}\right)\) |
| \(\chi_{2432}(275,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{125}{288}\right)\) | \(e\left(\frac{239}{288}\right)\) | \(e\left(\frac{17}{48}\right)\) | \(e\left(\frac{125}{144}\right)\) | \(e\left(\frac{89}{96}\right)\) | \(e\left(\frac{1}{288}\right)\) | \(e\left(\frac{19}{72}\right)\) | \(e\left(\frac{41}{72}\right)\) | \(e\left(\frac{227}{288}\right)\) | \(e\left(\frac{65}{144}\right)\) |
| \(\chi_{2432}(283,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{163}{288}\right)\) | \(e\left(\frac{49}{288}\right)\) | \(e\left(\frac{31}{48}\right)\) | \(e\left(\frac{19}{144}\right)\) | \(e\left(\frac{7}{96}\right)\) | \(e\left(\frac{287}{288}\right)\) | \(e\left(\frac{53}{72}\right)\) | \(e\left(\frac{31}{72}\right)\) | \(e\left(\frac{61}{288}\right)\) | \(e\left(\frac{79}{144}\right)\) |
| \(\chi_{2432}(291,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{185}{288}\right)\) | \(e\left(\frac{227}{288}\right)\) | \(e\left(\frac{29}{48}\right)\) | \(e\left(\frac{41}{144}\right)\) | \(e\left(\frac{5}{96}\right)\) | \(e\left(\frac{13}{288}\right)\) | \(e\left(\frac{31}{72}\right)\) | \(e\left(\frac{29}{72}\right)\) | \(e\left(\frac{71}{288}\right)\) | \(e\left(\frac{125}{144}\right)\) |
| \(\chi_{2432}(339,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{13}{288}\right)\) | \(e\left(\frac{223}{288}\right)\) | \(e\left(\frac{1}{48}\right)\) | \(e\left(\frac{13}{144}\right)\) | \(e\left(\frac{73}{96}\right)\) | \(e\left(\frac{113}{288}\right)\) | \(e\left(\frac{59}{72}\right)\) | \(e\left(\frac{25}{72}\right)\) | \(e\left(\frac{19}{288}\right)\) | \(e\left(\frac{1}{144}\right)\) |
| \(\chi_{2432}(347,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{115}{288}\right)\) | \(e\left(\frac{1}{288}\right)\) | \(e\left(\frac{31}{48}\right)\) | \(e\left(\frac{115}{144}\right)\) | \(e\left(\frac{55}{96}\right)\) | \(e\left(\frac{47}{288}\right)\) | \(e\left(\frac{29}{72}\right)\) | \(e\left(\frac{55}{72}\right)\) | \(e\left(\frac{13}{288}\right)\) | \(e\left(\frac{31}{144}\right)\) |
| \(\chi_{2432}(403,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{29}{288}\right)\) | \(e\left(\frac{143}{288}\right)\) | \(e\left(\frac{17}{48}\right)\) | \(e\left(\frac{29}{144}\right)\) | \(e\left(\frac{89}{96}\right)\) | \(e\left(\frac{97}{288}\right)\) | \(e\left(\frac{43}{72}\right)\) | \(e\left(\frac{17}{72}\right)\) | \(e\left(\frac{131}{288}\right)\) | \(e\left(\frac{113}{144}\right)\) |
| \(\chi_{2432}(427,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{287}{288}\right)\) | \(e\left(\frac{5}{288}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{143}{144}\right)\) | \(e\left(\frac{83}{96}\right)\) | \(e\left(\frac{235}{288}\right)\) | \(e\left(\frac{1}{72}\right)\) | \(e\left(\frac{59}{72}\right)\) | \(e\left(\frac{65}{288}\right)\) | \(e\left(\frac{11}{144}\right)\) |
| \(\chi_{2432}(435,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{181}{288}\right)\) | \(e\left(\frac{247}{288}\right)\) | \(e\left(\frac{25}{48}\right)\) | \(e\left(\frac{37}{144}\right)\) | \(e\left(\frac{49}{96}\right)\) | \(e\left(\frac{89}{288}\right)\) | \(e\left(\frac{35}{72}\right)\) | \(e\left(\frac{49}{72}\right)\) | \(e\left(\frac{43}{288}\right)\) | \(e\left(\frac{25}{144}\right)\) |
| \(\chi_{2432}(443,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{59}{288}\right)\) | \(e\left(\frac{281}{288}\right)\) | \(e\left(\frac{23}{48}\right)\) | \(e\left(\frac{59}{144}\right)\) | \(e\left(\frac{95}{96}\right)\) | \(e\left(\frac{247}{288}\right)\) | \(e\left(\frac{13}{72}\right)\) | \(e\left(\frac{47}{72}\right)\) | \(e\left(\frac{197}{288}\right)\) | \(e\left(\frac{71}{144}\right)\) |
| \(\chi_{2432}(491,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{175}{288}\right)\) | \(e\left(\frac{277}{288}\right)\) | \(e\left(\frac{43}{48}\right)\) | \(e\left(\frac{31}{144}\right)\) | \(e\left(\frac{67}{96}\right)\) | \(e\left(\frac{59}{288}\right)\) | \(e\left(\frac{41}{72}\right)\) | \(e\left(\frac{43}{72}\right)\) | \(e\left(\frac{145}{288}\right)\) | \(e\left(\frac{91}{144}\right)\) |
| \(\chi_{2432}(499,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{133}{288}\right)\) | \(e\left(\frac{199}{288}\right)\) | \(e\left(\frac{25}{48}\right)\) | \(e\left(\frac{133}{144}\right)\) | \(e\left(\frac{1}{96}\right)\) | \(e\left(\frac{137}{288}\right)\) | \(e\left(\frac{11}{72}\right)\) | \(e\left(\frac{1}{72}\right)\) | \(e\left(\frac{283}{288}\right)\) | \(e\left(\frac{121}{144}\right)\) |
| \(\chi_{2432}(555,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{191}{288}\right)\) | \(e\left(\frac{197}{288}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{47}{144}\right)\) | \(e\left(\frac{83}{96}\right)\) | \(e\left(\frac{43}{288}\right)\) | \(e\left(\frac{25}{72}\right)\) | \(e\left(\frac{35}{72}\right)\) | \(e\left(\frac{257}{288}\right)\) | \(e\left(\frac{59}{144}\right)\) |
| \(\chi_{2432}(579,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{17}{288}\right)\) | \(e\left(\frac{203}{288}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{17}{144}\right)\) | \(e\left(\frac{29}{96}\right)\) | \(e\left(\frac{37}{288}\right)\) | \(e\left(\frac{55}{72}\right)\) | \(e\left(\frac{5}{72}\right)\) | \(e\left(\frac{47}{288}\right)\) | \(e\left(\frac{101}{144}\right)\) |
| \(\chi_{2432}(587,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{55}{288}\right)\) | \(e\left(\frac{13}{288}\right)\) | \(e\left(\frac{19}{48}\right)\) | \(e\left(\frac{55}{144}\right)\) | \(e\left(\frac{43}{96}\right)\) | \(e\left(\frac{35}{288}\right)\) | \(e\left(\frac{17}{72}\right)\) | \(e\left(\frac{67}{72}\right)\) | \(e\left(\frac{169}{288}\right)\) | \(e\left(\frac{115}{144}\right)\) |
| \(\chi_{2432}(595,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{77}{288}\right)\) | \(e\left(\frac{191}{288}\right)\) | \(e\left(\frac{17}{48}\right)\) | \(e\left(\frac{77}{144}\right)\) | \(e\left(\frac{41}{96}\right)\) | \(e\left(\frac{49}{288}\right)\) | \(e\left(\frac{67}{72}\right)\) | \(e\left(\frac{65}{72}\right)\) | \(e\left(\frac{179}{288}\right)\) | \(e\left(\frac{17}{144}\right)\) |
| \(\chi_{2432}(643,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{193}{288}\right)\) | \(e\left(\frac{187}{288}\right)\) | \(e\left(\frac{37}{48}\right)\) | \(e\left(\frac{49}{144}\right)\) | \(e\left(\frac{13}{96}\right)\) | \(e\left(\frac{149}{288}\right)\) | \(e\left(\frac{23}{72}\right)\) | \(e\left(\frac{61}{72}\right)\) | \(e\left(\frac{127}{288}\right)\) | \(e\left(\frac{37}{144}\right)\) |
| \(\chi_{2432}(651,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{7}{288}\right)\) | \(e\left(\frac{253}{288}\right)\) | \(e\left(\frac{19}{48}\right)\) | \(e\left(\frac{7}{144}\right)\) | \(e\left(\frac{91}{96}\right)\) | \(e\left(\frac{83}{288}\right)\) | \(e\left(\frac{65}{72}\right)\) | \(e\left(\frac{19}{72}\right)\) | \(e\left(\frac{121}{288}\right)\) | \(e\left(\frac{67}{144}\right)\) |
| \(\chi_{2432}(707,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{209}{288}\right)\) | \(e\left(\frac{107}{288}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{65}{144}\right)\) | \(e\left(\frac{29}{96}\right)\) | \(e\left(\frac{133}{288}\right)\) | \(e\left(\frac{7}{72}\right)\) | \(e\left(\frac{53}{72}\right)\) | \(e\left(\frac{239}{288}\right)\) | \(e\left(\frac{5}{144}\right)\) |
| \(\chi_{2432}(731,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{179}{288}\right)\) | \(e\left(\frac{257}{288}\right)\) | \(e\left(\frac{47}{48}\right)\) | \(e\left(\frac{35}{144}\right)\) | \(e\left(\frac{23}{96}\right)\) | \(e\left(\frac{271}{288}\right)\) | \(e\left(\frac{37}{72}\right)\) | \(e\left(\frac{23}{72}\right)\) | \(e\left(\frac{173}{288}\right)\) | \(e\left(\frac{47}{144}\right)\) |
| \(\chi_{2432}(739,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{73}{288}\right)\) | \(e\left(\frac{211}{288}\right)\) | \(e\left(\frac{13}{48}\right)\) | \(e\left(\frac{73}{144}\right)\) | \(e\left(\frac{85}{96}\right)\) | \(e\left(\frac{125}{288}\right)\) | \(e\left(\frac{71}{72}\right)\) | \(e\left(\frac{13}{72}\right)\) | \(e\left(\frac{151}{288}\right)\) | \(e\left(\frac{61}{144}\right)\) |
| \(\chi_{2432}(747,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{239}{288}\right)\) | \(e\left(\frac{245}{288}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{95}{144}\right)\) | \(e\left(\frac{35}{96}\right)\) | \(e\left(\frac{283}{288}\right)\) | \(e\left(\frac{49}{72}\right)\) | \(e\left(\frac{11}{72}\right)\) | \(e\left(\frac{17}{288}\right)\) | \(e\left(\frac{107}{144}\right)\) |
| \(\chi_{2432}(795,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{67}{288}\right)\) | \(e\left(\frac{241}{288}\right)\) | \(e\left(\frac{31}{48}\right)\) | \(e\left(\frac{67}{144}\right)\) | \(e\left(\frac{7}{96}\right)\) | \(e\left(\frac{95}{288}\right)\) | \(e\left(\frac{5}{72}\right)\) | \(e\left(\frac{7}{72}\right)\) | \(e\left(\frac{253}{288}\right)\) | \(e\left(\frac{127}{144}\right)\) |