from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3332, base_ring=CyclotomicField(336))
M = H._module
chi = DirichletCharacter(H, M([0,232,105]))
chi.galois_orbit()
[g,chi] = znchar(Mod(5,3332))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(3332\) | |
Conductor: | \(833\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(336\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from 833.bn | 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: | $\Q(\zeta_{336})$ |
Fixed field: | Number field defined by a degree 336 polynomial (not computed) |
First 31 of 96 characters in Galois orbit
Character | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(23\) | \(25\) | \(27\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{3332}(5,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{336}\right)\) | \(e\left(\frac{197}{336}\right)\) | \(e\left(\frac{1}{168}\right)\) | \(e\left(\frac{271}{336}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{33}{56}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{311}{336}\right)\) | \(e\left(\frac{29}{168}\right)\) | \(e\left(\frac{1}{112}\right)\) |
\(\chi_{3332}(45,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{59}{336}\right)\) | \(e\left(\frac{199}{336}\right)\) | \(e\left(\frac{59}{168}\right)\) | \(e\left(\frac{197}{336}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{43}{56}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{205}{336}\right)\) | \(e\left(\frac{31}{168}\right)\) | \(e\left(\frac{59}{112}\right)\) |
\(\chi_{3332}(61,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{151}{336}\right)\) | \(e\left(\frac{179}{336}\right)\) | \(e\left(\frac{151}{168}\right)\) | \(e\left(\frac{265}{336}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{55}{56}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{257}{336}\right)\) | \(e\left(\frac{11}{168}\right)\) | \(e\left(\frac{39}{112}\right)\) |
\(\chi_{3332}(73,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{65}{336}\right)\) | \(e\left(\frac{37}{336}\right)\) | \(e\left(\frac{65}{168}\right)\) | \(e\left(\frac{143}{336}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{17}{56}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{55}{336}\right)\) | \(e\left(\frac{37}{168}\right)\) | \(e\left(\frac{65}{112}\right)\) |
\(\chi_{3332}(173,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{157}{336}\right)\) | \(e\left(\frac{17}{336}\right)\) | \(e\left(\frac{157}{168}\right)\) | \(e\left(\frac{211}{336}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{29}{56}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{107}{336}\right)\) | \(e\left(\frac{17}{168}\right)\) | \(e\left(\frac{45}{112}\right)\) |
\(\chi_{3332}(201,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{85}{336}\right)\) | \(e\left(\frac{281}{336}\right)\) | \(e\left(\frac{85}{168}\right)\) | \(e\left(\frac{187}{336}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{5}{56}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{227}{336}\right)\) | \(e\left(\frac{113}{168}\right)\) | \(e\left(\frac{85}{112}\right)\) |
\(\chi_{3332}(241,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{269}{336}\right)\) | \(e\left(\frac{241}{336}\right)\) | \(e\left(\frac{101}{168}\right)\) | \(e\left(\frac{323}{336}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{29}{56}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{331}{336}\right)\) | \(e\left(\frac{73}{168}\right)\) | \(e\left(\frac{45}{112}\right)\) |
\(\chi_{3332}(269,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{149}{336}\right)\) | \(e\left(\frac{121}{336}\right)\) | \(e\left(\frac{149}{168}\right)\) | \(e\left(\frac{59}{336}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{45}{56}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{307}{336}\right)\) | \(e\left(\frac{121}{168}\right)\) | \(e\left(\frac{37}{112}\right)\) |
\(\chi_{3332}(369,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{336}\right)\) | \(e\left(\frac{269}{336}\right)\) | \(e\left(\frac{73}{168}\right)\) | \(e\left(\frac{295}{336}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{1}{56}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{191}{336}\right)\) | \(e\left(\frac{101}{168}\right)\) | \(e\left(\frac{73}{112}\right)\) |
\(\chi_{3332}(381,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{336}\right)\) | \(e\left(\frac{187}{336}\right)\) | \(e\left(\frac{47}{168}\right)\) | \(e\left(\frac{305}{336}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{39}{56}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{169}{336}\right)\) | \(e\left(\frac{19}{168}\right)\) | \(e\left(\frac{47}{112}\right)\) |
\(\chi_{3332}(397,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{211}{336}\right)\) | \(e\left(\frac{239}{336}\right)\) | \(e\left(\frac{43}{168}\right)\) | \(e\left(\frac{61}{336}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{19}{56}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{101}{336}\right)\) | \(e\left(\frac{71}{168}\right)\) | \(e\left(\frac{99}{112}\right)\) |
\(\chi_{3332}(437,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{185}{336}\right)\) | \(e\left(\frac{157}{336}\right)\) | \(e\left(\frac{17}{168}\right)\) | \(e\left(\frac{71}{336}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{1}{56}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{79}{336}\right)\) | \(e\left(\frac{157}{168}\right)\) | \(e\left(\frac{73}{112}\right)\) |
\(\chi_{3332}(453,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{235}{336}\right)\) | \(e\left(\frac{263}{336}\right)\) | \(e\left(\frac{67}{168}\right)\) | \(e\left(\frac{181}{336}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{27}{56}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{173}{336}\right)\) | \(e\left(\frac{95}{168}\right)\) | \(e\left(\frac{11}{112}\right)\) |
\(\chi_{3332}(465,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{275}{336}\right)\) | \(e\left(\frac{79}{336}\right)\) | \(e\left(\frac{107}{168}\right)\) | \(e\left(\frac{269}{336}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{3}{56}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{181}{336}\right)\) | \(e\left(\frac{79}{168}\right)\) | \(e\left(\frac{51}{112}\right)\) |
\(\chi_{3332}(481,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{289}{336}\right)\) | \(e\left(\frac{149}{336}\right)\) | \(e\left(\frac{121}{168}\right)\) | \(e\left(\frac{31}{336}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{17}{56}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{167}{336}\right)\) | \(e\left(\frac{149}{168}\right)\) | \(e\left(\frac{65}{112}\right)\) |
\(\chi_{3332}(537,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{103}{336}\right)\) | \(e\left(\frac{131}{336}\right)\) | \(e\left(\frac{103}{168}\right)\) | \(e\left(\frac{25}{336}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{39}{56}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{113}{336}\right)\) | \(e\left(\frac{131}{168}\right)\) | \(e\left(\frac{103}{112}\right)\) |
\(\chi_{3332}(549,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{209}{336}\right)\) | \(e\left(\frac{181}{336}\right)\) | \(e\left(\frac{41}{168}\right)\) | \(e\left(\frac{191}{336}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{9}{56}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{151}{336}\right)\) | \(e\left(\frac{13}{168}\right)\) | \(e\left(\frac{97}{112}\right)\) |
\(\chi_{3332}(605,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{263}{336}\right)\) | \(e\left(\frac{67}{336}\right)\) | \(e\left(\frac{95}{168}\right)\) | \(e\left(\frac{41}{336}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{55}{56}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{145}{336}\right)\) | \(e\left(\frac{67}{168}\right)\) | \(e\left(\frac{39}{112}\right)\) |
\(\chi_{3332}(649,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{109}{336}\right)\) | \(e\left(\frac{305}{336}\right)\) | \(e\left(\frac{109}{168}\right)\) | \(e\left(\frac{307}{336}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{299}{336}\right)\) | \(e\left(\frac{137}{168}\right)\) | \(e\left(\frac{109}{112}\right)\) |
\(\chi_{3332}(677,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{336}\right)\) | \(e\left(\frac{233}{336}\right)\) | \(e\left(\frac{37}{168}\right)\) | \(e\left(\frac{283}{336}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{45}{56}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{83}{336}\right)\) | \(e\left(\frac{65}{168}\right)\) | \(e\left(\frac{37}{112}\right)\) |
\(\chi_{3332}(745,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{293}{336}\right)\) | \(e\left(\frac{265}{336}\right)\) | \(e\left(\frac{125}{168}\right)\) | \(e\left(\frac{107}{336}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{37}{56}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{67}{336}\right)\) | \(e\left(\frac{97}{168}\right)\) | \(e\left(\frac{69}{112}\right)\) |
\(\chi_{3332}(789,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{127}{336}\right)\) | \(e\left(\frac{155}{336}\right)\) | \(e\left(\frac{127}{168}\right)\) | \(e\left(\frac{145}{336}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{47}{56}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{185}{336}\right)\) | \(e\left(\frac{155}{168}\right)\) | \(e\left(\frac{15}{112}\right)\) |
\(\chi_{3332}(845,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{25}{336}\right)\) | \(e\left(\frac{221}{336}\right)\) | \(e\left(\frac{25}{168}\right)\) | \(e\left(\frac{55}{336}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{41}{56}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{47}{336}\right)\) | \(e\left(\frac{53}{168}\right)\) | \(e\left(\frac{25}{112}\right)\) |
\(\chi_{3332}(857,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{191}{336}\right)\) | \(e\left(\frac{331}{336}\right)\) | \(e\left(\frac{23}{168}\right)\) | \(e\left(\frac{17}{336}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{31}{56}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{265}{336}\right)\) | \(e\left(\frac{163}{168}\right)\) | \(e\left(\frac{79}{112}\right)\) |
\(\chi_{3332}(873,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{163}{336}\right)\) | \(e\left(\frac{191}{336}\right)\) | \(e\left(\frac{163}{168}\right)\) | \(e\left(\frac{157}{336}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{3}{56}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{293}{336}\right)\) | \(e\left(\frac{23}{168}\right)\) | \(e\left(\frac{51}{112}\right)\) |
\(\chi_{3332}(929,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{187}{336}\right)\) | \(e\left(\frac{215}{336}\right)\) | \(e\left(\frac{19}{168}\right)\) | \(e\left(\frac{277}{336}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{11}{56}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{29}{336}\right)\) | \(e\left(\frac{47}{168}\right)\) | \(e\left(\frac{75}{112}\right)\) |
\(\chi_{3332}(941,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{83}{336}\right)\) | \(e\left(\frac{223}{336}\right)\) | \(e\left(\frac{83}{168}\right)\) | \(e\left(\frac{317}{336}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{51}{56}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{277}{336}\right)\) | \(e\left(\frac{55}{168}\right)\) | \(e\left(\frac{83}{112}\right)\) |
\(\chi_{3332}(957,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{241}{336}\right)\) | \(e\left(\frac{101}{336}\right)\) | \(e\left(\frac{73}{168}\right)\) | \(e\left(\frac{127}{336}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{1}{56}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{23}{336}\right)\) | \(e\left(\frac{101}{168}\right)\) | \(e\left(\frac{17}{112}\right)\) |
\(\chi_{3332}(997,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{336}\right)\) | \(e\left(\frac{151}{336}\right)\) | \(e\left(\frac{11}{168}\right)\) | \(e\left(\frac{293}{336}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{27}{56}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{61}{336}\right)\) | \(e\left(\frac{151}{168}\right)\) | \(e\left(\frac{11}{112}\right)\) |
\(\chi_{3332}(1013,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{55}{336}\right)\) | \(e\left(\frac{83}{336}\right)\) | \(e\left(\frac{55}{168}\right)\) | \(e\left(\frac{121}{336}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{23}{56}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{305}{336}\right)\) | \(e\left(\frac{83}{168}\right)\) | \(e\left(\frac{55}{112}\right)\) |
\(\chi_{3332}(1025,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{336}\right)\) | \(e\left(\frac{325}{336}\right)\) | \(e\left(\frac{17}{168}\right)\) | \(e\left(\frac{239}{336}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{1}{56}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{247}{336}\right)\) | \(e\left(\frac{157}{168}\right)\) | \(e\left(\frac{17}{112}\right)\) |