from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(14994, base_ring=CyclotomicField(336))
M = H._module
chi = DirichletCharacter(H, M([56,320,147]))
chi.galois_orbit()
[g,chi] = znchar(Mod(11,14994))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(14994\) | |
| Conductor: | \(7497\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(336\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 7497.hp | 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 | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{14994}(11,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{215}{336}\right)\) | \(e\left(\frac{109}{336}\right)\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{197}{336}\right)\) | \(e\left(\frac{47}{168}\right)\) | \(e\left(\frac{335}{336}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{307}{336}\right)\) | \(e\left(\frac{313}{336}\right)\) |
| \(\chi_{14994}(23,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{336}\right)\) | \(e\left(\frac{197}{336}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{205}{336}\right)\) | \(e\left(\frac{31}{168}\right)\) | \(e\left(\frac{103}{336}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{299}{336}\right)\) | \(e\left(\frac{17}{336}\right)\) |
| \(\chi_{14994}(401,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{163}{336}\right)\) | \(e\left(\frac{17}{336}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{265}{336}\right)\) | \(e\left(\frac{163}{168}\right)\) | \(e\left(\frac{43}{336}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{239}{336}\right)\) | \(e\left(\frac{317}{336}\right)\) |
| \(\chi_{14994}(515,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{149}{336}\right)\) | \(e\left(\frac{199}{336}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{335}{336}\right)\) | \(e\left(\frac{149}{168}\right)\) | \(e\left(\frac{29}{336}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{169}{336}\right)\) | \(e\left(\frac{331}{336}\right)\) |
| \(\chi_{14994}(641,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{269}{336}\right)\) | \(e\left(\frac{127}{336}\right)\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{23}{336}\right)\) | \(e\left(\frac{101}{168}\right)\) | \(e\left(\frac{5}{336}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{145}{336}\right)\) | \(e\left(\frac{115}{336}\right)\) |
| \(\chi_{14994}(653,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{139}{336}\right)\) | \(e\left(\frac{233}{336}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{193}{336}\right)\) | \(e\left(\frac{139}{168}\right)\) | \(e\left(\frac{115}{336}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{311}{336}\right)\) | \(e\left(\frac{293}{336}\right)\) |
| \(\chi_{14994}(779,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{169}{336}\right)\) | \(e\left(\frac{131}{336}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{283}{336}\right)\) | \(e\left(\frac{1}{168}\right)\) | \(e\left(\frac{193}{336}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{221}{336}\right)\) | \(e\left(\frac{71}{336}\right)\) |
| \(\chi_{14994}(1031,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{103}{336}\right)\) | \(e\left(\frac{221}{336}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{85}{336}\right)\) | \(e\left(\frac{103}{168}\right)\) | \(e\left(\frac{223}{336}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{83}{336}\right)\) | \(e\left(\frac{89}{336}\right)\) |
| \(\chi_{14994}(1397,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{65}{336}\right)\) | \(e\left(\frac{283}{336}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{83}{336}\right)\) | \(e\left(\frac{65}{168}\right)\) | \(e\left(\frac{281}{336}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{85}{336}\right)\) | \(e\left(\frac{79}{336}\right)\) |
| \(\chi_{14994}(1523,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{227}{336}\right)\) | \(e\left(\frac{1}{336}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{233}{336}\right)\) | \(e\left(\frac{59}{168}\right)\) | \(e\left(\frac{299}{336}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{271}{336}\right)\) | \(e\left(\frac{157}{336}\right)\) |
| \(\chi_{14994}(1535,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{181}{336}\right)\) | \(e\left(\frac{23}{336}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{319}{336}\right)\) | \(e\left(\frac{13}{168}\right)\) | \(e\left(\frac{157}{336}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{185}{336}\right)\) | \(e\left(\frac{251}{336}\right)\) |
| \(\chi_{14994}(1661,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{253}{336}\right)\) | \(e\left(\frac{47}{336}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{199}{336}\right)\) | \(e\left(\frac{85}{168}\right)\) | \(e\left(\frac{277}{336}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{305}{336}\right)\) | \(e\left(\frac{323}{336}\right)\) |
| \(\chi_{14994}(1775,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{299}{336}\right)\) | \(e\left(\frac{25}{336}\right)\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{113}{336}\right)\) | \(e\left(\frac{131}{168}\right)\) | \(e\left(\frac{83}{336}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{55}{336}\right)\) | \(e\left(\frac{229}{336}\right)\) |
| \(\chi_{14994}(1901,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{336}\right)\) | \(e\left(\frac{163}{336}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{11}{336}\right)\) | \(e\left(\frac{41}{168}\right)\) | \(e\left(\frac{17}{336}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{157}{336}\right)\) | \(e\left(\frac{55}{336}\right)\) |
| \(\chi_{14994}(2153,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{336}\right)\) | \(e\left(\frac{61}{336}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{101}{336}\right)\) | \(e\left(\frac{71}{168}\right)\) | \(e\left(\frac{95}{336}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{67}{336}\right)\) | \(e\left(\frac{169}{336}\right)\) |
| \(\chi_{14994}(2165,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{336}\right)\) | \(e\left(\frac{101}{336}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{13}{336}\right)\) | \(e\left(\frac{79}{168}\right)\) | \(e\left(\frac{295}{336}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{155}{336}\right)\) | \(e\left(\frac{65}{336}\right)\) |
| \(\chi_{14994}(2417,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{97}{336}\right)\) | \(e\left(\frac{107}{336}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{67}{336}\right)\) | \(e\left(\frac{97}{168}\right)\) | \(e\left(\frac{73}{336}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{101}{336}\right)\) | \(e\left(\frac{335}{336}\right)\) |
| \(\chi_{14994}(2543,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{211}{336}\right)\) | \(e\left(\frac{257}{336}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{73}{336}\right)\) | \(e\left(\frac{43}{168}\right)\) | \(e\left(\frac{235}{336}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{95}{336}\right)\) | \(e\left(\frac{29}{336}\right)\) |
| \(\chi_{14994}(2657,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{336}\right)\) | \(e\left(\frac{151}{336}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{239}{336}\right)\) | \(e\left(\frac{5}{168}\right)\) | \(e\left(\frac{125}{336}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{265}{336}\right)\) | \(e\left(\frac{187}{336}\right)\) |
| \(\chi_{14994}(2783,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{125}{336}\right)\) | \(e\left(\frac{79}{336}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{263}{336}\right)\) | \(e\left(\frac{125}{168}\right)\) | \(e\left(\frac{101}{336}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{241}{336}\right)\) | \(e\left(\frac{307}{336}\right)\) |
| \(\chi_{14994}(2795,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{187}{336}\right)\) | \(e\left(\frac{137}{336}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{1}{336}\right)\) | \(e\left(\frac{19}{168}\right)\) | \(e\left(\frac{307}{336}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{167}{336}\right)\) | \(e\left(\frac{5}{336}\right)\) |
| \(\chi_{14994}(3173,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{151}{336}\right)\) | \(e\left(\frac{125}{336}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{229}{336}\right)\) | \(e\left(\frac{151}{168}\right)\) | \(e\left(\frac{79}{336}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{275}{336}\right)\) | \(e\left(\frac{137}{336}\right)\) |
| \(\chi_{14994}(3287,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{143}{336}\right)\) | \(e\left(\frac{85}{336}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{317}{336}\right)\) | \(e\left(\frac{143}{168}\right)\) | \(e\left(\frac{215}{336}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{187}{336}\right)\) | \(e\left(\frac{241}{336}\right)\) |
| \(\chi_{14994}(3539,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{257}{336}\right)\) | \(e\left(\frac{235}{336}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{323}{336}\right)\) | \(e\left(\frac{89}{168}\right)\) | \(e\left(\frac{41}{336}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{181}{336}\right)\) | \(e\left(\frac{271}{336}\right)\) |
| \(\chi_{14994}(3665,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{83}{336}\right)\) | \(e\left(\frac{289}{336}\right)\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{137}{336}\right)\) | \(e\left(\frac{83}{168}\right)\) | \(e\left(\frac{59}{336}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{31}{336}\right)\) | \(e\left(\frac{13}{336}\right)\) |
| \(\chi_{14994}(3677,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{229}{336}\right)\) | \(e\left(\frac{263}{336}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{127}{336}\right)\) | \(e\left(\frac{61}{168}\right)\) | \(e\left(\frac{13}{336}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{41}{336}\right)\) | \(e\left(\frac{299}{336}\right)\) |
| \(\chi_{14994}(3917,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{155}{336}\right)\) | \(e\left(\frac{313}{336}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{17}{336}\right)\) | \(e\left(\frac{155}{168}\right)\) | \(e\left(\frac{179}{336}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{151}{336}\right)\) | \(e\left(\frac{85}{336}\right)\) |
| \(\chi_{14994}(4043,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{233}{336}\right)\) | \(e\left(\frac{115}{336}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{251}{336}\right)\) | \(e\left(\frac{65}{168}\right)\) | \(e\left(\frac{113}{336}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{253}{336}\right)\) | \(e\left(\frac{247}{336}\right)\) |
| \(\chi_{14994}(4295,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{263}{336}\right)\) | \(e\left(\frac{13}{336}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{5}{336}\right)\) | \(e\left(\frac{95}{168}\right)\) | \(e\left(\frac{191}{336}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{163}{336}\right)\) | \(e\left(\frac{25}{336}\right)\) |
| \(\chi_{14994}(4307,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{127}{336}\right)\) | \(e\left(\frac{5}{336}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{157}{336}\right)\) | \(e\left(\frac{127}{168}\right)\) | \(e\left(\frac{151}{336}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{11}{336}\right)\) | \(e\left(\frac{113}{336}\right)\) |
| \(\chi_{14994}(4559,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{145}{336}\right)\) | \(e\left(\frac{11}{336}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{211}{336}\right)\) | \(e\left(\frac{145}{168}\right)\) | \(e\left(\frac{265}{336}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{293}{336}\right)\) | \(e\left(\frac{47}{336}\right)\) |