from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, base_ring=CyclotomicField(924))
M = H._module
chi = DirichletCharacter(H, M([154,84,33]))
chi.galois_orbit()
[g,chi] = znchar(Mod(2,6003))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(6003\) | |
| Conductor: | \(6003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(924\) | 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: | $\Q(\zeta_{924})$ |
| Fixed field: | Number field defined by a degree 924 polynomial (not computed) |
First 31 of 240 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{6003}(2,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{355}{924}\right)\) | \(e\left(\frac{355}{462}\right)\) | \(e\left(\frac{164}{231}\right)\) | \(e\left(\frac{190}{231}\right)\) | \(e\left(\frac{47}{308}\right)\) | \(e\left(\frac{29}{308}\right)\) | \(e\left(\frac{811}{924}\right)\) | \(e\left(\frac{115}{462}\right)\) | \(e\left(\frac{191}{924}\right)\) | \(e\left(\frac{124}{231}\right)\) |
| \(\chi_{6003}(32,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{851}{924}\right)\) | \(e\left(\frac{389}{462}\right)\) | \(e\left(\frac{127}{231}\right)\) | \(e\left(\frac{26}{231}\right)\) | \(e\left(\frac{235}{308}\right)\) | \(e\left(\frac{145}{308}\right)\) | \(e\left(\frac{359}{924}\right)\) | \(e\left(\frac{113}{462}\right)\) | \(e\left(\frac{31}{924}\right)\) | \(e\left(\frac{158}{231}\right)\) |
| \(\chi_{6003}(50,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{743}{924}\right)\) | \(e\left(\frac{281}{462}\right)\) | \(e\left(\frac{163}{231}\right)\) | \(e\left(\frac{17}{231}\right)\) | \(e\left(\frac{127}{308}\right)\) | \(e\left(\frac{157}{308}\right)\) | \(e\left(\frac{599}{924}\right)\) | \(e\left(\frac{65}{462}\right)\) | \(e\left(\frac{811}{924}\right)\) | \(e\left(\frac{50}{231}\right)\) |
| \(\chi_{6003}(77,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{647}{924}\right)\) | \(e\left(\frac{185}{462}\right)\) | \(e\left(\frac{118}{231}\right)\) | \(e\left(\frac{86}{231}\right)\) | \(e\left(\frac{31}{308}\right)\) | \(e\left(\frac{65}{308}\right)\) | \(e\left(\frac{299}{924}\right)\) | \(e\left(\frac{125}{462}\right)\) | \(e\left(\frac{67}{924}\right)\) | \(e\left(\frac{185}{231}\right)\) |
| \(\chi_{6003}(95,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{365}{924}\right)\) | \(e\left(\frac{365}{462}\right)\) | \(e\left(\frac{58}{231}\right)\) | \(e\left(\frac{101}{231}\right)\) | \(e\left(\frac{57}{308}\right)\) | \(e\left(\frac{199}{308}\right)\) | \(e\left(\frac{53}{924}\right)\) | \(e\left(\frac{359}{462}\right)\) | \(e\left(\frac{769}{924}\right)\) | \(e\left(\frac{134}{231}\right)\) |
| \(\chi_{6003}(101,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{499}{924}\right)\) | \(e\left(\frac{37}{462}\right)\) | \(e\left(\frac{116}{231}\right)\) | \(e\left(\frac{202}{231}\right)\) | \(e\left(\frac{191}{308}\right)\) | \(e\left(\frac{13}{308}\right)\) | \(e\left(\frac{799}{924}\right)\) | \(e\left(\frac{25}{462}\right)\) | \(e\left(\frac{383}{924}\right)\) | \(e\left(\frac{37}{231}\right)\) |
| \(\chi_{6003}(119,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{655}{924}\right)\) | \(e\left(\frac{193}{462}\right)\) | \(e\left(\frac{218}{231}\right)\) | \(e\left(\frac{61}{231}\right)\) | \(e\left(\frac{39}{308}\right)\) | \(e\left(\frac{201}{308}\right)\) | \(e\left(\frac{247}{924}\right)\) | \(e\left(\frac{43}{462}\right)\) | \(e\left(\frac{899}{924}\right)\) | \(e\left(\frac{193}{231}\right)\) |
| \(\chi_{6003}(131,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{485}{924}\right)\) | \(e\left(\frac{23}{462}\right)\) | \(e\left(\frac{172}{231}\right)\) | \(e\left(\frac{188}{231}\right)\) | \(e\left(\frac{177}{308}\right)\) | \(e\left(\frac{83}{308}\right)\) | \(e\left(\frac{197}{924}\right)\) | \(e\left(\frac{53}{462}\right)\) | \(e\left(\frac{313}{924}\right)\) | \(e\left(\frac{23}{231}\right)\) |
| \(\chi_{6003}(164,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{871}{924}\right)\) | \(e\left(\frac{409}{462}\right)\) | \(e\left(\frac{146}{231}\right)\) | \(e\left(\frac{79}{231}\right)\) | \(e\left(\frac{255}{308}\right)\) | \(e\left(\frac{177}{308}\right)\) | \(e\left(\frac{691}{924}\right)\) | \(e\left(\frac{139}{462}\right)\) | \(e\left(\frac{263}{924}\right)\) | \(e\left(\frac{178}{231}\right)\) |
| \(\chi_{6003}(200,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{529}{924}\right)\) | \(e\left(\frac{67}{462}\right)\) | \(e\left(\frac{29}{231}\right)\) | \(e\left(\frac{166}{231}\right)\) | \(e\left(\frac{221}{308}\right)\) | \(e\left(\frac{215}{308}\right)\) | \(e\left(\frac{373}{924}\right)\) | \(e\left(\frac{295}{462}\right)\) | \(e\left(\frac{269}{924}\right)\) | \(e\left(\frac{67}{231}\right)\) |
| \(\chi_{6003}(308,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{433}{924}\right)\) | \(e\left(\frac{433}{462}\right)\) | \(e\left(\frac{215}{231}\right)\) | \(e\left(\frac{4}{231}\right)\) | \(e\left(\frac{125}{308}\right)\) | \(e\left(\frac{123}{308}\right)\) | \(e\left(\frac{73}{924}\right)\) | \(e\left(\frac{355}{462}\right)\) | \(e\left(\frac{449}{924}\right)\) | \(e\left(\frac{202}{231}\right)\) |
| \(\chi_{6003}(311,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{239}{924}\right)\) | \(e\left(\frac{239}{462}\right)\) | \(e\left(\frac{100}{231}\right)\) | \(e\left(\frac{206}{231}\right)\) | \(e\left(\frac{239}{308}\right)\) | \(e\left(\frac{213}{308}\right)\) | \(e\left(\frac{179}{924}\right)\) | \(e\left(\frac{149}{462}\right)\) | \(e\left(\frac{139}{924}\right)\) | \(e\left(\frac{8}{231}\right)\) |
| \(\chi_{6003}(317,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{733}{924}\right)\) | \(e\left(\frac{271}{462}\right)\) | \(e\left(\frac{38}{231}\right)\) | \(e\left(\frac{106}{231}\right)\) | \(e\left(\frac{117}{308}\right)\) | \(e\left(\frac{295}{308}\right)\) | \(e\left(\frac{433}{924}\right)\) | \(e\left(\frac{283}{462}\right)\) | \(e\left(\frac{233}{924}\right)\) | \(e\left(\frac{40}{231}\right)\) |
| \(\chi_{6003}(338,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{815}{924}\right)\) | \(e\left(\frac{353}{462}\right)\) | \(e\left(\frac{139}{231}\right)\) | \(e\left(\frac{23}{231}\right)\) | \(e\left(\frac{199}{308}\right)\) | \(e\left(\frac{149}{308}\right)\) | \(e\left(\frac{131}{924}\right)\) | \(e\left(\frac{251}{462}\right)\) | \(e\left(\frac{907}{924}\right)\) | \(e\left(\frac{122}{231}\right)\) |
| \(\chi_{6003}(374,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{137}{924}\right)\) | \(e\left(\frac{137}{462}\right)\) | \(e\left(\frac{211}{231}\right)\) | \(e\left(\frac{5}{231}\right)\) | \(e\left(\frac{137}{308}\right)\) | \(e\left(\frac{19}{308}\right)\) | \(e\left(\frac{149}{924}\right)\) | \(e\left(\frac{155}{462}\right)\) | \(e\left(\frac{157}{924}\right)\) | \(e\left(\frac{137}{231}\right)\) |
| \(\chi_{6003}(380,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{151}{924}\right)\) | \(e\left(\frac{151}{462}\right)\) | \(e\left(\frac{155}{231}\right)\) | \(e\left(\frac{19}{231}\right)\) | \(e\left(\frac{151}{308}\right)\) | \(e\left(\frac{257}{308}\right)\) | \(e\left(\frac{751}{924}\right)\) | \(e\left(\frac{127}{462}\right)\) | \(e\left(\frac{227}{924}\right)\) | \(e\left(\frac{151}{231}\right)\) |
| \(\chi_{6003}(416,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{157}{924}\right)\) | \(e\left(\frac{157}{462}\right)\) | \(e\left(\frac{230}{231}\right)\) | \(e\left(\frac{58}{231}\right)\) | \(e\left(\frac{157}{308}\right)\) | \(e\left(\frac{51}{308}\right)\) | \(e\left(\frac{481}{924}\right)\) | \(e\left(\frac{181}{462}\right)\) | \(e\left(\frac{389}{924}\right)\) | \(e\left(\frac{157}{231}\right)\) |
| \(\chi_{6003}(443,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{841}{924}\right)\) | \(e\left(\frac{379}{462}\right)\) | \(e\left(\frac{2}{231}\right)\) | \(e\left(\frac{115}{231}\right)\) | \(e\left(\frac{225}{308}\right)\) | \(e\left(\frac{283}{308}\right)\) | \(e\left(\frac{193}{924}\right)\) | \(e\left(\frac{331}{462}\right)\) | \(e\left(\frac{377}{924}\right)\) | \(e\left(\frac{148}{231}\right)\) |
| \(\chi_{6003}(446,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{587}{924}\right)\) | \(e\left(\frac{125}{462}\right)\) | \(e\left(\frac{61}{231}\right)\) | \(e\left(\frac{158}{231}\right)\) | \(e\left(\frac{279}{308}\right)\) | \(e\left(\frac{277}{308}\right)\) | \(e\left(\frac{227}{924}\right)\) | \(e\left(\frac{47}{462}\right)\) | \(e\left(\frac{295}{924}\right)\) | \(e\left(\frac{125}{231}\right)\) |
| \(\chi_{6003}(491,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{845}{924}\right)\) | \(e\left(\frac{383}{462}\right)\) | \(e\left(\frac{52}{231}\right)\) | \(e\left(\frac{218}{231}\right)\) | \(e\left(\frac{229}{308}\right)\) | \(e\left(\frac{43}{308}\right)\) | \(e\left(\frac{629}{924}\right)\) | \(e\left(\frac{59}{462}\right)\) | \(e\left(\frac{793}{924}\right)\) | \(e\left(\frac{152}{231}\right)\) |
| \(\chi_{6003}(524,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{271}{924}\right)\) | \(e\left(\frac{271}{462}\right)\) | \(e\left(\frac{38}{231}\right)\) | \(e\left(\frac{106}{231}\right)\) | \(e\left(\frac{271}{308}\right)\) | \(e\left(\frac{141}{308}\right)\) | \(e\left(\frac{895}{924}\right)\) | \(e\left(\frac{283}{462}\right)\) | \(e\left(\frac{695}{924}\right)\) | \(e\left(\frac{40}{231}\right)\) |
| \(\chi_{6003}(533,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{391}{924}\right)\) | \(e\left(\frac{391}{462}\right)\) | \(e\left(\frac{152}{231}\right)\) | \(e\left(\frac{193}{231}\right)\) | \(e\left(\frac{83}{308}\right)\) | \(e\left(\frac{25}{308}\right)\) | \(e\left(\frac{115}{924}\right)\) | \(e\left(\frac{439}{462}\right)\) | \(e\left(\frac{239}{924}\right)\) | \(e\left(\frac{160}{231}\right)\) |
| \(\chi_{6003}(554,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{179}{924}\right)\) | \(e\left(\frac{179}{462}\right)\) | \(e\left(\frac{43}{231}\right)\) | \(e\left(\frac{47}{231}\right)\) | \(e\left(\frac{179}{308}\right)\) | \(e\left(\frac{117}{308}\right)\) | \(e\left(\frac{107}{924}\right)\) | \(e\left(\frac{71}{462}\right)\) | \(e\left(\frac{367}{924}\right)\) | \(e\left(\frac{179}{231}\right)\) |
| \(\chi_{6003}(578,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{145}{924}\right)\) | \(e\left(\frac{145}{462}\right)\) | \(e\left(\frac{80}{231}\right)\) | \(e\left(\frac{211}{231}\right)\) | \(e\left(\frac{145}{308}\right)\) | \(e\left(\frac{155}{308}\right)\) | \(e\left(\frac{97}{924}\right)\) | \(e\left(\frac{73}{462}\right)\) | \(e\left(\frac{65}{924}\right)\) | \(e\left(\frac{145}{231}\right)\) |
| \(\chi_{6003}(623,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{751}{924}\right)\) | \(e\left(\frac{289}{462}\right)\) | \(e\left(\frac{32}{231}\right)\) | \(e\left(\frac{223}{231}\right)\) | \(e\left(\frac{135}{308}\right)\) | \(e\left(\frac{293}{308}\right)\) | \(e\left(\frac{547}{924}\right)\) | \(e\left(\frac{445}{462}\right)\) | \(e\left(\frac{719}{924}\right)\) | \(e\left(\frac{58}{231}\right)\) |
| \(\chi_{6003}(653,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{653}{924}\right)\) | \(e\left(\frac{191}{462}\right)\) | \(e\left(\frac{193}{231}\right)\) | \(e\left(\frac{125}{231}\right)\) | \(e\left(\frac{37}{308}\right)\) | \(e\left(\frac{167}{308}\right)\) | \(e\left(\frac{29}{924}\right)\) | \(e\left(\frac{179}{462}\right)\) | \(e\left(\frac{229}{924}\right)\) | \(e\left(\frac{191}{231}\right)\) |
| \(\chi_{6003}(698,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{383}{924}\right)\) | \(e\left(\frac{383}{462}\right)\) | \(e\left(\frac{52}{231}\right)\) | \(e\left(\frac{218}{231}\right)\) | \(e\left(\frac{75}{308}\right)\) | \(e\left(\frac{197}{308}\right)\) | \(e\left(\frac{167}{924}\right)\) | \(e\left(\frac{59}{462}\right)\) | \(e\left(\frac{331}{924}\right)\) | \(e\left(\frac{152}{231}\right)\) |
| \(\chi_{6003}(722,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{697}{924}\right)\) | \(e\left(\frac{235}{462}\right)\) | \(e\left(\frac{50}{231}\right)\) | \(e\left(\frac{103}{231}\right)\) | \(e\left(\frac{81}{308}\right)\) | \(e\left(\frac{299}{308}\right)\) | \(e\left(\frac{205}{924}\right)\) | \(e\left(\frac{421}{462}\right)\) | \(e\left(\frac{185}{924}\right)\) | \(e\left(\frac{4}{231}\right)\) |
| \(\chi_{6003}(740,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{457}{924}\right)\) | \(e\left(\frac{457}{462}\right)\) | \(e\left(\frac{53}{231}\right)\) | \(e\left(\frac{160}{231}\right)\) | \(e\left(\frac{149}{308}\right)\) | \(e\left(\frac{223}{308}\right)\) | \(e\left(\frac{841}{924}\right)\) | \(e\left(\frac{109}{462}\right)\) | \(e\left(\frac{173}{924}\right)\) | \(e\left(\frac{226}{231}\right)\) |
| \(\chi_{6003}(752,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{924}\right)\) | \(e\left(\frac{89}{462}\right)\) | \(e\left(\frac{73}{231}\right)\) | \(e\left(\frac{155}{231}\right)\) | \(e\left(\frac{89}{308}\right)\) | \(e\left(\frac{127}{308}\right)\) | \(e\left(\frac{461}{924}\right)\) | \(e\left(\frac{185}{462}\right)\) | \(e\left(\frac{709}{924}\right)\) | \(e\left(\frac{89}{231}\right)\) |
| \(\chi_{6003}(785,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{607}{924}\right)\) | \(e\left(\frac{145}{462}\right)\) | \(e\left(\frac{80}{231}\right)\) | \(e\left(\frac{211}{231}\right)\) | \(e\left(\frac{299}{308}\right)\) | \(e\left(\frac{1}{308}\right)\) | \(e\left(\frac{559}{924}\right)\) | \(e\left(\frac{73}{462}\right)\) | \(e\left(\frac{527}{924}\right)\) | \(e\left(\frac{145}{231}\right)\) |