from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, base_ring=CyclotomicField(924))
M = H._module
chi = DirichletCharacter(H, M([154,378,825]))
chi.galois_orbit()
[g,chi] = znchar(Mod(11,6003))
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: | odd | 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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{6003}(11,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{811}{924}\right)\) | \(e\left(\frac{349}{462}\right)\) | \(e\left(\frac{409}{462}\right)\) | \(e\left(\frac{71}{462}\right)\) | \(e\left(\frac{195}{308}\right)\) | \(e\left(\frac{235}{308}\right)\) | \(e\left(\frac{157}{924}\right)\) | \(e\left(\frac{61}{462}\right)\) | \(e\left(\frac{29}{924}\right)\) | \(e\left(\frac{118}{231}\right)\) |
| \(\chi_{6003}(14,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{191}{924}\right)\) | \(e\left(\frac{191}{462}\right)\) | \(e\left(\frac{155}{462}\right)\) | \(e\left(\frac{19}{462}\right)\) | \(e\left(\frac{191}{308}\right)\) | \(e\left(\frac{167}{308}\right)\) | \(e\left(\frac{29}{924}\right)\) | \(e\left(\frac{179}{462}\right)\) | \(e\left(\frac{229}{924}\right)\) | \(e\left(\frac{191}{231}\right)\) |
| \(\chi_{6003}(56,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{901}{924}\right)\) | \(e\left(\frac{439}{462}\right)\) | \(e\left(\frac{349}{462}\right)\) | \(e\left(\frac{317}{462}\right)\) | \(e\left(\frac{285}{308}\right)\) | \(e\left(\frac{225}{308}\right)\) | \(e\left(\frac{727}{924}\right)\) | \(e\left(\frac{409}{462}\right)\) | \(e\left(\frac{611}{924}\right)\) | \(e\left(\frac{208}{231}\right)\) |
| \(\chi_{6003}(113,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{641}{924}\right)\) | \(e\left(\frac{179}{462}\right)\) | \(e\left(\frac{317}{462}\right)\) | \(e\left(\frac{325}{462}\right)\) | \(e\left(\frac{25}{308}\right)\) | \(e\left(\frac{117}{308}\right)\) | \(e\left(\frac{107}{924}\right)\) | \(e\left(\frac{71}{462}\right)\) | \(e\left(\frac{367}{924}\right)\) | \(e\left(\frac{179}{231}\right)\) |
| \(\chi_{6003}(155,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{577}{924}\right)\) | \(e\left(\frac{115}{462}\right)\) | \(e\left(\frac{103}{462}\right)\) | \(e\left(\frac{263}{462}\right)\) | \(e\left(\frac{269}{308}\right)\) | \(e\left(\frac{261}{308}\right)\) | \(e\left(\frac{523}{924}\right)\) | \(e\left(\frac{265}{462}\right)\) | \(e\left(\frac{179}{924}\right)\) | \(e\left(\frac{115}{231}\right)\) |
| \(\chi_{6003}(176,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{383}{924}\right)\) | \(e\left(\frac{383}{462}\right)\) | \(e\left(\frac{335}{462}\right)\) | \(e\left(\frac{205}{462}\right)\) | \(e\left(\frac{75}{308}\right)\) | \(e\left(\frac{43}{308}\right)\) | \(e\left(\frac{629}{924}\right)\) | \(e\left(\frac{59}{462}\right)\) | \(e\left(\frac{793}{924}\right)\) | \(e\left(\frac{152}{231}\right)\) |
| \(\chi_{6003}(182,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{421}{924}\right)\) | \(e\left(\frac{421}{462}\right)\) | \(e\left(\frac{361}{462}\right)\) | \(e\left(\frac{83}{462}\right)\) | \(e\left(\frac{113}{308}\right)\) | \(e\left(\frac{73}{308}\right)\) | \(e\left(\frac{151}{924}\right)\) | \(e\left(\frac{247}{462}\right)\) | \(e\left(\frac{587}{924}\right)\) | \(e\left(\frac{190}{231}\right)\) |
| \(\chi_{6003}(218,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{877}{924}\right)\) | \(e\left(\frac{415}{462}\right)\) | \(e\left(\frac{211}{462}\right)\) | \(e\left(\frac{5}{462}\right)\) | \(e\left(\frac{261}{308}\right)\) | \(e\left(\frac{125}{308}\right)\) | \(e\left(\frac{883}{924}\right)\) | \(e\left(\frac{193}{462}\right)\) | \(e\left(\frac{887}{924}\right)\) | \(e\left(\frac{184}{231}\right)\) |
| \(\chi_{6003}(221,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{125}{924}\right)\) | \(e\left(\frac{125}{462}\right)\) | \(e\left(\frac{353}{462}\right)\) | \(e\left(\frac{85}{462}\right)\) | \(e\left(\frac{125}{308}\right)\) | \(e\left(\frac{277}{308}\right)\) | \(e\left(\frac{227}{924}\right)\) | \(e\left(\frac{47}{462}\right)\) | \(e\left(\frac{295}{924}\right)\) | \(e\left(\frac{125}{231}\right)\) |
| \(\chi_{6003}(263,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{439}{924}\right)\) | \(e\left(\frac{439}{462}\right)\) | \(e\left(\frac{349}{462}\right)\) | \(e\left(\frac{317}{462}\right)\) | \(e\left(\frac{131}{308}\right)\) | \(e\left(\frac{71}{308}\right)\) | \(e\left(\frac{265}{924}\right)\) | \(e\left(\frac{409}{462}\right)\) | \(e\left(\frac{149}{924}\right)\) | \(e\left(\frac{208}{231}\right)\) |
| \(\chi_{6003}(272,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{391}{924}\right)\) | \(e\left(\frac{391}{462}\right)\) | \(e\left(\frac{73}{462}\right)\) | \(e\left(\frac{155}{462}\right)\) | \(e\left(\frac{83}{308}\right)\) | \(e\left(\frac{179}{308}\right)\) | \(e\left(\frac{577}{924}\right)\) | \(e\left(\frac{439}{462}\right)\) | \(e\left(\frac{701}{924}\right)\) | \(e\left(\frac{160}{231}\right)\) |
| \(\chi_{6003}(293,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{599}{924}\right)\) | \(e\left(\frac{137}{462}\right)\) | \(e\left(\frac{191}{462}\right)\) | \(e\left(\frac{241}{462}\right)\) | \(e\left(\frac{291}{308}\right)\) | \(e\left(\frac{19}{308}\right)\) | \(e\left(\frac{149}{924}\right)\) | \(e\left(\frac{155}{462}\right)\) | \(e\left(\frac{157}{924}\right)\) | \(e\left(\frac{137}{231}\right)\) |
| \(\chi_{6003}(329,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{353}{924}\right)\) | \(e\left(\frac{353}{462}\right)\) | \(e\left(\frac{47}{462}\right)\) | \(e\left(\frac{277}{462}\right)\) | \(e\left(\frac{45}{308}\right)\) | \(e\left(\frac{149}{308}\right)\) | \(e\left(\frac{131}{924}\right)\) | \(e\left(\frac{251}{462}\right)\) | \(e\left(\frac{907}{924}\right)\) | \(e\left(\frac{122}{231}\right)\) |
| \(\chi_{6003}(356,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{701}{924}\right)\) | \(e\left(\frac{239}{462}\right)\) | \(e\left(\frac{431}{462}\right)\) | \(e\left(\frac{181}{462}\right)\) | \(e\left(\frac{85}{308}\right)\) | \(e\left(\frac{213}{308}\right)\) | \(e\left(\frac{179}{924}\right)\) | \(e\left(\frac{149}{462}\right)\) | \(e\left(\frac{139}{924}\right)\) | \(e\left(\frac{8}{231}\right)\) |
| \(\chi_{6003}(362,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{247}{924}\right)\) | \(e\left(\frac{247}{462}\right)\) | \(e\left(\frac{169}{462}\right)\) | \(e\left(\frac{131}{462}\right)\) | \(e\left(\frac{247}{308}\right)\) | \(e\left(\frac{195}{308}\right)\) | \(e\left(\frac{589}{924}\right)\) | \(e\left(\frac{67}{462}\right)\) | \(e\left(\frac{509}{924}\right)\) | \(e\left(\frac{16}{231}\right)\) |
| \(\chi_{6003}(398,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{463}{924}\right)\) | \(e\left(\frac{1}{462}\right)\) | \(e\left(\frac{25}{462}\right)\) | \(e\left(\frac{167}{462}\right)\) | \(e\left(\frac{155}{308}\right)\) | \(e\left(\frac{171}{308}\right)\) | \(e\left(\frac{109}{924}\right)\) | \(e\left(\frac{163}{462}\right)\) | \(e\left(\frac{797}{924}\right)\) | \(e\left(\frac{1}{231}\right)\) |
| \(\chi_{6003}(425,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{283}{924}\right)\) | \(e\left(\frac{283}{462}\right)\) | \(e\left(\frac{145}{462}\right)\) | \(e\left(\frac{137}{462}\right)\) | \(e\left(\frac{283}{308}\right)\) | \(e\left(\frac{191}{308}\right)\) | \(e\left(\frac{817}{924}\right)\) | \(e\left(\frac{391}{462}\right)\) | \(e\left(\frac{557}{924}\right)\) | \(e\left(\frac{52}{231}\right)\) |
| \(\chi_{6003}(479,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{457}{924}\right)\) | \(e\left(\frac{457}{462}\right)\) | \(e\left(\frac{337}{462}\right)\) | \(e\left(\frac{89}{462}\right)\) | \(e\left(\frac{149}{308}\right)\) | \(e\left(\frac{69}{308}\right)\) | \(e\left(\frac{379}{924}\right)\) | \(e\left(\frac{109}{462}\right)\) | \(e\left(\frac{635}{924}\right)\) | \(e\left(\frac{226}{231}\right)\) |
| \(\chi_{6003}(536,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{23}{924}\right)\) | \(e\left(\frac{23}{462}\right)\) | \(e\left(\frac{113}{462}\right)\) | \(e\left(\frac{145}{462}\right)\) | \(e\left(\frac{23}{308}\right)\) | \(e\left(\frac{83}{308}\right)\) | \(e\left(\frac{197}{924}\right)\) | \(e\left(\frac{53}{462}\right)\) | \(e\left(\frac{313}{924}\right)\) | \(e\left(\frac{23}{231}\right)\) |
| \(\chi_{6003}(569,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{181}{924}\right)\) | \(e\left(\frac{181}{462}\right)\) | \(e\left(\frac{367}{462}\right)\) | \(e\left(\frac{197}{462}\right)\) | \(e\left(\frac{181}{308}\right)\) | \(e\left(\frac{305}{308}\right)\) | \(e\left(\frac{787}{924}\right)\) | \(e\left(\frac{397}{462}\right)\) | \(e\left(\frac{575}{924}\right)\) | \(e\left(\frac{181}{231}\right)\) |
| \(\chi_{6003}(572,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{827}{924}\right)\) | \(e\left(\frac{365}{462}\right)\) | \(e\left(\frac{347}{462}\right)\) | \(e\left(\frac{433}{462}\right)\) | \(e\left(\frac{211}{308}\right)\) | \(e\left(\frac{199}{308}\right)\) | \(e\left(\frac{53}{924}\right)\) | \(e\left(\frac{359}{462}\right)\) | \(e\left(\frac{769}{924}\right)\) | \(e\left(\frac{134}{231}\right)\) |
| \(\chi_{6003}(590,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{185}{924}\right)\) | \(e\left(\frac{185}{462}\right)\) | \(e\left(\frac{5}{462}\right)\) | \(e\left(\frac{403}{462}\right)\) | \(e\left(\frac{185}{308}\right)\) | \(e\left(\frac{65}{308}\right)\) | \(e\left(\frac{299}{924}\right)\) | \(e\left(\frac{125}{462}\right)\) | \(e\left(\frac{67}{924}\right)\) | \(e\left(\frac{185}{231}\right)\) |
| \(\chi_{6003}(617,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{281}{924}\right)\) | \(e\left(\frac{281}{462}\right)\) | \(e\left(\frac{95}{462}\right)\) | \(e\left(\frac{265}{462}\right)\) | \(e\left(\frac{281}{308}\right)\) | \(e\left(\frac{157}{308}\right)\) | \(e\left(\frac{599}{924}\right)\) | \(e\left(\frac{65}{462}\right)\) | \(e\left(\frac{811}{924}\right)\) | \(e\left(\frac{50}{231}\right)\) |
| \(\chi_{6003}(635,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{389}{924}\right)\) | \(e\left(\frac{389}{462}\right)\) | \(e\left(\frac{23}{462}\right)\) | \(e\left(\frac{283}{462}\right)\) | \(e\left(\frac{81}{308}\right)\) | \(e\left(\frac{145}{308}\right)\) | \(e\left(\frac{359}{924}\right)\) | \(e\left(\frac{113}{462}\right)\) | \(e\left(\frac{31}{924}\right)\) | \(e\left(\frac{158}{231}\right)\) |
| \(\chi_{6003}(641,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{739}{924}\right)\) | \(e\left(\frac{277}{462}\right)\) | \(e\left(\frac{457}{462}\right)\) | \(e\left(\frac{59}{462}\right)\) | \(e\left(\frac{123}{308}\right)\) | \(e\left(\frac{243}{308}\right)\) | \(e\left(\frac{625}{924}\right)\) | \(e\left(\frac{337}{462}\right)\) | \(e\left(\frac{857}{924}\right)\) | \(e\left(\frac{46}{231}\right)\) |
| \(\chi_{6003}(659,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{295}{924}\right)\) | \(e\left(\frac{295}{462}\right)\) | \(e\left(\frac{445}{462}\right)\) | \(e\left(\frac{293}{462}\right)\) | \(e\left(\frac{295}{308}\right)\) | \(e\left(\frac{87}{308}\right)\) | \(e\left(\frac{277}{924}\right)\) | \(e\left(\frac{37}{462}\right)\) | \(e\left(\frac{881}{924}\right)\) | \(e\left(\frac{64}{231}\right)\) |
| \(\chi_{6003}(677,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{241}{924}\right)\) | \(e\left(\frac{241}{462}\right)\) | \(e\left(\frac{19}{462}\right)\) | \(e\left(\frac{53}{462}\right)\) | \(e\left(\frac{241}{308}\right)\) | \(e\left(\frac{93}{308}\right)\) | \(e\left(\frac{859}{924}\right)\) | \(e\left(\frac{13}{462}\right)\) | \(e\left(\frac{347}{924}\right)\) | \(e\left(\frac{10}{231}\right)\) |
| \(\chi_{6003}(686,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{787}{924}\right)\) | \(e\left(\frac{325}{462}\right)\) | \(e\left(\frac{271}{462}\right)\) | \(e\left(\frac{221}{462}\right)\) | \(e\left(\frac{171}{308}\right)\) | \(e\left(\frac{135}{308}\right)\) | \(e\left(\frac{313}{924}\right)\) | \(e\left(\frac{307}{462}\right)\) | \(e\left(\frac{305}{924}\right)\) | \(e\left(\frac{94}{231}\right)\) |
| \(\chi_{6003}(704,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{169}{924}\right)\) | \(e\left(\frac{169}{462}\right)\) | \(e\left(\frac{67}{462}\right)\) | \(e\left(\frac{41}{462}\right)\) | \(e\left(\frac{169}{308}\right)\) | \(e\left(\frac{101}{308}\right)\) | \(e\left(\frac{403}{924}\right)\) | \(e\left(\frac{289}{462}\right)\) | \(e\left(\frac{251}{924}\right)\) | \(e\left(\frac{169}{231}\right)\) |
| \(\chi_{6003}(707,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{335}{924}\right)\) | \(e\left(\frac{335}{462}\right)\) | \(e\left(\frac{59}{462}\right)\) | \(e\left(\frac{43}{462}\right)\) | \(e\left(\frac{27}{308}\right)\) | \(e\left(\frac{151}{308}\right)\) | \(e\left(\frac{17}{924}\right)\) | \(e\left(\frac{89}{462}\right)\) | \(e\left(\frac{421}{924}\right)\) | \(e\left(\frac{104}{231}\right)\) |
| \(\chi_{6003}(743,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{881}{924}\right)\) | \(e\left(\frac{419}{462}\right)\) | \(e\left(\frac{311}{462}\right)\) | \(e\left(\frac{211}{462}\right)\) | \(e\left(\frac{265}{308}\right)\) | \(e\left(\frac{193}{308}\right)\) | \(e\left(\frac{395}{924}\right)\) | \(e\left(\frac{383}{462}\right)\) | \(e\left(\frac{379}{924}\right)\) | \(e\left(\frac{188}{231}\right)\) |