from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3267, base_ring=CyclotomicField(990))
M = H._module
chi = DirichletCharacter(H, M([55,9]))
chi.galois_orbit()
[g,chi] = znchar(Mod(2,3267))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(3267\) | |
| Conductor: | \(3267\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(990\) | 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: | $\Q(\zeta_{495})$ |
| Fixed field: | Number field defined by a degree 990 polynomial (not computed) |
First 31 of 240 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{3267}(2,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{32}{495}\right)\) | \(e\left(\frac{64}{495}\right)\) | \(e\left(\frac{941}{990}\right)\) | \(e\left(\frac{943}{990}\right)\) | \(e\left(\frac{32}{165}\right)\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{359}{990}\right)\) | \(e\left(\frac{17}{990}\right)\) | \(e\left(\frac{128}{495}\right)\) | \(e\left(\frac{46}{165}\right)\) |
| \(\chi_{3267}(29,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{104}{495}\right)\) | \(e\left(\frac{208}{495}\right)\) | \(e\left(\frac{707}{990}\right)\) | \(e\left(\frac{961}{990}\right)\) | \(e\left(\frac{104}{165}\right)\) | \(e\left(\frac{61}{66}\right)\) | \(e\left(\frac{53}{990}\right)\) | \(e\left(\frac{179}{990}\right)\) | \(e\left(\frac{416}{495}\right)\) | \(e\left(\frac{67}{165}\right)\) |
| \(\chi_{3267}(41,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{76}{495}\right)\) | \(e\left(\frac{152}{495}\right)\) | \(e\left(\frac{193}{990}\right)\) | \(e\left(\frac{569}{990}\right)\) | \(e\left(\frac{76}{165}\right)\) | \(e\left(\frac{23}{66}\right)\) | \(e\left(\frac{667}{990}\right)\) | \(e\left(\frac{721}{990}\right)\) | \(e\left(\frac{304}{495}\right)\) | \(e\left(\frac{68}{165}\right)\) |
| \(\chi_{3267}(50,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{478}{495}\right)\) | \(e\left(\frac{461}{495}\right)\) | \(e\left(\frac{289}{990}\right)\) | \(e\left(\frac{257}{990}\right)\) | \(e\left(\frac{148}{165}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{691}{990}\right)\) | \(e\left(\frac{223}{990}\right)\) | \(e\left(\frac{427}{495}\right)\) | \(e\left(\frac{89}{165}\right)\) |
| \(\chi_{3267}(68,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{202}{495}\right)\) | \(e\left(\frac{404}{495}\right)\) | \(e\left(\frac{31}{990}\right)\) | \(e\left(\frac{353}{990}\right)\) | \(e\left(\frac{37}{165}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{379}{990}\right)\) | \(e\left(\frac{757}{990}\right)\) | \(e\left(\frac{313}{495}\right)\) | \(e\left(\frac{146}{165}\right)\) |
| \(\chi_{3267}(74,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{386}{495}\right)\) | \(e\left(\frac{277}{495}\right)\) | \(e\left(\frac{863}{990}\right)\) | \(e\left(\frac{949}{990}\right)\) | \(e\left(\frac{56}{165}\right)\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{587}{990}\right)\) | \(e\left(\frac{731}{990}\right)\) | \(e\left(\frac{59}{495}\right)\) | \(e\left(\frac{163}{165}\right)\) |
| \(\chi_{3267}(83,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{158}{495}\right)\) | \(e\left(\frac{316}{495}\right)\) | \(e\left(\frac{779}{990}\right)\) | \(e\left(\frac{727}{990}\right)\) | \(e\left(\frac{158}{165}\right)\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{71}{990}\right)\) | \(e\left(\frac{53}{990}\right)\) | \(e\left(\frac{137}{495}\right)\) | \(e\left(\frac{124}{165}\right)\) |
| \(\chi_{3267}(95,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{184}{495}\right)\) | \(e\left(\frac{368}{495}\right)\) | \(e\left(\frac{337}{990}\right)\) | \(e\left(\frac{101}{990}\right)\) | \(e\left(\frac{19}{165}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{703}{990}\right)\) | \(e\left(\frac{469}{990}\right)\) | \(e\left(\frac{241}{495}\right)\) | \(e\left(\frac{17}{165}\right)\) |
| \(\chi_{3267}(101,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{287}{495}\right)\) | \(e\left(\frac{79}{495}\right)\) | \(e\left(\frac{71}{990}\right)\) | \(e\left(\frac{553}{990}\right)\) | \(e\left(\frac{122}{165}\right)\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{389}{990}\right)\) | \(e\left(\frac{137}{990}\right)\) | \(e\left(\frac{158}{495}\right)\) | \(e\left(\frac{31}{165}\right)\) |
| \(\chi_{3267}(128,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{224}{495}\right)\) | \(e\left(\frac{448}{495}\right)\) | \(e\left(\frac{647}{990}\right)\) | \(e\left(\frac{661}{990}\right)\) | \(e\left(\frac{59}{165}\right)\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{533}{990}\right)\) | \(e\left(\frac{119}{990}\right)\) | \(e\left(\frac{401}{495}\right)\) | \(e\left(\frac{157}{165}\right)\) |
| \(\chi_{3267}(140,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{16}{495}\right)\) | \(e\left(\frac{32}{495}\right)\) | \(e\left(\frac{223}{990}\right)\) | \(e\left(\frac{719}{990}\right)\) | \(e\left(\frac{16}{165}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{427}{990}\right)\) | \(e\left(\frac{751}{990}\right)\) | \(e\left(\frac{64}{495}\right)\) | \(e\left(\frac{23}{165}\right)\) |
| \(\chi_{3267}(149,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{495}\right)\) | \(e\left(\frac{26}{495}\right)\) | \(e\left(\frac{769}{990}\right)\) | \(e\left(\frac{677}{990}\right)\) | \(e\left(\frac{13}{165}\right)\) | \(e\left(\frac{53}{66}\right)\) | \(e\left(\frac{811}{990}\right)\) | \(e\left(\frac{703}{990}\right)\) | \(e\left(\frac{52}{495}\right)\) | \(e\left(\frac{29}{165}\right)\) |
| \(\chi_{3267}(167,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{457}{495}\right)\) | \(e\left(\frac{419}{495}\right)\) | \(e\left(\frac{151}{990}\right)\) | \(e\left(\frac{953}{990}\right)\) | \(e\left(\frac{127}{165}\right)\) | \(e\left(\frac{5}{66}\right)\) | \(e\left(\frac{409}{990}\right)\) | \(e\left(\frac{877}{990}\right)\) | \(e\left(\frac{343}{495}\right)\) | \(e\left(\frac{131}{165}\right)\) |
| \(\chi_{3267}(173,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{326}{495}\right)\) | \(e\left(\frac{157}{495}\right)\) | \(e\left(\frac{893}{990}\right)\) | \(e\left(\frac{109}{990}\right)\) | \(e\left(\frac{161}{165}\right)\) | \(e\left(\frac{37}{66}\right)\) | \(e\left(\frac{347}{990}\right)\) | \(e\left(\frac{761}{990}\right)\) | \(e\left(\frac{314}{495}\right)\) | \(e\left(\frac{118}{165}\right)\) |
| \(\chi_{3267}(182,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{188}{495}\right)\) | \(e\left(\frac{376}{495}\right)\) | \(e\left(\frac{269}{990}\right)\) | \(e\left(\frac{157}{990}\right)\) | \(e\left(\frac{23}{165}\right)\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{191}{990}\right)\) | \(e\left(\frac{533}{990}\right)\) | \(e\left(\frac{257}{495}\right)\) | \(e\left(\frac{64}{165}\right)\) |
| \(\chi_{3267}(194,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{304}{495}\right)\) | \(e\left(\frac{113}{495}\right)\) | \(e\left(\frac{277}{990}\right)\) | \(e\left(\frac{791}{990}\right)\) | \(e\left(\frac{139}{165}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{193}{990}\right)\) | \(e\left(\frac{409}{990}\right)\) | \(e\left(\frac{226}{495}\right)\) | \(e\left(\frac{107}{165}\right)\) |
| \(\chi_{3267}(200,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{495}\right)\) | \(e\left(\frac{94}{495}\right)\) | \(e\left(\frac{191}{990}\right)\) | \(e\left(\frac{163}{990}\right)\) | \(e\left(\frac{47}{165}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{419}{990}\right)\) | \(e\left(\frac{257}{990}\right)\) | \(e\left(\frac{188}{495}\right)\) | \(e\left(\frac{16}{165}\right)\) |
| \(\chi_{3267}(227,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{344}{495}\right)\) | \(e\left(\frac{193}{495}\right)\) | \(e\left(\frac{587}{990}\right)\) | \(e\left(\frac{361}{990}\right)\) | \(e\left(\frac{14}{165}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{23}{990}\right)\) | \(e\left(\frac{59}{990}\right)\) | \(e\left(\frac{386}{495}\right)\) | \(e\left(\frac{82}{165}\right)\) |
| \(\chi_{3267}(248,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{495}\right)\) | \(e\left(\frac{86}{495}\right)\) | \(e\left(\frac{259}{990}\right)\) | \(e\left(\frac{107}{990}\right)\) | \(e\left(\frac{43}{165}\right)\) | \(e\left(\frac{23}{66}\right)\) | \(e\left(\frac{931}{990}\right)\) | \(e\left(\frac{193}{990}\right)\) | \(e\left(\frac{172}{495}\right)\) | \(e\left(\frac{134}{165}\right)\) |
| \(\chi_{3267}(266,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{217}{495}\right)\) | \(e\left(\frac{434}{495}\right)\) | \(e\left(\frac{271}{990}\right)\) | \(e\left(\frac{563}{990}\right)\) | \(e\left(\frac{52}{165}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{439}{990}\right)\) | \(e\left(\frac{7}{990}\right)\) | \(e\left(\frac{373}{495}\right)\) | \(e\left(\frac{116}{165}\right)\) |
| \(\chi_{3267}(272,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{266}{495}\right)\) | \(e\left(\frac{37}{495}\right)\) | \(e\left(\frac{923}{990}\right)\) | \(e\left(\frac{259}{990}\right)\) | \(e\left(\frac{101}{165}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{107}{990}\right)\) | \(e\left(\frac{791}{990}\right)\) | \(e\left(\frac{74}{495}\right)\) | \(e\left(\frac{73}{165}\right)\) |
| \(\chi_{3267}(281,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{218}{495}\right)\) | \(e\left(\frac{436}{495}\right)\) | \(e\left(\frac{749}{990}\right)\) | \(e\left(\frac{577}{990}\right)\) | \(e\left(\frac{53}{165}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{311}{990}\right)\) | \(e\left(\frac{23}{990}\right)\) | \(e\left(\frac{377}{495}\right)\) | \(e\left(\frac{4}{165}\right)\) |
| \(\chi_{3267}(293,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{424}{495}\right)\) | \(e\left(\frac{353}{495}\right)\) | \(e\left(\frac{217}{990}\right)\) | \(e\left(\frac{491}{990}\right)\) | \(e\left(\frac{94}{165}\right)\) | \(e\left(\frac{5}{66}\right)\) | \(e\left(\frac{673}{990}\right)\) | \(e\left(\frac{349}{990}\right)\) | \(e\left(\frac{211}{495}\right)\) | \(e\left(\frac{32}{165}\right)\) |
| \(\chi_{3267}(299,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{302}{495}\right)\) | \(e\left(\frac{109}{495}\right)\) | \(e\left(\frac{311}{990}\right)\) | \(e\left(\frac{763}{990}\right)\) | \(e\left(\frac{137}{165}\right)\) | \(e\left(\frac{61}{66}\right)\) | \(e\left(\frac{449}{990}\right)\) | \(e\left(\frac{377}{990}\right)\) | \(e\left(\frac{218}{495}\right)\) | \(e\left(\frac{1}{165}\right)\) |
| \(\chi_{3267}(326,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{464}{495}\right)\) | \(e\left(\frac{433}{495}\right)\) | \(e\left(\frac{527}{990}\right)\) | \(e\left(\frac{61}{990}\right)\) | \(e\left(\frac{134}{165}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{503}{990}\right)\) | \(e\left(\frac{989}{990}\right)\) | \(e\left(\frac{371}{495}\right)\) | \(e\left(\frac{7}{165}\right)\) |
| \(\chi_{3267}(338,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{391}{495}\right)\) | \(e\left(\frac{287}{495}\right)\) | \(e\left(\frac{283}{990}\right)\) | \(e\left(\frac{29}{990}\right)\) | \(e\left(\frac{61}{165}\right)\) | \(e\left(\frac{5}{66}\right)\) | \(e\left(\frac{937}{990}\right)\) | \(e\left(\frac{811}{990}\right)\) | \(e\left(\frac{79}{495}\right)\) | \(e\left(\frac{98}{165}\right)\) |
| \(\chi_{3267}(347,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{495}\right)\) | \(e\left(\frac{146}{495}\right)\) | \(e\left(\frac{739}{990}\right)\) | \(e\left(\frac{527}{990}\right)\) | \(e\left(\frac{73}{165}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{61}{990}\right)\) | \(e\left(\frac{673}{990}\right)\) | \(e\left(\frac{292}{495}\right)\) | \(e\left(\frac{74}{165}\right)\) |
| \(\chi_{3267}(365,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{472}{495}\right)\) | \(e\left(\frac{449}{495}\right)\) | \(e\left(\frac{391}{990}\right)\) | \(e\left(\frac{173}{990}\right)\) | \(e\left(\frac{142}{165}\right)\) | \(e\left(\frac{23}{66}\right)\) | \(e\left(\frac{469}{990}\right)\) | \(e\left(\frac{127}{990}\right)\) | \(e\left(\frac{403}{495}\right)\) | \(e\left(\frac{101}{165}\right)\) |
| \(\chi_{3267}(371,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{206}{495}\right)\) | \(e\left(\frac{412}{495}\right)\) | \(e\left(\frac{953}{990}\right)\) | \(e\left(\frac{409}{990}\right)\) | \(e\left(\frac{41}{165}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{857}{990}\right)\) | \(e\left(\frac{821}{990}\right)\) | \(e\left(\frac{329}{495}\right)\) | \(e\left(\frac{28}{165}\right)\) |
| \(\chi_{3267}(380,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{248}{495}\right)\) | \(e\left(\frac{1}{495}\right)\) | \(e\left(\frac{239}{990}\right)\) | \(e\left(\frac{7}{990}\right)\) | \(e\left(\frac{83}{165}\right)\) | \(e\left(\frac{49}{66}\right)\) | \(e\left(\frac{431}{990}\right)\) | \(e\left(\frac{503}{990}\right)\) | \(e\left(\frac{2}{495}\right)\) | \(e\left(\frac{109}{165}\right)\) |
| \(\chi_{3267}(392,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{49}{495}\right)\) | \(e\left(\frac{98}{495}\right)\) | \(e\left(\frac{157}{990}\right)\) | \(e\left(\frac{191}{990}\right)\) | \(e\left(\frac{49}{165}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{163}{990}\right)\) | \(e\left(\frac{289}{990}\right)\) | \(e\left(\frac{196}{495}\right)\) | \(e\left(\frac{122}{165}\right)\) |