from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16335, base_ring=CyclotomicField(990))
M = H._module
chi = DirichletCharacter(H, M([880,0,981]))
chi.galois_orbit()
[g,chi] = znchar(Mod(61,16335))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(16335\) | |
| Conductor: | \(3267\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(990\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 3267.bu | 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: | $\Q(\zeta_{495})$ |
| Fixed field: | Number field defined by a degree 990 polynomial (not computed) |
First 22 of 240 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{16335}(61,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{871}{990}\right)\) | \(e\left(\frac{376}{495}\right)\) | \(e\left(\frac{157}{990}\right)\) | \(e\left(\frac{211}{330}\right)\) | \(e\left(\frac{191}{990}\right)\) | \(e\left(\frac{19}{495}\right)\) | \(e\left(\frac{257}{495}\right)\) | \(e\left(\frac{293}{330}\right)\) | \(e\left(\frac{301}{330}\right)\) | \(e\left(\frac{14}{99}\right)\) |
| \(\chi_{16335}(106,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{523}{990}\right)\) | \(e\left(\frac{28}{495}\right)\) | \(e\left(\frac{691}{990}\right)\) | \(e\left(\frac{193}{330}\right)\) | \(e\left(\frac{683}{990}\right)\) | \(e\left(\frac{112}{495}\right)\) | \(e\left(\frac{56}{495}\right)\) | \(e\left(\frac{329}{330}\right)\) | \(e\left(\frac{133}{330}\right)\) | \(e\left(\frac{20}{99}\right)\) |
| \(\chi_{16335}(151,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{697}{990}\right)\) | \(e\left(\frac{202}{495}\right)\) | \(e\left(\frac{919}{990}\right)\) | \(e\left(\frac{37}{330}\right)\) | \(e\left(\frac{437}{990}\right)\) | \(e\left(\frac{313}{495}\right)\) | \(e\left(\frac{404}{495}\right)\) | \(e\left(\frac{311}{330}\right)\) | \(e\left(\frac{217}{330}\right)\) | \(e\left(\frac{17}{99}\right)\) |
| \(\chi_{16335}(211,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{59}{990}\right)\) | \(e\left(\frac{59}{495}\right)\) | \(e\left(\frac{413}{990}\right)\) | \(e\left(\frac{59}{330}\right)\) | \(e\left(\frac{679}{990}\right)\) | \(e\left(\frac{236}{495}\right)\) | \(e\left(\frac{118}{495}\right)\) | \(e\left(\frac{157}{330}\right)\) | \(e\left(\frac{239}{330}\right)\) | \(e\left(\frac{28}{99}\right)\) |
| \(\chi_{16335}(376,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{469}{990}\right)\) | \(e\left(\frac{469}{495}\right)\) | \(e\left(\frac{313}{990}\right)\) | \(e\left(\frac{139}{330}\right)\) | \(e\left(\frac{179}{990}\right)\) | \(e\left(\frac{391}{495}\right)\) | \(e\left(\frac{443}{495}\right)\) | \(e\left(\frac{107}{330}\right)\) | \(e\left(\frac{289}{330}\right)\) | \(e\left(\frac{38}{99}\right)\) |
| \(\chi_{16335}(391,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{521}{990}\right)\) | \(e\left(\frac{26}{495}\right)\) | \(e\left(\frac{677}{990}\right)\) | \(e\left(\frac{191}{330}\right)\) | \(e\left(\frac{811}{990}\right)\) | \(e\left(\frac{104}{495}\right)\) | \(e\left(\frac{52}{495}\right)\) | \(e\left(\frac{223}{330}\right)\) | \(e\left(\frac{41}{330}\right)\) | \(e\left(\frac{61}{99}\right)\) |
| \(\chi_{16335}(436,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{443}{990}\right)\) | \(e\left(\frac{443}{495}\right)\) | \(e\left(\frac{131}{990}\right)\) | \(e\left(\frac{113}{330}\right)\) | \(e\left(\frac{853}{990}\right)\) | \(e\left(\frac{287}{495}\right)\) | \(e\left(\frac{391}{495}\right)\) | \(e\left(\frac{49}{330}\right)\) | \(e\left(\frac{83}{330}\right)\) | \(e\left(\frac{76}{99}\right)\) |
| \(\chi_{16335}(556,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{841}{990}\right)\) | \(e\left(\frac{346}{495}\right)\) | \(e\left(\frac{937}{990}\right)\) | \(e\left(\frac{181}{330}\right)\) | \(e\left(\frac{131}{990}\right)\) | \(e\left(\frac{394}{495}\right)\) | \(e\left(\frac{197}{495}\right)\) | \(e\left(\frac{23}{330}\right)\) | \(e\left(\frac{241}{330}\right)\) | \(e\left(\frac{35}{99}\right)\) |
| \(\chi_{16335}(601,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{403}{990}\right)\) | \(e\left(\frac{403}{495}\right)\) | \(e\left(\frac{841}{990}\right)\) | \(e\left(\frac{73}{330}\right)\) | \(e\left(\frac{443}{990}\right)\) | \(e\left(\frac{127}{495}\right)\) | \(e\left(\frac{311}{495}\right)\) | \(e\left(\frac{239}{330}\right)\) | \(e\left(\frac{223}{330}\right)\) | \(e\left(\frac{5}{99}\right)\) |
| \(\chi_{16335}(646,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{757}{990}\right)\) | \(e\left(\frac{262}{495}\right)\) | \(e\left(\frac{349}{990}\right)\) | \(e\left(\frac{97}{330}\right)\) | \(e\left(\frac{557}{990}\right)\) | \(e\left(\frac{58}{495}\right)\) | \(e\left(\frac{29}{495}\right)\) | \(e\left(\frac{191}{330}\right)\) | \(e\left(\frac{7}{330}\right)\) | \(e\left(\frac{74}{99}\right)\) |
| \(\chi_{16335}(706,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{299}{990}\right)\) | \(e\left(\frac{299}{495}\right)\) | \(e\left(\frac{113}{990}\right)\) | \(e\left(\frac{299}{330}\right)\) | \(e\left(\frac{169}{990}\right)\) | \(e\left(\frac{206}{495}\right)\) | \(e\left(\frac{103}{495}\right)\) | \(e\left(\frac{7}{330}\right)\) | \(e\left(\frac{59}{330}\right)\) | \(e\left(\frac{58}{99}\right)\) |
| \(\chi_{16335}(871,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{709}{990}\right)\) | \(e\left(\frac{214}{495}\right)\) | \(e\left(\frac{13}{990}\right)\) | \(e\left(\frac{49}{330}\right)\) | \(e\left(\frac{659}{990}\right)\) | \(e\left(\frac{361}{495}\right)\) | \(e\left(\frac{428}{495}\right)\) | \(e\left(\frac{287}{330}\right)\) | \(e\left(\frac{109}{330}\right)\) | \(e\left(\frac{68}{99}\right)\) |
| \(\chi_{16335}(886,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{491}{990}\right)\) | \(e\left(\frac{491}{495}\right)\) | \(e\left(\frac{467}{990}\right)\) | \(e\left(\frac{161}{330}\right)\) | \(e\left(\frac{751}{990}\right)\) | \(e\left(\frac{479}{495}\right)\) | \(e\left(\frac{487}{495}\right)\) | \(e\left(\frac{283}{330}\right)\) | \(e\left(\frac{311}{330}\right)\) | \(e\left(\frac{82}{99}\right)\) |
| \(\chi_{16335}(931,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{323}{990}\right)\) | \(e\left(\frac{323}{495}\right)\) | \(e\left(\frac{281}{990}\right)\) | \(e\left(\frac{323}{330}\right)\) | \(e\left(\frac{613}{990}\right)\) | \(e\left(\frac{302}{495}\right)\) | \(e\left(\frac{151}{495}\right)\) | \(e\left(\frac{289}{330}\right)\) | \(e\left(\frac{173}{330}\right)\) | \(e\left(\frac{61}{99}\right)\) |
| \(\chi_{16335}(976,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{137}{990}\right)\) | \(e\left(\frac{137}{495}\right)\) | \(e\left(\frac{959}{990}\right)\) | \(e\left(\frac{137}{330}\right)\) | \(e\left(\frac{637}{990}\right)\) | \(e\left(\frac{53}{495}\right)\) | \(e\left(\frac{274}{495}\right)\) | \(e\left(\frac{1}{330}\right)\) | \(e\left(\frac{197}{330}\right)\) | \(e\left(\frac{13}{99}\right)\) |
| \(\chi_{16335}(1051,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{811}{990}\right)\) | \(e\left(\frac{316}{495}\right)\) | \(e\left(\frac{727}{990}\right)\) | \(e\left(\frac{151}{330}\right)\) | \(e\left(\frac{71}{990}\right)\) | \(e\left(\frac{274}{495}\right)\) | \(e\left(\frac{137}{495}\right)\) | \(e\left(\frac{83}{330}\right)\) | \(e\left(\frac{181}{330}\right)\) | \(e\left(\frac{56}{99}\right)\) |
| \(\chi_{16335}(1096,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{283}{990}\right)\) | \(e\left(\frac{283}{495}\right)\) | \(e\left(\frac{1}{990}\right)\) | \(e\left(\frac{283}{330}\right)\) | \(e\left(\frac{203}{990}\right)\) | \(e\left(\frac{142}{495}\right)\) | \(e\left(\frac{71}{495}\right)\) | \(e\left(\frac{149}{330}\right)\) | \(e\left(\frac{313}{330}\right)\) | \(e\left(\frac{89}{99}\right)\) |
| \(\chi_{16335}(1141,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{817}{990}\right)\) | \(e\left(\frac{322}{495}\right)\) | \(e\left(\frac{769}{990}\right)\) | \(e\left(\frac{157}{330}\right)\) | \(e\left(\frac{677}{990}\right)\) | \(e\left(\frac{298}{495}\right)\) | \(e\left(\frac{149}{495}\right)\) | \(e\left(\frac{71}{330}\right)\) | \(e\left(\frac{127}{330}\right)\) | \(e\left(\frac{32}{99}\right)\) |
| \(\chi_{16335}(1366,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{949}{990}\right)\) | \(e\left(\frac{454}{495}\right)\) | \(e\left(\frac{703}{990}\right)\) | \(e\left(\frac{289}{330}\right)\) | \(e\left(\frac{149}{990}\right)\) | \(e\left(\frac{331}{495}\right)\) | \(e\left(\frac{413}{495}\right)\) | \(e\left(\frac{137}{330}\right)\) | \(e\left(\frac{259}{330}\right)\) | \(e\left(\frac{98}{99}\right)\) |
| \(\chi_{16335}(1381,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{461}{990}\right)\) | \(e\left(\frac{461}{495}\right)\) | \(e\left(\frac{257}{990}\right)\) | \(e\left(\frac{131}{330}\right)\) | \(e\left(\frac{691}{990}\right)\) | \(e\left(\frac{359}{495}\right)\) | \(e\left(\frac{427}{495}\right)\) | \(e\left(\frac{13}{330}\right)\) | \(e\left(\frac{251}{330}\right)\) | \(e\left(\frac{4}{99}\right)\) |
| \(\chi_{16335}(1426,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{203}{990}\right)\) | \(e\left(\frac{203}{495}\right)\) | \(e\left(\frac{431}{990}\right)\) | \(e\left(\frac{203}{330}\right)\) | \(e\left(\frac{373}{990}\right)\) | \(e\left(\frac{317}{495}\right)\) | \(e\left(\frac{406}{495}\right)\) | \(e\left(\frac{199}{330}\right)\) | \(e\left(\frac{263}{330}\right)\) | \(e\left(\frac{46}{99}\right)\) |
| \(\chi_{16335}(1471,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{197}{990}\right)\) | \(e\left(\frac{197}{495}\right)\) | \(e\left(\frac{389}{990}\right)\) | \(e\left(\frac{197}{330}\right)\) | \(e\left(\frac{757}{990}\right)\) | \(e\left(\frac{293}{495}\right)\) | \(e\left(\frac{394}{495}\right)\) | \(e\left(\frac{211}{330}\right)\) | \(e\left(\frac{317}{330}\right)\) | \(e\left(\frac{70}{99}\right)\) |