from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(259200, base_ring=CyclotomicField(2160))
M = H._module
chi = DirichletCharacter(H, M([1080,405,1960,1944]))
chi.galois_orbit()
[g,chi] = znchar(Mod(119,259200))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(259200\) | |
| Conductor: | \(129600\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2160\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 129600.vt | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | $\Q(\zeta_{2160})$ |
| Fixed field: | Number field defined by a degree 2160 polynomial (not computed) |
First 31 of 576 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{259200}(119,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{85}{216}\right)\) | \(e\left(\frac{1369}{2160}\right)\) | \(e\left(\frac{371}{2160}\right)\) | \(e\left(\frac{161}{180}\right)\) | \(e\left(\frac{409}{720}\right)\) | \(e\left(\frac{7}{1080}\right)\) | \(e\left(\frac{943}{2160}\right)\) | \(e\left(\frac{47}{135}\right)\) | \(e\left(\frac{647}{720}\right)\) | \(e\left(\frac{343}{1080}\right)\) |
| \(\chi_{259200}(839,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{216}\right)\) | \(e\left(\frac{583}{2160}\right)\) | \(e\left(\frac{797}{2160}\right)\) | \(e\left(\frac{47}{180}\right)\) | \(e\left(\frac{343}{720}\right)\) | \(e\left(\frac{769}{1080}\right)\) | \(e\left(\frac{1921}{2160}\right)\) | \(e\left(\frac{14}{135}\right)\) | \(e\left(\frac{569}{720}\right)\) | \(e\left(\frac{961}{1080}\right)\) |
| \(\chi_{259200}(1319,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{191}{216}\right)\) | \(e\left(\frac{779}{2160}\right)\) | \(e\left(\frac{361}{2160}\right)\) | \(e\left(\frac{31}{180}\right)\) | \(e\left(\frac{299}{720}\right)\) | \(e\left(\frac{557}{1080}\right)\) | \(e\left(\frac{1133}{2160}\right)\) | \(e\left(\frac{37}{135}\right)\) | \(e\left(\frac{517}{720}\right)\) | \(e\left(\frac{293}{1080}\right)\) |
| \(\chi_{259200}(1559,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{169}{216}\right)\) | \(e\left(\frac{1957}{2160}\right)\) | \(e\left(\frac{1223}{2160}\right)\) | \(e\left(\frac{113}{180}\right)\) | \(e\left(\frac{277}{720}\right)\) | \(e\left(\frac{451}{1080}\right)\) | \(e\left(\frac{739}{2160}\right)\) | \(e\left(\frac{116}{135}\right)\) | \(e\left(\frac{491}{720}\right)\) | \(e\left(\frac{499}{1080}\right)\) |
| \(\chi_{259200}(2039,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{197}{216}\right)\) | \(e\left(\frac{713}{2160}\right)\) | \(e\left(\frac{67}{2160}\right)\) | \(e\left(\frac{97}{180}\right)\) | \(e\left(\frac{233}{720}\right)\) | \(e\left(\frac{959}{1080}\right)\) | \(e\left(\frac{671}{2160}\right)\) | \(e\left(\frac{94}{135}\right)\) | \(e\left(\frac{439}{720}\right)\) | \(e\left(\frac{551}{1080}\right)\) |
| \(\chi_{259200}(2279,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{103}{216}\right)\) | \(e\left(\frac{1171}{2160}\right)\) | \(e\left(\frac{1649}{2160}\right)\) | \(e\left(\frac{179}{180}\right)\) | \(e\left(\frac{211}{720}\right)\) | \(e\left(\frac{133}{1080}\right)\) | \(e\left(\frac{1717}{2160}\right)\) | \(e\left(\frac{83}{135}\right)\) | \(e\left(\frac{413}{720}\right)\) | \(e\left(\frac{37}{1080}\right)\) |
| \(\chi_{259200}(2759,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{203}{216}\right)\) | \(e\left(\frac{647}{2160}\right)\) | \(e\left(\frac{1933}{2160}\right)\) | \(e\left(\frac{163}{180}\right)\) | \(e\left(\frac{167}{720}\right)\) | \(e\left(\frac{281}{1080}\right)\) | \(e\left(\frac{209}{2160}\right)\) | \(e\left(\frac{16}{135}\right)\) | \(e\left(\frac{361}{720}\right)\) | \(e\left(\frac{809}{1080}\right)\) |
| \(\chi_{259200}(3479,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{209}{216}\right)\) | \(e\left(\frac{581}{2160}\right)\) | \(e\left(\frac{1639}{2160}\right)\) | \(e\left(\frac{49}{180}\right)\) | \(e\left(\frac{101}{720}\right)\) | \(e\left(\frac{683}{1080}\right)\) | \(e\left(\frac{1907}{2160}\right)\) | \(e\left(\frac{73}{135}\right)\) | \(e\left(\frac{283}{720}\right)\) | \(e\left(\frac{1067}{1080}\right)\) |
| \(\chi_{259200}(3719,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{187}{216}\right)\) | \(e\left(\frac{1759}{2160}\right)\) | \(e\left(\frac{341}{2160}\right)\) | \(e\left(\frac{131}{180}\right)\) | \(e\left(\frac{79}{720}\right)\) | \(e\left(\frac{577}{1080}\right)\) | \(e\left(\frac{1513}{2160}\right)\) | \(e\left(\frac{17}{135}\right)\) | \(e\left(\frac{257}{720}\right)\) | \(e\left(\frac{193}{1080}\right)\) |
| \(\chi_{259200}(4439,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{121}{216}\right)\) | \(e\left(\frac{973}{2160}\right)\) | \(e\left(\frac{767}{2160}\right)\) | \(e\left(\frac{17}{180}\right)\) | \(e\left(\frac{13}{720}\right)\) | \(e\left(\frac{259}{1080}\right)\) | \(e\left(\frac{331}{2160}\right)\) | \(e\left(\frac{119}{135}\right)\) | \(e\left(\frac{179}{720}\right)\) | \(e\left(\frac{811}{1080}\right)\) |
| \(\chi_{259200}(4919,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{216}\right)\) | \(e\left(\frac{449}{2160}\right)\) | \(e\left(\frac{1051}{2160}\right)\) | \(e\left(\frac{1}{180}\right)\) | \(e\left(\frac{689}{720}\right)\) | \(e\left(\frac{407}{1080}\right)\) | \(e\left(\frac{983}{2160}\right)\) | \(e\left(\frac{52}{135}\right)\) | \(e\left(\frac{127}{720}\right)\) | \(e\left(\frac{503}{1080}\right)\) |
| \(\chi_{259200}(5159,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{55}{216}\right)\) | \(e\left(\frac{187}{2160}\right)\) | \(e\left(\frac{1193}{2160}\right)\) | \(e\left(\frac{83}{180}\right)\) | \(e\left(\frac{667}{720}\right)\) | \(e\left(\frac{1021}{1080}\right)\) | \(e\left(\frac{1309}{2160}\right)\) | \(e\left(\frac{86}{135}\right)\) | \(e\left(\frac{101}{720}\right)\) | \(e\left(\frac{349}{1080}\right)\) |
| \(\chi_{259200}(5639,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{216}\right)\) | \(e\left(\frac{383}{2160}\right)\) | \(e\left(\frac{757}{2160}\right)\) | \(e\left(\frac{67}{180}\right)\) | \(e\left(\frac{623}{720}\right)\) | \(e\left(\frac{809}{1080}\right)\) | \(e\left(\frac{521}{2160}\right)\) | \(e\left(\frac{109}{135}\right)\) | \(e\left(\frac{49}{720}\right)\) | \(e\left(\frac{761}{1080}\right)\) |
| \(\chi_{259200}(5879,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{205}{216}\right)\) | \(e\left(\frac{1561}{2160}\right)\) | \(e\left(\frac{1619}{2160}\right)\) | \(e\left(\frac{149}{180}\right)\) | \(e\left(\frac{601}{720}\right)\) | \(e\left(\frac{703}{1080}\right)\) | \(e\left(\frac{127}{2160}\right)\) | \(e\left(\frac{53}{135}\right)\) | \(e\left(\frac{23}{720}\right)\) | \(e\left(\frac{967}{1080}\right)\) |
| \(\chi_{259200}(6359,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{216}\right)\) | \(e\left(\frac{317}{2160}\right)\) | \(e\left(\frac{463}{2160}\right)\) | \(e\left(\frac{133}{180}\right)\) | \(e\left(\frac{557}{720}\right)\) | \(e\left(\frac{131}{1080}\right)\) | \(e\left(\frac{59}{2160}\right)\) | \(e\left(\frac{31}{135}\right)\) | \(e\left(\frac{691}{720}\right)\) | \(e\left(\frac{1019}{1080}\right)\) |
| \(\chi_{259200}(7079,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{216}\right)\) | \(e\left(\frac{251}{2160}\right)\) | \(e\left(\frac{169}{2160}\right)\) | \(e\left(\frac{19}{180}\right)\) | \(e\left(\frac{491}{720}\right)\) | \(e\left(\frac{533}{1080}\right)\) | \(e\left(\frac{1757}{2160}\right)\) | \(e\left(\frac{88}{135}\right)\) | \(e\left(\frac{613}{720}\right)\) | \(e\left(\frac{197}{1080}\right)\) |
| \(\chi_{259200}(7319,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{216}\right)\) | \(e\left(\frac{2149}{2160}\right)\) | \(e\left(\frac{311}{2160}\right)\) | \(e\left(\frac{101}{180}\right)\) | \(e\left(\frac{469}{720}\right)\) | \(e\left(\frac{67}{1080}\right)\) | \(e\left(\frac{2083}{2160}\right)\) | \(e\left(\frac{122}{135}\right)\) | \(e\left(\frac{587}{720}\right)\) | \(e\left(\frac{43}{1080}\right)\) |
| \(\chi_{259200}(8039,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{216}\right)\) | \(e\left(\frac{1363}{2160}\right)\) | \(e\left(\frac{737}{2160}\right)\) | \(e\left(\frac{167}{180}\right)\) | \(e\left(\frac{403}{720}\right)\) | \(e\left(\frac{829}{1080}\right)\) | \(e\left(\frac{901}{2160}\right)\) | \(e\left(\frac{89}{135}\right)\) | \(e\left(\frac{509}{720}\right)\) | \(e\left(\frac{661}{1080}\right)\) |
| \(\chi_{259200}(8519,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{35}{216}\right)\) | \(e\left(\frac{119}{2160}\right)\) | \(e\left(\frac{1741}{2160}\right)\) | \(e\left(\frac{151}{180}\right)\) | \(e\left(\frac{359}{720}\right)\) | \(e\left(\frac{257}{1080}\right)\) | \(e\left(\frac{833}{2160}\right)\) | \(e\left(\frac{67}{135}\right)\) | \(e\left(\frac{457}{720}\right)\) | \(e\left(\frac{713}{1080}\right)\) |
| \(\chi_{259200}(8759,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{157}{216}\right)\) | \(e\left(\frac{577}{2160}\right)\) | \(e\left(\frac{1163}{2160}\right)\) | \(e\left(\frac{53}{180}\right)\) | \(e\left(\frac{337}{720}\right)\) | \(e\left(\frac{511}{1080}\right)\) | \(e\left(\frac{1879}{2160}\right)\) | \(e\left(\frac{56}{135}\right)\) | \(e\left(\frac{431}{720}\right)\) | \(e\left(\frac{199}{1080}\right)\) |
| \(\chi_{259200}(9239,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{216}\right)\) | \(e\left(\frac{53}{2160}\right)\) | \(e\left(\frac{1447}{2160}\right)\) | \(e\left(\frac{37}{180}\right)\) | \(e\left(\frac{293}{720}\right)\) | \(e\left(\frac{659}{1080}\right)\) | \(e\left(\frac{371}{2160}\right)\) | \(e\left(\frac{124}{135}\right)\) | \(e\left(\frac{379}{720}\right)\) | \(e\left(\frac{971}{1080}\right)\) |
| \(\chi_{259200}(9479,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{91}{216}\right)\) | \(e\left(\frac{1951}{2160}\right)\) | \(e\left(\frac{1589}{2160}\right)\) | \(e\left(\frac{119}{180}\right)\) | \(e\left(\frac{271}{720}\right)\) | \(e\left(\frac{193}{1080}\right)\) | \(e\left(\frac{697}{2160}\right)\) | \(e\left(\frac{23}{135}\right)\) | \(e\left(\frac{353}{720}\right)\) | \(e\left(\frac{817}{1080}\right)\) |
| \(\chi_{259200}(9959,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{216}\right)\) | \(e\left(\frac{2147}{2160}\right)\) | \(e\left(\frac{1153}{2160}\right)\) | \(e\left(\frac{103}{180}\right)\) | \(e\left(\frac{227}{720}\right)\) | \(e\left(\frac{1061}{1080}\right)\) | \(e\left(\frac{2069}{2160}\right)\) | \(e\left(\frac{46}{135}\right)\) | \(e\left(\frac{301}{720}\right)\) | \(e\left(\frac{149}{1080}\right)\) |
| \(\chi_{259200}(10679,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{216}\right)\) | \(e\left(\frac{2081}{2160}\right)\) | \(e\left(\frac{859}{2160}\right)\) | \(e\left(\frac{169}{180}\right)\) | \(e\left(\frac{161}{720}\right)\) | \(e\left(\frac{383}{1080}\right)\) | \(e\left(\frac{1607}{2160}\right)\) | \(e\left(\frac{103}{135}\right)\) | \(e\left(\frac{223}{720}\right)\) | \(e\left(\frac{407}{1080}\right)\) |
| \(\chi_{259200}(10919,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{175}{216}\right)\) | \(e\left(\frac{379}{2160}\right)\) | \(e\left(\frac{281}{2160}\right)\) | \(e\left(\frac{71}{180}\right)\) | \(e\left(\frac{139}{720}\right)\) | \(e\left(\frac{637}{1080}\right)\) | \(e\left(\frac{493}{2160}\right)\) | \(e\left(\frac{92}{135}\right)\) | \(e\left(\frac{197}{720}\right)\) | \(e\left(\frac{973}{1080}\right)\) |
| \(\chi_{259200}(11639,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{109}{216}\right)\) | \(e\left(\frac{1753}{2160}\right)\) | \(e\left(\frac{707}{2160}\right)\) | \(e\left(\frac{137}{180}\right)\) | \(e\left(\frac{73}{720}\right)\) | \(e\left(\frac{319}{1080}\right)\) | \(e\left(\frac{1471}{2160}\right)\) | \(e\left(\frac{59}{135}\right)\) | \(e\left(\frac{119}{720}\right)\) | \(e\left(\frac{511}{1080}\right)\) |
| \(\chi_{259200}(12119,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{65}{216}\right)\) | \(e\left(\frac{1949}{2160}\right)\) | \(e\left(\frac{271}{2160}\right)\) | \(e\left(\frac{121}{180}\right)\) | \(e\left(\frac{29}{720}\right)\) | \(e\left(\frac{107}{1080}\right)\) | \(e\left(\frac{683}{2160}\right)\) | \(e\left(\frac{82}{135}\right)\) | \(e\left(\frac{67}{720}\right)\) | \(e\left(\frac{923}{1080}\right)\) |
| \(\chi_{259200}(12359,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{216}\right)\) | \(e\left(\frac{967}{2160}\right)\) | \(e\left(\frac{1133}{2160}\right)\) | \(e\left(\frac{23}{180}\right)\) | \(e\left(\frac{7}{720}\right)\) | \(e\left(\frac{1}{1080}\right)\) | \(e\left(\frac{289}{2160}\right)\) | \(e\left(\frac{26}{135}\right)\) | \(e\left(\frac{41}{720}\right)\) | \(e\left(\frac{49}{1080}\right)\) |
| \(\chi_{259200}(12839,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{216}\right)\) | \(e\left(\frac{1883}{2160}\right)\) | \(e\left(\frac{2137}{2160}\right)\) | \(e\left(\frac{7}{180}\right)\) | \(e\left(\frac{683}{720}\right)\) | \(e\left(\frac{509}{1080}\right)\) | \(e\left(\frac{221}{2160}\right)\) | \(e\left(\frac{4}{135}\right)\) | \(e\left(\frac{709}{720}\right)\) | \(e\left(\frac{101}{1080}\right)\) |
| \(\chi_{259200}(13079,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{193}{216}\right)\) | \(e\left(\frac{181}{2160}\right)\) | \(e\left(\frac{1559}{2160}\right)\) | \(e\left(\frac{89}{180}\right)\) | \(e\left(\frac{661}{720}\right)\) | \(e\left(\frac{763}{1080}\right)\) | \(e\left(\frac{1267}{2160}\right)\) | \(e\left(\frac{128}{135}\right)\) | \(e\left(\frac{683}{720}\right)\) | \(e\left(\frac{667}{1080}\right)\) |
| \(\chi_{259200}(13559,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{77}{216}\right)\) | \(e\left(\frac{1817}{2160}\right)\) | \(e\left(\frac{1843}{2160}\right)\) | \(e\left(\frac{73}{180}\right)\) | \(e\left(\frac{617}{720}\right)\) | \(e\left(\frac{911}{1080}\right)\) | \(e\left(\frac{1919}{2160}\right)\) | \(e\left(\frac{61}{135}\right)\) | \(e\left(\frac{631}{720}\right)\) | \(e\left(\frac{359}{1080}\right)\) |