from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4928, base_ring=CyclotomicField(120))
M = H._module
chi = DirichletCharacter(H, M([60,15,80,108]))
chi.galois_orbit()
[g,chi] = znchar(Mod(39,4928))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(4928\) | |
| Conductor: | \(2464\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 2464.es | 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: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
First 31 of 32 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{4928}(39,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{9}{40}\right)\) |
| \(\chi_{4928}(151,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{23}{40}\right)\) |
| \(\chi_{4928}(359,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{97}{120}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{17}{40}\right)\) |
| \(\chi_{4928}(695,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{91}{120}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{11}{40}\right)\) |
| \(\chi_{4928}(711,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{91}{120}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{37}{120}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{37}{40}\right)\) |
| \(\chi_{4928}(919,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{39}{40}\right)\) |
| \(\chi_{4928}(1031,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{13}{40}\right)\) |
| \(\chi_{4928}(1047,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{31}{40}\right)\) |
| \(\chi_{4928}(1271,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{37}{120}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{19}{40}\right)\) |
| \(\chi_{4928}(1383,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{33}{40}\right)\) |
| \(\chi_{4928}(1591,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{107}{120}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{27}{40}\right)\) |
| \(\chi_{4928}(1927,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{21}{40}\right)\) |
| \(\chi_{4928}(1943,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{120}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{7}{40}\right)\) |
| \(\chi_{4928}(2151,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{47}{120}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{9}{40}\right)\) |
| \(\chi_{4928}(2263,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{23}{40}\right)\) |
| \(\chi_{4928}(2279,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{1}{40}\right)\) |
| \(\chi_{4928}(2503,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{29}{40}\right)\) |
| \(\chi_{4928}(2615,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{43}{120}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{3}{40}\right)\) |
| \(\chi_{4928}(2823,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{120}\right)\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{37}{40}\right)\) |
| \(\chi_{4928}(3159,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{31}{40}\right)\) |
| \(\chi_{4928}(3175,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{97}{120}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{17}{40}\right)\) |
| \(\chi_{4928}(3383,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{19}{40}\right)\) |
| \(\chi_{4928}(3495,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{33}{40}\right)\) |
| \(\chi_{4928}(3511,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{91}{120}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{11}{40}\right)\) |
| \(\chi_{4928}(3735,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{97}{120}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{39}{40}\right)\) |
| \(\chi_{4928}(3847,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{13}{40}\right)\) |
| \(\chi_{4928}(4055,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{47}{120}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{7}{40}\right)\) |
| \(\chi_{4928}(4391,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{1}{40}\right)\) |
| \(\chi_{4928}(4407,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{107}{120}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{27}{40}\right)\) |
| \(\chi_{4928}(4615,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{107}{120}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{29}{40}\right)\) |
| \(\chi_{4928}(4727,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{120}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{3}{40}\right)\) |