from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6275, base_ring=CyclotomicField(50))
M = H._module
chi = DirichletCharacter(H, M([10,36]))
chi.galois_orbit()
[g,chi] = znchar(Mod(91,6275))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(6275\) | |
| Conductor: | \(6275\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(25\) | 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: | \(\Q(\zeta_{25})\) |
| Fixed field: | Number field defined by a degree 25 polynomial |
Characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{6275}(91,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{21}{25}\right)\) |
| \(\chi_{6275}(571,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{13}{25}\right)\) |
| \(\chi_{6275}(706,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{7}{25}\right)\) |
| \(\chi_{6275}(816,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{16}{25}\right)\) |
| \(\chi_{6275}(1271,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{18}{25}\right)\) |
| \(\chi_{6275}(1496,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{3}{25}\right)\) |
| \(\chi_{6275}(1531,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{22}{25}\right)\) |
| \(\chi_{6275}(1586,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{4}{25}\right)\) |
| \(\chi_{6275}(1761,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{9}{25}\right)\) |
| \(\chi_{6275}(2006,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{17}{25}\right)\) |
| \(\chi_{6275}(2711,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{14}{25}\right)\) |
| \(\chi_{6275}(2766,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{11}{25}\right)\) |
| \(\chi_{6275}(3386,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{19}{25}\right)\) |
| \(\chi_{6275}(4116,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{6}{25}\right)\) |
| \(\chi_{6275}(4331,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{2}{25}\right)\) |
| \(\chi_{6275}(4361,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{24}{25}\right)\) |
| \(\chi_{6275}(5071,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{23}{25}\right)\) |
| \(\chi_{6275}(5231,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{12}{25}\right)\) |
| \(\chi_{6275}(5396,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{8}{25}\right)\) |
| \(\chi_{6275}(6016,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{1}{25}\right)\) |