from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6275, base_ring=CyclotomicField(50))
M = H._module
chi = DirichletCharacter(H, M([20,14]))
chi.galois_orbit()
[g,chi] = znchar(Mod(331,6275))
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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{6275}(331,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{14}{25}\right)\) |
\(\chi_{6275}(506,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{19}{25}\right)\) |
\(\chi_{6275}(566,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{7}{25}\right)\) |
\(\chi_{6275}(996,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{16}{25}\right)\) |
\(\chi_{6275}(1346,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{11}{25}\right)\) |
\(\chi_{6275}(1456,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{24}{25}\right)\) |
\(\chi_{6275}(1466,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{17}{25}\right)\) |
\(\chi_{6275}(2071,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{6}{25}\right)\) |
\(\chi_{6275}(2131,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{4}{25}\right)\) |
\(\chi_{6275}(2561,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{18}{25}\right)\) |
\(\chi_{6275}(2886,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{3}{25}\right)\) |
\(\chi_{6275}(3106,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{9}{25}\right)\) |
\(\chi_{6275}(3216,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{12}{25}\right)\) |
\(\chi_{6275}(4021,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{1}{25}\right)\) |
\(\chi_{6275}(4041,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{2}{25}\right)\) |
\(\chi_{6275}(4336,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{8}{25}\right)\) |
\(\chi_{6275}(4516,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{22}{25}\right)\) |
\(\chi_{6275}(5036,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{13}{25}\right)\) |
\(\chi_{6275}(5261,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{23}{25}\right)\) |
\(\chi_{6275}(5371,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{21}{25}\right)\) |