from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7254, base_ring=CyclotomicField(30))
M = H._module
chi = DirichletCharacter(H, M([5,0,19]))
chi.galois_orbit()
[g,chi] = znchar(Mod(911,7254))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(7254\) | |
Conductor: | \(279\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(30\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from 279.be | 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: | \(\Q(\zeta_{15})\) |
Fixed field: | Number field defined by a degree 30 polynomial |
Characters in Galois orbit
Character | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(35\) | \(37\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{7254}(911,\cdot)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(1\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{7254}(1067,\cdot)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(1\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{7254}(2471,\cdot)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(1\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{7254}(2783,\cdot)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(1\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{7254}(3173,\cdot)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(1\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{7254}(6527,\cdot)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(1\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{7254}(6761,\cdot)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(1\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{7254}(7151,\cdot)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(1\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{6}\right)\) |