from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8352, base_ring=CyclotomicField(28))
M = H._module
chi = DirichletCharacter(H, M([14,0,0,25]))
chi.galois_orbit()
[g,chi] = znchar(Mod(127,8352))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(8352\) | |
| Conductor: | \(116\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(28\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 116.l | 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: | \(\Q(\zeta_{28})\) |
| Fixed field: | \(\Q(\zeta_{116})^+\) |
Characters in Galois orbit
| Character | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(31\) | \(35\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{8352}(127,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(-i\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{6}{7}\right)\) |
| \(\chi_{8352}(1279,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(-i\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{4}{7}\right)\) |
| \(\chi_{8352}(2143,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(i\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{4}{7}\right)\) |
| \(\chi_{8352}(3295,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(i\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{6}{7}\right)\) |
| \(\chi_{8352}(3871,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(-i\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{2}{7}\right)\) |
| \(\chi_{8352}(4447,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(i\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{3}{7}\right)\) |
| \(\chi_{8352}(4735,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(i\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{1}{7}\right)\) |
| \(\chi_{8352}(5599,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(-i\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{5}{7}\right)\) |
| \(\chi_{8352}(6175,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(i\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{5}{7}\right)\) |
| \(\chi_{8352}(7039,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(-i\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{1}{7}\right)\) |
| \(\chi_{8352}(7327,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(-i\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{3}{7}\right)\) |
| \(\chi_{8352}(7903,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(i\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{2}{7}\right)\) |