from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2163, base_ring=CyclotomicField(34))
M = H._module
chi = DirichletCharacter(H, M([0,0,1]))
chi.galois_orbit()
[g,chi] = znchar(Mod(22,2163))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(2163\) | |
| Conductor: | \(103\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(34\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 103.f | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | \(\Q(\zeta_{17})\) |
| Fixed field: | Number field defined by a degree 34 polynomial |
Characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{2163}(22,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{27}{34}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{6}{17}\right)\) |
| \(\chi_{2163}(106,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{7}{34}\right)\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{10}{17}\right)\) |
| \(\chi_{2163}(127,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{23}{34}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{9}{34}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{2}{17}\right)\) |
| \(\chi_{2163}(295,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{23}{34}\right)\) | \(e\left(\frac{7}{34}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{11}{17}\right)\) |
| \(\chi_{2163}(610,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{27}{34}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{9}{17}\right)\) |
| \(\chi_{2163}(904,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{3}{34}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{14}{17}\right)\) |
| \(\chi_{2163}(1072,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) |
| \(\chi_{2163}(1366,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{13}{17}\right)\) |
| \(\chi_{2163}(1408,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{27}{34}\right)\) | \(e\left(\frac{23}{34}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{7}{17}\right)\) |
| \(\chi_{2163}(1429,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{7}{34}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{9}{34}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{8}{17}\right)\) |
| \(\chi_{2163}(1555,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{31}{34}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{5}{17}\right)\) |
| \(\chi_{2163}(1576,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(e\left(\frac{3}{34}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{12}{17}\right)\) |
| \(\chi_{2163}(1618,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{15}{17}\right)\) |
| \(\chi_{2163}(1639,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{9}{34}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{31}{34}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{3}{17}\right)\) |
| \(\chi_{2163}(1891,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{31}{34}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{16}{17}\right)\) |
| \(\chi_{2163}(1996,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{3}{34}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{1}{17}\right)\) |