from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(828, base_ring=CyclotomicField(66))
M = H._module
chi = DirichletCharacter(H, M([0,22,42]))
chi.galois_orbit()
[g,chi] = znchar(Mod(13,828))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(828\) | |
Conductor: | \(207\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(33\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from 207.m | 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: | \(\Q(\zeta_{33})\) |
Fixed field: | 33.33.70011645999218458416472683122408534303895571350166174758601569.1 |
Characters in Galois orbit
Character | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(35\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{828}(13,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{8}{11}\right)\) |
\(\chi_{828}(25,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{9}{11}\right)\) |
\(\chi_{828}(49,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{6}{11}\right)\) |
\(\chi_{828}(85,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{3}{11}\right)\) |
\(\chi_{828}(121,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{4}{11}\right)\) |
\(\chi_{828}(133,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{10}{11}\right)\) |
\(\chi_{828}(169,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{5}{11}\right)\) |
\(\chi_{828}(193,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{1}{11}\right)\) |
\(\chi_{828}(265,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{2}{11}\right)\) |
\(\chi_{828}(301,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{9}{11}\right)\) |
\(\chi_{828}(349,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{7}{11}\right)\) |
\(\chi_{828}(409,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{10}{11}\right)\) |
\(\chi_{828}(445,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{5}{11}\right)\) |
\(\chi_{828}(565,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{8}{11}\right)\) |
\(\chi_{828}(601,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{6}{11}\right)\) |
\(\chi_{828}(625,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{7}{11}\right)\) |
\(\chi_{828}(637,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{3}{11}\right)\) |
\(\chi_{828}(673,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{4}{11}\right)\) |
\(\chi_{828}(745,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{1}{11}\right)\) |
\(\chi_{828}(817,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{2}{11}\right)\) |