from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7935, base_ring=CyclotomicField(46))
M = H._module
chi = DirichletCharacter(H, M([0,0,12]))
chi.galois_orbit()
[g,chi] = znchar(Mod(346,7935))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(7935\) | |
Conductor: | \(529\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(23\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from 529.e | 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: | \(\Q(\zeta_{23})\) |
Fixed field: | Number field defined by a degree 23 polynomial |
Characters in Galois orbit
Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{7935}(346,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) |
\(\chi_{7935}(691,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) |
\(\chi_{7935}(1036,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) |
\(\chi_{7935}(1381,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) |
\(\chi_{7935}(1726,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) |
\(\chi_{7935}(2071,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) |
\(\chi_{7935}(2416,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) |
\(\chi_{7935}(2761,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) |
\(\chi_{7935}(3106,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) |
\(\chi_{7935}(3451,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) |
\(\chi_{7935}(3796,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) |
\(\chi_{7935}(4141,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{2}{23}\right)\) |
\(\chi_{7935}(4486,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) |
\(\chi_{7935}(4831,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) |
\(\chi_{7935}(5176,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) |
\(\chi_{7935}(5521,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) |
\(\chi_{7935}(5866,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) |
\(\chi_{7935}(6211,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) |
\(\chi_{7935}(6556,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) |
\(\chi_{7935}(6901,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) |
\(\chi_{7935}(7246,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) |
\(\chi_{7935}(7591,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) |