from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4592, base_ring=CyclotomicField(40))
M = H._module
chi = DirichletCharacter(H, M([20,30,0,3]))
chi.galois_orbit()
[g,chi] = znchar(Mod(995,4592))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(4592\) | |
Conductor: | \(656\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(40\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from 656.bx | 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: | \(\Q(\zeta_{40})\) |
Fixed field: | 40.40.1027708468267178047292394722862044397918868556644399912781578154071083295594368567462835848740864.2 |
Characters in Galois orbit
Character | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{4592}(995,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(-i\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{4592}(1051,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(i\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{4592}(1163,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(i\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{4592}(1219,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(-i\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{4592}(2227,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(-i\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{4592}(2395,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(i\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{4592}(2507,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(i\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{4592}(2899,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(-i\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{4592}(3123,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(-i\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{4592}(3179,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(i\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{4592}(3627,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(i\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{4592}(3683,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(-i\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{4592}(3907,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(-i\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{4592}(4299,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(i\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{4592}(4411,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(i\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{4592}(4579,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(-i\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) |