from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7728, base_ring=CyclotomicField(44))
M = H._module
chi = DirichletCharacter(H, M([22,33,22,22,42]))
chi.galois_orbit()
[g,chi] = znchar(Mod(83,7728))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(7728\) | |
Conductor: | \(7728\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(44\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | 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: | \(\Q(\zeta_{44})\) |
Fixed field: | Number field defined by a degree 44 polynomial |
Characters in Galois orbit
Character | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{7728}(83,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) |
\(\chi_{7728}(251,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) |
\(\chi_{7728}(419,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{1}{22}\right)\) |
\(\chi_{7728}(755,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{15}{22}\right)\) |
\(\chi_{7728}(1091,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) |
\(\chi_{7728}(1259,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) |
\(\chi_{7728}(1763,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) |
\(\chi_{7728}(2435,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) |
\(\chi_{7728}(2771,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{9}{22}\right)\) |
\(\chi_{7728}(3779,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) |
\(\chi_{7728}(3947,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) |
\(\chi_{7728}(4115,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) |
\(\chi_{7728}(4283,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{1}{22}\right)\) |
\(\chi_{7728}(4619,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{15}{22}\right)\) |
\(\chi_{7728}(4955,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) |
\(\chi_{7728}(5123,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) |
\(\chi_{7728}(5627,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) |
\(\chi_{7728}(6299,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) |
\(\chi_{7728}(6635,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{9}{22}\right)\) |
\(\chi_{7728}(7643,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) |