from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(547, base_ring=CyclotomicField(78))
M = H._module
chi = DirichletCharacter(H, M([10]))
chi.galois_orbit()
[g,chi] = znchar(Mod(11,547))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(547\) | |
Conductor: | \(547\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(39\) | 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: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 39 polynomial |
Characters in Galois orbit
Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{547}(11,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{39}\right)\) | \(1\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(1\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{38}{39}\right)\) |
\(\chi_{547}(21,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{38}{39}\right)\) | \(1\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(1\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{8}{39}\right)\) |
\(\chi_{547}(47,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{39}\right)\) | \(1\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(1\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{4}{39}\right)\) |
\(\chi_{547}(54,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{14}{39}\right)\) | \(1\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(1\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{5}{39}\right)\) |
\(\chi_{547}(96,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{39}\right)\) | \(1\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(1\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{25}{39}\right)\) |
\(\chi_{547}(121,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{10}{39}\right)\) | \(1\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(1\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{37}{39}\right)\) |
\(\chi_{547}(129,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{39}\right)\) | \(1\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(1\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{23}{39}\right)\) |
\(\chi_{547}(136,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{39}\right)\) | \(1\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(1\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{29}{39}\right)\) |
\(\chi_{547}(181,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{28}{39}\right)\) | \(1\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(1\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{10}{39}\right)\) |
\(\chi_{547}(199,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{34}{39}\right)\) | \(1\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(1\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{1}{39}\right)\) |
\(\chi_{547}(217,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{39}\right)\) | \(1\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(1\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{2}{39}\right)\) |
\(\chi_{547}(231,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{39}\right)\) | \(1\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(1\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{7}{39}\right)\) |
\(\chi_{547}(233,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{25}{39}\right)\) | \(1\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(1\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{34}{39}\right)\) |
\(\chi_{547}(239,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{32}{39}\right)\) | \(1\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(1\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{17}{39}\right)\) |
\(\chi_{547}(296,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{35}{39}\right)\) | \(1\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(1\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{32}{39}\right)\) |
\(\chi_{547}(302,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{8}{39}\right)\) | \(1\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(1\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{14}{39}\right)\) |
\(\chi_{547}(325,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{39}\right)\) | \(1\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(1\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{22}{39}\right)\) |
\(\chi_{547}(402,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{16}{39}\right)\) | \(1\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(1\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{28}{39}\right)\) |
\(\chi_{547}(419,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{20}{39}\right)\) | \(1\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(1\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{35}{39}\right)\) |
\(\chi_{547}(441,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{39}\right)\) | \(1\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(1\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{16}{39}\right)\) |
\(\chi_{547}(445,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{22}{39}\right)\) | \(1\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(1\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{19}{39}\right)\) |
\(\chi_{547}(464,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{39}\right)\) | \(1\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(1\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{11}{39}\right)\) |
\(\chi_{547}(488,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{39}\right)\) | \(1\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(1\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{20}{39}\right)\) |
\(\chi_{547}(521,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{39}\right)\) | \(1\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(1\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{31}{39}\right)\) |