from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(987, base_ring=CyclotomicField(46))
M = H._module
chi = DirichletCharacter(H, M([23,23,30]))
chi.galois_orbit()
[g,chi] = znchar(Mod(83,987))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(987\) | |
| Conductor: | \(987\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(46\) | 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: | \(\Q(\zeta_{23})\) |
| Fixed field: | Number field defined by a degree 46 polynomial |
Characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{987}(83,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{46}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{3}{46}\right)\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{39}{46}\right)\) |
| \(\chi_{987}(209,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{25}{46}\right)\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{17}{46}\right)\) |
| \(\chi_{987}(230,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{7}{46}\right)\) | \(e\left(\frac{11}{46}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{45}{46}\right)\) |
| \(\chi_{987}(251,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{11}{46}\right)\) | \(e\left(\frac{21}{46}\right)\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{43}{46}\right)\) |
| \(\chi_{987}(272,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{25}{46}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{27}{46}\right)\) |
| \(\chi_{987}(314,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{7}{46}\right)\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{9}{46}\right)\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{25}{46}\right)\) |
| \(\chi_{987}(335,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{46}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{9}{46}\right)\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{31}{46}\right)\) |
| \(\chi_{987}(356,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{9}{46}\right)\) |
| \(\chi_{987}(440,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{35}{46}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{15}{46}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{7}{46}\right)\) |
| \(\chi_{987}(482,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{11}{46}\right)\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{13}{46}\right)\) |
| \(\chi_{987}(524,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{3}{46}\right)\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{17}{46}\right)\) | \(e\left(\frac{7}{46}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{37}{46}\right)\) |
| \(\chi_{987}(545,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{15}{46}\right)\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{35}{46}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{1}{46}\right)\) |
| \(\chi_{987}(566,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{25}{46}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{11}{46}\right)\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{5}{46}\right)\) |
| \(\chi_{987}(629,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{9}{46}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{21}{46}\right)\) | \(e\left(\frac{15}{46}\right)\) | \(e\left(\frac{17}{46}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{11}{46}\right)\) |
| \(\chi_{987}(692,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{25}{46}\right)\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{35}{46}\right)\) |
| \(\chi_{987}(713,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{15}{46}\right)\) |
| \(\chi_{987}(755,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{15}{46}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{35}{46}\right)\) | \(e\left(\frac{25}{46}\right)\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{3}{46}\right)\) |
| \(\chi_{987}(776,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{21}{46}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{17}{46}\right)\) | \(e\left(\frac{3}{46}\right)\) | \(e\left(\frac{35}{46}\right)\) | \(e\left(\frac{9}{46}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{41}{46}\right)\) |
| \(\chi_{987}(860,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{46}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{9}{46}\right)\) | \(e\left(\frac{7}{46}\right)\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{21}{46}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{19}{46}\right)\) |
| \(\chi_{987}(902,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{46}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{21}{46}\right)\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{3}{46}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{29}{46}\right)\) |
| \(\chi_{987}(944,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{35}{46}\right)\) | \(e\left(\frac{17}{46}\right)\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{33}{46}\right)\) |
| \(\chi_{987}(965,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{15}{46}\right)\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{21}{46}\right)\) |