from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(705, base_ring=CyclotomicField(46))
M = H._module
chi = DirichletCharacter(H, M([23,0,40]))
chi.galois_orbit()
[g,chi] = znchar(Mod(56,705))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(705\) | |
| Conductor: | \(141\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(46\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 141.h | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | \(\Q(\zeta_{23})\) |
| Fixed field: | 46.0.3516370336176915030779886015601767871077707157889593350075735586626118367196692091787.1 |
Characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{705}(56,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{7}{46}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{21}{46}\right)\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{3}{23}\right)\) |
| \(\chi_{705}(71,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{21}{46}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{17}{46}\right)\) | \(e\left(\frac{35}{46}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{11}{46}\right)\) | \(e\left(\frac{9}{23}\right)\) |
| \(\chi_{705}(101,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{3}{46}\right)\) | \(e\left(\frac{17}{46}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{7}{23}\right)\) |
| \(\chi_{705}(131,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{7}{46}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{2}{23}\right)\) |
| \(\chi_{705}(191,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{15}{46}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{25}{46}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{11}{46}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{21}{46}\right)\) | \(e\left(\frac{13}{23}\right)\) |
| \(\chi_{705}(206,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{9}{46}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{15}{46}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{25}{46}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{17}{23}\right)\) |
| \(\chi_{705}(251,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{21}{46}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{35}{46}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{25}{46}\right)\) | \(e\left(\frac{10}{23}\right)\) |
| \(\chi_{705}(296,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{46}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{9}{46}\right)\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{21}{23}\right)\) |
| \(\chi_{705}(341,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{11}{46}\right)\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{17}{46}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{18}{23}\right)\) |
| \(\chi_{705}(356,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{17}{46}\right)\) | \(e\left(\frac{16}{23}\right)\) |
| \(\chi_{705}(371,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{7}{46}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{11}{23}\right)\) |
| \(\chi_{705}(401,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{9}{46}\right)\) | \(e\left(\frac{22}{23}\right)\) |
| \(\chi_{705}(431,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{9}{46}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{19}{23}\right)\) |
| \(\chi_{705}(476,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{17}{46}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{4}{23}\right)\) |
| \(\chi_{705}(491,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{25}{46}\right)\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{20}{23}\right)\) |
| \(\chi_{705}(506,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{11}{46}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{3}{46}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{8}{23}\right)\) |
| \(\chi_{705}(521,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{35}{46}\right)\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{5}{23}\right)\) |
| \(\chi_{705}(551,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{21}{46}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{15}{46}\right)\) | \(e\left(\frac{6}{23}\right)\) |
| \(\chi_{705}(566,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{25}{46}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{11}{46}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{3}{46}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{35}{46}\right)\) | \(e\left(\frac{14}{23}\right)\) |
| \(\chi_{705}(581,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{35}{46}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{3}{46}\right)\) | \(e\left(\frac{15}{23}\right)\) |
| \(\chi_{705}(596,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{7}{46}\right)\) | \(e\left(\frac{9}{46}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{15}{46}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{1}{23}\right)\) |
| \(\chi_{705}(686,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{15}{46}\right)\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{7}{46}\right)\) | \(e\left(\frac{12}{23}\right)\) |