from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1444, base_ring=CyclotomicField(38))
M = H._module
chi = DirichletCharacter(H, M([0,5]))
chi.galois_orbit()
[g,chi] = znchar(Mod(37,1444))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(1444\) | |
Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(38\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from 361.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: | \(\Q(\zeta_{19})\) |
Fixed field: | 38.0.2233638411813024816853081773648251688534529753590642239923912316757382599022775822751448518259.1 |
Characters in Galois orbit
Character | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{1444}(37,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{11}{38}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{11}{38}\right)\) | \(e\left(\frac{31}{38}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{4}{19}\right)\) |
\(\chi_{1444}(113,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{33}{38}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{5}{19}\right)\) | \(e\left(\frac{33}{38}\right)\) | \(e\left(\frac{17}{38}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{3}{38}\right)\) | \(e\left(\frac{12}{19}\right)\) |
\(\chi_{1444}(189,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{17}{38}\right)\) | \(e\left(\frac{12}{19}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{17}{38}\right)\) | \(e\left(\frac{3}{38}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{5}{38}\right)\) | \(e\left(\frac{1}{19}\right)\) |
\(\chi_{1444}(265,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{27}{38}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{7}{38}\right)\) | \(e\left(\frac{9}{19}\right)\) |
\(\chi_{1444}(341,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{23}{38}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{12}{19}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{23}{38}\right)\) | \(e\left(\frac{13}{38}\right)\) | \(e\left(\frac{12}{19}\right)\) | \(e\left(\frac{9}{38}\right)\) | \(e\left(\frac{17}{19}\right)\) |
\(\chi_{1444}(417,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{7}{38}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{12}{19}\right)\) | \(e\left(\frac{7}{38}\right)\) | \(e\left(\frac{37}{38}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{11}{38}\right)\) | \(e\left(\frac{6}{19}\right)\) |
\(\chi_{1444}(493,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{29}{38}\right)\) | \(e\left(\frac{16}{19}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{29}{38}\right)\) | \(e\left(\frac{23}{38}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{13}{38}\right)\) | \(e\left(\frac{14}{19}\right)\) |
\(\chi_{1444}(569,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{13}{38}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{13}{38}\right)\) | \(e\left(\frac{9}{38}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{3}{19}\right)\) |
\(\chi_{1444}(645,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{35}{38}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{16}{19}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{35}{38}\right)\) | \(e\left(\frac{33}{38}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{17}{38}\right)\) | \(e\left(\frac{11}{19}\right)\) |
\(\chi_{1444}(797,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{38}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{16}{19}\right)\) | \(e\left(\frac{3}{38}\right)\) | \(e\left(\frac{5}{38}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{21}{38}\right)\) | \(e\left(\frac{8}{19}\right)\) |
\(\chi_{1444}(873,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{25}{38}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{25}{38}\right)\) | \(e\left(\frac{29}{38}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{23}{38}\right)\) | \(e\left(\frac{16}{19}\right)\) |
\(\chi_{1444}(949,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{9}{38}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{9}{38}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{25}{38}\right)\) | \(e\left(\frac{5}{19}\right)\) |
\(\chi_{1444}(1025,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{31}{38}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{12}{19}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{31}{38}\right)\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{27}{38}\right)\) | \(e\left(\frac{13}{19}\right)\) |
\(\chi_{1444}(1101,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{5}{19}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{25}{38}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{29}{38}\right)\) | \(e\left(\frac{2}{19}\right)\) |
\(\chi_{1444}(1177,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{37}{38}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{16}{19}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{37}{38}\right)\) | \(e\left(\frac{11}{38}\right)\) | \(e\left(\frac{16}{19}\right)\) | \(e\left(\frac{31}{38}\right)\) | \(e\left(\frac{10}{19}\right)\) |
\(\chi_{1444}(1253,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{21}{38}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{21}{38}\right)\) | \(e\left(\frac{35}{38}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{33}{38}\right)\) | \(e\left(\frac{18}{19}\right)\) |
\(\chi_{1444}(1329,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{38}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{5}{19}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{5}{38}\right)\) | \(e\left(\frac{21}{38}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{35}{38}\right)\) | \(e\left(\frac{7}{19}\right)\) |
\(\chi_{1444}(1405,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{27}{38}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{5}{19}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{27}{38}\right)\) | \(e\left(\frac{7}{38}\right)\) | \(e\left(\frac{5}{19}\right)\) | \(e\left(\frac{37}{38}\right)\) | \(e\left(\frac{15}{19}\right)\) |