from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(60))
M = H._module
chi = DirichletCharacter(H, M([30,39,10]))
chi.galois_orbit()
[g,chi] = znchar(Mod(17,1950))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(1950\) | |
Conductor: | \(975\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(60\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from 975.cy | 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: | \(\Q(\zeta_{60})\) |
Fixed field: | Number field defined by a degree 60 polynomial |
Characters in Galois orbit
Character | \(-1\) | \(1\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{1950}(17,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{1950}(23,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{1950}(173,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{1950}(413,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{1950}(563,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{1950}(647,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{1950}(797,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{1950}(803,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{1950}(953,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{1950}(1037,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{1950}(1187,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{1950}(1427,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{1950}(1577,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{1950}(1583,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{1950}(1733,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{1950}(1817,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{5}{12}\right)\) |