from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5950, base_ring=CyclotomicField(40))
M = H._module
chi = DirichletCharacter(H, M([6,20,25]))
chi.galois_orbit()
[g,chi] = znchar(Mod(433,5950))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(5950\) | |
Conductor: | \(2975\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(40\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from 2975.du | 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: | \(\Q(\zeta_{40})\) |
Fixed field: | Number field defined by a degree 40 polynomial |
Characters in Galois orbit
Character | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(33\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{5950}(433,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{19}{20}\right)\) |
\(\chi_{5950}(797,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{1}{20}\right)\) |
\(\chi_{5950}(937,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{17}{20}\right)\) |
\(\chi_{5950}(1063,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{7}{20}\right)\) |
\(\chi_{5950}(1623,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{3}{20}\right)\) |
\(\chi_{5950}(1987,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{17}{20}\right)\) |
\(\chi_{5950}(2127,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{13}{20}\right)\) |
\(\chi_{5950}(2253,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{11}{20}\right)\) |
\(\chi_{5950}(2813,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{7}{20}\right)\) |
\(\chi_{5950}(3177,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{13}{20}\right)\) |
\(\chi_{5950}(3317,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{9}{20}\right)\) |
\(\chi_{5950}(4003,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{11}{20}\right)\) |
\(\chi_{5950}(4367,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{9}{20}\right)\) |
\(\chi_{5950}(4633,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{19}{20}\right)\) |
\(\chi_{5950}(5697,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{1}{20}\right)\) |
\(\chi_{5950}(5823,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{3}{20}\right)\) |