↑

Properties

Label 2793.cb
Modulus 27932793
Conductor 133133
Order 1818
Real no
Primitive no
Minimal no
Parity odd

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2793, base_ring=CyclotomicField(18))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,15,8]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(313,2793))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 27932793
Conductor: 133133
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 1818
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 133.x
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ9)\Q(\zeta_{9})
Fixed field: 18.0.1369393352927188877370217151752183.2

Characters in Galois orbit

Character −1-1 11 22 44 55 88 1010 1111 1313 1616 1717 2020
χ2793(313,⋅)\chi_{2793}(313,\cdot) −1-1 11 e(19)e\left(\frac{1}{9}\right) e(29)e\left(\frac{2}{9}\right) e(518)e\left(\frac{5}{18}\right) e(13)e\left(\frac{1}{3}\right) e(718)e\left(\frac{7}{18}\right) e(23)e\left(\frac{2}{3}\right) e(1318)e\left(\frac{13}{18}\right) e(49)e\left(\frac{4}{9}\right) e(518)e\left(\frac{5}{18}\right) −1-1
χ2793(460,⋅)\chi_{2793}(460,\cdot) −1-1 11 e(79)e\left(\frac{7}{9}\right) e(59)e\left(\frac{5}{9}\right) e(1718)e\left(\frac{17}{18}\right) e(13)e\left(\frac{1}{3}\right) e(1318)e\left(\frac{13}{18}\right) e(23)e\left(\frac{2}{3}\right) e(118)e\left(\frac{1}{18}\right) e(19)e\left(\frac{1}{9}\right) e(1718)e\left(\frac{17}{18}\right) −1-1
χ2793(472,⋅)\chi_{2793}(472,\cdot) −1-1 11 e(59)e\left(\frac{5}{9}\right) e(19)e\left(\frac{1}{9}\right) e(718)e\left(\frac{7}{18}\right) e(23)e\left(\frac{2}{3}\right) e(1718)e\left(\frac{17}{18}\right) e(13)e\left(\frac{1}{3}\right) e(1118)e\left(\frac{11}{18}\right) e(29)e\left(\frac{2}{9}\right) e(718)e\left(\frac{7}{18}\right) −1-1
χ2793(1354,⋅)\chi_{2793}(1354,\cdot) −1-1 11 e(29)e\left(\frac{2}{9}\right) e(49)e\left(\frac{4}{9}\right) e(118)e\left(\frac{1}{18}\right) e(23)e\left(\frac{2}{3}\right) e(518)e\left(\frac{5}{18}\right) e(13)e\left(\frac{1}{3}\right) e(1718)e\left(\frac{17}{18}\right) e(89)e\left(\frac{8}{9}\right) e(118)e\left(\frac{1}{18}\right) −1-1
χ2793(2077,⋅)\chi_{2793}(2077,\cdot) −1-1 11 e(49)e\left(\frac{4}{9}\right) e(89)e\left(\frac{8}{9}\right) e(1118)e\left(\frac{11}{18}\right) e(13)e\left(\frac{1}{3}\right) e(118)e\left(\frac{1}{18}\right) e(23)e\left(\frac{2}{3}\right) e(718)e\left(\frac{7}{18}\right) e(79)e\left(\frac{7}{9}\right) e(1118)e\left(\frac{11}{18}\right) −1-1
χ2793(2677,⋅)\chi_{2793}(2677,\cdot) −1-1 11 e(89)e\left(\frac{8}{9}\right) e(79)e\left(\frac{7}{9}\right) e(1318)e\left(\frac{13}{18}\right) e(23)e\left(\frac{2}{3}\right) e(1118)e\left(\frac{11}{18}\right) e(13)e\left(\frac{1}{3}\right) e(518)e\left(\frac{5}{18}\right) e(59)e\left(\frac{5}{9}\right) e(1318)e\left(\frac{13}{18}\right) −1-1