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Properties

Label 2793.cg
Modulus 27932793
Conductor 399399
Order 1818
Real no
Primitive no
Minimal no
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2793, base_ring=CyclotomicField(18))
 
M = H._module
 
chi = DirichletCharacter(H, M([9,15,11]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(509,2793))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 27932793
Conductor: 399399
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 1818
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 399.by
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: Number field defined by a degree 18 polynomial

Characters in Galois orbit

Character −1-1 11 22 44 55 88 1010 1111 1313 1616 1717 2020
χ2793(509,⋅)\chi_{2793}(509,\cdot) −1-1 11 e(79)e\left(\frac{7}{9}\right) e(59)e\left(\frac{5}{9}\right) e(49)e\left(\frac{4}{9}\right) e(13)e\left(\frac{1}{3}\right) e(29)e\left(\frac{2}{9}\right) e(16)e\left(\frac{1}{6}\right) e(59)e\left(\frac{5}{9}\right) e(19)e\left(\frac{1}{9}\right) e(49)e\left(\frac{4}{9}\right) 11
χ2793(656,⋅)\chi_{2793}(656,\cdot) −1-1 11 e(19)e\left(\frac{1}{9}\right) e(29)e\left(\frac{2}{9}\right) e(79)e\left(\frac{7}{9}\right) e(13)e\left(\frac{1}{3}\right) e(89)e\left(\frac{8}{9}\right) e(16)e\left(\frac{1}{6}\right) e(29)e\left(\frac{2}{9}\right) e(49)e\left(\frac{4}{9}\right) e(79)e\left(\frac{7}{9}\right) 11
χ2793(668,⋅)\chi_{2793}(668,\cdot) −1-1 11 e(59)e\left(\frac{5}{9}\right) e(19)e\left(\frac{1}{9}\right) e(89)e\left(\frac{8}{9}\right) e(23)e\left(\frac{2}{3}\right) e(49)e\left(\frac{4}{9}\right) e(56)e\left(\frac{5}{6}\right) e(19)e\left(\frac{1}{9}\right) e(29)e\left(\frac{2}{9}\right) e(89)e\left(\frac{8}{9}\right) 11
χ2793(1256,⋅)\chi_{2793}(1256,\cdot) −1-1 11 e(89)e\left(\frac{8}{9}\right) e(79)e\left(\frac{7}{9}\right) e(29)e\left(\frac{2}{9}\right) e(23)e\left(\frac{2}{3}\right) e(19)e\left(\frac{1}{9}\right) e(56)e\left(\frac{5}{6}\right) e(79)e\left(\frac{7}{9}\right) e(59)e\left(\frac{5}{9}\right) e(29)e\left(\frac{2}{9}\right) 11
χ2793(1685,⋅)\chi_{2793}(1685,\cdot) −1-1 11 e(49)e\left(\frac{4}{9}\right) e(89)e\left(\frac{8}{9}\right) e(19)e\left(\frac{1}{9}\right) e(13)e\left(\frac{1}{3}\right) e(59)e\left(\frac{5}{9}\right) e(16)e\left(\frac{1}{6}\right) e(89)e\left(\frac{8}{9}\right) e(79)e\left(\frac{7}{9}\right) e(19)e\left(\frac{1}{9}\right) 11
χ2793(2579,⋅)\chi_{2793}(2579,\cdot) −1-1 11 e(29)e\left(\frac{2}{9}\right) e(49)e\left(\frac{4}{9}\right) e(59)e\left(\frac{5}{9}\right) e(23)e\left(\frac{2}{3}\right) e(79)e\left(\frac{7}{9}\right) e(56)e\left(\frac{5}{6}\right) e(49)e\left(\frac{4}{9}\right) e(89)e\left(\frac{8}{9}\right) e(59)e\left(\frac{5}{9}\right) 11