↑

Properties

Label 912.bo
Modulus 912912
Conductor 1919
Order 99
Real no
Primitive no
Minimal no
Parity even

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(912, base_ring=CyclotomicField(18))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,0,0,2]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(289,912))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 912912
Conductor: 1919
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 99
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 19.e
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ9)\Q(\zeta_{9})
Fixed field: Q(ζ19)+\Q(\zeta_{19})^+

Characters in Galois orbit

Character −1-1 11 55 77 1111 1313 1717 2323 2525 2929 3131 3535
χ912(289,⋅)\chi_{912}(289,\cdot) 11 11 e(79)e\left(\frac{7}{9}\right) e(23)e\left(\frac{2}{3}\right) e(13)e\left(\frac{1}{3}\right) e(59)e\left(\frac{5}{9}\right) e(19)e\left(\frac{1}{9}\right) e(29)e\left(\frac{2}{9}\right) e(59)e\left(\frac{5}{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)
χ912(385,⋅)\chi_{912}(385,\cdot) 11 11 e(29)e\left(\frac{2}{9}\right) e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\right) e(49)e\left(\frac{4}{9}\right) e(89)e\left(\frac{8}{9}\right) e(79)e\left(\frac{7}{9}\right) e(49)e\left(\frac{4}{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)
χ912(481,⋅)\chi_{912}(481,\cdot) 11 11 e(49)e\left(\frac{4}{9}\right) e(23)e\left(\frac{2}{3}\right) e(13)e\left(\frac{1}{3}\right) e(89)e\left(\frac{8}{9}\right) e(79)e\left(\frac{7}{9}\right) e(59)e\left(\frac{5}{9}\right) e(89)e\left(\frac{8}{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)
χ912(529,⋅)\chi_{912}(529,\cdot) 11 11 e(59)e\left(\frac{5}{9}\right) e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\right) e(19)e\left(\frac{1}{9}\right) e(29)e\left(\frac{2}{9}\right) e(49)e\left(\frac{4}{9}\right) e(19)e\left(\frac{1}{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)
χ912(625,⋅)\chi_{912}(625,\cdot) 11 11 e(89)e\left(\frac{8}{9}\right) e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\right) e(79)e\left(\frac{7}{9}\right) e(59)e\left(\frac{5}{9}\right) e(19)e\left(\frac{1}{9}\right) e(79)e\left(\frac{7}{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)
χ912(769,⋅)\chi_{912}(769,\cdot) 11 11 e(19)e\left(\frac{1}{9}\right) e(23)e\left(\frac{2}{3}\right) e(13)e\left(\frac{1}{3}\right) e(29)e\left(\frac{2}{9}\right) e(49)e\left(\frac{4}{9}\right) e(89)e\left(\frac{8}{9}\right) e(29)e\left(\frac{2}{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)