↑

Properties

Label 1710.co
Modulus 17101710
Conductor 855855
Order 1818
Real no
Primitive no
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1710, base_ring=CyclotomicField(18))
 
M = H._module
 
chi = DirichletCharacter(H, M([3,9,7]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(299,1710))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 17101710
Conductor: 855855
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 1818
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 855.co
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(ζ9)\Q(\zeta_{9})
Fixed field: 18.18.81623484842733584357749488935542564453125.2

Characters in Galois orbit

Character −1-1 11 77 1111 1313 1717 2323 2929 3131 3737 4141 4343
χ1710(299,⋅)\chi_{1710}(299,\cdot) 11 11 −1-1 e(56)e\left(\frac{5}{6}\right) e(79)e\left(\frac{7}{9}\right) e(89)e\left(\frac{8}{9}\right) e(19)e\left(\frac{1}{9}\right) e(79)e\left(\frac{7}{9}\right) e(16)e\left(\frac{1}{6}\right) 11 e(89)e\left(\frac{8}{9}\right) e(718)e\left(\frac{7}{18}\right)
χ1710(509,⋅)\chi_{1710}(509,\cdot) 11 11 −1-1 e(16)e\left(\frac{1}{6}\right) e(29)e\left(\frac{2}{9}\right) e(19)e\left(\frac{1}{9}\right) e(89)e\left(\frac{8}{9}\right) e(29)e\left(\frac{2}{9}\right) e(56)e\left(\frac{5}{6}\right) 11 e(19)e\left(\frac{1}{9}\right) e(1118)e\left(\frac{11}{18}\right)
χ1710(599,⋅)\chi_{1710}(599,\cdot) 11 11 −1-1 e(16)e\left(\frac{1}{6}\right) e(89)e\left(\frac{8}{9}\right) e(49)e\left(\frac{4}{9}\right) e(59)e\left(\frac{5}{9}\right) e(89)e\left(\frac{8}{9}\right) e(56)e\left(\frac{5}{6}\right) 11 e(49)e\left(\frac{4}{9}\right) e(1718)e\left(\frac{17}{18}\right)
χ1710(839,⋅)\chi_{1710}(839,\cdot) 11 11 −1-1 e(56)e\left(\frac{5}{6}\right) e(49)e\left(\frac{4}{9}\right) e(29)e\left(\frac{2}{9}\right) e(79)e\left(\frac{7}{9}\right) e(49)e\left(\frac{4}{9}\right) e(16)e\left(\frac{1}{6}\right) 11 e(29)e\left(\frac{2}{9}\right) e(1318)e\left(\frac{13}{18}\right)
χ1710(1199,⋅)\chi_{1710}(1199,\cdot) 11 11 −1-1 e(56)e\left(\frac{5}{6}\right) e(19)e\left(\frac{1}{9}\right) e(59)e\left(\frac{5}{9}\right) e(49)e\left(\frac{4}{9}\right) e(19)e\left(\frac{1}{9}\right) e(16)e\left(\frac{1}{6}\right) 11 e(59)e\left(\frac{5}{9}\right) e(118)e\left(\frac{1}{18}\right)
χ1710(1229,⋅)\chi_{1710}(1229,\cdot) 11 11 −1-1 e(16)e\left(\frac{1}{6}\right) e(59)e\left(\frac{5}{9}\right) e(79)e\left(\frac{7}{9}\right) e(29)e\left(\frac{2}{9}\right) e(59)e\left(\frac{5}{9}\right) e(56)e\left(\frac{5}{6}\right) 11 e(79)e\left(\frac{7}{9}\right) e(518)e\left(\frac{5}{18}\right)