↑

Properties

Label 8800.oc
Modulus 88008800
Conductor 88008800
Order 4040
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8800, base_ring=CyclotomicField(40))
 
M = H._module
 
chi = DirichletCharacter(H, M([20,35,24,12]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(371,8800))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 88008800
Conductor: 88008800
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 4040
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
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(ζ40)\Q(\zeta_{40})
Fixed field: Number field defined by a degree 40 polynomial

Characters in Galois orbit

Character −1-1 11 33 77 99 1313 1717 1919 2121 2323 2727 2929
χ8800(371,⋅)\chi_{8800}(371,\cdot) 11 11 e(2940)e\left(\frac{29}{40}\right) e(720)e\left(\frac{7}{20}\right) e(920)e\left(\frac{9}{20}\right) e(3340)e\left(\frac{33}{40}\right) 11 e(1340)e\left(\frac{13}{40}\right) e(340)e\left(\frac{3}{40}\right) e(720)e\left(\frac{7}{20}\right) e(740)e\left(\frac{7}{40}\right) e(3740)e\left(\frac{37}{40}\right)
χ8800(611,⋅)\chi_{8800}(611,\cdot) 11 11 e(1740)e\left(\frac{17}{40}\right) e(1120)e\left(\frac{11}{20}\right) e(1720)e\left(\frac{17}{20}\right) e(2940)e\left(\frac{29}{40}\right) 11 e(940)e\left(\frac{9}{40}\right) e(3940)e\left(\frac{39}{40}\right) e(1120)e\left(\frac{11}{20}\right) e(1140)e\left(\frac{11}{40}\right) e(140)e\left(\frac{1}{40}\right)
χ8800(931,⋅)\chi_{8800}(931,\cdot) 11 11 e(140)e\left(\frac{1}{40}\right) e(320)e\left(\frac{3}{20}\right) e(120)e\left(\frac{1}{20}\right) e(3740)e\left(\frac{37}{40}\right) 11 e(1740)e\left(\frac{17}{40}\right) e(740)e\left(\frac{7}{40}\right) e(320)e\left(\frac{3}{20}\right) e(340)e\left(\frac{3}{40}\right) e(3340)e\left(\frac{33}{40}\right)
χ8800(1091,⋅)\chi_{8800}(1091,\cdot) 11 11 e(3340)e\left(\frac{33}{40}\right) e(1920)e\left(\frac{19}{20}\right) e(1320)e\left(\frac{13}{20}\right) e(2140)e\left(\frac{21}{40}\right) 11 e(140)e\left(\frac{1}{40}\right) e(3140)e\left(\frac{31}{40}\right) e(1920)e\left(\frac{19}{20}\right) e(1940)e\left(\frac{19}{40}\right) e(940)e\left(\frac{9}{40}\right)
χ8800(2571,⋅)\chi_{8800}(2571,\cdot) 11 11 e(3940)e\left(\frac{39}{40}\right) e(1720)e\left(\frac{17}{20}\right) e(1920)e\left(\frac{19}{20}\right) e(340)e\left(\frac{3}{40}\right) 11 e(2340)e\left(\frac{23}{40}\right) e(3340)e\left(\frac{33}{40}\right) e(1720)e\left(\frac{17}{20}\right) e(3740)e\left(\frac{37}{40}\right) e(740)e\left(\frac{7}{40}\right)
χ8800(2811,⋅)\chi_{8800}(2811,\cdot) 11 11 e(2740)e\left(\frac{27}{40}\right) e(120)e\left(\frac{1}{20}\right) e(720)e\left(\frac{7}{20}\right) e(3940)e\left(\frac{39}{40}\right) 11 e(1940)e\left(\frac{19}{40}\right) e(2940)e\left(\frac{29}{40}\right) e(120)e\left(\frac{1}{20}\right) e(140)e\left(\frac{1}{40}\right) e(1140)e\left(\frac{11}{40}\right)
χ8800(3131,⋅)\chi_{8800}(3131,\cdot) 11 11 e(1140)e\left(\frac{11}{40}\right) e(1320)e\left(\frac{13}{20}\right) e(1120)e\left(\frac{11}{20}\right) e(740)e\left(\frac{7}{40}\right) 11 e(2740)e\left(\frac{27}{40}\right) e(3740)e\left(\frac{37}{40}\right) e(1320)e\left(\frac{13}{20}\right) e(3340)e\left(\frac{33}{40}\right) e(340)e\left(\frac{3}{40}\right)
χ8800(3291,⋅)\chi_{8800}(3291,\cdot) 11 11 e(340)e\left(\frac{3}{40}\right) e(920)e\left(\frac{9}{20}\right) e(320)e\left(\frac{3}{20}\right) e(3140)e\left(\frac{31}{40}\right) 11 e(1140)e\left(\frac{11}{40}\right) e(2140)e\left(\frac{21}{40}\right) e(920)e\left(\frac{9}{20}\right) e(940)e\left(\frac{9}{40}\right) e(1940)e\left(\frac{19}{40}\right)
χ8800(4771,⋅)\chi_{8800}(4771,\cdot) 11 11 e(940)e\left(\frac{9}{40}\right) e(720)e\left(\frac{7}{20}\right) e(920)e\left(\frac{9}{20}\right) e(1340)e\left(\frac{13}{40}\right) 11 e(3340)e\left(\frac{33}{40}\right) e(2340)e\left(\frac{23}{40}\right) e(720)e\left(\frac{7}{20}\right) e(2740)e\left(\frac{27}{40}\right) e(1740)e\left(\frac{17}{40}\right)
χ8800(5011,⋅)\chi_{8800}(5011,\cdot) 11 11 e(3740)e\left(\frac{37}{40}\right) e(1120)e\left(\frac{11}{20}\right) e(1720)e\left(\frac{17}{20}\right) e(940)e\left(\frac{9}{40}\right) 11 e(2940)e\left(\frac{29}{40}\right) e(1940)e\left(\frac{19}{40}\right) e(1120)e\left(\frac{11}{20}\right) e(3140)e\left(\frac{31}{40}\right) e(2140)e\left(\frac{21}{40}\right)
χ8800(5331,⋅)\chi_{8800}(5331,\cdot) 11 11 e(2140)e\left(\frac{21}{40}\right) e(320)e\left(\frac{3}{20}\right) e(120)e\left(\frac{1}{20}\right) e(1740)e\left(\frac{17}{40}\right) 11 e(3740)e\left(\frac{37}{40}\right) e(2740)e\left(\frac{27}{40}\right) e(320)e\left(\frac{3}{20}\right) e(2340)e\left(\frac{23}{40}\right) e(1340)e\left(\frac{13}{40}\right)
χ8800(5491,⋅)\chi_{8800}(5491,\cdot) 11 11 e(1340)e\left(\frac{13}{40}\right) e(1920)e\left(\frac{19}{20}\right) e(1320)e\left(\frac{13}{20}\right) e(140)e\left(\frac{1}{40}\right) 11 e(2140)e\left(\frac{21}{40}\right) e(1140)e\left(\frac{11}{40}\right) e(1920)e\left(\frac{19}{20}\right) e(3940)e\left(\frac{39}{40}\right) e(2940)e\left(\frac{29}{40}\right)
χ8800(6971,⋅)\chi_{8800}(6971,\cdot) 11 11 e(1940)e\left(\frac{19}{40}\right) e(1720)e\left(\frac{17}{20}\right) e(1920)e\left(\frac{19}{20}\right) e(2340)e\left(\frac{23}{40}\right) 11 e(340)e\left(\frac{3}{40}\right) e(1340)e\left(\frac{13}{40}\right) e(1720)e\left(\frac{17}{20}\right) e(1740)e\left(\frac{17}{40}\right) e(2740)e\left(\frac{27}{40}\right)
χ8800(7211,⋅)\chi_{8800}(7211,\cdot) 11 11 e(740)e\left(\frac{7}{40}\right) e(120)e\left(\frac{1}{20}\right) e(720)e\left(\frac{7}{20}\right) e(1940)e\left(\frac{19}{40}\right) 11 e(3940)e\left(\frac{39}{40}\right) e(940)e\left(\frac{9}{40}\right) e(120)e\left(\frac{1}{20}\right) e(2140)e\left(\frac{21}{40}\right) e(3140)e\left(\frac{31}{40}\right)
χ8800(7531,⋅)\chi_{8800}(7531,\cdot) 11 11 e(3140)e\left(\frac{31}{40}\right) e(1320)e\left(\frac{13}{20}\right) e(1120)e\left(\frac{11}{20}\right) e(2740)e\left(\frac{27}{40}\right) 11 e(740)e\left(\frac{7}{40}\right) e(1740)e\left(\frac{17}{40}\right) e(1320)e\left(\frac{13}{20}\right) e(1340)e\left(\frac{13}{40}\right) e(2340)e\left(\frac{23}{40}\right)
χ8800(7691,⋅)\chi_{8800}(7691,\cdot) 11 11 e(2340)e\left(\frac{23}{40}\right) e(920)e\left(\frac{9}{20}\right) e(320)e\left(\frac{3}{20}\right) e(1140)e\left(\frac{11}{40}\right) 11 e(3140)e\left(\frac{31}{40}\right) e(140)e\left(\frac{1}{40}\right) e(920)e\left(\frac{9}{20}\right) e(2940)e\left(\frac{29}{40}\right) e(3940)e\left(\frac{39}{40}\right)