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Properties

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

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8800, base_ring=CyclotomicField(40))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,25,22,20]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(373,8800))
 
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(373,⋅)\chi_{8800}(373,\cdot) 11 11 e(2940)e\left(\frac{29}{40}\right) −1-1 e(920)e\left(\frac{9}{20}\right) e(1340)e\left(\frac{13}{40}\right) e(320)e\left(\frac{3}{20}\right) e(3140)e\left(\frac{31}{40}\right) e(940)e\left(\frac{9}{40}\right) e(45)e\left(\frac{4}{5}\right) e(740)e\left(\frac{7}{40}\right) e(1940)e\left(\frac{19}{40}\right)
χ8800(637,⋅)\chi_{8800}(637,\cdot) 11 11 e(1140)e\left(\frac{11}{40}\right) −1-1 e(1120)e\left(\frac{11}{20}\right) e(2740)e\left(\frac{27}{40}\right) e(1720)e\left(\frac{17}{20}\right) e(940)e\left(\frac{9}{40}\right) e(3140)e\left(\frac{31}{40}\right) e(15)e\left(\frac{1}{5}\right) e(3340)e\left(\frac{33}{40}\right) e(2140)e\left(\frac{21}{40}\right)
χ8800(1253,⋅)\chi_{8800}(1253,\cdot) 11 11 e(3340)e\left(\frac{33}{40}\right) −1-1 e(1320)e\left(\frac{13}{20}\right) e(140)e\left(\frac{1}{40}\right) e(1120)e\left(\frac{11}{20}\right) e(2740)e\left(\frac{27}{40}\right) e(1340)e\left(\frac{13}{40}\right) e(35)e\left(\frac{3}{5}\right) e(1940)e\left(\frac{19}{40}\right) e(2340)e\left(\frac{23}{40}\right)
χ8800(1517,⋅)\chi_{8800}(1517,\cdot) 11 11 e(740)e\left(\frac{7}{40}\right) −1-1 e(720)e\left(\frac{7}{20}\right) e(3940)e\left(\frac{39}{40}\right) e(920)e\left(\frac{9}{20}\right) e(1340)e\left(\frac{13}{40}\right) e(2740)e\left(\frac{27}{40}\right) e(25)e\left(\frac{2}{5}\right) e(2140)e\left(\frac{21}{40}\right) e(1740)e\left(\frac{17}{40}\right)
χ8800(2133,⋅)\chi_{8800}(2133,\cdot) 11 11 e(3740)e\left(\frac{37}{40}\right) −1-1 e(1720)e\left(\frac{17}{20}\right) e(2940)e\left(\frac{29}{40}\right) e(1920)e\left(\frac{19}{20}\right) e(2340)e\left(\frac{23}{40}\right) e(1740)e\left(\frac{17}{40}\right) e(25)e\left(\frac{2}{5}\right) e(3140)e\left(\frac{31}{40}\right) e(2740)e\left(\frac{27}{40}\right)
χ8800(2397,⋅)\chi_{8800}(2397,\cdot) 11 11 e(340)e\left(\frac{3}{40}\right) −1-1 e(320)e\left(\frac{3}{20}\right) e(1140)e\left(\frac{11}{40}\right) e(120)e\left(\frac{1}{20}\right) e(1740)e\left(\frac{17}{40}\right) e(2340)e\left(\frac{23}{40}\right) e(35)e\left(\frac{3}{5}\right) e(940)e\left(\frac{9}{40}\right) e(1340)e\left(\frac{13}{40}\right)
χ8800(3013,⋅)\chi_{8800}(3013,\cdot) 11 11 e(140)e\left(\frac{1}{40}\right) −1-1 e(120)e\left(\frac{1}{20}\right) e(1740)e\left(\frac{17}{40}\right) e(720)e\left(\frac{7}{20}\right) e(1940)e\left(\frac{19}{40}\right) e(2140)e\left(\frac{21}{40}\right) e(15)e\left(\frac{1}{5}\right) e(340)e\left(\frac{3}{40}\right) e(3140)e\left(\frac{31}{40}\right)
χ8800(3277,⋅)\chi_{8800}(3277,\cdot) 11 11 e(3940)e\left(\frac{39}{40}\right) −1-1 e(1920)e\left(\frac{19}{20}\right) e(2340)e\left(\frac{23}{40}\right) e(1320)e\left(\frac{13}{20}\right) e(2140)e\left(\frac{21}{40}\right) e(1940)e\left(\frac{19}{40}\right) e(45)e\left(\frac{4}{5}\right) e(3740)e\left(\frac{37}{40}\right) e(940)e\left(\frac{9}{40}\right)
χ8800(4773,⋅)\chi_{8800}(4773,\cdot) 11 11 e(940)e\left(\frac{9}{40}\right) −1-1 e(920)e\left(\frac{9}{20}\right) e(3340)e\left(\frac{33}{40}\right) e(320)e\left(\frac{3}{20}\right) e(1140)e\left(\frac{11}{40}\right) e(2940)e\left(\frac{29}{40}\right) e(45)e\left(\frac{4}{5}\right) e(2740)e\left(\frac{27}{40}\right) e(3940)e\left(\frac{39}{40}\right)
χ8800(5037,⋅)\chi_{8800}(5037,\cdot) 11 11 e(3140)e\left(\frac{31}{40}\right) −1-1 e(1120)e\left(\frac{11}{20}\right) e(740)e\left(\frac{7}{40}\right) e(1720)e\left(\frac{17}{20}\right) e(2940)e\left(\frac{29}{40}\right) e(1140)e\left(\frac{11}{40}\right) e(15)e\left(\frac{1}{5}\right) e(1340)e\left(\frac{13}{40}\right) e(140)e\left(\frac{1}{40}\right)
χ8800(5653,⋅)\chi_{8800}(5653,\cdot) 11 11 e(1340)e\left(\frac{13}{40}\right) −1-1 e(1320)e\left(\frac{13}{20}\right) e(2140)e\left(\frac{21}{40}\right) e(1120)e\left(\frac{11}{20}\right) e(740)e\left(\frac{7}{40}\right) e(3340)e\left(\frac{33}{40}\right) e(35)e\left(\frac{3}{5}\right) e(3940)e\left(\frac{39}{40}\right) e(340)e\left(\frac{3}{40}\right)
χ8800(5917,⋅)\chi_{8800}(5917,\cdot) 11 11 e(2740)e\left(\frac{27}{40}\right) −1-1 e(720)e\left(\frac{7}{20}\right) e(1940)e\left(\frac{19}{40}\right) e(920)e\left(\frac{9}{20}\right) e(3340)e\left(\frac{33}{40}\right) e(740)e\left(\frac{7}{40}\right) e(25)e\left(\frac{2}{5}\right) e(140)e\left(\frac{1}{40}\right) e(3740)e\left(\frac{37}{40}\right)
χ8800(6533,⋅)\chi_{8800}(6533,\cdot) 11 11 e(1740)e\left(\frac{17}{40}\right) −1-1 e(1720)e\left(\frac{17}{20}\right) e(940)e\left(\frac{9}{40}\right) e(1920)e\left(\frac{19}{20}\right) e(340)e\left(\frac{3}{40}\right) e(3740)e\left(\frac{37}{40}\right) e(25)e\left(\frac{2}{5}\right) e(1140)e\left(\frac{11}{40}\right) e(740)e\left(\frac{7}{40}\right)
χ8800(6797,⋅)\chi_{8800}(6797,\cdot) 11 11 e(2340)e\left(\frac{23}{40}\right) −1-1 e(320)e\left(\frac{3}{20}\right) e(3140)e\left(\frac{31}{40}\right) e(120)e\left(\frac{1}{20}\right) e(3740)e\left(\frac{37}{40}\right) e(340)e\left(\frac{3}{40}\right) e(35)e\left(\frac{3}{5}\right) e(2940)e\left(\frac{29}{40}\right) e(3340)e\left(\frac{33}{40}\right)
χ8800(7413,⋅)\chi_{8800}(7413,\cdot) 11 11 e(2140)e\left(\frac{21}{40}\right) −1-1 e(120)e\left(\frac{1}{20}\right) e(3740)e\left(\frac{37}{40}\right) e(720)e\left(\frac{7}{20}\right) e(3940)e\left(\frac{39}{40}\right) e(140)e\left(\frac{1}{40}\right) e(15)e\left(\frac{1}{5}\right) e(2340)e\left(\frac{23}{40}\right) e(1140)e\left(\frac{11}{40}\right)
χ8800(7677,⋅)\chi_{8800}(7677,\cdot) 11 11 e(1940)e\left(\frac{19}{40}\right) −1-1 e(1920)e\left(\frac{19}{20}\right) e(340)e\left(\frac{3}{40}\right) e(1320)e\left(\frac{13}{20}\right) e(140)e\left(\frac{1}{40}\right) e(3940)e\left(\frac{39}{40}\right) e(45)e\left(\frac{4}{5}\right) e(1740)e\left(\frac{17}{40}\right) e(2940)e\left(\frac{29}{40}\right)