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Properties

Label 8800.lo
Modulus 88008800
Conductor 17601760
Order 4040
Real no
Primitive no
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([0,15,30,4]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(893,8800))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 88008800
Conductor: 17601760
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 4040
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 1760.ds
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: 40.40.1314880012449506220994309247746612403564809108378301093397843089030698237952000000000000000000000000000000.2

Characters in Galois orbit

Character −1-1 11 33 77 99 1313 1717 1919 2121 2323 2727 2929
χ8800(893,⋅)\chi_{8800}(893,\cdot) 11 11 e(740)e\left(\frac{7}{40}\right) e(15)e\left(\frac{1}{5}\right) e(720)e\left(\frac{7}{20}\right) e(3940)e\left(\frac{39}{40}\right) e(320)e\left(\frac{3}{20}\right) e(1740)e\left(\frac{17}{40}\right) e(38)e\left(\frac{3}{8}\right) −1-1 e(2140)e\left(\frac{21}{40}\right) e(1340)e\left(\frac{13}{40}\right)
χ8800(1157,⋅)\chi_{8800}(1157,\cdot) 11 11 e(3740)e\left(\frac{37}{40}\right) e(15)e\left(\frac{1}{5}\right) e(1720)e\left(\frac{17}{20}\right) e(2940)e\left(\frac{29}{40}\right) e(1320)e\left(\frac{13}{20}\right) e(2740)e\left(\frac{27}{40}\right) e(18)e\left(\frac{1}{8}\right) −1-1 e(3140)e\left(\frac{31}{40}\right) e(2340)e\left(\frac{23}{40}\right)
χ8800(1293,⋅)\chi_{8800}(1293,\cdot) 11 11 e(340)e\left(\frac{3}{40}\right) e(45)e\left(\frac{4}{5}\right) e(320)e\left(\frac{3}{20}\right) e(1140)e\left(\frac{11}{40}\right) e(720)e\left(\frac{7}{20}\right) e(1340)e\left(\frac{13}{40}\right) e(78)e\left(\frac{7}{8}\right) −1-1 e(940)e\left(\frac{9}{40}\right) e(1740)e\left(\frac{17}{40}\right)
χ8800(1557,⋅)\chi_{8800}(1557,\cdot) 11 11 e(3340)e\left(\frac{33}{40}\right) e(45)e\left(\frac{4}{5}\right) e(1320)e\left(\frac{13}{20}\right) e(140)e\left(\frac{1}{40}\right) e(1720)e\left(\frac{17}{20}\right) e(2340)e\left(\frac{23}{40}\right) e(58)e\left(\frac{5}{8}\right) −1-1 e(1940)e\left(\frac{19}{40}\right) e(2740)e\left(\frac{27}{40}\right)
χ8800(2493,⋅)\chi_{8800}(2493,\cdot) 11 11 e(3940)e\left(\frac{39}{40}\right) e(25)e\left(\frac{2}{5}\right) e(1920)e\left(\frac{19}{20}\right) e(2340)e\left(\frac{23}{40}\right) e(1120)e\left(\frac{11}{20}\right) e(940)e\left(\frac{9}{40}\right) e(38)e\left(\frac{3}{8}\right) −1-1 e(3740)e\left(\frac{37}{40}\right) e(2140)e\left(\frac{21}{40}\right)
χ8800(2757,⋅)\chi_{8800}(2757,\cdot) 11 11 e(2940)e\left(\frac{29}{40}\right) e(25)e\left(\frac{2}{5}\right) e(920)e\left(\frac{9}{20}\right) e(1340)e\left(\frac{13}{40}\right) e(120)e\left(\frac{1}{20}\right) e(1940)e\left(\frac{19}{40}\right) e(18)e\left(\frac{1}{8}\right) −1-1 e(740)e\left(\frac{7}{40}\right) e(3140)e\left(\frac{31}{40}\right)
χ8800(3693,⋅)\chi_{8800}(3693,\cdot) 11 11 e(1140)e\left(\frac{11}{40}\right) e(35)e\left(\frac{3}{5}\right) e(1120)e\left(\frac{11}{20}\right) e(2740)e\left(\frac{27}{40}\right) e(1920)e\left(\frac{19}{20}\right) e(2140)e\left(\frac{21}{40}\right) e(78)e\left(\frac{7}{8}\right) −1-1 e(3340)e\left(\frac{33}{40}\right) e(940)e\left(\frac{9}{40}\right)
χ8800(3957,⋅)\chi_{8800}(3957,\cdot) 11 11 e(140)e\left(\frac{1}{40}\right) e(35)e\left(\frac{3}{5}\right) e(120)e\left(\frac{1}{20}\right) e(1740)e\left(\frac{17}{40}\right) e(920)e\left(\frac{9}{20}\right) e(3140)e\left(\frac{31}{40}\right) e(58)e\left(\frac{5}{8}\right) −1-1 e(340)e\left(\frac{3}{40}\right) e(1940)e\left(\frac{19}{40}\right)
χ8800(5293,⋅)\chi_{8800}(5293,\cdot) 11 11 e(2740)e\left(\frac{27}{40}\right) e(15)e\left(\frac{1}{5}\right) e(720)e\left(\frac{7}{20}\right) e(1940)e\left(\frac{19}{40}\right) e(320)e\left(\frac{3}{20}\right) e(3740)e\left(\frac{37}{40}\right) e(78)e\left(\frac{7}{8}\right) −1-1 e(140)e\left(\frac{1}{40}\right) e(3340)e\left(\frac{33}{40}\right)
χ8800(5557,⋅)\chi_{8800}(5557,\cdot) 11 11 e(1740)e\left(\frac{17}{40}\right) e(15)e\left(\frac{1}{5}\right) e(1720)e\left(\frac{17}{20}\right) e(940)e\left(\frac{9}{40}\right) e(1320)e\left(\frac{13}{20}\right) e(740)e\left(\frac{7}{40}\right) e(58)e\left(\frac{5}{8}\right) −1-1 e(1140)e\left(\frac{11}{40}\right) e(340)e\left(\frac{3}{40}\right)
χ8800(5693,⋅)\chi_{8800}(5693,\cdot) 11 11 e(2340)e\left(\frac{23}{40}\right) e(45)e\left(\frac{4}{5}\right) e(320)e\left(\frac{3}{20}\right) e(3140)e\left(\frac{31}{40}\right) e(720)e\left(\frac{7}{20}\right) e(3340)e\left(\frac{33}{40}\right) e(38)e\left(\frac{3}{8}\right) −1-1 e(2940)e\left(\frac{29}{40}\right) e(3740)e\left(\frac{37}{40}\right)
χ8800(5957,⋅)\chi_{8800}(5957,\cdot) 11 11 e(1340)e\left(\frac{13}{40}\right) e(45)e\left(\frac{4}{5}\right) e(1320)e\left(\frac{13}{20}\right) e(2140)e\left(\frac{21}{40}\right) e(1720)e\left(\frac{17}{20}\right) e(340)e\left(\frac{3}{40}\right) e(18)e\left(\frac{1}{8}\right) −1-1 e(3940)e\left(\frac{39}{40}\right) e(740)e\left(\frac{7}{40}\right)
χ8800(6893,⋅)\chi_{8800}(6893,\cdot) 11 11 e(1940)e\left(\frac{19}{40}\right) e(25)e\left(\frac{2}{5}\right) e(1920)e\left(\frac{19}{20}\right) e(340)e\left(\frac{3}{40}\right) e(1120)e\left(\frac{11}{20}\right) e(2940)e\left(\frac{29}{40}\right) e(78)e\left(\frac{7}{8}\right) −1-1 e(1740)e\left(\frac{17}{40}\right) e(140)e\left(\frac{1}{40}\right)
χ8800(7157,⋅)\chi_{8800}(7157,\cdot) 11 11 e(940)e\left(\frac{9}{40}\right) e(25)e\left(\frac{2}{5}\right) e(920)e\left(\frac{9}{20}\right) e(3340)e\left(\frac{33}{40}\right) e(120)e\left(\frac{1}{20}\right) e(3940)e\left(\frac{39}{40}\right) e(58)e\left(\frac{5}{8}\right) −1-1 e(2740)e\left(\frac{27}{40}\right) e(1140)e\left(\frac{11}{40}\right)
χ8800(8093,⋅)\chi_{8800}(8093,\cdot) 11 11 e(3140)e\left(\frac{31}{40}\right) e(35)e\left(\frac{3}{5}\right) e(1120)e\left(\frac{11}{20}\right) e(740)e\left(\frac{7}{40}\right) e(1920)e\left(\frac{19}{20}\right) e(140)e\left(\frac{1}{40}\right) e(38)e\left(\frac{3}{8}\right) −1-1 e(1340)e\left(\frac{13}{40}\right) e(2940)e\left(\frac{29}{40}\right)
χ8800(8357,⋅)\chi_{8800}(8357,\cdot) 11 11 e(2140)e\left(\frac{21}{40}\right) e(35)e\left(\frac{3}{5}\right) e(120)e\left(\frac{1}{20}\right) e(3740)e\left(\frac{37}{40}\right) e(920)e\left(\frac{9}{20}\right) e(1140)e\left(\frac{11}{40}\right) e(18)e\left(\frac{1}{8}\right) −1-1 e(2340)e\left(\frac{23}{40}\right) e(3940)e\left(\frac{39}{40}\right)