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Properties

Label 8800.nn
Modulus 88008800
Conductor 352352
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([0,35,0,8]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(301,8800))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 88008800
Conductor: 352352
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 4040
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 352.bf
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: 40.40.96430685261162182749113906515642066253992366248338958954046471967872161601814528.1

Characters in Galois orbit

Character −1-1 11 33 77 99 1313 1717 1919 2121 2323 2727 2929
χ8800(301,⋅)\chi_{8800}(301,\cdot) 11 11 e(940)e\left(\frac{9}{40}\right) e(320)e\left(\frac{3}{20}\right) e(920)e\left(\frac{9}{20}\right) e(1340)e\left(\frac{13}{40}\right) e(310)e\left(\frac{3}{10}\right) e(2940)e\left(\frac{29}{40}\right) e(38)e\left(\frac{3}{8}\right) ii e(2740)e\left(\frac{27}{40}\right) e(140)e\left(\frac{1}{40}\right)
χ8800(1301,⋅)\chi_{8800}(1301,\cdot) 11 11 e(1140)e\left(\frac{11}{40}\right) e(1720)e\left(\frac{17}{20}\right) e(1120)e\left(\frac{11}{20}\right) e(740)e\left(\frac{7}{40}\right) e(710)e\left(\frac{7}{10}\right) e(3140)e\left(\frac{31}{40}\right) e(18)e\left(\frac{1}{8}\right) −i-i e(3340)e\left(\frac{33}{40}\right) e(1940)e\left(\frac{19}{40}\right)
χ8800(1501,⋅)\chi_{8800}(1501,\cdot) 11 11 e(1340)e\left(\frac{13}{40}\right) e(1120)e\left(\frac{11}{20}\right) e(1320)e\left(\frac{13}{20}\right) e(140)e\left(\frac{1}{40}\right) e(110)e\left(\frac{1}{10}\right) e(3340)e\left(\frac{33}{40}\right) e(78)e\left(\frac{7}{8}\right) ii e(3940)e\left(\frac{39}{40}\right) e(3740)e\left(\frac{37}{40}\right)
χ8800(1901,⋅)\chi_{8800}(1901,\cdot) 11 11 e(1740)e\left(\frac{17}{40}\right) e(1920)e\left(\frac{19}{20}\right) e(1720)e\left(\frac{17}{20}\right) e(2940)e\left(\frac{29}{40}\right) e(910)e\left(\frac{9}{10}\right) e(3740)e\left(\frac{37}{40}\right) e(38)e\left(\frac{3}{8}\right) ii e(1140)e\left(\frac{11}{40}\right) e(3340)e\left(\frac{33}{40}\right)
χ8800(2501,⋅)\chi_{8800}(2501,\cdot) 11 11 e(3940)e\left(\frac{39}{40}\right) e(1320)e\left(\frac{13}{20}\right) e(1920)e\left(\frac{19}{20}\right) e(340)e\left(\frac{3}{40}\right) e(310)e\left(\frac{3}{10}\right) e(1940)e\left(\frac{19}{40}\right) e(58)e\left(\frac{5}{8}\right) −i-i e(3740)e\left(\frac{37}{40}\right) e(3140)e\left(\frac{31}{40}\right)
χ8800(3501,⋅)\chi_{8800}(3501,\cdot) 11 11 e(140)e\left(\frac{1}{40}\right) e(720)e\left(\frac{7}{20}\right) e(120)e\left(\frac{1}{20}\right) e(3740)e\left(\frac{37}{40}\right) e(710)e\left(\frac{7}{10}\right) e(2140)e\left(\frac{21}{40}\right) e(38)e\left(\frac{3}{8}\right) ii e(340)e\left(\frac{3}{40}\right) e(940)e\left(\frac{9}{40}\right)
χ8800(3701,⋅)\chi_{8800}(3701,\cdot) 11 11 e(340)e\left(\frac{3}{40}\right) e(120)e\left(\frac{1}{20}\right) e(320)e\left(\frac{3}{20}\right) e(3140)e\left(\frac{31}{40}\right) e(110)e\left(\frac{1}{10}\right) e(2340)e\left(\frac{23}{40}\right) e(18)e\left(\frac{1}{8}\right) −i-i e(940)e\left(\frac{9}{40}\right) e(2740)e\left(\frac{27}{40}\right)
χ8800(4101,⋅)\chi_{8800}(4101,\cdot) 11 11 e(740)e\left(\frac{7}{40}\right) e(920)e\left(\frac{9}{20}\right) e(720)e\left(\frac{7}{20}\right) e(1940)e\left(\frac{19}{40}\right) e(910)e\left(\frac{9}{10}\right) e(2740)e\left(\frac{27}{40}\right) e(58)e\left(\frac{5}{8}\right) −i-i e(2140)e\left(\frac{21}{40}\right) e(2340)e\left(\frac{23}{40}\right)
χ8800(4701,⋅)\chi_{8800}(4701,\cdot) 11 11 e(2940)e\left(\frac{29}{40}\right) e(320)e\left(\frac{3}{20}\right) e(920)e\left(\frac{9}{20}\right) e(3340)e\left(\frac{33}{40}\right) e(310)e\left(\frac{3}{10}\right) e(940)e\left(\frac{9}{40}\right) e(78)e\left(\frac{7}{8}\right) ii e(740)e\left(\frac{7}{40}\right) e(2140)e\left(\frac{21}{40}\right)
χ8800(5701,⋅)\chi_{8800}(5701,\cdot) 11 11 e(3140)e\left(\frac{31}{40}\right) e(1720)e\left(\frac{17}{20}\right) e(1120)e\left(\frac{11}{20}\right) e(2740)e\left(\frac{27}{40}\right) e(710)e\left(\frac{7}{10}\right) e(1140)e\left(\frac{11}{40}\right) e(58)e\left(\frac{5}{8}\right) −i-i e(1340)e\left(\frac{13}{40}\right) e(3940)e\left(\frac{39}{40}\right)
χ8800(5901,⋅)\chi_{8800}(5901,\cdot) 11 11 e(3340)e\left(\frac{33}{40}\right) e(1120)e\left(\frac{11}{20}\right) e(1320)e\left(\frac{13}{20}\right) e(2140)e\left(\frac{21}{40}\right) e(110)e\left(\frac{1}{10}\right) e(1340)e\left(\frac{13}{40}\right) e(38)e\left(\frac{3}{8}\right) ii e(1940)e\left(\frac{19}{40}\right) e(1740)e\left(\frac{17}{40}\right)
χ8800(6301,⋅)\chi_{8800}(6301,\cdot) 11 11 e(3740)e\left(\frac{37}{40}\right) e(1920)e\left(\frac{19}{20}\right) e(1720)e\left(\frac{17}{20}\right) e(940)e\left(\frac{9}{40}\right) e(910)e\left(\frac{9}{10}\right) e(1740)e\left(\frac{17}{40}\right) e(78)e\left(\frac{7}{8}\right) ii e(3140)e\left(\frac{31}{40}\right) e(1340)e\left(\frac{13}{40}\right)
χ8800(6901,⋅)\chi_{8800}(6901,\cdot) 11 11 e(1940)e\left(\frac{19}{40}\right) e(1320)e\left(\frac{13}{20}\right) e(1920)e\left(\frac{19}{20}\right) e(2340)e\left(\frac{23}{40}\right) e(310)e\left(\frac{3}{10}\right) e(3940)e\left(\frac{39}{40}\right) e(18)e\left(\frac{1}{8}\right) −i-i e(1740)e\left(\frac{17}{40}\right) e(1140)e\left(\frac{11}{40}\right)
χ8800(7901,⋅)\chi_{8800}(7901,\cdot) 11 11 e(2140)e\left(\frac{21}{40}\right) e(720)e\left(\frac{7}{20}\right) e(120)e\left(\frac{1}{20}\right) e(1740)e\left(\frac{17}{40}\right) e(710)e\left(\frac{7}{10}\right) e(140)e\left(\frac{1}{40}\right) e(78)e\left(\frac{7}{8}\right) ii e(2340)e\left(\frac{23}{40}\right) e(2940)e\left(\frac{29}{40}\right)
χ8800(8101,⋅)\chi_{8800}(8101,\cdot) 11 11 e(2340)e\left(\frac{23}{40}\right) e(120)e\left(\frac{1}{20}\right) e(320)e\left(\frac{3}{20}\right) e(1140)e\left(\frac{11}{40}\right) e(110)e\left(\frac{1}{10}\right) e(340)e\left(\frac{3}{40}\right) e(58)e\left(\frac{5}{8}\right) −i-i e(2940)e\left(\frac{29}{40}\right) e(740)e\left(\frac{7}{40}\right)
χ8800(8501,⋅)\chi_{8800}(8501,\cdot) 11 11 e(2740)e\left(\frac{27}{40}\right) e(920)e\left(\frac{9}{20}\right) e(720)e\left(\frac{7}{20}\right) e(3940)e\left(\frac{39}{40}\right) e(910)e\left(\frac{9}{10}\right) e(740)e\left(\frac{7}{40}\right) e(18)e\left(\frac{1}{8}\right) −i-i e(140)e\left(\frac{1}{40}\right) e(340)e\left(\frac{3}{40}\right)