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Properties

Label 800.bz
Modulus 800800
Conductor 800800
Order 4040
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(800, base_ring=CyclotomicField(40))
 
M = H._module
 
chi = DirichletCharacter(H, M([20,35,36]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(19,800))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 800800
Conductor: 800800
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: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ40)\Q(\zeta_{40})
Fixed field: 40.0.15474250491067253436239052800000000000000000000000000000000000000000000000000000000000000000000.1

Characters in Galois orbit

Character −1-1 11 33 77 99 1111 1313 1717 1919 2121 2323 2727
χ800(19,⋅)\chi_{800}(19,\cdot) −1-1 11 e(1740)e\left(\frac{17}{40}\right) −i-i e(1720)e\left(\frac{17}{20}\right) e(1140)e\left(\frac{11}{40}\right) e(940)e\left(\frac{9}{40}\right) e(15)e\left(\frac{1}{5}\right) e(3340)e\left(\frac{33}{40}\right) e(740)e\left(\frac{7}{40}\right) e(1320)e\left(\frac{13}{20}\right) e(1140)e\left(\frac{11}{40}\right)
χ800(59,⋅)\chi_{800}(59,\cdot) −1-1 11 e(3140)e\left(\frac{31}{40}\right) ii e(1120)e\left(\frac{11}{20}\right) e(1340)e\left(\frac{13}{40}\right) e(740)e\left(\frac{7}{40}\right) e(35)e\left(\frac{3}{5}\right) e(3940)e\left(\frac{39}{40}\right) e(140)e\left(\frac{1}{40}\right) e(1920)e\left(\frac{19}{20}\right) e(1340)e\left(\frac{13}{40}\right)
χ800(139,⋅)\chi_{800}(139,\cdot) −1-1 11 e(1940)e\left(\frac{19}{40}\right) ii e(1920)e\left(\frac{19}{20}\right) e(1740)e\left(\frac{17}{40}\right) e(340)e\left(\frac{3}{40}\right) e(25)e\left(\frac{2}{5}\right) e(1140)e\left(\frac{11}{40}\right) e(2940)e\left(\frac{29}{40}\right) e(1120)e\left(\frac{11}{20}\right) e(1740)e\left(\frac{17}{40}\right)
χ800(179,⋅)\chi_{800}(179,\cdot) −1-1 11 e(3340)e\left(\frac{33}{40}\right) −i-i e(1320)e\left(\frac{13}{20}\right) e(1940)e\left(\frac{19}{40}\right) e(140)e\left(\frac{1}{40}\right) e(45)e\left(\frac{4}{5}\right) e(1740)e\left(\frac{17}{40}\right) e(2340)e\left(\frac{23}{40}\right) e(1720)e\left(\frac{17}{20}\right) e(1940)e\left(\frac{19}{40}\right)
χ800(219,⋅)\chi_{800}(219,\cdot) −1-1 11 e(740)e\left(\frac{7}{40}\right) ii e(720)e\left(\frac{7}{20}\right) e(2140)e\left(\frac{21}{40}\right) e(3940)e\left(\frac{39}{40}\right) e(15)e\left(\frac{1}{5}\right) e(2340)e\left(\frac{23}{40}\right) e(1740)e\left(\frac{17}{40}\right) e(320)e\left(\frac{3}{20}\right) e(2140)e\left(\frac{21}{40}\right)
χ800(259,⋅)\chi_{800}(259,\cdot) −1-1 11 e(2140)e\left(\frac{21}{40}\right) −i-i e(120)e\left(\frac{1}{20}\right) e(2340)e\left(\frac{23}{40}\right) e(3740)e\left(\frac{37}{40}\right) e(35)e\left(\frac{3}{5}\right) e(2940)e\left(\frac{29}{40}\right) e(1140)e\left(\frac{11}{40}\right) e(920)e\left(\frac{9}{20}\right) e(2340)e\left(\frac{23}{40}\right)
χ800(339,⋅)\chi_{800}(339,\cdot) −1-1 11 e(940)e\left(\frac{9}{40}\right) −i-i e(920)e\left(\frac{9}{20}\right) e(2740)e\left(\frac{27}{40}\right) e(3340)e\left(\frac{33}{40}\right) e(25)e\left(\frac{2}{5}\right) e(140)e\left(\frac{1}{40}\right) e(3940)e\left(\frac{39}{40}\right) e(120)e\left(\frac{1}{20}\right) e(2740)e\left(\frac{27}{40}\right)
χ800(379,⋅)\chi_{800}(379,\cdot) −1-1 11 e(2340)e\left(\frac{23}{40}\right) ii e(320)e\left(\frac{3}{20}\right) e(2940)e\left(\frac{29}{40}\right) e(3140)e\left(\frac{31}{40}\right) e(45)e\left(\frac{4}{5}\right) e(740)e\left(\frac{7}{40}\right) e(3340)e\left(\frac{33}{40}\right) e(720)e\left(\frac{7}{20}\right) e(2940)e\left(\frac{29}{40}\right)
χ800(419,⋅)\chi_{800}(419,\cdot) −1-1 11 e(3740)e\left(\frac{37}{40}\right) −i-i e(1720)e\left(\frac{17}{20}\right) e(3140)e\left(\frac{31}{40}\right) e(2940)e\left(\frac{29}{40}\right) e(15)e\left(\frac{1}{5}\right) e(1340)e\left(\frac{13}{40}\right) e(2740)e\left(\frac{27}{40}\right) e(1320)e\left(\frac{13}{20}\right) e(3140)e\left(\frac{31}{40}\right)
χ800(459,⋅)\chi_{800}(459,\cdot) −1-1 11 e(1140)e\left(\frac{11}{40}\right) ii e(1120)e\left(\frac{11}{20}\right) e(3340)e\left(\frac{33}{40}\right) e(2740)e\left(\frac{27}{40}\right) e(35)e\left(\frac{3}{5}\right) e(1940)e\left(\frac{19}{40}\right) e(2140)e\left(\frac{21}{40}\right) e(1920)e\left(\frac{19}{20}\right) e(3340)e\left(\frac{33}{40}\right)
χ800(539,⋅)\chi_{800}(539,\cdot) −1-1 11 e(3940)e\left(\frac{39}{40}\right) ii e(1920)e\left(\frac{19}{20}\right) e(3740)e\left(\frac{37}{40}\right) e(2340)e\left(\frac{23}{40}\right) e(25)e\left(\frac{2}{5}\right) e(3140)e\left(\frac{31}{40}\right) e(940)e\left(\frac{9}{40}\right) e(1120)e\left(\frac{11}{20}\right) e(3740)e\left(\frac{37}{40}\right)
χ800(579,⋅)\chi_{800}(579,\cdot) −1-1 11 e(1340)e\left(\frac{13}{40}\right) −i-i e(1320)e\left(\frac{13}{20}\right) e(3940)e\left(\frac{39}{40}\right) e(2140)e\left(\frac{21}{40}\right) e(45)e\left(\frac{4}{5}\right) e(3740)e\left(\frac{37}{40}\right) e(340)e\left(\frac{3}{40}\right) e(1720)e\left(\frac{17}{20}\right) e(3940)e\left(\frac{39}{40}\right)
χ800(619,⋅)\chi_{800}(619,\cdot) −1-1 11 e(2740)e\left(\frac{27}{40}\right) ii e(720)e\left(\frac{7}{20}\right) e(140)e\left(\frac{1}{40}\right) e(1940)e\left(\frac{19}{40}\right) e(15)e\left(\frac{1}{5}\right) e(340)e\left(\frac{3}{40}\right) e(3740)e\left(\frac{37}{40}\right) e(320)e\left(\frac{3}{20}\right) e(140)e\left(\frac{1}{40}\right)
χ800(659,⋅)\chi_{800}(659,\cdot) −1-1 11 e(140)e\left(\frac{1}{40}\right) −i-i e(120)e\left(\frac{1}{20}\right) e(340)e\left(\frac{3}{40}\right) e(1740)e\left(\frac{17}{40}\right) e(35)e\left(\frac{3}{5}\right) e(940)e\left(\frac{9}{40}\right) e(3140)e\left(\frac{31}{40}\right) e(920)e\left(\frac{9}{20}\right) e(340)e\left(\frac{3}{40}\right)
χ800(739,⋅)\chi_{800}(739,\cdot) −1-1 11 e(2940)e\left(\frac{29}{40}\right) −i-i e(920)e\left(\frac{9}{20}\right) e(740)e\left(\frac{7}{40}\right) e(1340)e\left(\frac{13}{40}\right) e(25)e\left(\frac{2}{5}\right) e(2140)e\left(\frac{21}{40}\right) e(1940)e\left(\frac{19}{40}\right) e(120)e\left(\frac{1}{20}\right) e(740)e\left(\frac{7}{40}\right)
χ800(779,⋅)\chi_{800}(779,\cdot) −1-1 11 e(340)e\left(\frac{3}{40}\right) ii e(320)e\left(\frac{3}{20}\right) e(940)e\left(\frac{9}{40}\right) e(1140)e\left(\frac{11}{40}\right) e(45)e\left(\frac{4}{5}\right) e(2740)e\left(\frac{27}{40}\right) e(1340)e\left(\frac{13}{40}\right) e(720)e\left(\frac{7}{20}\right) e(940)e\left(\frac{9}{40}\right)