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Properties

Label 2016.fb
Modulus 20162016
Conductor 20162016
Order 2424
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(2016, base_ring=CyclotomicField(24))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,3,20,12]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(293,2016))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 20162016
Conductor: 20162016
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 2424
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(ζ24)\Q(\zeta_{24})
Fixed field: 24.24.20574592712627357116606755731219706996406776278896607232.1

Characters in Galois orbit

Character −1-1 11 55 1111 1313 1717 1919 2323 2525 2929 3131 3737
χ2016(293,⋅)\chi_{2016}(293,\cdot) 11 11 e(1924)e\left(\frac{19}{24}\right) e(1124)e\left(\frac{11}{24}\right) e(124)e\left(\frac{1}{24}\right) −1-1 e(38)e\left(\frac{3}{8}\right) e(1112)e\left(\frac{11}{12}\right) e(712)e\left(\frac{7}{12}\right) e(524)e\left(\frac{5}{24}\right) e(16)e\left(\frac{1}{6}\right) e(18)e\left(\frac{1}{8}\right)
χ2016(461,⋅)\chi_{2016}(461,\cdot) 11 11 e(524)e\left(\frac{5}{24}\right) e(1324)e\left(\frac{13}{24}\right) e(2324)e\left(\frac{23}{24}\right) −1-1 e(58)e\left(\frac{5}{8}\right) e(112)e\left(\frac{1}{12}\right) e(512)e\left(\frac{5}{12}\right) e(1924)e\left(\frac{19}{24}\right) e(56)e\left(\frac{5}{6}\right) e(78)e\left(\frac{7}{8}\right)
χ2016(797,⋅)\chi_{2016}(797,\cdot) 11 11 e(124)e\left(\frac{1}{24}\right) e(1724)e\left(\frac{17}{24}\right) e(1924)e\left(\frac{19}{24}\right) −1-1 e(18)e\left(\frac{1}{8}\right) e(512)e\left(\frac{5}{12}\right) e(112)e\left(\frac{1}{12}\right) e(2324)e\left(\frac{23}{24}\right) e(16)e\left(\frac{1}{6}\right) e(38)e\left(\frac{3}{8}\right)
χ2016(965,⋅)\chi_{2016}(965,\cdot) 11 11 e(1124)e\left(\frac{11}{24}\right) e(1924)e\left(\frac{19}{24}\right) e(1724)e\left(\frac{17}{24}\right) −1-1 e(38)e\left(\frac{3}{8}\right) e(712)e\left(\frac{7}{12}\right) e(1112)e\left(\frac{11}{12}\right) e(1324)e\left(\frac{13}{24}\right) e(56)e\left(\frac{5}{6}\right) e(18)e\left(\frac{1}{8}\right)
χ2016(1301,⋅)\chi_{2016}(1301,\cdot) 11 11 e(724)e\left(\frac{7}{24}\right) e(2324)e\left(\frac{23}{24}\right) e(1324)e\left(\frac{13}{24}\right) −1-1 e(78)e\left(\frac{7}{8}\right) e(1112)e\left(\frac{11}{12}\right) e(712)e\left(\frac{7}{12}\right) e(1724)e\left(\frac{17}{24}\right) e(16)e\left(\frac{1}{6}\right) e(58)e\left(\frac{5}{8}\right)
χ2016(1469,⋅)\chi_{2016}(1469,\cdot) 11 11 e(1724)e\left(\frac{17}{24}\right) e(124)e\left(\frac{1}{24}\right) e(1124)e\left(\frac{11}{24}\right) −1-1 e(18)e\left(\frac{1}{8}\right) e(112)e\left(\frac{1}{12}\right) e(512)e\left(\frac{5}{12}\right) e(724)e\left(\frac{7}{24}\right) e(56)e\left(\frac{5}{6}\right) e(38)e\left(\frac{3}{8}\right)
χ2016(1805,⋅)\chi_{2016}(1805,\cdot) 11 11 e(1324)e\left(\frac{13}{24}\right) e(524)e\left(\frac{5}{24}\right) e(724)e\left(\frac{7}{24}\right) −1-1 e(58)e\left(\frac{5}{8}\right) e(512)e\left(\frac{5}{12}\right) e(112)e\left(\frac{1}{12}\right) e(1124)e\left(\frac{11}{24}\right) e(16)e\left(\frac{1}{6}\right) e(78)e\left(\frac{7}{8}\right)
χ2016(1973,⋅)\chi_{2016}(1973,\cdot) 11 11 e(2324)e\left(\frac{23}{24}\right) e(724)e\left(\frac{7}{24}\right) e(524)e\left(\frac{5}{24}\right) −1-1 e(78)e\left(\frac{7}{8}\right) e(712)e\left(\frac{7}{12}\right) e(1112)e\left(\frac{11}{12}\right) e(124)e\left(\frac{1}{24}\right) e(56)e\left(\frac{5}{6}\right) e(58)e\left(\frac{5}{8}\right)