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Properties

Label 4032.ga
Modulus 40324032
Conductor 20162016
Order 2424
Real no
Primitive no
Minimal no
Parity even

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4032, base_ring=CyclotomicField(24))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,9,16,8]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(457,4032))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 40324032
Conductor: 20162016
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 2424
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 2016.fs
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ24)\Q(\zeta_{24})
Fixed field: Number field defined by a degree 24 polynomial

Characters in Galois orbit

Character −1-1 11 55 1111 1313 1717 1919 2323 2525 2929 3131 3737
χ4032(457,⋅)\chi_{4032}(457,\cdot) 11 11 e(38)e\left(\frac{3}{8}\right) e(78)e\left(\frac{7}{8}\right) e(2324)e\left(\frac{23}{24}\right) e(56)e\left(\frac{5}{6}\right) e(724)e\left(\frac{7}{24}\right) ii −i-i e(1924)e\left(\frac{19}{24}\right) e(23)e\left(\frac{2}{3}\right) e(124)e\left(\frac{1}{24}\right)
χ4032(697,⋅)\chi_{4032}(697,\cdot) 11 11 e(58)e\left(\frac{5}{8}\right) e(18)e\left(\frac{1}{8}\right) e(124)e\left(\frac{1}{24}\right) e(16)e\left(\frac{1}{6}\right) e(1724)e\left(\frac{17}{24}\right) −i-i ii e(524)e\left(\frac{5}{24}\right) e(13)e\left(\frac{1}{3}\right) e(2324)e\left(\frac{23}{24}\right)
χ4032(1465,⋅)\chi_{4032}(1465,\cdot) 11 11 e(58)e\left(\frac{5}{8}\right) e(18)e\left(\frac{1}{8}\right) e(1724)e\left(\frac{17}{24}\right) e(56)e\left(\frac{5}{6}\right) e(124)e\left(\frac{1}{24}\right) −i-i ii e(1324)e\left(\frac{13}{24}\right) e(23)e\left(\frac{2}{3}\right) e(724)e\left(\frac{7}{24}\right)
χ4032(1705,⋅)\chi_{4032}(1705,\cdot) 11 11 e(78)e\left(\frac{7}{8}\right) e(38)e\left(\frac{3}{8}\right) e(1924)e\left(\frac{19}{24}\right) e(16)e\left(\frac{1}{6}\right) e(1124)e\left(\frac{11}{24}\right) ii −i-i e(2324)e\left(\frac{23}{24}\right) e(13)e\left(\frac{1}{3}\right) e(524)e\left(\frac{5}{24}\right)
χ4032(2473,⋅)\chi_{4032}(2473,\cdot) 11 11 e(78)e\left(\frac{7}{8}\right) e(38)e\left(\frac{3}{8}\right) e(1124)e\left(\frac{11}{24}\right) e(56)e\left(\frac{5}{6}\right) e(1924)e\left(\frac{19}{24}\right) ii −i-i e(724)e\left(\frac{7}{24}\right) e(23)e\left(\frac{2}{3}\right) e(1324)e\left(\frac{13}{24}\right)
χ4032(2713,⋅)\chi_{4032}(2713,\cdot) 11 11 e(18)e\left(\frac{1}{8}\right) e(58)e\left(\frac{5}{8}\right) e(1324)e\left(\frac{13}{24}\right) e(16)e\left(\frac{1}{6}\right) e(524)e\left(\frac{5}{24}\right) −i-i ii e(1724)e\left(\frac{17}{24}\right) e(13)e\left(\frac{1}{3}\right) e(1124)e\left(\frac{11}{24}\right)
χ4032(3481,⋅)\chi_{4032}(3481,\cdot) 11 11 e(18)e\left(\frac{1}{8}\right) e(58)e\left(\frac{5}{8}\right) e(524)e\left(\frac{5}{24}\right) e(56)e\left(\frac{5}{6}\right) e(1324)e\left(\frac{13}{24}\right) −i-i ii e(124)e\left(\frac{1}{24}\right) e(23)e\left(\frac{2}{3}\right) e(1924)e\left(\frac{19}{24}\right)
χ4032(3721,⋅)\chi_{4032}(3721,\cdot) 11 11 e(38)e\left(\frac{3}{8}\right) e(78)e\left(\frac{7}{8}\right) e(724)e\left(\frac{7}{24}\right) e(16)e\left(\frac{1}{6}\right) e(2324)e\left(\frac{23}{24}\right) ii −i-i e(1124)e\left(\frac{11}{24}\right) e(13)e\left(\frac{1}{3}\right) e(1724)e\left(\frac{17}{24}\right)