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Properties

Label 3744.iq
Modulus 37443744
Conductor 37443744
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(3744, base_ring=CyclotomicField(24))
 
M = H._module
 
chi = DirichletCharacter(H, M([12,21,16,14]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(115,3744))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 37443744
Conductor: 37443744
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: 24.24.58941814124004967164712359225739836985369047739311632559462382829568.2

Characters in Galois orbit

Character −1-1 11 55 77 1111 1717 1919 2323 2525 2929 3131 3535
χ3744(115,⋅)\chi_{3744}(115,\cdot) 11 11 e(1124)e\left(\frac{11}{24}\right) e(13)e\left(\frac{1}{3}\right) e(58)e\left(\frac{5}{8}\right) e(23)e\left(\frac{2}{3}\right) e(1324)e\left(\frac{13}{24}\right) e(1112)e\left(\frac{11}{12}\right) e(1112)e\left(\frac{11}{12}\right) e(58)e\left(\frac{5}{8}\right) e(112)e\left(\frac{1}{12}\right) e(1924)e\left(\frac{19}{24}\right)
χ3744(787,⋅)\chi_{3744}(787,\cdot) 11 11 e(1924)e\left(\frac{19}{24}\right) e(23)e\left(\frac{2}{3}\right) e(58)e\left(\frac{5}{8}\right) e(13)e\left(\frac{1}{3}\right) e(524)e\left(\frac{5}{24}\right) e(712)e\left(\frac{7}{12}\right) e(712)e\left(\frac{7}{12}\right) e(58)e\left(\frac{5}{8}\right) e(512)e\left(\frac{5}{12}\right) e(1124)e\left(\frac{11}{24}\right)
χ3744(1579,⋅)\chi_{3744}(1579,\cdot) 11 11 e(124)e\left(\frac{1}{24}\right) e(23)e\left(\frac{2}{3}\right) e(78)e\left(\frac{7}{8}\right) e(13)e\left(\frac{1}{3}\right) e(2324)e\left(\frac{23}{24}\right) e(112)e\left(\frac{1}{12}\right) e(112)e\left(\frac{1}{12}\right) e(78)e\left(\frac{7}{8}\right) e(1112)e\left(\frac{11}{12}\right) e(1724)e\left(\frac{17}{24}\right)
χ3744(1627,⋅)\chi_{3744}(1627,\cdot) 11 11 e(524)e\left(\frac{5}{24}\right) e(13)e\left(\frac{1}{3}\right) e(38)e\left(\frac{3}{8}\right) e(23)e\left(\frac{2}{3}\right) e(1924)e\left(\frac{19}{24}\right) e(512)e\left(\frac{5}{12}\right) e(512)e\left(\frac{5}{12}\right) e(38)e\left(\frac{3}{8}\right) e(712)e\left(\frac{7}{12}\right) e(1324)e\left(\frac{13}{24}\right)
χ3744(1987,⋅)\chi_{3744}(1987,\cdot) 11 11 e(2324)e\left(\frac{23}{24}\right) e(13)e\left(\frac{1}{3}\right) e(18)e\left(\frac{1}{8}\right) e(23)e\left(\frac{2}{3}\right) e(124)e\left(\frac{1}{24}\right) e(1112)e\left(\frac{11}{12}\right) e(1112)e\left(\frac{11}{12}\right) e(18)e\left(\frac{1}{8}\right) e(112)e\left(\frac{1}{12}\right) e(724)e\left(\frac{7}{24}\right)
χ3744(2659,⋅)\chi_{3744}(2659,\cdot) 11 11 e(724)e\left(\frac{7}{24}\right) e(23)e\left(\frac{2}{3}\right) e(18)e\left(\frac{1}{8}\right) e(13)e\left(\frac{1}{3}\right) e(1724)e\left(\frac{17}{24}\right) e(712)e\left(\frac{7}{12}\right) e(712)e\left(\frac{7}{12}\right) e(18)e\left(\frac{1}{8}\right) e(512)e\left(\frac{5}{12}\right) e(2324)e\left(\frac{23}{24}\right)
χ3744(3451,⋅)\chi_{3744}(3451,\cdot) 11 11 e(1324)e\left(\frac{13}{24}\right) e(23)e\left(\frac{2}{3}\right) e(38)e\left(\frac{3}{8}\right) e(13)e\left(\frac{1}{3}\right) e(1124)e\left(\frac{11}{24}\right) e(112)e\left(\frac{1}{12}\right) e(112)e\left(\frac{1}{12}\right) e(38)e\left(\frac{3}{8}\right) e(1112)e\left(\frac{11}{12}\right) e(524)e\left(\frac{5}{24}\right)
χ3744(3499,⋅)\chi_{3744}(3499,\cdot) 11 11 e(1724)e\left(\frac{17}{24}\right) e(13)e\left(\frac{1}{3}\right) e(78)e\left(\frac{7}{8}\right) e(23)e\left(\frac{2}{3}\right) e(724)e\left(\frac{7}{24}\right) e(512)e\left(\frac{5}{12}\right) e(512)e\left(\frac{5}{12}\right) e(78)e\left(\frac{7}{8}\right) e(712)e\left(\frac{7}{12}\right) e(124)e\left(\frac{1}{24}\right)