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Properties

Label 4160.it
Modulus 41604160
Conductor 20802080
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(4160, base_ring=CyclotomicField(24))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,9,6,22]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(137,4160))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 41604160
Conductor: 20802080
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 2424
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 2080.hn
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 33 77 99 1111 1717 1919 2121 2323 2727 2929
χ4160(137,⋅)\chi_{4160}(137,\cdot) 11 11 e(1324)e\left(\frac{13}{24}\right) e(112)e\left(\frac{1}{12}\right) e(112)e\left(\frac{1}{12}\right) e(724)e\left(\frac{7}{24}\right) e(712)e\left(\frac{7}{12}\right) e(1724)e\left(\frac{17}{24}\right) e(58)e\left(\frac{5}{8}\right) e(16)e\left(\frac{1}{6}\right) e(58)e\left(\frac{5}{8}\right) e(724)e\left(\frac{7}{24}\right)
χ4160(297,⋅)\chi_{4160}(297,\cdot) 11 11 e(1724)e\left(\frac{17}{24}\right) e(512)e\left(\frac{5}{12}\right) e(512)e\left(\frac{5}{12}\right) e(1124)e\left(\frac{11}{24}\right) e(1112)e\left(\frac{11}{12}\right) e(1324)e\left(\frac{13}{24}\right) e(18)e\left(\frac{1}{8}\right) e(56)e\left(\frac{5}{6}\right) e(18)e\left(\frac{1}{8}\right) e(1124)e\left(\frac{11}{24}\right)
χ4160(1913,⋅)\chi_{4160}(1913,\cdot) 11 11 e(1124)e\left(\frac{11}{24}\right) e(1112)e\left(\frac{11}{12}\right) e(1112)e\left(\frac{11}{12}\right) e(1724)e\left(\frac{17}{24}\right) e(512)e\left(\frac{5}{12}\right) e(724)e\left(\frac{7}{24}\right) e(38)e\left(\frac{3}{8}\right) e(56)e\left(\frac{5}{6}\right) e(38)e\left(\frac{3}{8}\right) e(1724)e\left(\frac{17}{24}\right)
χ4160(2073,⋅)\chi_{4160}(2073,\cdot) 11 11 e(724)e\left(\frac{7}{24}\right) e(712)e\left(\frac{7}{12}\right) e(712)e\left(\frac{7}{12}\right) e(1324)e\left(\frac{13}{24}\right) e(112)e\left(\frac{1}{12}\right) e(1124)e\left(\frac{11}{24}\right) e(78)e\left(\frac{7}{8}\right) e(16)e\left(\frac{1}{6}\right) e(78)e\left(\frac{7}{8}\right) e(1324)e\left(\frac{13}{24}\right)
χ4160(2217,⋅)\chi_{4160}(2217,\cdot) 11 11 e(124)e\left(\frac{1}{24}\right) e(112)e\left(\frac{1}{12}\right) e(112)e\left(\frac{1}{12}\right) e(1924)e\left(\frac{19}{24}\right) e(712)e\left(\frac{7}{12}\right) e(524)e\left(\frac{5}{24}\right) e(18)e\left(\frac{1}{8}\right) e(16)e\left(\frac{1}{6}\right) e(18)e\left(\frac{1}{8}\right) e(1924)e\left(\frac{19}{24}\right)
χ4160(2377,⋅)\chi_{4160}(2377,\cdot) 11 11 e(524)e\left(\frac{5}{24}\right) e(512)e\left(\frac{5}{12}\right) e(512)e\left(\frac{5}{12}\right) e(2324)e\left(\frac{23}{24}\right) e(1112)e\left(\frac{11}{12}\right) e(124)e\left(\frac{1}{24}\right) e(58)e\left(\frac{5}{8}\right) e(56)e\left(\frac{5}{6}\right) e(58)e\left(\frac{5}{8}\right) e(2324)e\left(\frac{23}{24}\right)
χ4160(3993,⋅)\chi_{4160}(3993,\cdot) 11 11 e(2324)e\left(\frac{23}{24}\right) e(1112)e\left(\frac{11}{12}\right) e(1112)e\left(\frac{11}{12}\right) e(524)e\left(\frac{5}{24}\right) e(512)e\left(\frac{5}{12}\right) e(1924)e\left(\frac{19}{24}\right) e(78)e\left(\frac{7}{8}\right) e(56)e\left(\frac{5}{6}\right) e(78)e\left(\frac{7}{8}\right) e(524)e\left(\frac{5}{24}\right)
χ4160(4153,⋅)\chi_{4160}(4153,\cdot) 11 11 e(1924)e\left(\frac{19}{24}\right) e(712)e\left(\frac{7}{12}\right) e(712)e\left(\frac{7}{12}\right) e(124)e\left(\frac{1}{24}\right) e(112)e\left(\frac{1}{12}\right) e(2324)e\left(\frac{23}{24}\right) e(38)e\left(\frac{3}{8}\right) e(16)e\left(\frac{1}{6}\right) e(38)e\left(\frac{3}{8}\right) e(124)e\left(\frac{1}{24}\right)