Properties

Label 4160.457
Modulus 41604160
Conductor 20802080
Order 2424
Real no
Primitive no
Minimal no
Parity even

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4160, base_ring=CyclotomicField(24)) M = H._module chi = DirichletCharacter(H, M([0,9,6,2]))
 
Copy content pari:[g,chi] = znchar(Mod(457,4160))
 

Basic properties

Modulus: 41604160
Conductor: 20802080
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 2424
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from χ2080(1757,)\chi_{2080}(1757,\cdot)
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Galois orbit 4160.iq

χ4160(457,)\chi_{4160}(457,\cdot) χ4160(617,)\chi_{4160}(617,\cdot) χ4160(1593,)\chi_{4160}(1593,\cdot) χ4160(1753,)\chi_{4160}(1753,\cdot) χ4160(2537,)\chi_{4160}(2537,\cdot) χ4160(2697,)\chi_{4160}(2697,\cdot) χ4160(3673,)\chi_{4160}(3673,\cdot) χ4160(3833,)\chi_{4160}(3833,\cdot)

Copy content sage:chi.galois_orbit()
 
Copy content pari:order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

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

Values on generators

(4031,261,2497,1601)(4031,261,2497,1601)(1,e(38),i,e(112))(1,e\left(\frac{3}{8}\right),i,e\left(\frac{1}{12}\right))

First values

aa 1-1113377991111171719192121232327272929
χ4160(457,a) \chi_{ 4160 }(457, a) 1111e(524)e\left(\frac{5}{24}\right)e(1112)e\left(\frac{11}{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(58)e\left(\frac{5}{8}\right)e(2324)e\left(\frac{23}{24}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ4160(457,a)   \chi_{ 4160 }(457,a) \; at   a=\;a = e.g. 2