Properties

Label 7488.5147
Modulus 74887488
Conductor 24962496
Order 1616
Real no
Primitive no
Minimal yes
Parity even

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7488, base_ring=CyclotomicField(16)) M = H._module chi = DirichletCharacter(H, M([8,9,8,8]))
 
Copy content pari:[g,chi] = znchar(Mod(5147,7488))
 

Basic properties

Modulus: 74887488
Conductor: 24962496
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 1616
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from χ2496(155,)\chi_{2496}(155,\cdot)
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Galois orbit 7488.ij

χ7488(467,)\chi_{7488}(467,\cdot) χ7488(1403,)\chi_{7488}(1403,\cdot) χ7488(2339,)\chi_{7488}(2339,\cdot) χ7488(3275,)\chi_{7488}(3275,\cdot) χ7488(4211,)\chi_{7488}(4211,\cdot) χ7488(5147,)\chi_{7488}(5147,\cdot) χ7488(6083,)\chi_{7488}(6083,\cdot) χ7488(7019,)\chi_{7488}(7019,\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(ζ16)\Q(\zeta_{16})
Fixed field: 16.16.3235091090906039146864124182111715328.1

Values on generators

(703,6085,5825,5761)(703,6085,5825,5761)(1,e(916),1,1)(-1,e\left(\frac{9}{16}\right),-1,-1)

First values

aa 1-111557711111717191923232525292931313535
χ7488(5147,a) \chi_{ 7488 }(5147, a) 1111e(916)e\left(\frac{9}{16}\right)e(58)e\left(\frac{5}{8}\right)e(516)e\left(\frac{5}{16}\right)iie(1516)e\left(\frac{15}{16}\right)e(78)e\left(\frac{7}{8}\right)e(18)e\left(\frac{1}{8}\right)e(1116)e\left(\frac{11}{16}\right)1-1e(316)e\left(\frac{3}{16}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ7488(5147,a)   \chi_{ 7488 }(5147,a) \; at   a=\;a = e.g. 2