Properties

Label 28900.7449
Modulus 2890028900
Conductor 8585
Order 1616
Real no
Primitive no
Minimal no
Parity odd

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(28900, base_ring=CyclotomicField(16)) M = H._module chi = DirichletCharacter(H, M([0,8,1]))
 
Copy content pari:[g,chi] = znchar(Mod(7449,28900))
 

Basic properties

Modulus: 2890028900
Conductor: 8585
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 χ85(54,)\chi_{85}(54,\cdot)
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Galois orbit 28900.bp

χ28900(249,)\chi_{28900}(249,\cdot) χ28900(4549,)\chi_{28900}(4549,\cdot) χ28900(5649,)\chi_{28900}(5649,\cdot) χ28900(7449,)\chi_{28900}(7449,\cdot) χ28900(16249,)\chi_{28900}(16249,\cdot) χ28900(18049,)\chi_{28900}(18049,\cdot) χ28900(19149,)\chi_{28900}(19149,\cdot) χ28900(23449,)\chi_{28900}(23449,\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: 16.0.1118134004496021794140625.1

Values on generators

(14451,24277,23701)(14451,24277,23701)(1,1,e(116))(1,-1,e\left(\frac{1}{16}\right))

First values

aa 1-1113377991111131319192121232327272929
χ28900(7449,a) \chi_{ 28900 }(7449, a) 1-111e(916)e\left(\frac{9}{16}\right)e(316)e\left(\frac{3}{16}\right)e(18)e\left(\frac{1}{8}\right)e(716)e\left(\frac{7}{16}\right)i-ie(78)e\left(\frac{7}{8}\right)i-ie(716)e\left(\frac{7}{16}\right)e(1116)e\left(\frac{11}{16}\right)e(1316)e\left(\frac{13}{16}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ28900(7449,a)   \chi_{ 28900 }(7449,a) \; at   a=\;a = e.g. 2