Properties

Label 3360.421
Modulus 33603360
Conductor 3232
Order 88
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(3360, base_ring=CyclotomicField(8)) M = H._module chi = DirichletCharacter(H, M([0,1,0,0,0]))
 
Copy content pari:[g,chi] = znchar(Mod(421,3360))
 

Basic properties

Modulus: 33603360
Conductor: 3232
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 88
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from χ32(5,)\chi_{32}(5,\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 3360.en

χ3360(421,)\chi_{3360}(421,\cdot) χ3360(1261,)\chi_{3360}(1261,\cdot) χ3360(2101,)\chi_{3360}(2101,\cdot) χ3360(2941,)\chi_{3360}(2941,\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(ζ8)\Q(\zeta_{8})
Fixed field: Q(ζ32)+\Q(\zeta_{32})^+

Values on generators

(1471,421,1121,2017,1921)(1471,421,1121,2017,1921)(1,e(18),1,1,1)(1,e\left(\frac{1}{8}\right),1,1,1)

First values

aa 1-1111111131317171919232329293131373741414343
χ3360(421,a) \chi_{ 3360 }(421, a) 1111e(58)e\left(\frac{5}{8}\right)e(78)e\left(\frac{7}{8}\right)1-1e(78)e\left(\frac{7}{8}\right)i-ie(38)e\left(\frac{3}{8}\right)11e(18)e\left(\frac{1}{8}\right)i-ie(58)e\left(\frac{5}{8}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ3360(421,a)   \chi_{ 3360 }(421,a) \; at   a=\;a = e.g. 2