Properties

Label 3267.928
Modulus 32673267
Conductor 9999
Order 1515
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(3267, base_ring=CyclotomicField(30)) M = H._module chi = DirichletCharacter(H, M([10,6]))
 
Copy content pari:[g,chi] = znchar(Mod(928,3267))
 

Basic properties

Modulus: 32673267
Conductor: 9999
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 1515
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from χ99(4,)\chi_{99}(4,\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 3267.o

χ3267(856,)\chi_{3267}(856,\cdot) χ3267(874,)\chi_{3267}(874,\cdot) χ3267(928,)\chi_{3267}(928,\cdot) χ3267(1576,)\chi_{3267}(1576,\cdot) χ3267(1963,)\chi_{3267}(1963,\cdot) χ3267(2017,)\chi_{3267}(2017,\cdot) χ3267(2665,)\chi_{3267}(2665,\cdot) χ3267(3034,)\chi_{3267}(3034,\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(ζ15)\Q(\zeta_{15})
Fixed field: 15.15.10943023107606534329121.1

Values on generators

(3026,244)(3026,244)(e(13),e(15))(e\left(\frac{1}{3}\right),e\left(\frac{1}{5}\right))

First values

aa 1-111224455778810101313141416161717
χ3267(928,a) \chi_{ 3267 }(928, a) 1111e(815)e\left(\frac{8}{15}\right)e(115)e\left(\frac{1}{15}\right)e(715)e\left(\frac{7}{15}\right)e(1115)e\left(\frac{11}{15}\right)e(35)e\left(\frac{3}{5}\right)11e(1315)e\left(\frac{13}{15}\right)e(415)e\left(\frac{4}{15}\right)e(215)e\left(\frac{2}{15}\right)e(45)e\left(\frac{4}{5}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ3267(928,a)   \chi_{ 3267 }(928,a) \; at   a=\;a = e.g. 2