Properties

Label 7800.3347
Modulus 78007800
Conductor 78007800
Order 6060
Real no
Primitive yes
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(7800, base_ring=CyclotomicField(60)) M = H._module chi = DirichletCharacter(H, M([30,30,30,51,25]))
 
Copy content pari:[g,chi] = znchar(Mod(3347,7800))
 

Basic properties

Modulus: 78007800
Conductor: 78007800
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 6060
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: yes
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 7800.kp

χ7800(227,)\chi_{7800}(227,\cdot) χ7800(323,)\chi_{7800}(323,\cdot) χ7800(587,)\chi_{7800}(587,\cdot) χ7800(683,)\chi_{7800}(683,\cdot) χ7800(1787,)\chi_{7800}(1787,\cdot) χ7800(1883,)\chi_{7800}(1883,\cdot) χ7800(2147,)\chi_{7800}(2147,\cdot) χ7800(3347,)\chi_{7800}(3347,\cdot) χ7800(3803,)\chi_{7800}(3803,\cdot) χ7800(5003,)\chi_{7800}(5003,\cdot) χ7800(5267,)\chi_{7800}(5267,\cdot) χ7800(5363,)\chi_{7800}(5363,\cdot) χ7800(6467,)\chi_{7800}(6467,\cdot) χ7800(6563,)\chi_{7800}(6563,\cdot) χ7800(6827,)\chi_{7800}(6827,\cdot) χ7800(6923,)\chi_{7800}(6923,\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(ζ60)\Q(\zeta_{60})
Fixed field: Number field defined by a degree 60 polynomial

Values on generators

(1951,3901,5201,7177,4201)(1951,3901,5201,7177,4201)(1,1,1,e(1720),e(512))(-1,-1,-1,e\left(\frac{17}{20}\right),e\left(\frac{5}{12}\right))

First values

aa 1-11177111117171919232329293131373741414343
χ7800(3347,a) \chi_{ 7800 }(3347, a) 1111e(13)e\left(\frac{1}{3}\right)e(160)e\left(\frac{1}{60}\right)e(2360)e\left(\frac{23}{60}\right)e(2360)e\left(\frac{23}{60}\right)e(3160)e\left(\frac{31}{60}\right)e(1130)e\left(\frac{11}{30}\right)e(120)e\left(\frac{1}{20}\right)e(115)e\left(\frac{1}{15}\right)e(1960)e\left(\frac{19}{60}\right)e(712)e\left(\frac{7}{12}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ7800(3347,a)   \chi_{ 7800 }(3347,a) \; at   a=\;a = e.g. 2