Properties

Label 4840.1253
Modulus 48404840
Conductor 48404840
Order 4444
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(4840, base_ring=CyclotomicField(44)) M = H._module chi = DirichletCharacter(H, M([0,22,33,10]))
 
Copy content pari:[g,chi] = znchar(Mod(1253,4840))
 

Basic properties

Modulus: 48404840
Conductor: 48404840
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 4444
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 4840.cq

χ4840(197,)\chi_{4840}(197,\cdot) χ4840(373,)\chi_{4840}(373,\cdot) χ4840(637,)\chi_{4840}(637,\cdot) χ4840(813,)\chi_{4840}(813,\cdot) χ4840(1077,)\chi_{4840}(1077,\cdot) χ4840(1253,)\chi_{4840}(1253,\cdot) χ4840(1517,)\chi_{4840}(1517,\cdot) χ4840(1957,)\chi_{4840}(1957,\cdot) χ4840(2133,)\chi_{4840}(2133,\cdot) χ4840(2397,)\chi_{4840}(2397,\cdot) χ4840(2573,)\chi_{4840}(2573,\cdot) χ4840(2837,)\chi_{4840}(2837,\cdot) χ4840(3013,)\chi_{4840}(3013,\cdot) χ4840(3277,)\chi_{4840}(3277,\cdot) χ4840(3453,)\chi_{4840}(3453,\cdot) χ4840(3717,)\chi_{4840}(3717,\cdot) χ4840(3893,)\chi_{4840}(3893,\cdot) χ4840(4157,)\chi_{4840}(4157,\cdot) χ4840(4333,)\chi_{4840}(4333,\cdot) χ4840(4773,)\chi_{4840}(4773,\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(ζ44)\Q(\zeta_{44})
Fixed field: 44.44.212907048724487789150739362720525788138562346514417698933058002742934795048229975182497632223232000000000000000000000000000000000.1

Values on generators

(3631,2421,1937,4721)(3631,2421,1937,4721)(1,1,i,e(522))(1,-1,-i,e\left(\frac{5}{22}\right))

First values

aa 1-1113377991313171719192121232327272929
χ4840(1253,a) \chi_{ 4840 }(1253, a) 1111i-ie(1544)e\left(\frac{15}{44}\right)1-1e(3144)e\left(\frac{31}{44}\right)e(3944)e\left(\frac{39}{44}\right)e(1922)e\left(\frac{19}{22}\right)e(111)e\left(\frac{1}{11}\right)e(744)e\left(\frac{7}{44}\right)iie(1922)e\left(\frac{19}{22}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ4840(1253,a)   \chi_{ 4840 }(1253,a) \; at   a=\;a = e.g. 2