Properties

Label 2664.245
Modulus 26642664
Conductor 26642664
Order 1212
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(2664, base_ring=CyclotomicField(12)) M = H._module chi = DirichletCharacter(H, M([0,6,2,5]))
 
Copy content pari:[g,chi] = znchar(Mod(245,2664))
 

Basic properties

Modulus: 26642664
Conductor: 26642664
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 1212
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 2664.er

χ2664(245,)\chi_{2664}(245,\cdot) χ2664(1229,)\chi_{2664}(1229,\cdot) χ2664(1805,)\chi_{2664}(1805,\cdot) χ2664(1901,)\chi_{2664}(1901,\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(ζ12)\Q(\zeta_{12})
Fixed field: 12.12.18069305958469626327361639415808.2

Values on generators

(1999,1333,2369,1297)(1999,1333,2369,1297)(1,1,e(16),e(512))(1,-1,e\left(\frac{1}{6}\right),e\left(\frac{5}{12}\right))

First values

aa 1-111557711111313171719192323252529293131
χ2664(245,a) \chi_{ 2664 }(245, a) 1111e(1112)e\left(\frac{11}{12}\right)11e(16)e\left(\frac{1}{6}\right)e(512)e\left(\frac{5}{12}\right)e(512)e\left(\frac{5}{12}\right)e(112)e\left(\frac{1}{12}\right)e(112)e\left(\frac{1}{12}\right)e(56)e\left(\frac{5}{6}\right)e(512)e\left(\frac{5}{12}\right)e(112)e\left(\frac{1}{12}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ2664(245,a)   \chi_{ 2664 }(245,a) \; at   a=\;a = e.g. 2