Properties

Label 7056.dk
Modulus 70567056
Conductor 4949
Order 77
Real no
Primitive no
Minimal no
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7056, base_ring=CyclotomicField(14)) M = H._module chi = DirichletCharacter(H, M([0,0,0,6])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(1009,7056)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 70567056
Conductor: 4949
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 77
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 49.e
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)
 

Related number fields

Field of values: Q(ζ7)\Q(\zeta_{7})
Fixed field: 7.7.13841287201.1

Characters in Galois orbit

Character 1-1 11 55 1111 1313 1717 1919 2323 2525 2929 3131 3737
χ7056(1009,)\chi_{7056}(1009,\cdot) 11 11 e(37)e\left(\frac{3}{7}\right) e(17)e\left(\frac{1}{7}\right) e(17)e\left(\frac{1}{7}\right) e(57)e\left(\frac{5}{7}\right) 11 e(27)e\left(\frac{2}{7}\right) e(67)e\left(\frac{6}{7}\right) e(57)e\left(\frac{5}{7}\right) 11 e(57)e\left(\frac{5}{7}\right)
χ7056(2017,)\chi_{7056}(2017,\cdot) 11 11 e(67)e\left(\frac{6}{7}\right) e(27)e\left(\frac{2}{7}\right) e(27)e\left(\frac{2}{7}\right) e(37)e\left(\frac{3}{7}\right) 11 e(47)e\left(\frac{4}{7}\right) e(57)e\left(\frac{5}{7}\right) e(37)e\left(\frac{3}{7}\right) 11 e(37)e\left(\frac{3}{7}\right)
χ7056(3025,)\chi_{7056}(3025,\cdot) 11 11 e(27)e\left(\frac{2}{7}\right) e(37)e\left(\frac{3}{7}\right) e(37)e\left(\frac{3}{7}\right) e(17)e\left(\frac{1}{7}\right) 11 e(67)e\left(\frac{6}{7}\right) e(47)e\left(\frac{4}{7}\right) e(17)e\left(\frac{1}{7}\right) 11 e(17)e\left(\frac{1}{7}\right)
χ7056(4033,)\chi_{7056}(4033,\cdot) 11 11 e(57)e\left(\frac{5}{7}\right) e(47)e\left(\frac{4}{7}\right) e(47)e\left(\frac{4}{7}\right) e(67)e\left(\frac{6}{7}\right) 11 e(17)e\left(\frac{1}{7}\right) e(37)e\left(\frac{3}{7}\right) e(67)e\left(\frac{6}{7}\right) 11 e(67)e\left(\frac{6}{7}\right)
χ7056(5041,)\chi_{7056}(5041,\cdot) 11 11 e(17)e\left(\frac{1}{7}\right) e(57)e\left(\frac{5}{7}\right) e(57)e\left(\frac{5}{7}\right) e(47)e\left(\frac{4}{7}\right) 11 e(37)e\left(\frac{3}{7}\right) e(27)e\left(\frac{2}{7}\right) e(47)e\left(\frac{4}{7}\right) 11 e(47)e\left(\frac{4}{7}\right)
χ7056(6049,)\chi_{7056}(6049,\cdot) 11 11 e(47)e\left(\frac{4}{7}\right) e(67)e\left(\frac{6}{7}\right) e(67)e\left(\frac{6}{7}\right) e(27)e\left(\frac{2}{7}\right) 11 e(57)e\left(\frac{5}{7}\right) e(17)e\left(\frac{1}{7}\right) e(27)e\left(\frac{2}{7}\right) 11 e(27)e\left(\frac{2}{7}\right)