↑

Properties

Label 71.d
Modulus 7171
Conductor 7171
Order 77
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(71, base_ring=CyclotomicField(14)) M = H._module chi = DirichletCharacter(H, M([8])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(20,71)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 7171
Conductor: 7171
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: 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)
 

Related number fields

Field of values: Q(ζ7)\Q(\zeta_{7})
Fixed field: 7.7.128100283921.1

Characters in Galois orbit

Character −1-1 11 22 33 44 55 66 77 88 99 1010 1111
χ71(20,⋅)\chi_{71}(20,\cdot) 11 11 e(37)e\left(\frac{3}{7}\right) e(67)e\left(\frac{6}{7}\right) e(67)e\left(\frac{6}{7}\right) 11 e(27)e\left(\frac{2}{7}\right) e(47)e\left(\frac{4}{7}\right) e(27)e\left(\frac{2}{7}\right) e(57)e\left(\frac{5}{7}\right) e(37)e\left(\frac{3}{7}\right) e(57)e\left(\frac{5}{7}\right)
χ71(30,⋅)\chi_{71}(30,\cdot) 11 11 e(17)e\left(\frac{1}{7}\right) e(27)e\left(\frac{2}{7}\right) e(27)e\left(\frac{2}{7}\right) 11 e(37)e\left(\frac{3}{7}\right) e(67)e\left(\frac{6}{7}\right) e(37)e\left(\frac{3}{7}\right) e(47)e\left(\frac{4}{7}\right) e(17)e\left(\frac{1}{7}\right) e(47)e\left(\frac{4}{7}\right)
χ71(32,⋅)\chi_{71}(32,\cdot) 11 11 e(47)e\left(\frac{4}{7}\right) e(17)e\left(\frac{1}{7}\right) e(17)e\left(\frac{1}{7}\right) 11 e(57)e\left(\frac{5}{7}\right) e(37)e\left(\frac{3}{7}\right) e(57)e\left(\frac{5}{7}\right) e(27)e\left(\frac{2}{7}\right) e(47)e\left(\frac{4}{7}\right) e(27)e\left(\frac{2}{7}\right)
χ71(37,⋅)\chi_{71}(37,\cdot) 11 11 e(57)e\left(\frac{5}{7}\right) e(37)e\left(\frac{3}{7}\right) e(37)e\left(\frac{3}{7}\right) 11 e(17)e\left(\frac{1}{7}\right) e(27)e\left(\frac{2}{7}\right) e(17)e\left(\frac{1}{7}\right) e(67)e\left(\frac{6}{7}\right) e(57)e\left(\frac{5}{7}\right) e(67)e\left(\frac{6}{7}\right)
χ71(45,⋅)\chi_{71}(45,\cdot) 11 11 e(67)e\left(\frac{6}{7}\right) e(57)e\left(\frac{5}{7}\right) e(57)e\left(\frac{5}{7}\right) 11 e(47)e\left(\frac{4}{7}\right) e(17)e\left(\frac{1}{7}\right) e(47)e\left(\frac{4}{7}\right) e(37)e\left(\frac{3}{7}\right) e(67)e\left(\frac{6}{7}\right) e(37)e\left(\frac{3}{7}\right)
χ71(48,⋅)\chi_{71}(48,\cdot) 11 11 e(27)e\left(\frac{2}{7}\right) e(47)e\left(\frac{4}{7}\right) e(47)e\left(\frac{4}{7}\right) 11 e(67)e\left(\frac{6}{7}\right) e(57)e\left(\frac{5}{7}\right) e(67)e\left(\frac{6}{7}\right) e(17)e\left(\frac{1}{7}\right) e(27)e\left(\frac{2}{7}\right) e(17)e\left(\frac{1}{7}\right)