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Properties

Label 87.g
Modulus 8787
Conductor 2929
Order 77
Real no
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(87, base_ring=CyclotomicField(14))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,6]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(7,87))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 8787
Conductor: 2929
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 77
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 29.d
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ7)\Q(\zeta_{7})
Fixed field: 7.7.594823321.1

Characters in Galois orbit

Character −1-1 11 22 44 55 77 88 1010 1111 1313 1414 1616
χ87(7,⋅)\chi_{87}(7,\cdot) 11 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(17)e\left(\frac{1}{7}\right) e(27)e\left(\frac{2}{7}\right) e(67)e\left(\frac{6}{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) e(57)e\left(\frac{5}{7}\right)
χ87(16,⋅)\chi_{87}(16,\cdot) 11 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(57)e\left(\frac{5}{7}\right) e(37)e\left(\frac{3}{7}\right) e(27)e\left(\frac{2}{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) e(47)e\left(\frac{4}{7}\right)
χ87(25,⋅)\chi_{87}(25,\cdot) 11 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(67)e\left(\frac{6}{7}\right) e(57)e\left(\frac{5}{7}\right) e(17)e\left(\frac{1}{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) e(27)e\left(\frac{2}{7}\right)
χ87(49,⋅)\chi_{87}(49,\cdot) 11 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(27)e\left(\frac{2}{7}\right) e(47)e\left(\frac{4}{7}\right) e(57)e\left(\frac{5}{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) e(37)e\left(\frac{3}{7}\right)
χ87(52,⋅)\chi_{87}(52,\cdot) 11 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(47)e\left(\frac{4}{7}\right) e(17)e\left(\frac{1}{7}\right) e(37)e\left(\frac{3}{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) e(67)e\left(\frac{6}{7}\right)
χ87(82,⋅)\chi_{87}(82,\cdot) 11 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(37)e\left(\frac{3}{7}\right) e(67)e\left(\frac{6}{7}\right) e(47)e\left(\frac{4}{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) e(17)e\left(\frac{1}{7}\right)