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Properties

Label 1183.be
Modulus 11831183
Conductor 169169
Order 1313
Real no
Primitive no
Minimal yes
Parity even

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1183, base_ring=CyclotomicField(26))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,22]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(92,1183))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 11831183
Conductor: 169169
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 1313
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 169.g
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(ζ13)\Q(\zeta_{13})
Fixed field: 13.13.542800770374370512771595361.1

Characters in Galois orbit

Character −1-1 11 22 33 44 55 66 88 99 1010 1111 1212
χ1183(92,⋅)\chi_{1183}(92,\cdot) 11 11 e(1113)e\left(\frac{11}{13}\right) e(1213)e\left(\frac{12}{13}\right) e(913)e\left(\frac{9}{13}\right) e(813)e\left(\frac{8}{13}\right) e(1013)e\left(\frac{10}{13}\right) e(713)e\left(\frac{7}{13}\right) e(1113)e\left(\frac{11}{13}\right) e(613)e\left(\frac{6}{13}\right) e(213)e\left(\frac{2}{13}\right) e(813)e\left(\frac{8}{13}\right)
χ1183(183,⋅)\chi_{1183}(183,\cdot) 11 11 e(913)e\left(\frac{9}{13}\right) e(1113)e\left(\frac{11}{13}\right) e(513)e\left(\frac{5}{13}\right) e(313)e\left(\frac{3}{13}\right) e(713)e\left(\frac{7}{13}\right) e(113)e\left(\frac{1}{13}\right) e(913)e\left(\frac{9}{13}\right) e(1213)e\left(\frac{12}{13}\right) e(413)e\left(\frac{4}{13}\right) e(313)e\left(\frac{3}{13}\right)
χ1183(274,⋅)\chi_{1183}(274,\cdot) 11 11 e(713)e\left(\frac{7}{13}\right) e(1013)e\left(\frac{10}{13}\right) e(113)e\left(\frac{1}{13}\right) e(1113)e\left(\frac{11}{13}\right) e(413)e\left(\frac{4}{13}\right) e(813)e\left(\frac{8}{13}\right) e(713)e\left(\frac{7}{13}\right) e(513)e\left(\frac{5}{13}\right) e(613)e\left(\frac{6}{13}\right) e(1113)e\left(\frac{11}{13}\right)
χ1183(365,⋅)\chi_{1183}(365,\cdot) 11 11 e(513)e\left(\frac{5}{13}\right) e(913)e\left(\frac{9}{13}\right) e(1013)e\left(\frac{10}{13}\right) e(613)e\left(\frac{6}{13}\right) e(113)e\left(\frac{1}{13}\right) e(213)e\left(\frac{2}{13}\right) e(513)e\left(\frac{5}{13}\right) e(1113)e\left(\frac{11}{13}\right) e(813)e\left(\frac{8}{13}\right) e(613)e\left(\frac{6}{13}\right)
χ1183(456,⋅)\chi_{1183}(456,\cdot) 11 11 e(313)e\left(\frac{3}{13}\right) e(813)e\left(\frac{8}{13}\right) e(613)e\left(\frac{6}{13}\right) e(113)e\left(\frac{1}{13}\right) e(1113)e\left(\frac{11}{13}\right) e(913)e\left(\frac{9}{13}\right) e(313)e\left(\frac{3}{13}\right) e(413)e\left(\frac{4}{13}\right) e(1013)e\left(\frac{10}{13}\right) e(113)e\left(\frac{1}{13}\right)
χ1183(547,⋅)\chi_{1183}(547,\cdot) 11 11 e(113)e\left(\frac{1}{13}\right) e(713)e\left(\frac{7}{13}\right) e(213)e\left(\frac{2}{13}\right) e(913)e\left(\frac{9}{13}\right) e(813)e\left(\frac{8}{13}\right) e(313)e\left(\frac{3}{13}\right) e(113)e\left(\frac{1}{13}\right) e(1013)e\left(\frac{10}{13}\right) e(1213)e\left(\frac{12}{13}\right) e(913)e\left(\frac{9}{13}\right)
χ1183(638,⋅)\chi_{1183}(638,\cdot) 11 11 e(1213)e\left(\frac{12}{13}\right) e(613)e\left(\frac{6}{13}\right) e(1113)e\left(\frac{11}{13}\right) e(413)e\left(\frac{4}{13}\right) e(513)e\left(\frac{5}{13}\right) e(1013)e\left(\frac{10}{13}\right) e(1213)e\left(\frac{12}{13}\right) e(313)e\left(\frac{3}{13}\right) e(113)e\left(\frac{1}{13}\right) e(413)e\left(\frac{4}{13}\right)
χ1183(729,⋅)\chi_{1183}(729,\cdot) 11 11 e(1013)e\left(\frac{10}{13}\right) e(513)e\left(\frac{5}{13}\right) e(713)e\left(\frac{7}{13}\right) e(1213)e\left(\frac{12}{13}\right) e(213)e\left(\frac{2}{13}\right) e(413)e\left(\frac{4}{13}\right) e(1013)e\left(\frac{10}{13}\right) e(913)e\left(\frac{9}{13}\right) e(313)e\left(\frac{3}{13}\right) e(1213)e\left(\frac{12}{13}\right)
χ1183(820,⋅)\chi_{1183}(820,\cdot) 11 11 e(813)e\left(\frac{8}{13}\right) e(413)e\left(\frac{4}{13}\right) e(313)e\left(\frac{3}{13}\right) e(713)e\left(\frac{7}{13}\right) e(1213)e\left(\frac{12}{13}\right) e(1113)e\left(\frac{11}{13}\right) e(813)e\left(\frac{8}{13}\right) e(213)e\left(\frac{2}{13}\right) e(513)e\left(\frac{5}{13}\right) e(713)e\left(\frac{7}{13}\right)
χ1183(911,⋅)\chi_{1183}(911,\cdot) 11 11 e(613)e\left(\frac{6}{13}\right) e(313)e\left(\frac{3}{13}\right) e(1213)e\left(\frac{12}{13}\right) e(213)e\left(\frac{2}{13}\right) e(913)e\left(\frac{9}{13}\right) e(513)e\left(\frac{5}{13}\right) e(613)e\left(\frac{6}{13}\right) e(813)e\left(\frac{8}{13}\right) e(713)e\left(\frac{7}{13}\right) e(213)e\left(\frac{2}{13}\right)
χ1183(1002,⋅)\chi_{1183}(1002,\cdot) 11 11 e(413)e\left(\frac{4}{13}\right) e(213)e\left(\frac{2}{13}\right) e(813)e\left(\frac{8}{13}\right) e(1013)e\left(\frac{10}{13}\right) e(613)e\left(\frac{6}{13}\right) e(1213)e\left(\frac{12}{13}\right) e(413)e\left(\frac{4}{13}\right) e(113)e\left(\frac{1}{13}\right) e(913)e\left(\frac{9}{13}\right) e(1013)e\left(\frac{10}{13}\right)
χ1183(1093,⋅)\chi_{1183}(1093,\cdot) 11 11 e(213)e\left(\frac{2}{13}\right) e(113)e\left(\frac{1}{13}\right) e(413)e\left(\frac{4}{13}\right) e(513)e\left(\frac{5}{13}\right) e(313)e\left(\frac{3}{13}\right) e(613)e\left(\frac{6}{13}\right) e(213)e\left(\frac{2}{13}\right) e(713)e\left(\frac{7}{13}\right) e(1113)e\left(\frac{11}{13}\right) e(513)e\left(\frac{5}{13}\right)