Properties

Label 92.e
Modulus $92$
Conductor $23$
Order $11$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(92, base_ring=CyclotomicField(22))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,10]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(9,92))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(92\)
Conductor: \(23\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(11\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 23.c
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: \(\Q(\zeta_{11})\)
Fixed field: \(\Q(\zeta_{23})^+\)

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(21\)
\(\chi_{92}(9,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{92}(13,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{92}(25,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{92}(29,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{92}(41,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{92}(49,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{92}(73,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{92}(77,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{92}(81,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{92}(85,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{8}{11}\right)\)