Properties

Conductor 121
Order 11
Real no
Primitive no
Minimal yes
Parity even
Orbit label 2541.y

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(2541)
 
sage: chi = H[232]
 
pari: [g,chi] = znchar(Mod(232,2541))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 121
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 11
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 2541.y
Orbit index = 25

Galois orbit

sage: chi.sage_character().galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{2541}(232,\cdot)\) \(\chi_{2541}(463,\cdot)\) \(\chi_{2541}(694,\cdot)\) \(\chi_{2541}(925,\cdot)\) \(\chi_{2541}(1156,\cdot)\) \(\chi_{2541}(1387,\cdot)\) \(\chi_{2541}(1618,\cdot)\) \(\chi_{2541}(1849,\cdot)\) \(\chi_{2541}(2080,\cdot)\) \(\chi_{2541}(2311,\cdot)\)

Values on generators

\((848,1816,2059)\) → \((1,1,e\left(\frac{2}{11}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{4}{11}\right)\)\(e\left(\frac{5}{11}\right)\)\(e\left(\frac{6}{11}\right)\)\(e\left(\frac{7}{11}\right)\)\(e\left(\frac{4}{11}\right)\)\(e\left(\frac{8}{11}\right)\)\(e\left(\frac{10}{11}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{9}{11}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{11})\)