Properties

Conductor 161
Order 22
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4025.bo

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(4025)
 
sage: chi = H[76]
 
pari: [g,chi] = znchar(Mod(76,4025))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 161
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 22
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 = 4025.bo
Orbit index = 41

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 ]
 

\(\chi_{4025}(76,\cdot)\) \(\chi_{4025}(251,\cdot)\) \(\chi_{4025}(776,\cdot)\) \(\chi_{4025}(2176,\cdot)\) \(\chi_{4025}(2351,\cdot)\) \(\chi_{4025}(2526,\cdot)\) \(\chi_{4025}(2701,\cdot)\) \(\chi_{4025}(3051,\cdot)\) \(\chi_{4025}(3401,\cdot)\) \(\chi_{4025}(3576,\cdot)\)

Values on generators

\((2577,1151,3501)\) → \((1,-1,e\left(\frac{19}{22}\right))\)

Values

-1123468911121316
\(1\)\(1\)\(e\left(\frac{8}{11}\right)\)\(e\left(\frac{7}{22}\right)\)\(e\left(\frac{5}{11}\right)\)\(e\left(\frac{1}{22}\right)\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{7}{11}\right)\)\(e\left(\frac{17}{22}\right)\)\(e\left(\frac{17}{22}\right)\)\(e\left(\frac{13}{22}\right)\)\(e\left(\frac{10}{11}\right)\)
value at  e.g. 2

Related number fields

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