Properties

Conductor 77
Order 10
Real no
Primitive no
Minimal no
Parity even
Orbit label 2541.w

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[118]
 
pari: [g,chi] = znchar(Mod(118,2541))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 77
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 10
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = no
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 2541.w
Orbit index = 23

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 ]
 

\(\chi_{2541}(118,\cdot)\) \(\chi_{2541}(475,\cdot)\) \(\chi_{2541}(1546,\cdot)\) \(\chi_{2541}(2218,\cdot)\)

Values on generators

\((848,1816,2059)\) → \((1,-1,e\left(\frac{3}{10}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{9}{10}\right)\)\(1\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{3}{10}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{5})\)