Properties

Conductor 2541
Order 66
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 2541.bv

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[32]
 
pari: [g,chi] = znchar(Mod(32,2541))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2541
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 66
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 2541.bv
Orbit index = 48

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 ]
 

\(\chi_{2541}(32,\cdot)\) \(\chi_{2541}(65,\cdot)\) \(\chi_{2541}(263,\cdot)\) \(\chi_{2541}(296,\cdot)\) \(\chi_{2541}(494,\cdot)\) \(\chi_{2541}(527,\cdot)\) \(\chi_{2541}(758,\cdot)\) \(\chi_{2541}(956,\cdot)\) \(\chi_{2541}(989,\cdot)\) \(\chi_{2541}(1187,\cdot)\) \(\chi_{2541}(1220,\cdot)\) \(\chi_{2541}(1418,\cdot)\) \(\chi_{2541}(1649,\cdot)\) \(\chi_{2541}(1682,\cdot)\) \(\chi_{2541}(1880,\cdot)\) \(\chi_{2541}(1913,\cdot)\) \(\chi_{2541}(2111,\cdot)\) \(\chi_{2541}(2144,\cdot)\) \(\chi_{2541}(2342,\cdot)\) \(\chi_{2541}(2375,\cdot)\)

Values on generators

\((848,1816,2059)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{1}{22}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{29}{33}\right)\)\(e\left(\frac{25}{33}\right)\)\(e\left(\frac{13}{66}\right)\)\(e\left(\frac{7}{11}\right)\)\(e\left(\frac{5}{66}\right)\)\(e\left(\frac{13}{22}\right)\)\(e\left(\frac{17}{33}\right)\)\(e\left(\frac{13}{33}\right)\)\(e\left(\frac{7}{66}\right)\)\(e\left(\frac{21}{22}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{33})\)