Properties

Conductor 2541
Order 330
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 2541.cg

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[2]
 
pari: [g,chi] = znchar(Mod(2,2541))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2541
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 330
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.cg
Orbit index = 59

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 ]
 

\(\chi_{2541}(2,\cdot)\) \(\chi_{2541}(74,\cdot)\) \(\chi_{2541}(95,\cdot)\) \(\chi_{2541}(107,\cdot)\) \(\chi_{2541}(116,\cdot)\) \(\chi_{2541}(128,\cdot)\) \(\chi_{2541}(149,\cdot)\) \(\chi_{2541}(200,\cdot)\) \(\chi_{2541}(305,\cdot)\) \(\chi_{2541}(326,\cdot)\) \(\chi_{2541}(338,\cdot)\) \(\chi_{2541}(347,\cdot)\) \(\chi_{2541}(359,\cdot)\) \(\chi_{2541}(380,\cdot)\) \(\chi_{2541}(431,\cdot)\) \(\chi_{2541}(464,\cdot)\) \(\chi_{2541}(536,\cdot)\) \(\chi_{2541}(557,\cdot)\) \(\chi_{2541}(569,\cdot)\) \(\chi_{2541}(590,\cdot)\) \(\chi_{2541}(611,\cdot)\) \(\chi_{2541}(662,\cdot)\) \(\chi_{2541}(695,\cdot)\) \(\chi_{2541}(767,\cdot)\) \(\chi_{2541}(788,\cdot)\) \(\chi_{2541}(800,\cdot)\) \(\chi_{2541}(809,\cdot)\) \(\chi_{2541}(821,\cdot)\) \(\chi_{2541}(842,\cdot)\) \(\chi_{2541}(893,\cdot)\) ...

Values on generators

\((848,1816,2059)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{1}{110}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{29}{165}\right)\)\(e\left(\frac{58}{165}\right)\)\(e\left(\frac{277}{330}\right)\)\(e\left(\frac{29}{55}\right)\)\(e\left(\frac{1}{66}\right)\)\(e\left(\frac{101}{110}\right)\)\(e\left(\frac{116}{165}\right)\)\(e\left(\frac{46}{165}\right)\)\(e\left(\frac{139}{330}\right)\)\(e\left(\frac{21}{110}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{165})\)