Properties

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

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[5]
 
pari: [g,chi] = znchar(Mod(5,2541))
 

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.ci
Orbit index = 61

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 ]
 

\(\chi_{2541}(5,\cdot)\) \(\chi_{2541}(26,\cdot)\) \(\chi_{2541}(38,\cdot)\) \(\chi_{2541}(47,\cdot)\) \(\chi_{2541}(59,\cdot)\) \(\chi_{2541}(80,\cdot)\) \(\chi_{2541}(152,\cdot)\) \(\chi_{2541}(185,\cdot)\) \(\chi_{2541}(236,\cdot)\) \(\chi_{2541}(257,\cdot)\) \(\chi_{2541}(278,\cdot)\) \(\chi_{2541}(290,\cdot)\) \(\chi_{2541}(311,\cdot)\) \(\chi_{2541}(383,\cdot)\) \(\chi_{2541}(416,\cdot)\) \(\chi_{2541}(467,\cdot)\) \(\chi_{2541}(488,\cdot)\) \(\chi_{2541}(500,\cdot)\) \(\chi_{2541}(509,\cdot)\) \(\chi_{2541}(521,\cdot)\) \(\chi_{2541}(542,\cdot)\) \(\chi_{2541}(647,\cdot)\) \(\chi_{2541}(698,\cdot)\) \(\chi_{2541}(719,\cdot)\) \(\chi_{2541}(731,\cdot)\) \(\chi_{2541}(740,\cdot)\) \(\chi_{2541}(752,\cdot)\) \(\chi_{2541}(773,\cdot)\) \(\chi_{2541}(845,\cdot)\) \(\chi_{2541}(878,\cdot)\) ...

Values on generators

\((848,1816,2059)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{37}{55}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{277}{330}\right)\)\(e\left(\frac{112}{165}\right)\)\(e\left(\frac{74}{165}\right)\)\(e\left(\frac{57}{110}\right)\)\(e\left(\frac{19}{66}\right)\)\(e\left(\frac{49}{110}\right)\)\(e\left(\frac{59}{165}\right)\)\(e\left(\frac{49}{165}\right)\)\(e\left(\frac{1}{330}\right)\)\(e\left(\frac{7}{55}\right)\)
value at  e.g. 2

Related number fields

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