Properties

Conductor 847
Order 165
Real no
Primitive no
Minimal yes
Parity even
Orbit label 2541.ce

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[4]
 
pari: [g,chi] = znchar(Mod(4,2541))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 847
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 165
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 = 2541.ce
Orbit index = 57

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 ]
 

\(\chi_{2541}(4,\cdot)\) \(\chi_{2541}(16,\cdot)\) \(\chi_{2541}(25,\cdot)\) \(\chi_{2541}(37,\cdot)\) \(\chi_{2541}(58,\cdot)\) \(\chi_{2541}(163,\cdot)\) \(\chi_{2541}(214,\cdot)\) \(\chi_{2541}(235,\cdot)\) \(\chi_{2541}(247,\cdot)\) \(\chi_{2541}(256,\cdot)\) \(\chi_{2541}(268,\cdot)\) \(\chi_{2541}(289,\cdot)\) \(\chi_{2541}(361,\cdot)\) \(\chi_{2541}(394,\cdot)\) \(\chi_{2541}(445,\cdot)\) \(\chi_{2541}(466,\cdot)\) \(\chi_{2541}(478,\cdot)\) \(\chi_{2541}(499,\cdot)\) \(\chi_{2541}(520,\cdot)\) \(\chi_{2541}(592,\cdot)\) \(\chi_{2541}(625,\cdot)\) \(\chi_{2541}(676,\cdot)\) \(\chi_{2541}(697,\cdot)\) \(\chi_{2541}(709,\cdot)\) \(\chi_{2541}(718,\cdot)\) \(\chi_{2541}(730,\cdot)\) \(\chi_{2541}(751,\cdot)\) \(\chi_{2541}(823,\cdot)\) \(\chi_{2541}(907,\cdot)\) \(\chi_{2541}(940,\cdot)\) ...

Values on generators

\((848,1816,2059)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{1}{55}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{58}{165}\right)\)\(e\left(\frac{116}{165}\right)\)\(e\left(\frac{112}{165}\right)\)\(e\left(\frac{3}{55}\right)\)\(e\left(\frac{1}{33}\right)\)\(e\left(\frac{46}{55}\right)\)\(e\left(\frac{67}{165}\right)\)\(e\left(\frac{92}{165}\right)\)\(e\left(\frac{139}{165}\right)\)\(e\left(\frac{21}{55}\right)\)
value at  e.g. 2

Related number fields

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