Properties

Conductor 121
Order 55
Real no
Primitive no
Minimal yes
Parity even
Orbit label 2541.bp

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[64]
 
pari: [g,chi] = znchar(Mod(64,2541))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 121
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 55
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.bp
Orbit index = 42

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 ]
 

\(\chi_{2541}(64,\cdot)\) \(\chi_{2541}(169,\cdot)\) \(\chi_{2541}(190,\cdot)\) \(\chi_{2541}(295,\cdot)\) \(\chi_{2541}(379,\cdot)\) \(\chi_{2541}(400,\cdot)\) \(\chi_{2541}(421,\cdot)\) \(\chi_{2541}(526,\cdot)\) \(\chi_{2541}(610,\cdot)\) \(\chi_{2541}(631,\cdot)\) \(\chi_{2541}(652,\cdot)\) \(\chi_{2541}(757,\cdot)\) \(\chi_{2541}(841,\cdot)\) \(\chi_{2541}(862,\cdot)\) \(\chi_{2541}(883,\cdot)\) \(\chi_{2541}(988,\cdot)\) \(\chi_{2541}(1072,\cdot)\) \(\chi_{2541}(1093,\cdot)\) \(\chi_{2541}(1114,\cdot)\) \(\chi_{2541}(1303,\cdot)\) \(\chi_{2541}(1324,\cdot)\) \(\chi_{2541}(1345,\cdot)\) \(\chi_{2541}(1450,\cdot)\) \(\chi_{2541}(1534,\cdot)\) \(\chi_{2541}(1555,\cdot)\) \(\chi_{2541}(1681,\cdot)\) \(\chi_{2541}(1765,\cdot)\) \(\chi_{2541}(1786,\cdot)\) \(\chi_{2541}(1807,\cdot)\) \(\chi_{2541}(1912,\cdot)\) ...

Values on generators

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

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{3}{55}\right)\)\(e\left(\frac{6}{55}\right)\)\(e\left(\frac{2}{55}\right)\)\(e\left(\frac{9}{55}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{28}{55}\right)\)\(e\left(\frac{12}{55}\right)\)\(e\left(\frac{37}{55}\right)\)\(e\left(\frac{29}{55}\right)\)\(e\left(\frac{8}{55}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{55})\)