Properties

Conductor 237
Order 26
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4029.br

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(4029)
 
sage: chi = H[137]
 
pari: [g,chi] = znchar(Mod(137,4029))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 237
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 26
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 = 4029.br
Orbit index = 44

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 ]
 

\(\chi_{4029}(137,\cdot)\) \(\chi_{4029}(545,\cdot)\) \(\chi_{4029}(647,\cdot)\) \(\chi_{4029}(851,\cdot)\) \(\chi_{4029}(902,\cdot)\) \(\chi_{4029}(1412,\cdot)\) \(\chi_{4029}(1463,\cdot)\) \(\chi_{4029}(2585,\cdot)\) \(\chi_{4029}(3095,\cdot)\) \(\chi_{4029}(3503,\cdot)\) \(\chi_{4029}(3809,\cdot)\) \(\chi_{4029}(3962,\cdot)\)

Values on generators

\((2687,3556,3163)\) → \((-1,1,e\left(\frac{5}{26}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{7}{26}\right)\)\(e\left(\frac{7}{13}\right)\)\(e\left(\frac{11}{26}\right)\)\(e\left(\frac{5}{26}\right)\)\(e\left(\frac{21}{26}\right)\)\(e\left(\frac{9}{13}\right)\)\(e\left(\frac{15}{26}\right)\)\(e\left(\frac{7}{13}\right)\)\(e\left(\frac{6}{13}\right)\)\(e\left(\frac{1}{13}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{13})\)