Properties

Conductor 79
Order 13
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4029.bc

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[52]
 
pari: [g,chi] = znchar(Mod(52,4029))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 79
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 13
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.bc
Orbit index = 29

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 ]
 

\(\chi_{4029}(52,\cdot)\) \(\chi_{4029}(460,\cdot)\) \(\chi_{4029}(970,\cdot)\) \(\chi_{4029}(2092,\cdot)\) \(\chi_{4029}(2143,\cdot)\) \(\chi_{4029}(2653,\cdot)\) \(\chi_{4029}(2704,\cdot)\) \(\chi_{4029}(2908,\cdot)\) \(\chi_{4029}(3010,\cdot)\) \(\chi_{4029}(3418,\cdot)\) \(\chi_{4029}(3622,\cdot)\) \(\chi_{4029}(3775,\cdot)\)

Values on generators

\((2687,3556,3163)\) → \((1,1,e\left(\frac{7}{13}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{2}{13}\right)\)\(e\left(\frac{4}{13}\right)\)\(e\left(\frac{5}{13}\right)\)\(e\left(\frac{7}{13}\right)\)\(e\left(\frac{6}{13}\right)\)\(e\left(\frac{7}{13}\right)\)\(e\left(\frac{8}{13}\right)\)\(e\left(\frac{4}{13}\right)\)\(e\left(\frac{9}{13}\right)\)\(e\left(\frac{8}{13}\right)\)
value at  e.g. 2

Related number fields

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