Properties

Conductor 1343
Order 48
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4029.bw

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[214]
 
pari: [g,chi] = znchar(Mod(214,4029))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1343
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 48
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.bw
Orbit index = 49

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 ]
 

\(\chi_{4029}(214,\cdot)\) \(\chi_{4029}(925,\cdot)\) \(\chi_{4029}(1051,\cdot)\) \(\chi_{4029}(1162,\cdot)\) \(\chi_{4029}(1399,\cdot)\) \(\chi_{4029}(1525,\cdot)\) \(\chi_{4029}(1762,\cdot)\) \(\chi_{4029}(1873,\cdot)\) \(\chi_{4029}(1999,\cdot)\) \(\chi_{4029}(2710,\cdot)\) \(\chi_{4029}(2947,\cdot)\) \(\chi_{4029}(3184,\cdot)\) \(\chi_{4029}(3295,\cdot)\) \(\chi_{4029}(3658,\cdot)\) \(\chi_{4029}(3769,\cdot)\) \(\chi_{4029}(4006,\cdot)\)

Values on generators

\((2687,3556,3163)\) → \((1,e\left(\frac{3}{16}\right),e\left(\frac{5}{6}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{23}{24}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{29}{48}\right)\)\(e\left(\frac{11}{48}\right)\)\(e\left(\frac{7}{8}\right)\)\(e\left(\frac{9}{16}\right)\)\(e\left(\frac{47}{48}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{3}{16}\right)\)\(e\left(\frac{5}{6}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{48})\)