Properties

Conductor 1343
Order 104
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4029.cj

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[100]
 
pari: [g,chi] = znchar(Mod(100,4029))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1343
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 104
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.cj
Orbit index = 62

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 ]
 

\(\chi_{4029}(100,\cdot)\) \(\chi_{4029}(196,\cdot)\) \(\chi_{4029}(223,\cdot)\) \(\chi_{4029}(247,\cdot)\) \(\chi_{4029}(304,\cdot)\) \(\chi_{4029}(433,\cdot)\) \(\chi_{4029}(457,\cdot)\) \(\chi_{4029}(484,\cdot)\) \(\chi_{4029}(733,\cdot)\) \(\chi_{4029}(757,\cdot)\) \(\chi_{4029}(763,\cdot)\) \(\chi_{4029}(808,\cdot)\) \(\chi_{4029}(994,\cdot)\) \(\chi_{4029}(1012,\cdot)\) \(\chi_{4029}(1045,\cdot)\) \(\chi_{4029}(1114,\cdot)\) \(\chi_{4029}(1171,\cdot)\) \(\chi_{4029}(1249,\cdot)\) \(\chi_{4029}(1351,\cdot)\) \(\chi_{4029}(1522,\cdot)\) \(\chi_{4029}(1681,\cdot)\) \(\chi_{4029}(1726,\cdot)\) \(\chi_{4029}(1759,\cdot)\) \(\chi_{4029}(1855,\cdot)\) \(\chi_{4029}(1879,\cdot)\) \(\chi_{4029}(1906,\cdot)\) \(\chi_{4029}(1963,\cdot)\) \(\chi_{4029}(2116,\cdot)\) \(\chi_{4029}(2185,\cdot)\) \(\chi_{4029}(2416,\cdot)\) ...

Values on generators

\((2687,3556,3163)\) → \((1,e\left(\frac{3}{8}\right),e\left(\frac{9}{13}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{1}{52}\right)\)\(e\left(\frac{1}{26}\right)\)\(e\left(\frac{83}{104}\right)\)\(e\left(\frac{85}{104}\right)\)\(e\left(\frac{3}{52}\right)\)\(e\left(\frac{85}{104}\right)\)\(e\left(\frac{73}{104}\right)\)\(e\left(\frac{1}{26}\right)\)\(e\left(\frac{87}{104}\right)\)\(e\left(\frac{1}{13}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{104})\)