Properties

Conductor 1343
Order 208
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4029.ct

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[58]
 
pari: [g,chi] = znchar(Mod(58,4029))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1343
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 208
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.ct
Orbit index = 72

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 ]
 

\(\chi_{4029}(58,\cdot)\) \(\chi_{4029}(61,\cdot)\) \(\chi_{4029}(91,\cdot)\) \(\chi_{4029}(112,\cdot)\) \(\chi_{4029}(148,\cdot)\) \(\chi_{4029}(175,\cdot)\) \(\chi_{4029}(199,\cdot)\) \(\chi_{4029}(295,\cdot)\) \(\chi_{4029}(328,\cdot)\) \(\chi_{4029}(343,\cdot)\) \(\chi_{4029}(385,\cdot)\) \(\chi_{4029}(436,\cdot)\) \(\chi_{4029}(466,\cdot)\) \(\chi_{4029}(532,\cdot)\) \(\chi_{4029}(568,\cdot)\) \(\chi_{4029}(622,\cdot)\) \(\chi_{4029}(649,\cdot)\) \(\chi_{4029}(673,\cdot)\) \(\chi_{4029}(703,\cdot)\) \(\chi_{4029}(772,\cdot)\) \(\chi_{4029}(802,\cdot)\) \(\chi_{4029}(805,\cdot)\) \(\chi_{4029}(823,\cdot)\) \(\chi_{4029}(847,\cdot)\) \(\chi_{4029}(940,\cdot)\) \(\chi_{4029}(1006,\cdot)\) \(\chi_{4029}(1009,\cdot)\) \(\chi_{4029}(1042,\cdot)\) \(\chi_{4029}(1060,\cdot)\) \(\chi_{4029}(1246,\cdot)\) ...

Values on generators

\((2687,3556,3163)\) → \((1,e\left(\frac{11}{16}\right),e\left(\frac{5}{26}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{41}{104}\right)\)\(e\left(\frac{41}{52}\right)\)\(e\left(\frac{75}{208}\right)\)\(e\left(\frac{157}{208}\right)\)\(e\left(\frac{19}{104}\right)\)\(e\left(\frac{157}{208}\right)\)\(e\left(\frac{185}{208}\right)\)\(e\left(\frac{15}{52}\right)\)\(e\left(\frac{31}{208}\right)\)\(e\left(\frac{15}{26}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{208})\)