Properties

Conductor 1343
Order 78
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4029.cf

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[16]
 
pari: [g,chi] = znchar(Mod(16,4029))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1343
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 78
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.cf
Orbit index = 58

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 ]
 

\(\chi_{4029}(16,\cdot)\) \(\chi_{4029}(169,\cdot)\) \(\chi_{4029}(730,\cdot)\) \(\chi_{4029}(832,\cdot)\) \(\chi_{4029}(1036,\cdot)\) \(\chi_{4029}(1138,\cdot)\) \(\chi_{4029}(1189,\cdot)\) \(\chi_{4029}(1393,\cdot)\) \(\chi_{4029}(1495,\cdot)\) \(\chi_{4029}(1546,\cdot)\) \(\chi_{4029}(1699,\cdot)\) \(\chi_{4029}(2056,\cdot)\) \(\chi_{4029}(2158,\cdot)\) \(\chi_{4029}(2209,\cdot)\) \(\chi_{4029}(2311,\cdot)\) \(\chi_{4029}(2770,\cdot)\) \(\chi_{4029}(2974,\cdot)\) \(\chi_{4029}(3331,\cdot)\) \(\chi_{4029}(3433,\cdot)\) \(\chi_{4029}(3586,\cdot)\) \(\chi_{4029}(3739,\cdot)\) \(\chi_{4029}(3841,\cdot)\) \(\chi_{4029}(3943,\cdot)\) \(\chi_{4029}(3994,\cdot)\)

Values on generators

\((2687,3556,3163)\) → \((1,-1,e\left(\frac{8}{39}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{32}{39}\right)\)\(e\left(\frac{25}{39}\right)\)\(e\left(\frac{17}{78}\right)\)\(e\left(\frac{29}{78}\right)\)\(e\left(\frac{6}{13}\right)\)\(e\left(\frac{1}{26}\right)\)\(e\left(\frac{35}{78}\right)\)\(e\left(\frac{38}{39}\right)\)\(e\left(\frac{5}{26}\right)\)\(e\left(\frac{11}{39}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{39})\)