Properties

Conductor 237
Order 78
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4029.cb

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[35]
 
pari: [g,chi] = znchar(Mod(35,4029))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 237
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.cb
Orbit index = 54

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 ]
 

\(\chi_{4029}(35,\cdot)\) \(\chi_{4029}(86,\cdot)\) \(\chi_{4029}(188,\cdot)\) \(\chi_{4029}(290,\cdot)\) \(\chi_{4029}(443,\cdot)\) \(\chi_{4029}(596,\cdot)\) \(\chi_{4029}(698,\cdot)\) \(\chi_{4029}(1055,\cdot)\) \(\chi_{4029}(1259,\cdot)\) \(\chi_{4029}(1718,\cdot)\) \(\chi_{4029}(1820,\cdot)\) \(\chi_{4029}(1871,\cdot)\) \(\chi_{4029}(1973,\cdot)\) \(\chi_{4029}(2330,\cdot)\) \(\chi_{4029}(2483,\cdot)\) \(\chi_{4029}(2534,\cdot)\) \(\chi_{4029}(2636,\cdot)\) \(\chi_{4029}(2840,\cdot)\) \(\chi_{4029}(2891,\cdot)\) \(\chi_{4029}(2993,\cdot)\) \(\chi_{4029}(3197,\cdot)\) \(\chi_{4029}(3299,\cdot)\) \(\chi_{4029}(3860,\cdot)\) \(\chi_{4029}(4013,\cdot)\)

Values on generators

\((2687,3556,3163)\) → \((-1,1,e\left(\frac{37}{78}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{31}{78}\right)\)\(e\left(\frac{31}{39}\right)\)\(e\left(\frac{71}{78}\right)\)\(e\left(\frac{11}{78}\right)\)\(e\left(\frac{5}{26}\right)\)\(e\left(\frac{4}{13}\right)\)\(e\left(\frac{59}{78}\right)\)\(e\left(\frac{5}{39}\right)\)\(e\left(\frac{7}{13}\right)\)\(e\left(\frac{23}{39}\right)\)
value at  e.g. 2

Related number fields

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