Properties

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

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[305]
 
pari: [g,chi] = znchar(Mod(305,4029))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4029
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 = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 4029.ce
Orbit index = 57

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 ]
 

\(\chi_{4029}(305,\cdot)\) \(\chi_{4029}(458,\cdot)\) \(\chi_{4029}(509,\cdot)\) \(\chi_{4029}(560,\cdot)\) \(\chi_{4029}(662,\cdot)\) \(\chi_{4029}(764,\cdot)\) \(\chi_{4029}(917,\cdot)\) \(\chi_{4029}(1070,\cdot)\) \(\chi_{4029}(1172,\cdot)\) \(\chi_{4029}(1529,\cdot)\) \(\chi_{4029}(1733,\cdot)\) \(\chi_{4029}(2192,\cdot)\) \(\chi_{4029}(2294,\cdot)\) \(\chi_{4029}(2345,\cdot)\) \(\chi_{4029}(2447,\cdot)\) \(\chi_{4029}(2804,\cdot)\) \(\chi_{4029}(2957,\cdot)\) \(\chi_{4029}(3008,\cdot)\) \(\chi_{4029}(3110,\cdot)\) \(\chi_{4029}(3314,\cdot)\) \(\chi_{4029}(3365,\cdot)\) \(\chi_{4029}(3467,\cdot)\) \(\chi_{4029}(3671,\cdot)\) \(\chi_{4029}(3773,\cdot)\)

Values on generators

\((2687,3556,3163)\) → \((-1,-1,e\left(\frac{29}{78}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{77}{78}\right)\)\(e\left(\frac{38}{39}\right)\)\(e\left(\frac{2}{39}\right)\)\(e\left(\frac{8}{39}\right)\)\(e\left(\frac{25}{26}\right)\)\(e\left(\frac{1}{26}\right)\)\(e\left(\frac{11}{39}\right)\)\(e\left(\frac{25}{39}\right)\)\(e\left(\frac{5}{26}\right)\)\(e\left(\frac{37}{39}\right)\)
value at  e.g. 2

Related number fields

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