Properties

Conductor 4029
Order 312
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4029.cw

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[53]
 
pari: [g,chi] = znchar(Mod(53,4029))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4029
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 312
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.cw
Orbit index = 75

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 ]
 

\(\chi_{4029}(53,\cdot)\) \(\chi_{4029}(59,\cdot)\) \(\chi_{4029}(77,\cdot)\) \(\chi_{4029}(161,\cdot)\) \(\chi_{4029}(206,\cdot)\) \(\chi_{4029}(212,\cdot)\) \(\chi_{4029}(314,\cdot)\) \(\chi_{4029}(359,\cdot)\) \(\chi_{4029}(434,\cdot)\) \(\chi_{4029}(461,\cdot)\) \(\chi_{4029}(542,\cdot)\) \(\chi_{4029}(587,\cdot)\) \(\chi_{4029}(638,\cdot)\) \(\chi_{4029}(671,\cdot)\) \(\chi_{4029}(695,\cdot)\) \(\chi_{4029}(740,\cdot)\) \(\chi_{4029}(746,\cdot)\) \(\chi_{4029}(797,\cdot)\) \(\chi_{4029}(818,\cdot)\) \(\chi_{4029}(824,\cdot)\) \(\chi_{4029}(875,\cdot)\) \(\chi_{4029}(899,\cdot)\) \(\chi_{4029}(944,\cdot)\) \(\chi_{4029}(977,\cdot)\) \(\chi_{4029}(995,\cdot)\) \(\chi_{4029}(1001,\cdot)\) \(\chi_{4029}(1022,\cdot)\) \(\chi_{4029}(1097,\cdot)\) \(\chi_{4029}(1154,\cdot)\) \(\chi_{4029}(1181,\cdot)\) ...

Values on generators

\((2687,3556,3163)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{77}{78}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{109}{156}\right)\)\(e\left(\frac{31}{78}\right)\)\(e\left(\frac{25}{312}\right)\)\(e\left(\frac{295}{312}\right)\)\(e\left(\frac{5}{52}\right)\)\(e\left(\frac{81}{104}\right)\)\(e\left(\frac{235}{312}\right)\)\(e\left(\frac{5}{78}\right)\)\(e\left(\frac{67}{104}\right)\)\(e\left(\frac{31}{39}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{312})\)