Properties

Conductor 4031
Order 644
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4031.bq

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(4031)
 
sage: chi = H[8]
 
pari: [g,chi] = znchar(Mod(8,4031))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4031
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 644
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 = 4031.bq
Orbit index = 43

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 ]
 

\(\chi_{4031}(8,\cdot)\) \(\chi_{4031}(10,\cdot)\) \(\chi_{4031}(14,\cdot)\) \(\chi_{4031}(27,\cdot)\) \(\chi_{4031}(39,\cdot)\) \(\chi_{4031}(48,\cdot)\) \(\chi_{4031}(60,\cdot)\) \(\chi_{4031}(76,\cdot)\) \(\chi_{4031}(84,\cdot)\) \(\chi_{4031}(95,\cdot)\) \(\chi_{4031}(105,\cdot)\) \(\chi_{4031}(147,\cdot)\) \(\chi_{4031}(153,\cdot)\) \(\chi_{4031}(166,\cdot)\) \(\chi_{4031}(172,\cdot)\) \(\chi_{4031}(201,\cdot)\) \(\chi_{4031}(213,\cdot)\) \(\chi_{4031}(214,\cdot)\) \(\chi_{4031}(221,\cdot)\) \(\chi_{4031}(234,\cdot)\) \(\chi_{4031}(242,\cdot)\) \(\chi_{4031}(272,\cdot)\) \(\chi_{4031}(288,\cdot)\) \(\chi_{4031}(292,\cdot)\) \(\chi_{4031}(301,\cdot)\) \(\chi_{4031}(305,\cdot)\) \(\chi_{4031}(311,\cdot)\) \(\chi_{4031}(317,\cdot)\) \(\chi_{4031}(337,\cdot)\) \(\chi_{4031}(338,\cdot)\) ...

Values on generators

\((3337,697)\) → \((e\left(\frac{3}{28}\right),e\left(\frac{1}{46}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{83}{644}\right)\)\(e\left(\frac{275}{644}\right)\)\(e\left(\frac{83}{322}\right)\)\(e\left(\frac{73}{322}\right)\)\(e\left(\frac{179}{322}\right)\)\(e\left(\frac{60}{161}\right)\)\(e\left(\frac{249}{644}\right)\)\(e\left(\frac{275}{322}\right)\)\(e\left(\frac{229}{644}\right)\)\(e\left(\frac{213}{644}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{644})\)