Properties

Conductor 4031
Order 483
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4031.bo

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[7]
 
pari: [g,chi] = znchar(Mod(7,4031))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4031
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 483
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.bo
Orbit index = 41

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 ]
 

\(\chi_{4031}(7,\cdot)\) \(\chi_{4031}(16,\cdot)\) \(\chi_{4031}(20,\cdot)\) \(\chi_{4031}(24,\cdot)\) \(\chi_{4031}(25,\cdot)\) \(\chi_{4031}(49,\cdot)\) \(\chi_{4031}(54,\cdot)\) \(\chi_{4031}(78,\cdot)\) \(\chi_{4031}(81,\cdot)\) \(\chi_{4031}(83,\cdot)\) \(\chi_{4031}(107,\cdot)\) \(\chi_{4031}(136,\cdot)\) \(\chi_{4031}(152,\cdot)\) \(\chi_{4031}(168,\cdot)\) \(\chi_{4031}(169,\cdot)\) \(\chi_{4031}(170,\cdot)\) \(\chi_{4031}(190,\cdot)\) \(\chi_{4031}(210,\cdot)\) \(\chi_{4031}(228,\cdot)\) \(\chi_{4031}(252,\cdot)\) \(\chi_{4031}(256,\cdot)\) \(\chi_{4031}(257,\cdot)\) \(\chi_{4031}(285,\cdot)\) \(\chi_{4031}(306,\cdot)\) \(\chi_{4031}(313,\cdot)\) \(\chi_{4031}(315,\cdot)\) \(\chi_{4031}(344,\cdot)\) \(\chi_{4031}(364,\cdot)\) \(\chi_{4031}(400,\cdot)\) \(\chi_{4031}(402,\cdot)\) ...

Values on generators

\((3337,697)\) → \((e\left(\frac{3}{7}\right),e\left(\frac{25}{69}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{382}{483}\right)\)\(e\left(\frac{482}{483}\right)\)\(e\left(\frac{281}{483}\right)\)\(e\left(\frac{284}{483}\right)\)\(e\left(\frac{127}{161}\right)\)\(e\left(\frac{125}{483}\right)\)\(e\left(\frac{60}{161}\right)\)\(e\left(\frac{481}{483}\right)\)\(e\left(\frac{61}{161}\right)\)\(e\left(\frac{121}{483}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{483})\)