Properties

Conductor 4031
Order 276
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4031.bk

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[249]
 
pari: [g,chi] = znchar(Mod(249,4031))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4031
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 276
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.bk
Orbit index = 37

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 ]
 

\(\chi_{4031}(12,\cdot)\) \(\chi_{4031}(17,\cdot)\) \(\chi_{4031}(70,\cdot)\) \(\chi_{4031}(104,\cdot)\) \(\chi_{4031}(128,\cdot)\) \(\chi_{4031}(157,\cdot)\) \(\chi_{4031}(249,\cdot)\) \(\chi_{4031}(273,\cdot)\) \(\chi_{4031}(331,\cdot)\) \(\chi_{4031}(336,\cdot)\) \(\chi_{4031}(389,\cdot)\) \(\chi_{4031}(505,\cdot)\) \(\chi_{4031}(510,\cdot)\) \(\chi_{4031}(568,\cdot)\) \(\chi_{4031}(626,\cdot)\) \(\chi_{4031}(679,\cdot)\) \(\chi_{4031}(684,\cdot)\) \(\chi_{4031}(713,\cdot)\) \(\chi_{4031}(829,\cdot)\) \(\chi_{4031}(853,\cdot)\) \(\chi_{4031}(887,\cdot)\) \(\chi_{4031}(945,\cdot)\) \(\chi_{4031}(969,\cdot)\) \(\chi_{4031}(1061,\cdot)\) \(\chi_{4031}(1114,\cdot)\) \(\chi_{4031}(1235,\cdot)\) \(\chi_{4031}(1409,\cdot)\) \(\chi_{4031}(1462,\cdot)\) \(\chi_{4031}(1491,\cdot)\) \(\chi_{4031}(1520,\cdot)\) ...

Values on generators

\((3337,697)\) → \((-i,e\left(\frac{25}{138}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{257}{276}\right)\)\(e\left(\frac{49}{276}\right)\)\(e\left(\frac{119}{138}\right)\)\(e\left(\frac{11}{138}\right)\)\(e\left(\frac{5}{46}\right)\)\(e\left(\frac{4}{69}\right)\)\(e\left(\frac{73}{92}\right)\)\(e\left(\frac{49}{138}\right)\)\(e\left(\frac{1}{92}\right)\)\(e\left(\frac{143}{276}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{276})\)