Properties

Conductor 4031
Order 138
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4031.bf

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[28]
 
pari: [g,chi] = znchar(Mod(28,4031))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4031
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 138
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.bf
Orbit index = 32

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 ]
 

\(\chi_{4031}(28,\cdot)\) \(\chi_{4031}(86,\cdot)\) \(\chi_{4031}(144,\cdot)\) \(\chi_{4031}(260,\cdot)\) \(\chi_{4031}(289,\cdot)\) \(\chi_{4031}(347,\cdot)\) \(\chi_{4031}(405,\cdot)\) \(\chi_{4031}(463,\cdot)\) \(\chi_{4031}(637,\cdot)\) \(\chi_{4031}(724,\cdot)\) \(\chi_{4031}(869,\cdot)\) \(\chi_{4031}(956,\cdot)\) \(\chi_{4031}(1014,\cdot)\) \(\chi_{4031}(1072,\cdot)\) \(\chi_{4031}(1159,\cdot)\) \(\chi_{4031}(1275,\cdot)\) \(\chi_{4031}(1420,\cdot)\) \(\chi_{4031}(1507,\cdot)\) \(\chi_{4031}(1536,\cdot)\) \(\chi_{4031}(1681,\cdot)\) \(\chi_{4031}(1739,\cdot)\) \(\chi_{4031}(1971,\cdot)\) \(\chi_{4031}(2000,\cdot)\) \(\chi_{4031}(2029,\cdot)\) \(\chi_{4031}(2116,\cdot)\) \(\chi_{4031}(2174,\cdot)\) \(\chi_{4031}(2203,\cdot)\) \(\chi_{4031}(2261,\cdot)\) \(\chi_{4031}(2290,\cdot)\) \(\chi_{4031}(2348,\cdot)\) ...

Values on generators

\((3337,697)\) → \((-1,e\left(\frac{26}{69}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{121}{138}\right)\)\(e\left(\frac{131}{138}\right)\)\(e\left(\frac{52}{69}\right)\)\(e\left(\frac{28}{69}\right)\)\(e\left(\frac{19}{23}\right)\)\(e\left(\frac{58}{69}\right)\)\(e\left(\frac{29}{46}\right)\)\(e\left(\frac{62}{69}\right)\)\(e\left(\frac{13}{46}\right)\)\(e\left(\frac{19}{138}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{69})\)