Properties

Conductor 4031
Order 92
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4031.bd

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[75]
 
pari: [g,chi] = znchar(Mod(75,4031))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4031
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 92
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.bd
Orbit index = 30

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 ]
 

\(\chi_{4031}(75,\cdot)\) \(\chi_{4031}(133,\cdot)\) \(\chi_{4031}(162,\cdot)\) \(\chi_{4031}(215,\cdot)\) \(\chi_{4031}(244,\cdot)\) \(\chi_{4031}(360,\cdot)\) \(\chi_{4031}(365,\cdot)\) \(\chi_{4031}(476,\cdot)\) \(\chi_{4031}(650,\cdot)\) \(\chi_{4031}(771,\cdot)\) \(\chi_{4031}(800,\cdot)\) \(\chi_{4031}(882,\cdot)\) \(\chi_{4031}(916,\cdot)\) \(\chi_{4031}(1032,\cdot)\) \(\chi_{4031}(1172,\cdot)\) \(\chi_{4031}(1206,\cdot)\) \(\chi_{4031}(1259,\cdot)\) \(\chi_{4031}(1346,\cdot)\) \(\chi_{4031}(1404,\cdot)\) \(\chi_{4031}(1438,\cdot)\) \(\chi_{4031}(1728,\cdot)\) \(\chi_{4031}(1752,\cdot)\) \(\chi_{4031}(1815,\cdot)\) \(\chi_{4031}(1902,\cdot)\) \(\chi_{4031}(1960,\cdot)\) \(\chi_{4031}(2308,\cdot)\) \(\chi_{4031}(2390,\cdot)\) \(\chi_{4031}(2535,\cdot)\) \(\chi_{4031}(2564,\cdot)\) \(\chi_{4031}(2651,\cdot)\) ...

Values on generators

\((3337,697)\) → \((-i,e\left(\frac{25}{46}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{27}{92}\right)\)\(e\left(\frac{3}{92}\right)\)\(e\left(\frac{27}{46}\right)\)\(e\left(\frac{11}{46}\right)\)\(e\left(\frac{15}{46}\right)\)\(e\left(\frac{4}{23}\right)\)\(e\left(\frac{81}{92}\right)\)\(e\left(\frac{3}{46}\right)\)\(e\left(\frac{49}{92}\right)\)\(e\left(\frac{5}{92}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{92})\)