Properties

Conductor 4031
Order 161
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4031.bi

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[36]
 
pari: [g,chi] = znchar(Mod(36,4031))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4031
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 161
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.bi
Orbit index = 35

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 ]
 

\(\chi_{4031}(36,\cdot)\) \(\chi_{4031}(45,\cdot)\) \(\chi_{4031}(52,\cdot)\) \(\chi_{4031}(65,\cdot)\) \(\chi_{4031}(112,\cdot)\) \(\chi_{4031}(194,\cdot)\) \(\chi_{4031}(219,\cdot)\) \(\chi_{4031}(239,\cdot)\) \(\chi_{4031}(255,\cdot)\) \(\chi_{4031}(268,\cdot)\) \(\chi_{4031}(284,\cdot)\) \(\chi_{4031}(314,\cdot)\) \(\chi_{4031}(335,\cdot)\) \(\chi_{4031}(342,\cdot)\) \(\chi_{4031}(343,\cdot)\) \(\chi_{4031}(355,\cdot)\) \(\chi_{4031}(384,\cdot)\) \(\chi_{4031}(451,\cdot)\) \(\chi_{4031}(480,\cdot)\) \(\chi_{4031}(517,\cdot)\) \(\chi_{4031}(529,\cdot)\) \(\chi_{4031}(542,\cdot)\) \(\chi_{4031}(546,\cdot)\) \(\chi_{4031}(600,\cdot)\) \(\chi_{4031}(633,\cdot)\) \(\chi_{4031}(662,\cdot)\) \(\chi_{4031}(687,\cdot)\) \(\chi_{4031}(750,\cdot)\) \(\chi_{4031}(774,\cdot)\) \(\chi_{4031}(807,\cdot)\) ...

Values on generators

\((3337,697)\) → \((e\left(\frac{3}{7}\right),e\left(\frac{14}{23}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{6}{161}\right)\)\(e\left(\frac{16}{161}\right)\)\(e\left(\frac{12}{161}\right)\)\(e\left(\frac{125}{161}\right)\)\(e\left(\frac{22}{161}\right)\)\(e\left(\frac{93}{161}\right)\)\(e\left(\frac{18}{161}\right)\)\(e\left(\frac{32}{161}\right)\)\(e\left(\frac{131}{161}\right)\)\(e\left(\frac{157}{161}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{161})\)