Properties

Conductor 4031
Order 322
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4031.bl

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[6]
 
pari: [g,chi] = znchar(Mod(6,4031))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4031
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 322
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.bl
Orbit index = 38

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 ]
 

\(\chi_{4031}(6,\cdot)\) \(\chi_{4031}(34,\cdot)\) \(\chi_{4031}(63,\cdot)\) \(\chi_{4031}(64,\cdot)\) \(\chi_{4031}(80,\cdot)\) \(\chi_{4031}(91,\cdot)\) \(\chi_{4031}(100,\cdot)\) \(\chi_{4031}(125,\cdot)\) \(\chi_{4031}(129,\cdot)\) \(\chi_{4031}(183,\cdot)\) \(\chi_{4031}(196,\cdot)\) \(\chi_{4031}(216,\cdot)\) \(\chi_{4031}(245,\cdot)\) \(\chi_{4031}(270,\cdot)\) \(\chi_{4031}(312,\cdot)\) \(\chi_{4031}(323,\cdot)\) \(\chi_{4031}(341,\cdot)\) \(\chi_{4031}(357,\cdot)\) \(\chi_{4031}(390,\cdot)\) \(\chi_{4031}(469,\cdot)\) \(\chi_{4031}(497,\cdot)\) \(\chi_{4031}(613,\cdot)\) \(\chi_{4031}(647,\cdot)\) \(\chi_{4031}(672,\cdot)\) \(\chi_{4031}(701,\cdot)\) \(\chi_{4031}(729,\cdot)\) \(\chi_{4031}(731,\cdot)\) \(\chi_{4031}(747,\cdot)\) \(\chi_{4031}(758,\cdot)\) \(\chi_{4031}(759,\cdot)\) ...

Values on generators

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

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{167}{322}\right)\)\(e\left(\frac{177}{322}\right)\)\(e\left(\frac{6}{161}\right)\)\(e\left(\frac{143}{161}\right)\)\(e\left(\frac{11}{161}\right)\)\(e\left(\frac{127}{161}\right)\)\(e\left(\frac{179}{322}\right)\)\(e\left(\frac{16}{161}\right)\)\(e\left(\frac{131}{322}\right)\)\(e\left(\frac{157}{322}\right)\)
value at  e.g. 2

Related number fields

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