Properties

Conductor 2805
Order 80
Real No
Primitive No
Parity Even
Orbit Label 5610.fk

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(5610)
 
sage: chi = H[107]
 
pari: [g,chi] = znchar(Mod(107,5610))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2805
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 80
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 5610.fk
Orbit index = 141

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 ]
 

\(\chi_{5610}(107,\cdot)\) \(\chi_{5610}(167,\cdot)\) \(\chi_{5610}(437,\cdot)\) \(\chi_{5610}(503,\cdot)\) \(\chi_{5610}(623,\cdot)\) \(\chi_{5610}(677,\cdot)\) \(\chi_{5610}(887,\cdot)\) \(\chi_{5610}(1163,\cdot)\) \(\chi_{5610}(1553,\cdot)\) \(\chi_{5610}(2063,\cdot)\) \(\chi_{5610}(2147,\cdot)\) \(\chi_{5610}(2153,\cdot)\) \(\chi_{5610}(2207,\cdot)\) \(\chi_{5610}(2417,\cdot)\) \(\chi_{5610}(2477,\cdot)\) \(\chi_{5610}(2543,\cdot)\) \(\chi_{5610}(2657,\cdot)\) \(\chi_{5610}(2987,\cdot)\) \(\chi_{5610}(3053,\cdot)\) \(\chi_{5610}(3203,\cdot)\) \(\chi_{5610}(3593,\cdot)\) \(\chi_{5610}(3713,\cdot)\) \(\chi_{5610}(3737,\cdot)\) \(\chi_{5610}(4187,\cdot)\) \(\chi_{5610}(4193,\cdot)\) \(\chi_{5610}(4457,\cdot)\) \(\chi_{5610}(4517,\cdot)\) \(\chi_{5610}(4583,\cdot)\) \(\chi_{5610}(4703,\cdot)\) \(\chi_{5610}(4967,\cdot)\) ...

Inducing primitive character

\(\chi_{2805}(107,\cdot)\)

Values on generators

\((1871,3367,1531,3301)\) → \((-1,i,e\left(\frac{3}{10}\right),e\left(\frac{5}{16}\right))\)

Values

-117131923293137414347
\(1\)\(1\)\(e\left(\frac{63}{80}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{31}{40}\right)\)\(e\left(\frac{15}{16}\right)\)\(e\left(\frac{13}{80}\right)\)\(e\left(\frac{49}{80}\right)\)\(e\left(\frac{13}{80}\right)\)\(e\left(\frac{67}{80}\right)\)\(e\left(\frac{7}{8}\right)\)\(e\left(\frac{2}{5}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{80})\)