Properties

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

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[269]
 
pari: [g,chi] = znchar(Mod(269,5610))
 

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.fg
Orbit index = 137

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 ]
 

\(\chi_{5610}(269,\cdot)\) \(\chi_{5610}(449,\cdot)\) \(\chi_{5610}(719,\cdot)\) \(\chi_{5610}(779,\cdot)\) \(\chi_{5610}(839,\cdot)\) \(\chi_{5610}(929,\cdot)\) \(\chi_{5610}(1049,\cdot)\) \(\chi_{5610}(1439,\cdot)\) \(\chi_{5610}(1499,\cdot)\) \(\chi_{5610}(1829,\cdot)\) \(\chi_{5610}(2249,\cdot)\) \(\chi_{5610}(2369,\cdot)\) \(\chi_{5610}(2489,\cdot)\) \(\chi_{5610}(2579,\cdot)\) \(\chi_{5610}(2759,\cdot)\) \(\chi_{5610}(2819,\cdot)\) \(\chi_{5610}(3029,\cdot)\) \(\chi_{5610}(3089,\cdot)\) \(\chi_{5610}(3359,\cdot)\) \(\chi_{5610}(3479,\cdot)\) \(\chi_{5610}(3899,\cdot)\) \(\chi_{5610}(4019,\cdot)\) \(\chi_{5610}(4349,\cdot)\) \(\chi_{5610}(4409,\cdot)\) \(\chi_{5610}(4559,\cdot)\) \(\chi_{5610}(4799,\cdot)\) \(\chi_{5610}(4889,\cdot)\) \(\chi_{5610}(5009,\cdot)\) \(\chi_{5610}(5069,\cdot)\) \(\chi_{5610}(5129,\cdot)\) ...

Inducing primitive character

\(\chi_{2805}(269,\cdot)\)

Values on generators

\((1871,3367,1531,3301)\) → \((-1,-1,e\left(\frac{2}{5}\right),e\left(\frac{9}{16}\right))\)

Values

-117131923293137414347
\(1\)\(1\)\(e\left(\frac{39}{80}\right)\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{3}{40}\right)\)\(e\left(\frac{7}{16}\right)\)\(e\left(\frac{49}{80}\right)\)\(e\left(\frac{37}{80}\right)\)\(e\left(\frac{69}{80}\right)\)\(e\left(\frac{71}{80}\right)\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{9}{20}\right)\)
value at  e.g. 2

Related number fields

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