Properties

Conductor 2805
Order 40
Real No
Primitive No
Parity Even
Orbit Label 5610.ep

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[257]
 
pari: [g,chi] = znchar(Mod(257,5610))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2805
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 40
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.ep
Orbit index = 120

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 ]
 

\(\chi_{5610}(257,\cdot)\) \(\chi_{5610}(383,\cdot)\) \(\chi_{5610}(773,\cdot)\) \(\chi_{5610}(797,\cdot)\) \(\chi_{5610}(1307,\cdot)\) \(\chi_{5610}(1787,\cdot)\) \(\chi_{5610}(2297,\cdot)\) \(\chi_{5610}(2303,\cdot)\) \(\chi_{5610}(2423,\cdot)\) \(\chi_{5610}(3347,\cdot)\) \(\chi_{5610}(3833,\cdot)\) \(\chi_{5610}(3953,\cdot)\) \(\chi_{5610}(4337,\cdot)\) \(\chi_{5610}(4343,\cdot)\) \(\chi_{5610}(4877,\cdot)\) \(\chi_{5610}(5483,\cdot)\)

Inducing primitive character

\(\chi_{2805}(257,\cdot)\)

Values on generators

\((1871,3367,1531,3301)\) → \((-1,i,e\left(\frac{1}{5}\right),e\left(\frac{7}{8}\right))\)

Values

-117131923293137414347
\(1\)\(1\)\(e\left(\frac{11}{40}\right)\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{31}{40}\right)\)\(e\left(\frac{3}{40}\right)\)\(e\left(\frac{21}{40}\right)\)\(e\left(\frac{29}{40}\right)\)\(-1\)\(e\left(\frac{17}{20}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{40})\)