Properties

Conductor 85
Order 16
Real No
Primitive No
Parity Even
Orbit Label 5610.cw

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[133]
 
pari: [g,chi] = znchar(Mod(133,5610))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 85
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 16
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.cw
Orbit index = 75

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 ]
 

\(\chi_{5610}(133,\cdot)\) \(\chi_{5610}(397,\cdot)\) \(\chi_{5610}(1387,\cdot)\) \(\chi_{5610}(2047,\cdot)\) \(\chi_{5610}(2113,\cdot)\) \(\chi_{5610}(2443,\cdot)\) \(\chi_{5610}(3037,\cdot)\) \(\chi_{5610}(4423,\cdot)\)

Inducing primitive character

\(\chi_{85}(48,\cdot)\)

Values on generators

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

Values

-117131923293137414347
\(1\)\(1\)\(e\left(\frac{15}{16}\right)\)\(-1\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{11}{16}\right)\)\(e\left(\frac{13}{16}\right)\)\(e\left(\frac{1}{16}\right)\)\(e\left(\frac{5}{16}\right)\)\(e\left(\frac{3}{16}\right)\)\(e\left(\frac{3}{8}\right)\)\(1\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{16})\)