Properties

Conductor 403
Order 15
Real No
Primitive No
Parity Even
Orbit Label 4030.ee

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(4030)
 
sage: chi = H[3461]
 
pari: [g,chi] = znchar(Mod(3461,4030))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 403
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 15
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 = 4030.ee
Orbit index = 109

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 ]
 

\(\chi_{4030}(731,\cdot)\) \(\chi_{4030}(1361,\cdot)\) \(\chi_{4030}(1901,\cdot)\) \(\chi_{4030}(2401,\cdot)\) \(\chi_{4030}(2551,\cdot)\) \(\chi_{4030}(2921,\cdot)\) \(\chi_{4030}(3181,\cdot)\) \(\chi_{4030}(3461,\cdot)\)

Inducing primitive character

\(\chi_{403}(237,\cdot)\)

Values on generators

\((807,1861,2731)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{4}{15}\right))\)

Values

-1137911171921232729
\(1\)\(1\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{2}{15}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{7}{15}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{11}{15}\right)\)\(e\left(\frac{11}{15}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{11}{15}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{15})\)