Properties

Conductor 2015
Order 12
Real No
Primitive Yes
Parity Even
Orbit Label 2015.cy

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(2015)
 
sage: chi = H[987]
 
pari: [g,chi] = znchar(Mod(987,2015))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2015
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 12
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = Yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 2015.cy
Orbit index = 77

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 ]
 

\(\chi_{2015}(688,\cdot)\) \(\chi_{2015}(987,\cdot)\) \(\chi_{2015}(1793,\cdot)\) \(\chi_{2015}(1897,\cdot)\)

Values on generators

\((807,1861,716)\) → \((i,-1,e\left(\frac{1}{6}\right))\)

Values

-112346789111214
\(1\)\(1\)\(-i\)\(e\left(\frac{11}{12}\right)\)\(-1\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{5}{12}\right)\)\(i\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{1}{6}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{12})\)