Properties

Modulus 2015
Conductor 2015
Order 60
Real no
Primitive yes
Minimal yes
Parity odd
Orbit label 2015.gm

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(2015)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([15,10,16]))
 
pari: [g,chi] = znchar(Mod(82,2015))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 2015
Conductor = 2015
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 60
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = odd
Orbit label = 2015.gm
Orbit index = 169

Galois orbit

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{2015}(82,\cdot)\) \(\chi_{2015}(173,\cdot)\) \(\chi_{2015}(348,\cdot)\) \(\chi_{2015}(537,\cdot)\) \(\chi_{2015}(608,\cdot)\) \(\chi_{2015}(803,\cdot)\) \(\chi_{2015}(888,\cdot)\) \(\chi_{2015}(1037,\cdot)\) \(\chi_{2015}(1187,\cdot)\) \(\chi_{2015}(1343,\cdot)\) \(\chi_{2015}(1382,\cdot)\) \(\chi_{2015}(1557,\cdot)\) \(\chi_{2015}(1817,\cdot)\) \(\chi_{2015}(1843,\cdot)\) \(\chi_{2015}(1993,\cdot)\) \(\chi_{2015}(2012,\cdot)\)

Values on generators

\((807,1861,716)\) → \((i,e\left(\frac{1}{6}\right),e\left(\frac{4}{15}\right))\)

Values

-112346789111214
\(-1\)\(1\)\(e\left(\frac{49}{60}\right)\)\(e\left(\frac{41}{60}\right)\)\(e\left(\frac{19}{30}\right)\)\(-1\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{19}{60}\right)\)\(e\left(\frac{11}{30}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{60})\)