Properties

Modulus 2015
Conductor 403
Order 60
Real no
Primitive no
Minimal yes
Parity odd
Orbit label 2015.hd

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([0,25,4]))
 
pari: [g,chi] = znchar(Mod(71,2015))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 2015
Conductor = 403
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 = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = odd
Orbit label = 2015.hd
Orbit index = 186

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 ]
 

\(\chi_{2015}(71,\cdot)\) \(\chi_{2015}(76,\cdot)\) \(\chi_{2015}(111,\cdot)\) \(\chi_{2015}(236,\cdot)\) \(\chi_{2015}(266,\cdot)\) \(\chi_{2015}(431,\cdot)\) \(\chi_{2015}(596,\cdot)\) \(\chi_{2015}(826,\cdot)\) \(\chi_{2015}(856,\cdot)\) \(\chi_{2015}(981,\cdot)\) \(\chi_{2015}(1051,\cdot)\) \(\chi_{2015}(1281,\cdot)\) \(\chi_{2015}(1436,\cdot)\) \(\chi_{2015}(1471,\cdot)\) \(\chi_{2015}(1931,\cdot)\) \(\chi_{2015}(1991,\cdot)\)

Values on generators

\((807,1861,716)\) → \((1,e\left(\frac{5}{12}\right),e\left(\frac{1}{15}\right))\)

Values

-112346789111214
\(-1\)\(1\)\(e\left(\frac{1}{60}\right)\)\(e\left(\frac{11}{15}\right)\)\(e\left(\frac{1}{30}\right)\)\(-i\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{7}{15}\right)\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{23}{30}\right)\)\(e\left(\frac{7}{15}\right)\)
value at  e.g. 2

Related number fields

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