Properties

Conductor 2015
Order 60
Real No
Primitive No
Parity Even
Orbit Label 4030.gk

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[1657]
 
pari: [g,chi] = znchar(Mod(1657,4030))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
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 = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 4030.gk
Orbit index = 167

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 ]
 

\(\chi_{4030}(293,\cdot)\) \(\chi_{4030}(617,\cdot)\) \(\chi_{4030}(813,\cdot)\) \(\chi_{4030}(847,\cdot)\) \(\chi_{4030}(1073,\cdot)\) \(\chi_{4030}(1103,\cdot)\) \(\chi_{4030}(1497,\cdot)\) \(\chi_{4030}(1657,\cdot)\) \(\chi_{4030}(2177,\cdot)\) \(\chi_{4030}(2273,\cdot)\) \(\chi_{4030}(2407,\cdot)\) \(\chi_{4030}(2437,\cdot)\) \(\chi_{4030}(2923,\cdot)\) \(\chi_{4030}(3283,\cdot)\) \(\chi_{4030}(3707,\cdot)\) \(\chi_{4030}(3833,\cdot)\)

Inducing primitive character

\(\chi_{2015}(1657,\cdot)\)

Values on generators

\((807,1861,2731)\) → \((i,e\left(\frac{5}{12}\right),e\left(\frac{11}{15}\right))\)

Values

-1137911171921232729
\(1\)\(1\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{47}{60}\right)\)\(e\left(\frac{13}{60}\right)\)\(e\left(\frac{31}{60}\right)\)\(e\left(\frac{31}{60}\right)\)\(e\left(\frac{43}{60}\right)\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{23}{30}\right)\)
value at  e.g. 2

Related number fields

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