Properties

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

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[2659]
 
pari: [g,chi] = znchar(Mod(2659,4030))
 

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.fw
Orbit index = 153

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 ]
 

\(\chi_{4030}(189,\cdot)\) \(\chi_{4030}(509,\cdot)\) \(\chi_{4030}(539,\cdot)\) \(\chi_{4030}(799,\cdot)\) \(\chi_{4030}(1129,\cdot)\) \(\chi_{4030}(1319,\cdot)\) \(\chi_{4030}(1809,\cdot)\) \(\chi_{4030}(2359,\cdot)\) \(\chi_{4030}(2399,\cdot)\) \(\chi_{4030}(2429,\cdot)\) \(\chi_{4030}(2659,\cdot)\) \(\chi_{4030}(2719,\cdot)\) \(\chi_{4030}(3179,\cdot)\) \(\chi_{4030}(3339,\cdot)\) \(\chi_{4030}(3369,\cdot)\) \(\chi_{4030}(3989,\cdot)\)

Inducing primitive character

\(\chi_{2015}(644,\cdot)\)

Values on generators

\((807,1861,2731)\) → \((-1,e\left(\frac{11}{12}\right),e\left(\frac{13}{30}\right))\)

Values

-1137911171921232729
\(1\)\(1\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{43}{60}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{23}{60}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{19}{60}\right)\)\(e\left(\frac{19}{60}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{17}{30}\right)\)
value at  e.g. 2

Related number fields

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