Properties

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

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[1543]
 
pari: [g,chi] = znchar(Mod(1543,4030))
 

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.gy
Orbit index = 181

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 ]
 

\(\chi_{4030}(393,\cdot)\) \(\chi_{4030}(477,\cdot)\) \(\chi_{4030}(737,\cdot)\) \(\chi_{4030}(757,\cdot)\) \(\chi_{4030}(1257,\cdot)\) \(\chi_{4030}(1283,\cdot)\) \(\chi_{4030}(1543,\cdot)\) \(\chi_{4030}(1563,\cdot)\) \(\chi_{4030}(2057,\cdot)\) \(\chi_{4030}(2063,\cdot)\) \(\chi_{4030}(2297,\cdot)\) \(\chi_{4030}(2863,\cdot)\) \(\chi_{4030}(2967,\cdot)\) \(\chi_{4030}(3103,\cdot)\) \(\chi_{4030}(3617,\cdot)\) \(\chi_{4030}(3773,\cdot)\)

Inducing primitive character

\(\chi_{2015}(1543,\cdot)\)

Values on generators

\((807,1861,2731)\) → \((-i,e\left(\frac{2}{3}\right),e\left(\frac{13}{30}\right))\)

Values

-1137911171921232729
\(1\)\(1\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{13}{60}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{19}{30}\right)\)\(e\left(\frac{7}{60}\right)\)\(e\left(\frac{17}{30}\right)\)\(e\left(\frac{17}{30}\right)\)\(e\left(\frac{37}{60}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{1}{15}\right)\)
value at  e.g. 2

Related number fields

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