Properties

Conductor 2015
Order 60
Real No
Primitive Yes
Parity Even
Orbit Label 2015.ge

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(2015)
 
sage: chi = H[189]
 
pari: [g,chi] = znchar(Mod(189,2015))
 

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 = Yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 2015.ge
Orbit index = 161

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 ]
 

\(\chi_{2015}(189,\cdot)\) \(\chi_{2015}(344,\cdot)\) \(\chi_{2015}(384,\cdot)\) \(\chi_{2015}(414,\cdot)\) \(\chi_{2015}(509,\cdot)\) \(\chi_{2015}(539,\cdot)\) \(\chi_{2015}(644,\cdot)\) \(\chi_{2015}(704,\cdot)\) \(\chi_{2015}(799,\cdot)\) \(\chi_{2015}(1129,\cdot)\) \(\chi_{2015}(1164,\cdot)\) \(\chi_{2015}(1319,\cdot)\) \(\chi_{2015}(1324,\cdot)\) \(\chi_{2015}(1354,\cdot)\) \(\chi_{2015}(1809,\cdot)\) \(\chi_{2015}(1974,\cdot)\)

Values on generators

\((807,1861,716)\) → \((-1,e\left(\frac{11}{12}\right),e\left(\frac{1}{30}\right))\)

Values

-112346789111214
\(1\)\(1\)\(e\left(\frac{13}{60}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{31}{60}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{11}{60}\right)\)\(e\left(\frac{19}{30}\right)\)\(e\left(\frac{11}{15}\right)\)
value at  e.g. 2

Related number fields

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