Properties

Conductor 9900
Order 60
Real No
Primitive Yes
Parity Even
Orbit Label 9900.mc

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(9900)
 
sage: chi = H[5123]
 
pari: [g,chi] = znchar(Mod(5123,9900))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 9900
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 = 9900.mc
Orbit index = 315

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 ]
 

\(\chi_{9900}(83,\cdot)\) \(\chi_{9900}(887,\cdot)\) \(\chi_{9900}(1427,\cdot)\) \(\chi_{9900}(1667,\cdot)\) \(\chi_{9900}(1823,\cdot)\) \(\chi_{9900}(2147,\cdot)\) \(\chi_{9900}(3263,\cdot)\) \(\chi_{9900}(4187,\cdot)\) \(\chi_{9900}(4727,\cdot)\) \(\chi_{9900}(5123,\cdot)\) \(\chi_{9900}(5447,\cdot)\) \(\chi_{9900}(6503,\cdot)\) \(\chi_{9900}(6563,\cdot)\) \(\chi_{9900}(6683,\cdot)\) \(\chi_{9900}(8267,\cdot)\) \(\chi_{9900}(9803,\cdot)\)

Values on generators

\((4951,5501,2377,4501)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{11}{20}\right),e\left(\frac{3}{10}\right))\)

Values

-117131719232931374143
\(1\)\(1\)\(e\left(\frac{1}{60}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{23}{60}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{1}{30}\right)\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{14}{15}\right)\)\(e\left(\frac{11}{12}\right)\)
value at  e.g. 2

Related number fields

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