Properties

Conductor 9900
Order 30
Real No
Primitive Yes
Parity Even
Orbit Label 9900.hx

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[79]
 
pari: [g,chi] = znchar(Mod(79,9900))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 9900
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 30
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.hx
Orbit index = 206

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 ]
 

\(\chi_{9900}(79,\cdot)\) \(\chi_{9900}(1339,\cdot)\) \(\chi_{9900}(3379,\cdot)\) \(\chi_{9900}(4219,\cdot)\) \(\chi_{9900}(4639,\cdot)\) \(\chi_{9900}(4759,\cdot)\) \(\chi_{9900}(7519,\cdot)\) \(\chi_{9900}(8059,\cdot)\)

Values on generators

\((4951,5501,2377,4501)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{1}{10}\right),e\left(\frac{1}{10}\right))\)

Values

-117131719232931374143
\(1\)\(1\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{14}{15}\right)\)\(e\left(\frac{17}{30}\right)\)\(e\left(\frac{7}{30}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{1}{30}\right)\)\(e\left(\frac{1}{6}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{15})\)