Properties

Conductor 9900
Order 30
Real no
Primitive yes
Minimal yes
Parity odd
Orbit label 9900.hq

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(9900)
 
sage: chi = H[131]
 
pari: [g,chi] = znchar(Mod(131,9900))
 

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
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = odd
Orbit label = 9900.hq
Orbit index = 199

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 ]
 

\(\chi_{9900}(131,\cdot)\) \(\chi_{9900}(2111,\cdot)\) \(\chi_{9900}(3431,\cdot)\) \(\chi_{9900}(4091,\cdot)\) \(\chi_{9900}(5411,\cdot)\) \(\chi_{9900}(6071,\cdot)\) \(\chi_{9900}(7391,\cdot)\) \(\chi_{9900}(9371,\cdot)\)

Values on generators

\((4951,5501,2377,4501)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{2}{5}\right),-1)\)

Values

-117131719232931374143
\(-1\)\(1\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{23}{30}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{1}{15}\right)\)\(e\left(\frac{2}{15}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{4}{15}\right)\)\(e\left(\frac{1}{3}\right)\)
value at  e.g. 2

Related number fields

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