Properties

Conductor 3004
Order 750
Real No
Primitive No
Parity Even
Orbit Label 6008.ci

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(6008)
 
sage: chi = H[15]
 
pari: [g,chi] = znchar(Mod(15,6008))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 3004
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 750
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 = 6008.ci
Orbit index = 61

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 ]
 

\(\chi_{6008}(15,\cdot)\) \(\chi_{6008}(31,\cdot)\) \(\chi_{6008}(39,\cdot)\) \(\chi_{6008}(55,\cdot)\) \(\chi_{6008}(63,\cdot)\) \(\chi_{6008}(79,\cdot)\) \(\chi_{6008}(103,\cdot)\) \(\chi_{6008}(135,\cdot)\) \(\chi_{6008}(143,\cdot)\) \(\chi_{6008}(159,\cdot)\) \(\chi_{6008}(175,\cdot)\) \(\chi_{6008}(231,\cdot)\) \(\chi_{6008}(263,\cdot)\) \(\chi_{6008}(279,\cdot)\) \(\chi_{6008}(335,\cdot)\) \(\chi_{6008}(351,\cdot)\) \(\chi_{6008}(375,\cdot)\) \(\chi_{6008}(431,\cdot)\) \(\chi_{6008}(487,\cdot)\) \(\chi_{6008}(495,\cdot)\) \(\chi_{6008}(591,\cdot)\) \(\chi_{6008}(599,\cdot)\) \(\chi_{6008}(607,\cdot)\) \(\chi_{6008}(623,\cdot)\) \(\chi_{6008}(647,\cdot)\) \(\chi_{6008}(711,\cdot)\) \(\chi_{6008}(735,\cdot)\) \(\chi_{6008}(775,\cdot)\) \(\chi_{6008}(839,\cdot)\) \(\chi_{6008}(847,\cdot)\) ...

Inducing primitive character

\(\chi_{3004}(15,\cdot)\)

Values on generators

\((1503,3005,1505)\) → \((-1,1,e\left(\frac{737}{750}\right))\)

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{181}{375}\right)\)\(e\left(\frac{91}{375}\right)\)\(e\left(\frac{27}{125}\right)\)\(e\left(\frac{362}{375}\right)\)\(e\left(\frac{8}{75}\right)\)\(e\left(\frac{73}{375}\right)\)\(e\left(\frac{272}{375}\right)\)\(e\left(\frac{223}{750}\right)\)\(e\left(\frac{641}{750}\right)\)\(e\left(\frac{262}{375}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{375})\)