Properties

Conductor 3004
Order 250
Real No
Primitive No
Parity Even
Orbit Label 6008.bz

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[7]
 
pari: [g,chi] = znchar(Mod(7,6008))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 3004
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 250
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.bz
Orbit index = 52

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 ]
 

\(\chi_{6008}(7,\cdot)\) \(\chi_{6008}(111,\cdot)\) \(\chi_{6008}(183,\cdot)\) \(\chi_{6008}(239,\cdot)\) \(\chi_{6008}(327,\cdot)\) \(\chi_{6008}(343,\cdot)\) \(\chi_{6008}(383,\cdot)\) \(\chi_{6008}(391,\cdot)\) \(\chi_{6008}(407,\cdot)\) \(\chi_{6008}(415,\cdot)\) \(\chi_{6008}(447,\cdot)\) \(\chi_{6008}(463,\cdot)\) \(\chi_{6008}(543,\cdot)\) \(\chi_{6008}(687,\cdot)\) \(\chi_{6008}(743,\cdot)\) \(\chi_{6008}(807,\cdot)\) \(\chi_{6008}(927,\cdot)\) \(\chi_{6008}(967,\cdot)\) \(\chi_{6008}(1079,\cdot)\) \(\chi_{6008}(1135,\cdot)\) \(\chi_{6008}(1199,\cdot)\) \(\chi_{6008}(1215,\cdot)\) \(\chi_{6008}(1231,\cdot)\) \(\chi_{6008}(1295,\cdot)\) \(\chi_{6008}(1311,\cdot)\) \(\chi_{6008}(1351,\cdot)\) \(\chi_{6008}(1431,\cdot)\) \(\chi_{6008}(1639,\cdot)\) \(\chi_{6008}(1743,\cdot)\) \(\chi_{6008}(1823,\cdot)\) ...

Inducing primitive character

\(\chi_{3004}(7,\cdot)\)

Values on generators

\((1503,3005,1505)\) → \((-1,1,e\left(\frac{217}{250}\right))\)

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{46}{125}\right)\)\(e\left(\frac{106}{125}\right)\)\(e\left(\frac{71}{125}\right)\)\(e\left(\frac{92}{125}\right)\)\(e\left(\frac{3}{25}\right)\)\(e\left(\frac{118}{125}\right)\)\(e\left(\frac{27}{125}\right)\)\(e\left(\frac{143}{250}\right)\)\(e\left(\frac{31}{250}\right)\)\(e\left(\frac{117}{125}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{125})\)