Properties

Conductor 6008
Order 750
Real No
Primitive Yes
Parity Even
Orbit Label 6008.ch

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[5]
 
pari: [g,chi] = znchar(Mod(5,6008))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6008
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 = Yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 6008.ch
Orbit index = 60

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 ]
 

\(\chi_{6008}(5,\cdot)\) \(\chi_{6008}(13,\cdot)\) \(\chi_{6008}(21,\cdot)\) \(\chi_{6008}(37,\cdot)\) \(\chi_{6008}(77,\cdot)\) \(\chi_{6008}(109,\cdot)\) \(\chi_{6008}(149,\cdot)\) \(\chi_{6008}(181,\cdot)\) \(\chi_{6008}(245,\cdot)\) \(\chi_{6008}(269,\cdot)\) \(\chi_{6008}(309,\cdot)\) \(\chi_{6008}(333,\cdot)\) \(\chi_{6008}(397,\cdot)\) \(\chi_{6008}(461,\cdot)\) \(\chi_{6008}(469,\cdot)\) \(\chi_{6008}(477,\cdot)\) \(\chi_{6008}(549,\cdot)\) \(\chi_{6008}(581,\cdot)\) \(\chi_{6008}(613,\cdot)\) \(\chi_{6008}(669,\cdot)\) \(\chi_{6008}(853,\cdot)\) \(\chi_{6008}(893,\cdot)\) \(\chi_{6008}(925,\cdot)\) \(\chi_{6008}(965,\cdot)\) \(\chi_{6008}(981,\cdot)\) \(\chi_{6008}(989,\cdot)\) \(\chi_{6008}(1029,\cdot)\) \(\chi_{6008}(1053,\cdot)\) \(\chi_{6008}(1077,\cdot)\) \(\chi_{6008}(1093,\cdot)\) ...

Values on generators

\((1503,3005,1505)\) → \((1,-1,e\left(\frac{368}{375}\right))\)

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{361}{750}\right)\)\(e\left(\frac{571}{750}\right)\)\(e\left(\frac{106}{125}\right)\)\(e\left(\frac{361}{375}\right)\)\(e\left(\frac{23}{150}\right)\)\(e\left(\frac{13}{750}\right)\)\(e\left(\frac{91}{375}\right)\)\(e\left(\frac{322}{375}\right)\)\(e\left(\frac{373}{750}\right)\)\(e\left(\frac{247}{750}\right)\)
value at  e.g. 2

Related number fields

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