Properties

Conductor 6008
Order 150
Real No
Primitive Yes
Parity Even
Orbit Label 6008.br

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[61]
 
pari: [g,chi] = znchar(Mod(61,6008))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6008
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 150
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.br
Orbit index = 44

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 ]
 

\(\chi_{6008}(61,\cdot)\) \(\chi_{6008}(197,\cdot)\) \(\chi_{6008}(229,\cdot)\) \(\chi_{6008}(405,\cdot)\) \(\chi_{6008}(637,\cdot)\) \(\chi_{6008}(717,\cdot)\) \(\chi_{6008}(837,\cdot)\) \(\chi_{6008}(941,\cdot)\) \(\chi_{6008}(1125,\cdot)\) \(\chi_{6008}(1373,\cdot)\) \(\chi_{6008}(1621,\cdot)\) \(\chi_{6008}(1901,\cdot)\) \(\chi_{6008}(1973,\cdot)\) \(\chi_{6008}(2133,\cdot)\) \(\chi_{6008}(2141,\cdot)\) \(\chi_{6008}(2285,\cdot)\) \(\chi_{6008}(2437,\cdot)\) \(\chi_{6008}(2453,\cdot)\) \(\chi_{6008}(2549,\cdot)\) \(\chi_{6008}(2781,\cdot)\) \(\chi_{6008}(3125,\cdot)\) \(\chi_{6008}(3277,\cdot)\) \(\chi_{6008}(3885,\cdot)\) \(\chi_{6008}(3949,\cdot)\) \(\chi_{6008}(4133,\cdot)\) \(\chi_{6008}(4613,\cdot)\) \(\chi_{6008}(4637,\cdot)\) \(\chi_{6008}(4669,\cdot)\) \(\chi_{6008}(4805,\cdot)\) \(\chi_{6008}(4813,\cdot)\) ...

Values on generators

\((1503,3005,1505)\) → \((1,-1,e\left(\frac{56}{75}\right))\)

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{37}{150}\right)\)\(e\left(\frac{7}{150}\right)\)\(e\left(\frac{2}{25}\right)\)\(e\left(\frac{37}{75}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{121}{150}\right)\)\(e\left(\frac{22}{75}\right)\)\(e\left(\frac{49}{75}\right)\)\(e\left(\frac{91}{150}\right)\)\(e\left(\frac{49}{150}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{75})\)