Properties

Conductor 3004
Order 150
Real No
Primitive No
Parity Even
Orbit Label 6008.bv

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[223]
 
pari: [g,chi] = znchar(Mod(223,6008))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 3004
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 = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 6008.bv
Orbit index = 48

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 ]
 

\(\chi_{6008}(223,\cdot)\) \(\chi_{6008}(455,\cdot)\) \(\chi_{6008}(551,\cdot)\) \(\chi_{6008}(567,\cdot)\) \(\chi_{6008}(719,\cdot)\) \(\chi_{6008}(863,\cdot)\) \(\chi_{6008}(871,\cdot)\) \(\chi_{6008}(1031,\cdot)\) \(\chi_{6008}(1103,\cdot)\) \(\chi_{6008}(1383,\cdot)\) \(\chi_{6008}(1631,\cdot)\) \(\chi_{6008}(1879,\cdot)\) \(\chi_{6008}(2063,\cdot)\) \(\chi_{6008}(2167,\cdot)\) \(\chi_{6008}(2287,\cdot)\) \(\chi_{6008}(2367,\cdot)\) \(\chi_{6008}(2599,\cdot)\) \(\chi_{6008}(2775,\cdot)\) \(\chi_{6008}(2807,\cdot)\) \(\chi_{6008}(2943,\cdot)\) \(\chi_{6008}(3015,\cdot)\) \(\chi_{6008}(3087,\cdot)\) \(\chi_{6008}(3247,\cdot)\) \(\chi_{6008}(3255,\cdot)\) \(\chi_{6008}(3383,\cdot)\) \(\chi_{6008}(3471,\cdot)\) \(\chi_{6008}(3575,\cdot)\) \(\chi_{6008}(3703,\cdot)\) \(\chi_{6008}(3863,\cdot)\) \(\chi_{6008}(4055,\cdot)\) ...

Inducing primitive character

\(\chi_{3004}(223,\cdot)\)

Values on generators

\((1503,3005,1505)\) → \((-1,1,e\left(\frac{101}{150}\right))\)

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{13}{75}\right)\)\(e\left(\frac{43}{75}\right)\)\(e\left(\frac{21}{25}\right)\)\(e\left(\frac{26}{75}\right)\)\(e\left(\frac{14}{15}\right)\)\(e\left(\frac{4}{75}\right)\)\(e\left(\frac{56}{75}\right)\)\(e\left(\frac{79}{150}\right)\)\(e\left(\frac{143}{150}\right)\)\(e\left(\frac{1}{75}\right)\)
value at  e.g. 2

Related number fields

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