Properties

Conductor 751
Order 375
Real No
Primitive No
Parity Even
Orbit Label 6008.ce

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[9]
 
pari: [g,chi] = znchar(Mod(9,6008))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 751
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 375
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.ce
Orbit index = 57

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 ]
 

\(\chi_{6008}(9,\cdot)\) \(\chi_{6008}(25,\cdot)\) \(\chi_{6008}(33,\cdot)\) \(\chi_{6008}(65,\cdot)\) \(\chi_{6008}(81,\cdot)\) \(\chi_{6008}(89,\cdot)\) \(\chi_{6008}(97,\cdot)\) \(\chi_{6008}(105,\cdot)\) \(\chi_{6008}(169,\cdot)\) \(\chi_{6008}(201,\cdot)\) \(\chi_{6008}(217,\cdot)\) \(\chi_{6008}(225,\cdot)\) \(\chi_{6008}(233,\cdot)\) \(\chi_{6008}(265,\cdot)\) \(\chi_{6008}(289,\cdot)\) \(\chi_{6008}(297,\cdot)\) \(\chi_{6008}(361,\cdot)\) \(\chi_{6008}(385,\cdot)\) \(\chi_{6008}(401,\cdot)\) \(\chi_{6008}(441,\cdot)\) \(\chi_{6008}(465,\cdot)\) \(\chi_{6008}(529,\cdot)\) \(\chi_{6008}(553,\cdot)\) \(\chi_{6008}(585,\cdot)\) \(\chi_{6008}(593,\cdot)\) \(\chi_{6008}(601,\cdot)\) \(\chi_{6008}(625,\cdot)\) \(\chi_{6008}(641,\cdot)\) \(\chi_{6008}(689,\cdot)\) \(\chi_{6008}(697,\cdot)\) ...

Inducing primitive character

\(\chi_{751}(9,\cdot)\)

Values on generators

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

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{1}{375}\right)\)\(e\left(\frac{361}{375}\right)\)\(e\left(\frac{92}{125}\right)\)\(e\left(\frac{2}{375}\right)\)\(e\left(\frac{68}{75}\right)\)\(e\left(\frac{133}{375}\right)\)\(e\left(\frac{362}{375}\right)\)\(e\left(\frac{329}{375}\right)\)\(e\left(\frac{268}{375}\right)\)\(e\left(\frac{277}{375}\right)\)
value at  e.g. 2

Related number fields

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