Properties

Conductor 751
Order 125
Real No
Primitive No
Parity Even
Orbit Label 6008.bp

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[1241]
 
pari: [g,chi] = znchar(Mod(1241,6008))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 751
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 125
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.bp
Orbit index = 42

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 ]
 

\(\chi_{6008}(49,\cdot)\) \(\chi_{6008}(185,\cdot)\) \(\chi_{6008}(249,\cdot)\) \(\chi_{6008}(305,\cdot)\) \(\chi_{6008}(433,\cdot)\) \(\chi_{6008}(457,\cdot)\) \(\chi_{6008}(545,\cdot)\) \(\chi_{6008}(617,\cdot)\) \(\chi_{6008}(681,\cdot)\) \(\chi_{6008}(729,\cdot)\) \(\chi_{6008}(745,\cdot)\) \(\chi_{6008}(761,\cdot)\) \(\chi_{6008}(777,\cdot)\) \(\chi_{6008}(793,\cdot)\) \(\chi_{6008}(905,\cdot)\) \(\chi_{6008}(1145,\cdot)\) \(\chi_{6008}(1241,\cdot)\) \(\chi_{6008}(1281,\cdot)\) \(\chi_{6008}(1329,\cdot)\) \(\chi_{6008}(1345,\cdot)\) \(\chi_{6008}(1545,\cdot)\) \(\chi_{6008}(1689,\cdot)\) \(\chi_{6008}(1849,\cdot)\) \(\chi_{6008}(1921,\cdot)\) \(\chi_{6008}(1937,\cdot)\) \(\chi_{6008}(2025,\cdot)\) \(\chi_{6008}(2033,\cdot)\) \(\chi_{6008}(2097,\cdot)\) \(\chi_{6008}(2129,\cdot)\) \(\chi_{6008}(2185,\cdot)\) ...

Inducing primitive character

\(\chi_{751}(490,\cdot)\)

Values on generators

\((1503,3005,1505)\) → \((1,1,e\left(\frac{34}{125}\right))\)

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{34}{125}\right)\)\(e\left(\frac{24}{125}\right)\)\(e\left(\frac{9}{125}\right)\)\(e\left(\frac{68}{125}\right)\)\(e\left(\frac{12}{25}\right)\)\(e\left(\frac{22}{125}\right)\)\(e\left(\frac{58}{125}\right)\)\(e\left(\frac{61}{125}\right)\)\(e\left(\frac{112}{125}\right)\)\(e\left(\frac{43}{125}\right)\)
value at  e.g. 2

Related number fields

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