Properties

Conductor 751
Order 25
Real No
Primitive No
Parity Even
Orbit Label 6008.z

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[193]
 
pari: [g,chi] = znchar(Mod(193,6008))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 751
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 25
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.z
Orbit index = 26

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 ]
 

\(\chi_{6008}(193,\cdot)\) \(\chi_{6008}(481,\cdot)\) \(\chi_{6008}(913,\cdot)\) \(\chi_{6008}(1201,\cdot)\) \(\chi_{6008}(1217,\cdot)\) \(\chi_{6008}(1417,\cdot)\) \(\chi_{6008}(1553,\cdot)\) \(\chi_{6008}(1673,\cdot)\) \(\chi_{6008}(1681,\cdot)\) \(\chi_{6008}(1977,\cdot)\) \(\chi_{6008}(2001,\cdot)\) \(\chi_{6008}(2601,\cdot)\) \(\chi_{6008}(2673,\cdot)\) \(\chi_{6008}(2809,\cdot)\) \(\chi_{6008}(3057,\cdot)\) \(\chi_{6008}(3121,\cdot)\) \(\chi_{6008}(3329,\cdot)\) \(\chi_{6008}(3489,\cdot)\) \(\chi_{6008}(4465,\cdot)\) \(\chi_{6008}(5209,\cdot)\)

Inducing primitive character

\(\chi_{751}(193,\cdot)\)

Values on generators

\((1503,3005,1505)\) → \((1,1,e\left(\frac{19}{25}\right))\)

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{19}{25}\right)\)\(e\left(\frac{9}{25}\right)\)\(e\left(\frac{19}{25}\right)\)\(e\left(\frac{13}{25}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{2}{25}\right)\)\(e\left(\frac{3}{25}\right)\)\(e\left(\frac{1}{25}\right)\)\(e\left(\frac{17}{25}\right)\)\(e\left(\frac{13}{25}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{25})\)