Properties

Conductor 500
Order 50
Real No
Primitive No
Parity Odd
Orbit Label 4000.cf

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(4000)
 
sage: chi = H[159]
 
pari: [g,chi] = znchar(Mod(159,4000))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 500
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 50
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 = Odd
Orbit label = 4000.cf
Orbit index = 58

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 ]
 

\(\chi_{4000}(159,\cdot)\) \(\chi_{4000}(319,\cdot)\) \(\chi_{4000}(479,\cdot)\) \(\chi_{4000}(639,\cdot)\) \(\chi_{4000}(959,\cdot)\) \(\chi_{4000}(1119,\cdot)\) \(\chi_{4000}(1279,\cdot)\) \(\chi_{4000}(1439,\cdot)\) \(\chi_{4000}(1759,\cdot)\) \(\chi_{4000}(1919,\cdot)\) \(\chi_{4000}(2079,\cdot)\) \(\chi_{4000}(2239,\cdot)\) \(\chi_{4000}(2559,\cdot)\) \(\chi_{4000}(2719,\cdot)\) \(\chi_{4000}(2879,\cdot)\) \(\chi_{4000}(3039,\cdot)\) \(\chi_{4000}(3359,\cdot)\) \(\chi_{4000}(3519,\cdot)\) \(\chi_{4000}(3679,\cdot)\) \(\chi_{4000}(3839,\cdot)\)

Inducing primitive character

\(\chi_{500}(159,\cdot)\)

Values on generators

\((2751,2501,1377)\) → \((-1,1,e\left(\frac{37}{50}\right))\)

Values

-1137911131719212327
\(-1\)\(1\)\(e\left(\frac{17}{25}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{9}{25}\right)\)\(e\left(\frac{37}{50}\right)\)\(e\left(\frac{43}{50}\right)\)\(e\left(\frac{1}{50}\right)\)\(e\left(\frac{41}{50}\right)\)\(e\left(\frac{2}{25}\right)\)\(e\left(\frac{11}{25}\right)\)\(e\left(\frac{1}{25}\right)\)
value at  e.g. 2

Related number fields

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