Properties

Conductor 2000
Order 100
Real no
Primitive no
Minimal no
Parity even
Orbit label 4000.cv

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[23]
 
pari: [g,chi] = znchar(Mod(23,4000))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2000
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 100
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = no
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 4000.cv
Orbit index = 74

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 ]
 

\(\chi_{4000}(23,\cdot)\) \(\chi_{4000}(167,\cdot)\) \(\chi_{4000}(183,\cdot)\) \(\chi_{4000}(327,\cdot)\) \(\chi_{4000}(487,\cdot)\) \(\chi_{4000}(503,\cdot)\) \(\chi_{4000}(647,\cdot)\) \(\chi_{4000}(663,\cdot)\) \(\chi_{4000}(823,\cdot)\) \(\chi_{4000}(967,\cdot)\) \(\chi_{4000}(983,\cdot)\) \(\chi_{4000}(1127,\cdot)\) \(\chi_{4000}(1287,\cdot)\) \(\chi_{4000}(1303,\cdot)\) \(\chi_{4000}(1447,\cdot)\) \(\chi_{4000}(1463,\cdot)\) \(\chi_{4000}(1623,\cdot)\) \(\chi_{4000}(1767,\cdot)\) \(\chi_{4000}(1783,\cdot)\) \(\chi_{4000}(1927,\cdot)\) \(\chi_{4000}(2087,\cdot)\) \(\chi_{4000}(2103,\cdot)\) \(\chi_{4000}(2247,\cdot)\) \(\chi_{4000}(2263,\cdot)\) \(\chi_{4000}(2423,\cdot)\) \(\chi_{4000}(2567,\cdot)\) \(\chi_{4000}(2583,\cdot)\) \(\chi_{4000}(2727,\cdot)\) \(\chi_{4000}(2887,\cdot)\) \(\chi_{4000}(2903,\cdot)\) ...

Values on generators

\((2751,2501,1377)\) → \((-1,-i,e\left(\frac{31}{100}\right))\)

Values

-1137911131719212327
\(1\)\(1\)\(e\left(\frac{23}{25}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{21}{25}\right)\)\(e\left(\frac{81}{100}\right)\)\(e\left(\frac{17}{50}\right)\)\(e\left(\frac{63}{100}\right)\)\(e\left(\frac{33}{100}\right)\)\(e\left(\frac{27}{100}\right)\)\(e\left(\frac{61}{100}\right)\)\(e\left(\frac{19}{25}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{100})\)