Properties

Conductor 1000
Order 100
Real no
Primitive no
Minimal no
Parity even
Orbit label 4000.cr

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[47]
 
pari: [g,chi] = znchar(Mod(47,4000))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1000
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.cr
Orbit index = 70

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 ]
 

\(\chi_{4000}(47,\cdot)\) \(\chi_{4000}(303,\cdot)\) \(\chi_{4000}(367,\cdot)\) \(\chi_{4000}(463,\cdot)\) \(\chi_{4000}(527,\cdot)\) \(\chi_{4000}(623,\cdot)\) \(\chi_{4000}(687,\cdot)\) \(\chi_{4000}(783,\cdot)\) \(\chi_{4000}(847,\cdot)\) \(\chi_{4000}(1103,\cdot)\) \(\chi_{4000}(1167,\cdot)\) \(\chi_{4000}(1263,\cdot)\) \(\chi_{4000}(1327,\cdot)\) \(\chi_{4000}(1423,\cdot)\) \(\chi_{4000}(1487,\cdot)\) \(\chi_{4000}(1583,\cdot)\) \(\chi_{4000}(1647,\cdot)\) \(\chi_{4000}(1903,\cdot)\) \(\chi_{4000}(1967,\cdot)\) \(\chi_{4000}(2063,\cdot)\) \(\chi_{4000}(2127,\cdot)\) \(\chi_{4000}(2223,\cdot)\) \(\chi_{4000}(2287,\cdot)\) \(\chi_{4000}(2383,\cdot)\) \(\chi_{4000}(2447,\cdot)\) \(\chi_{4000}(2703,\cdot)\) \(\chi_{4000}(2767,\cdot)\) \(\chi_{4000}(2863,\cdot)\) \(\chi_{4000}(2927,\cdot)\) \(\chi_{4000}(3023,\cdot)\) ...

Values on generators

\((2751,2501,1377)\) → \((-1,-1,e\left(\frac{97}{100}\right))\)

Values

-1137911131719212327
\(1\)\(1\)\(e\left(\frac{79}{100}\right)\)\(e\left(\frac{19}{20}\right)\)\(e\left(\frac{29}{50}\right)\)\(e\left(\frac{18}{25}\right)\)\(e\left(\frac{33}{100}\right)\)\(e\left(\frac{81}{100}\right)\)\(e\left(\frac{23}{50}\right)\)\(e\left(\frac{37}{50}\right)\)\(e\left(\frac{57}{100}\right)\)\(e\left(\frac{37}{100}\right)\)
value at  e.g. 2

Related number fields

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