Properties

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

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[9]
 
pari: [g,chi] = znchar(Mod(9,4000))
 

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.cn
Orbit index = 66

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 ]
 

\(\chi_{4000}(9,\cdot)\) \(\chi_{4000}(89,\cdot)\) \(\chi_{4000}(169,\cdot)\) \(\chi_{4000}(329,\cdot)\) \(\chi_{4000}(409,\cdot)\) \(\chi_{4000}(489,\cdot)\) \(\chi_{4000}(569,\cdot)\) \(\chi_{4000}(729,\cdot)\) \(\chi_{4000}(809,\cdot)\) \(\chi_{4000}(889,\cdot)\) \(\chi_{4000}(969,\cdot)\) \(\chi_{4000}(1129,\cdot)\) \(\chi_{4000}(1209,\cdot)\) \(\chi_{4000}(1289,\cdot)\) \(\chi_{4000}(1369,\cdot)\) \(\chi_{4000}(1529,\cdot)\) \(\chi_{4000}(1609,\cdot)\) \(\chi_{4000}(1689,\cdot)\) \(\chi_{4000}(1769,\cdot)\) \(\chi_{4000}(1929,\cdot)\) \(\chi_{4000}(2009,\cdot)\) \(\chi_{4000}(2089,\cdot)\) \(\chi_{4000}(2169,\cdot)\) \(\chi_{4000}(2329,\cdot)\) \(\chi_{4000}(2409,\cdot)\) \(\chi_{4000}(2489,\cdot)\) \(\chi_{4000}(2569,\cdot)\) \(\chi_{4000}(2729,\cdot)\) \(\chi_{4000}(2809,\cdot)\) \(\chi_{4000}(2889,\cdot)\) ...

Values on generators

\((2751,2501,1377)\) → \((1,-i,e\left(\frac{7}{50}\right))\)

Values

-1137911131719212327
\(1\)\(1\)\(e\left(\frac{23}{100}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{23}{50}\right)\)\(e\left(\frac{39}{100}\right)\)\(e\left(\frac{71}{100}\right)\)\(e\left(\frac{11}{50}\right)\)\(e\left(\frac{77}{100}\right)\)\(e\left(\frac{63}{100}\right)\)\(e\left(\frac{21}{25}\right)\)\(e\left(\frac{69}{100}\right)\)
value at  e.g. 2

Related number fields

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