Properties

Conductor 4000
Order 200
Real no
Primitive yes
Minimal yes
Parity odd
Orbit label 4000.dc

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[59]
 
pari: [g,chi] = znchar(Mod(59,4000))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4000
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 200
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = odd
Orbit label = 4000.dc
Orbit index = 81

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 ]
 

\(\chi_{4000}(19,\cdot)\) \(\chi_{4000}(59,\cdot)\) \(\chi_{4000}(139,\cdot)\) \(\chi_{4000}(179,\cdot)\) \(\chi_{4000}(219,\cdot)\) \(\chi_{4000}(259,\cdot)\) \(\chi_{4000}(339,\cdot)\) \(\chi_{4000}(379,\cdot)\) \(\chi_{4000}(419,\cdot)\) \(\chi_{4000}(459,\cdot)\) \(\chi_{4000}(539,\cdot)\) \(\chi_{4000}(579,\cdot)\) \(\chi_{4000}(619,\cdot)\) \(\chi_{4000}(659,\cdot)\) \(\chi_{4000}(739,\cdot)\) \(\chi_{4000}(779,\cdot)\) \(\chi_{4000}(819,\cdot)\) \(\chi_{4000}(859,\cdot)\) \(\chi_{4000}(939,\cdot)\) \(\chi_{4000}(979,\cdot)\) \(\chi_{4000}(1019,\cdot)\) \(\chi_{4000}(1059,\cdot)\) \(\chi_{4000}(1139,\cdot)\) \(\chi_{4000}(1179,\cdot)\) \(\chi_{4000}(1219,\cdot)\) \(\chi_{4000}(1259,\cdot)\) \(\chi_{4000}(1339,\cdot)\) \(\chi_{4000}(1379,\cdot)\) \(\chi_{4000}(1419,\cdot)\) \(\chi_{4000}(1459,\cdot)\) ...

Values on generators

\((2751,2501,1377)\) → \((-1,e\left(\frac{1}{8}\right),e\left(\frac{17}{50}\right))\)

Values

-1137911131719212327
\(-1\)\(1\)\(e\left(\frac{51}{200}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{51}{100}\right)\)\(e\left(\frac{193}{200}\right)\)\(e\left(\frac{27}{200}\right)\)\(e\left(\frac{8}{25}\right)\)\(e\left(\frac{99}{200}\right)\)\(e\left(\frac{181}{200}\right)\)\(e\left(\frac{79}{100}\right)\)\(e\left(\frac{153}{200}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{200})\)