Properties

Conductor 2593
Order 2592
Real no
Primitive yes
Minimal yes
Parity odd
Orbit label 2593.bd

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(2593)
 
sage: chi = H[138]
 
pari: [g,chi] = znchar(Mod(138,2593))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2593
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 2592
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 = 2593.bd
Orbit index = 30

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 ]
 

\(\chi_{2593}(7,\cdot)\) \(\chi_{2593}(10,\cdot)\) \(\chi_{2593}(11,\cdot)\) \(\chi_{2593}(13,\cdot)\) \(\chi_{2593}(14,\cdot)\) \(\chi_{2593}(15,\cdot)\) \(\chi_{2593}(20,\cdot)\) \(\chi_{2593}(21,\cdot)\) \(\chi_{2593}(26,\cdot)\) \(\chi_{2593}(29,\cdot)\) \(\chi_{2593}(30,\cdot)\) \(\chi_{2593}(39,\cdot)\) \(\chi_{2593}(44,\cdot)\) \(\chi_{2593}(45,\cdot)\) \(\chi_{2593}(46,\cdot)\) \(\chi_{2593}(56,\cdot)\) \(\chi_{2593}(61,\cdot)\) \(\chi_{2593}(66,\cdot)\) \(\chi_{2593}(69,\cdot)\) \(\chi_{2593}(80,\cdot)\) \(\chi_{2593}(83,\cdot)\) \(\chi_{2593}(84,\cdot)\) \(\chi_{2593}(85,\cdot)\) \(\chi_{2593}(88,\cdot)\) \(\chi_{2593}(89,\cdot)\) \(\chi_{2593}(92,\cdot)\) \(\chi_{2593}(97,\cdot)\) \(\chi_{2593}(99,\cdot)\) \(\chi_{2593}(104,\cdot)\) \(\chi_{2593}(109,\cdot)\) ...

Values on generators

\(7\) → \(e\left(\frac{1055}{2592}\right)\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{64}{81}\right)\)\(e\left(\frac{251}{648}\right)\)\(e\left(\frac{47}{81}\right)\)\(e\left(\frac{23}{32}\right)\)\(e\left(\frac{115}{648}\right)\)\(e\left(\frac{1055}{2592}\right)\)\(e\left(\frac{10}{27}\right)\)\(e\left(\frac{251}{324}\right)\)\(e\left(\frac{1319}{2592}\right)\)\(e\left(\frac{2443}{2592}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{2592})\)