Properties

Label 1183.289
Modulus $1183$
Conductor $1183$
Order $39$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1183, base_ring=CyclotomicField(78))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([26,68]))
 
pari: [g,chi] = znchar(Mod(289,1183))
 

Basic properties

Modulus: \(1183\)
Conductor: \(1183\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(39\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1183.bi

\(\chi_{1183}(16,\cdot)\) \(\chi_{1183}(74,\cdot)\) \(\chi_{1183}(107,\cdot)\) \(\chi_{1183}(165,\cdot)\) \(\chi_{1183}(198,\cdot)\) \(\chi_{1183}(256,\cdot)\) \(\chi_{1183}(289,\cdot)\) \(\chi_{1183}(347,\cdot)\) \(\chi_{1183}(380,\cdot)\) \(\chi_{1183}(438,\cdot)\) \(\chi_{1183}(471,\cdot)\) \(\chi_{1183}(562,\cdot)\) \(\chi_{1183}(620,\cdot)\) \(\chi_{1183}(711,\cdot)\) \(\chi_{1183}(744,\cdot)\) \(\chi_{1183}(802,\cdot)\) \(\chi_{1183}(835,\cdot)\) \(\chi_{1183}(893,\cdot)\) \(\chi_{1183}(926,\cdot)\) \(\chi_{1183}(984,\cdot)\) \(\chi_{1183}(1017,\cdot)\) \(\chi_{1183}(1075,\cdot)\) \(\chi_{1183}(1108,\cdot)\) \(\chi_{1183}(1166,\cdot)\)

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: $\Q(\zeta_{39})$
Fixed field: 39.39.253721406991290895924770503111827676888647505643788160579278763946491805765758913183386148271215912203961.2

Values on generators

\((339,1016)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{34}{39}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(8\)\(9\)\(10\)\(11\)\(12\)
\(1\)\(1\)\(e\left(\frac{7}{13}\right)\)\(e\left(\frac{17}{39}\right)\)\(e\left(\frac{1}{13}\right)\)\(e\left(\frac{20}{39}\right)\)\(e\left(\frac{38}{39}\right)\)\(e\left(\frac{8}{13}\right)\)\(e\left(\frac{34}{39}\right)\)\(e\left(\frac{2}{39}\right)\)\(e\left(\frac{5}{39}\right)\)\(e\left(\frac{20}{39}\right)\)
value at e.g. 2