Properties

Label 3549.11
Modulus $3549$
Conductor $3549$
Order $156$
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(3549, base_ring=CyclotomicField(156))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([78,104,103]))
 
pari: [g,chi] = znchar(Mod(11,3549))
 

Basic properties

Modulus: \(3549\)
Conductor: \(3549\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(156\)
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 3549.el

\(\chi_{3549}(11,\cdot)\) \(\chi_{3549}(149,\cdot)\) \(\chi_{3549}(158,\cdot)\) \(\chi_{3549}(254,\cdot)\) \(\chi_{3549}(284,\cdot)\) \(\chi_{3549}(422,\cdot)\) \(\chi_{3549}(431,\cdot)\) \(\chi_{3549}(527,\cdot)\) \(\chi_{3549}(557,\cdot)\) \(\chi_{3549}(704,\cdot)\) \(\chi_{3549}(800,\cdot)\) \(\chi_{3549}(830,\cdot)\) \(\chi_{3549}(968,\cdot)\) \(\chi_{3549}(977,\cdot)\) \(\chi_{3549}(1073,\cdot)\) \(\chi_{3549}(1241,\cdot)\) \(\chi_{3549}(1250,\cdot)\) \(\chi_{3549}(1346,\cdot)\) \(\chi_{3549}(1376,\cdot)\) \(\chi_{3549}(1514,\cdot)\) \(\chi_{3549}(1523,\cdot)\) \(\chi_{3549}(1619,\cdot)\) \(\chi_{3549}(1649,\cdot)\) \(\chi_{3549}(1787,\cdot)\) \(\chi_{3549}(1796,\cdot)\) \(\chi_{3549}(1892,\cdot)\) \(\chi_{3549}(1922,\cdot)\) \(\chi_{3549}(2060,\cdot)\) \(\chi_{3549}(2069,\cdot)\) \(\chi_{3549}(2165,\cdot)\) ...

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: $\Q(\zeta_{156})$
Fixed field: Number field defined by a degree 156 polynomial (not computed)

Values on generators

\((1184,1522,3382)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{103}{156}\right))\)

Values

\(-1\)\(1\)\(2\)\(4\)\(5\)\(8\)\(10\)\(11\)\(16\)\(17\)\(19\)\(20\)
\(1\)\(1\)\(e\left(\frac{77}{156}\right)\)\(e\left(\frac{77}{78}\right)\)\(e\left(\frac{121}{156}\right)\)\(e\left(\frac{25}{52}\right)\)\(e\left(\frac{7}{26}\right)\)\(e\left(\frac{9}{52}\right)\)\(e\left(\frac{38}{39}\right)\)\(e\left(\frac{22}{39}\right)\)\(i\)\(e\left(\frac{119}{156}\right)\)
value at e.g. 2