Properties

Label 3549.136
Modulus $3549$
Conductor $1183$
Order $156$
Real no
Primitive no
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([0,26,149]))
 
pari: [g,chi] = znchar(Mod(136,3549))
 

Basic properties

Modulus: \(3549\)
Conductor: \(1183\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(156\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1183}(136,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3549.eo

\(\chi_{3549}(136,\cdot)\) \(\chi_{3549}(145,\cdot)\) \(\chi_{3549}(241,\cdot)\) \(\chi_{3549}(271,\cdot)\) \(\chi_{3549}(409,\cdot)\) \(\chi_{3549}(514,\cdot)\) \(\chi_{3549}(544,\cdot)\) \(\chi_{3549}(682,\cdot)\) \(\chi_{3549}(691,\cdot)\) \(\chi_{3549}(787,\cdot)\) \(\chi_{3549}(817,\cdot)\) \(\chi_{3549}(955,\cdot)\) \(\chi_{3549}(964,\cdot)\) \(\chi_{3549}(1060,\cdot)\) \(\chi_{3549}(1090,\cdot)\) \(\chi_{3549}(1228,\cdot)\) \(\chi_{3549}(1237,\cdot)\) \(\chi_{3549}(1363,\cdot)\) \(\chi_{3549}(1501,\cdot)\) \(\chi_{3549}(1510,\cdot)\) \(\chi_{3549}(1606,\cdot)\) \(\chi_{3549}(1636,\cdot)\) \(\chi_{3549}(1774,\cdot)\) \(\chi_{3549}(1783,\cdot)\) \(\chi_{3549}(1879,\cdot)\) \(\chi_{3549}(1909,\cdot)\) \(\chi_{3549}(2056,\cdot)\) \(\chi_{3549}(2152,\cdot)\) \(\chi_{3549}(2182,\cdot)\) \(\chi_{3549}(2320,\cdot)\) ...

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

\((1184,1522,3382)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{149}{156}\right))\)

Values

\(-1\)\(1\)\(2\)\(4\)\(5\)\(8\)\(10\)\(11\)\(16\)\(17\)\(19\)\(20\)
\(1\)\(1\)\(e\left(\frac{15}{52}\right)\)\(e\left(\frac{15}{26}\right)\)\(e\left(\frac{67}{156}\right)\)\(e\left(\frac{45}{52}\right)\)\(e\left(\frac{28}{39}\right)\)\(e\left(\frac{7}{156}\right)\)\(e\left(\frac{2}{13}\right)\)\(e\left(\frac{8}{13}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{1}{156}\right)\)
value at e.g. 2