Properties

Label 3549.274
Modulus $3549$
Conductor $169$
Order $13$
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(26))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,0,14]))
 
pari: [g,chi] = znchar(Mod(274,3549))
 

Basic properties

Modulus: \(3549\)
Conductor: \(169\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(13\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{169}(105,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3549.ci

\(\chi_{3549}(274,\cdot)\) \(\chi_{3549}(547,\cdot)\) \(\chi_{3549}(820,\cdot)\) \(\chi_{3549}(1093,\cdot)\) \(\chi_{3549}(1366,\cdot)\) \(\chi_{3549}(1639,\cdot)\) \(\chi_{3549}(1912,\cdot)\) \(\chi_{3549}(2185,\cdot)\) \(\chi_{3549}(2458,\cdot)\) \(\chi_{3549}(2731,\cdot)\) \(\chi_{3549}(3004,\cdot)\) \(\chi_{3549}(3277,\cdot)\)

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: \(\Q(\zeta_{13})\)
Fixed field: 13.13.542800770374370512771595361.1

Values on generators

\((1184,1522,3382)\) → \((1,1,e\left(\frac{7}{13}\right))\)

Values

\(-1\)\(1\)\(2\)\(4\)\(5\)\(8\)\(10\)\(11\)\(16\)\(17\)\(19\)\(20\)
\(1\)\(1\)\(e\left(\frac{7}{13}\right)\)\(e\left(\frac{1}{13}\right)\)\(e\left(\frac{11}{13}\right)\)\(e\left(\frac{8}{13}\right)\)\(e\left(\frac{5}{13}\right)\)\(e\left(\frac{6}{13}\right)\)\(e\left(\frac{2}{13}\right)\)\(e\left(\frac{8}{13}\right)\)\(1\)\(e\left(\frac{12}{13}\right)\)
value at e.g. 2