Properties

Label 3549.64
Modulus $3549$
Conductor $169$
Order $26$
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([0,0,1]))
 
pari: [g,chi] = znchar(Mod(64,3549))
 

Basic properties

Modulus: \(3549\)
Conductor: \(169\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(26\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{169}(64,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3549.co

\(\chi_{3549}(64,\cdot)\) \(\chi_{3549}(610,\cdot)\) \(\chi_{3549}(883,\cdot)\) \(\chi_{3549}(1156,\cdot)\) \(\chi_{3549}(1429,\cdot)\) \(\chi_{3549}(1702,\cdot)\) \(\chi_{3549}(1975,\cdot)\) \(\chi_{3549}(2248,\cdot)\) \(\chi_{3549}(2521,\cdot)\) \(\chi_{3549}(2794,\cdot)\) \(\chi_{3549}(3067,\cdot)\) \(\chi_{3549}(3340,\cdot)\)

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: 26.26.3830224792147131369362629348887201408953937846517364173.1

Values on generators

\((1184,1522,3382)\) → \((1,1,e\left(\frac{1}{26}\right))\)

Values

\(-1\)\(1\)\(2\)\(4\)\(5\)\(8\)\(10\)\(11\)\(16\)\(17\)\(19\)\(20\)
\(1\)\(1\)\(e\left(\frac{1}{26}\right)\)\(e\left(\frac{1}{13}\right)\)\(e\left(\frac{9}{26}\right)\)\(e\left(\frac{3}{26}\right)\)\(e\left(\frac{5}{13}\right)\)\(e\left(\frac{25}{26}\right)\)\(e\left(\frac{2}{13}\right)\)\(e\left(\frac{8}{13}\right)\)\(-1\)\(e\left(\frac{11}{26}\right)\)
value at e.g. 2