Properties

Label 3549.100
Modulus $3549$
Conductor $1183$
Order $39$
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(78))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,26,10]))
 
pari: [g,chi] = znchar(Mod(100,3549))
 

Basic properties

Modulus: \(3549\)
Conductor: \(1183\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(39\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1183}(100,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3549.cs

\(\chi_{3549}(100,\cdot)\) \(\chi_{3549}(172,\cdot)\) \(\chi_{3549}(373,\cdot)\) \(\chi_{3549}(445,\cdot)\) \(\chi_{3549}(646,\cdot)\) \(\chi_{3549}(718,\cdot)\) \(\chi_{3549}(919,\cdot)\) \(\chi_{3549}(1192,\cdot)\) \(\chi_{3549}(1264,\cdot)\) \(\chi_{3549}(1465,\cdot)\) \(\chi_{3549}(1537,\cdot)\) \(\chi_{3549}(1738,\cdot)\) \(\chi_{3549}(1810,\cdot)\) \(\chi_{3549}(2011,\cdot)\) \(\chi_{3549}(2083,\cdot)\) \(\chi_{3549}(2284,\cdot)\) \(\chi_{3549}(2356,\cdot)\) \(\chi_{3549}(2629,\cdot)\) \(\chi_{3549}(2830,\cdot)\) \(\chi_{3549}(2902,\cdot)\) \(\chi_{3549}(3103,\cdot)\) \(\chi_{3549}(3175,\cdot)\) \(\chi_{3549}(3376,\cdot)\) \(\chi_{3549}(3448,\cdot)\)

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: 39.39.253721406991290895924770503111827676888647505643788160579278763946491805765758913183386148271215912203961.1

Values on generators

\((1184,1522,3382)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{5}{39}\right))\)

Values

\(-1\)\(1\)\(2\)\(4\)\(5\)\(8\)\(10\)\(11\)\(16\)\(17\)\(19\)\(20\)
\(1\)\(1\)\(e\left(\frac{31}{39}\right)\)\(e\left(\frac{23}{39}\right)\)\(e\left(\frac{32}{39}\right)\)\(e\left(\frac{5}{13}\right)\)\(e\left(\frac{8}{13}\right)\)\(e\left(\frac{7}{13}\right)\)\(e\left(\frac{7}{39}\right)\)\(e\left(\frac{2}{39}\right)\)\(1\)\(e\left(\frac{16}{39}\right)\)
value at e.g. 2