Properties

Label 3549.62
Modulus $3549$
Conductor $3549$
Order $78$
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(78))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([39,39,11]))
 
pari: [g,chi] = znchar(Mod(62,3549))
 

Basic properties

Modulus: \(3549\)
Conductor: \(3549\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(78\)
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.dv

\(\chi_{3549}(62,\cdot)\) \(\chi_{3549}(251,\cdot)\) \(\chi_{3549}(335,\cdot)\) \(\chi_{3549}(524,\cdot)\) \(\chi_{3549}(608,\cdot)\) \(\chi_{3549}(797,\cdot)\) \(\chi_{3549}(881,\cdot)\) \(\chi_{3549}(1070,\cdot)\) \(\chi_{3549}(1154,\cdot)\) \(\chi_{3549}(1343,\cdot)\) \(\chi_{3549}(1427,\cdot)\) \(\chi_{3549}(1616,\cdot)\) \(\chi_{3549}(1700,\cdot)\) \(\chi_{3549}(1889,\cdot)\) \(\chi_{3549}(1973,\cdot)\) \(\chi_{3549}(2162,\cdot)\) \(\chi_{3549}(2246,\cdot)\) \(\chi_{3549}(2435,\cdot)\) \(\chi_{3549}(2519,\cdot)\) \(\chi_{3549}(2708,\cdot)\) \(\chi_{3549}(2792,\cdot)\) \(\chi_{3549}(2981,\cdot)\) \(\chi_{3549}(3254,\cdot)\) \(\chi_{3549}(3338,\cdot)\)

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: Number field defined by a degree 78 polynomial

Values on generators

\((1184,1522,3382)\) → \((-1,-1,e\left(\frac{11}{78}\right))\)

Values

\(-1\)\(1\)\(2\)\(4\)\(5\)\(8\)\(10\)\(11\)\(16\)\(17\)\(19\)\(20\)
\(1\)\(1\)\(e\left(\frac{25}{39}\right)\)\(e\left(\frac{11}{39}\right)\)\(e\left(\frac{7}{26}\right)\)\(e\left(\frac{12}{13}\right)\)\(e\left(\frac{71}{78}\right)\)\(e\left(\frac{1}{39}\right)\)\(e\left(\frac{22}{39}\right)\)\(e\left(\frac{23}{39}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{43}{78}\right)\)
value at e.g. 2