Properties

Label 3549.17
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([39,13,73]))
 
pari: [g,chi] = znchar(Mod(17,3549))
 

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.cy

\(\chi_{3549}(17,\cdot)\) \(\chi_{3549}(257,\cdot)\) \(\chi_{3549}(290,\cdot)\) \(\chi_{3549}(563,\cdot)\) \(\chi_{3549}(803,\cdot)\) \(\chi_{3549}(836,\cdot)\) \(\chi_{3549}(1076,\cdot)\) \(\chi_{3549}(1109,\cdot)\) \(\chi_{3549}(1349,\cdot)\) \(\chi_{3549}(1382,\cdot)\) \(\chi_{3549}(1622,\cdot)\) \(\chi_{3549}(1655,\cdot)\) \(\chi_{3549}(1895,\cdot)\) \(\chi_{3549}(1928,\cdot)\) \(\chi_{3549}(2168,\cdot)\) \(\chi_{3549}(2201,\cdot)\) \(\chi_{3549}(2441,\cdot)\) \(\chi_{3549}(2474,\cdot)\) \(\chi_{3549}(2714,\cdot)\) \(\chi_{3549}(2747,\cdot)\) \(\chi_{3549}(2987,\cdot)\) \(\chi_{3549}(3260,\cdot)\) \(\chi_{3549}(3293,\cdot)\) \(\chi_{3549}(3533,\cdot)\)

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

\((1184,1522,3382)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{73}{78}\right))\)

Values

\(-1\)\(1\)\(2\)\(4\)\(5\)\(8\)\(10\)\(11\)\(16\)\(17\)\(19\)\(20\)
\(1\)\(1\)\(e\left(\frac{10}{13}\right)\)\(e\left(\frac{7}{13}\right)\)\(e\left(\frac{59}{78}\right)\)\(e\left(\frac{4}{13}\right)\)\(e\left(\frac{41}{78}\right)\)\(e\left(\frac{22}{39}\right)\)\(e\left(\frac{1}{13}\right)\)\(e\left(\frac{4}{13}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{23}{78}\right)\)
value at e.g. 2