Properties

Label 2736.385
Modulus $2736$
Conductor $171$
Order $9$
Real no
Primitive no
Minimal no
Parity even

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(2736, base_ring=CyclotomicField(18))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,0,12,16]))
 
pari: [g,chi] = znchar(Mod(385,2736))
 

Basic properties

Modulus: \(2736\)
Conductor: \(171\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(9\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{171}(43,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2736.dm

\(\chi_{2736}(385,\cdot)\) \(\chi_{2736}(481,\cdot)\) \(\chi_{2736}(529,\cdot)\) \(\chi_{2736}(769,\cdot)\) \(\chi_{2736}(1201,\cdot)\) \(\chi_{2736}(1537,\cdot)\)

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: \(\Q(\zeta_{9})\)
Fixed field: 9.9.9025761726072081.2

Values on generators

\((1711,2053,1217,1009)\) → \((1,1,e\left(\frac{2}{3}\right),e\left(\frac{8}{9}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(17\)\(23\)\(25\)\(29\)\(31\)\(35\)
\(1\)\(1\)\(e\left(\frac{5}{9}\right)\)\(1\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{8}{9}\right)\)\(e\left(\frac{1}{9}\right)\)\(e\left(\frac{1}{9}\right)\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{5}{9}\right)\)
value at e.g. 2