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Properties

Label 9016.1327
Modulus $9016$
Conductor $4508$
Order $462$
Real no
Primitive no
Minimal no
Parity odd

Related objects

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Show commands: Magma / Pari/GP / SageMath
Copy content comment:Define the Dirichlet character
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9016, base_ring=CyclotomicField(462)) M = H._module chi = DirichletCharacter(H, M([231,0,110,168]))
 
Copy content gp:[g,chi] = znchar(Mod(1327, 9016))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("9016.1327");
 

Basic properties

Modulus: \(9016\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(4508\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(462\)
Copy content comment:Order
 
Copy content sage:chi.multiplicative_order()
 
Copy content gp:charorder(g,chi)
 
Copy content magma:Order(chi);
 
Real: no
Copy content comment:Whether the character is real
 
Copy content sage:chi.multiplicative_order() <= 2
 
Copy content gp:charorder(g,chi) <= 2
 
Copy content magma:Order(chi) le 2;
 
Primitive: no, induced from \(\chi_{4508}(1327,\cdot)\)
Copy content comment:If the character is primitive
 
Copy content sage:chi.is_primitive()
 
Copy content gp:#znconreyconductor(g,chi)==1
 
Copy content magma:IsPrimitive(chi);
 
Minimal: no
Parity: odd
Copy content comment:Parity
 
Copy content sage:chi.is_odd()
 
Copy content gp:zncharisodd(g,chi)
 
Copy content magma:IsOdd(chi);
 

Galois orbit 9016.et

\(\chi_{9016}(39,\cdot)\) \(\chi_{9016}(95,\cdot)\) \(\chi_{9016}(151,\cdot)\) \(\chi_{9016}(303,\cdot)\) \(\chi_{9016}(487,\cdot)\) \(\chi_{9016}(583,\cdot)\) \(\chi_{9016}(639,\cdot)\) \(\chi_{9016}(767,\cdot)\) \(\chi_{9016}(807,\cdot)\) \(\chi_{9016}(823,\cdot)\) \(\chi_{9016}(975,\cdot)\) \(\chi_{9016}(991,\cdot)\) \(\chi_{9016}(1087,\cdot)\) \(\chi_{9016}(1143,\cdot)\) \(\chi_{9016}(1159,\cdot)\) \(\chi_{9016}(1199,\cdot)\) \(\chi_{9016}(1271,\cdot)\) \(\chi_{9016}(1327,\cdot)\) \(\chi_{9016}(1383,\cdot)\) \(\chi_{9016}(1591,\cdot)\) \(\chi_{9016}(1775,\cdot)\) \(\chi_{9016}(1871,\cdot)\) \(\chi_{9016}(1927,\cdot)\) \(\chi_{9016}(2055,\cdot)\) \(\chi_{9016}(2095,\cdot)\) \(\chi_{9016}(2111,\cdot)\) \(\chi_{9016}(2151,\cdot)\) \(\chi_{9016}(2263,\cdot)\) \(\chi_{9016}(2279,\cdot)\) \(\chi_{9016}(2335,\cdot)\) ...

Copy content comment:Galois orbit
 
Copy content sage:chi.galois_orbit()
 
Copy content gp:order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 
Copy content magma:order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };
 

Related number fields

Field of values: $\Q(\zeta_{231})$
Fixed field: Number field defined by a degree 462 polynomial (not computed)

Values on generators

\((2255,4509,1473,1569)\) → \((-1,1,e\left(\frac{5}{21}\right),e\left(\frac{4}{11}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(9\)\(11\)\(13\)\(15\)\(17\)\(19\)\(25\)\(27\)
\( \chi_{ 9016 }(1327, a) \) \(-1\)\(1\)\(e\left(\frac{257}{462}\right)\)\(e\left(\frac{62}{231}\right)\)\(e\left(\frac{26}{231}\right)\)\(e\left(\frac{137}{462}\right)\)\(e\left(\frac{73}{77}\right)\)\(e\left(\frac{127}{154}\right)\)\(e\left(\frac{115}{231}\right)\)\(e\left(\frac{19}{66}\right)\)\(e\left(\frac{124}{231}\right)\)\(e\left(\frac{103}{154}\right)\)
Copy content comment:Value of chi at x
 
Copy content sage:chi(x)
 
Copy content gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
 
Copy content magma:chi(x)
 
\( \chi_{ 9016 }(1327,a) \;\) at \(\;a = \) e.g. 2