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Properties

Label 6534.283
Modulus $6534$
Conductor $3267$
Order $990$
Real no
Primitive no
Minimal yes
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(6534, base_ring=CyclotomicField(990)) M = H._module chi = DirichletCharacter(H, M([440,207]))
 
Copy content gp:[g,chi] = znchar(Mod(283, 6534))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("6534.283");
 

Basic properties

Modulus: \(6534\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(3267\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(990\)
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 \(\chi_{3267}(283,\cdot)\)
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: yes
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 6534.bv

\(\chi_{6534}(7,\cdot)\) \(\chi_{6534}(13,\cdot)\) \(\chi_{6534}(61,\cdot)\) \(\chi_{6534}(79,\cdot)\) \(\chi_{6534}(85,\cdot)\) \(\chi_{6534}(139,\cdot)\) \(\chi_{6534}(151,\cdot)\) \(\chi_{6534}(193,\cdot)\) \(\chi_{6534}(205,\cdot)\) \(\chi_{6534}(211,\cdot)\) \(\chi_{6534}(259,\cdot)\) \(\chi_{6534}(277,\cdot)\) \(\chi_{6534}(283,\cdot)\) \(\chi_{6534}(337,\cdot)\) \(\chi_{6534}(349,\cdot)\) \(\chi_{6534}(391,\cdot)\) \(\chi_{6534}(409,\cdot)\) \(\chi_{6534}(535,\cdot)\) \(\chi_{6534}(547,\cdot)\) \(\chi_{6534}(589,\cdot)\) \(\chi_{6534}(601,\cdot)\) \(\chi_{6534}(607,\cdot)\) \(\chi_{6534}(655,\cdot)\) \(\chi_{6534}(673,\cdot)\) \(\chi_{6534}(679,\cdot)\) \(\chi_{6534}(733,\cdot)\) \(\chi_{6534}(745,\cdot)\) \(\chi_{6534}(787,\cdot)\) \(\chi_{6534}(799,\cdot)\) \(\chi_{6534}(805,\cdot)\) ...

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: $\Q(\zeta_{495})$
Fixed field: Number field defined by a degree 990 polynomial (not computed)

Values on generators

\((6293,3511)\) → \((e\left(\frac{4}{9}\right),e\left(\frac{23}{110}\right))\)

First values

\(a\) \(-1\)\(1\)\(5\)\(7\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\( \chi_{ 6534 }(283, a) \) \(-1\)\(1\)\(e\left(\frac{344}{495}\right)\)\(e\left(\frac{569}{990}\right)\)\(e\left(\frac{667}{990}\right)\)\(e\left(\frac{301}{330}\right)\)\(e\left(\frac{227}{330}\right)\)\(e\left(\frac{52}{99}\right)\)\(e\left(\frac{193}{495}\right)\)\(e\left(\frac{989}{990}\right)\)\(e\left(\frac{431}{495}\right)\)\(e\left(\frac{89}{330}\right)\)
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)
 
\( \chi_{ 6534 }(283,a) \;\) at \(\;a = \) e.g. 2