Properties

Label 8033.11
Modulus $8033$
Conductor $8033$
Order $1932$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(8033)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([1725,49]))
 
pari: [g,chi] = znchar(Mod(11,8033))
 

Basic properties

Modulus: \(8033\)
Conductor: \(8033\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(1932\)
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 8033.db

\(\chi_{8033}(11,\cdot)\) \(\chi_{8033}(31,\cdot)\) \(\chi_{8033}(43,\cdot)\) \(\chi_{8033}(44,\cdot)\) \(\chi_{8033}(68,\cdot)\) \(\chi_{8033}(97,\cdot)\) \(\chi_{8033}(98,\cdot)\) \(\chi_{8033}(124,\cdot)\) \(\chi_{8033}(126,\cdot)\) \(\chi_{8033}(127,\cdot)\) \(\chi_{8033}(137,\cdot)\) \(\chi_{8033}(143,\cdot)\) \(\chi_{8033}(163,\cdot)\) \(\chi_{8033}(172,\cdot)\) \(\chi_{8033}(176,\cdot)\) \(\chi_{8033}(184,\cdot)\) \(\chi_{8033}(205,\cdot)\) \(\chi_{8033}(221,\cdot)\) \(\chi_{8033}(253,\cdot)\) \(\chi_{8033}(259,\cdot)\) \(\chi_{8033}(263,\cdot)\) \(\chi_{8033}(271,\cdot)\) \(\chi_{8033}(272,\cdot)\) \(\chi_{8033}(327,\cdot)\) \(\chi_{8033}(330,\cdot)\) \(\chi_{8033}(333,\cdot)\) \(\chi_{8033}(345,\cdot)\) \(\chi_{8033}(374,\cdot)\) \(\chi_{8033}(380,\cdot)\) \(\chi_{8033}(388,\cdot)\) ...

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Values on generators

\((5541,1944)\) → \((e\left(\frac{25}{28}\right),e\left(\frac{7}{276}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{100}{161}\right)\)\(e\left(\frac{449}{1932}\right)\)\(e\left(\frac{39}{161}\right)\)\(e\left(\frac{1291}{1932}\right)\)\(e\left(\frac{1649}{1932}\right)\)\(e\left(\frac{263}{966}\right)\)\(e\left(\frac{139}{161}\right)\)\(e\left(\frac{449}{966}\right)\)\(e\left(\frac{559}{1932}\right)\)\(e\left(\frac{241}{483}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{1932})$
Fixed field: Number field defined by a degree 1932 polynomial