Properties

Label 8033.2
Modulus $8033$
Conductor $8033$
Order $644$
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([23,343]))
 
pari: [g,chi] = znchar(Mod(2,8033))
 

Basic properties

Modulus: \(8033\)
Conductor: \(8033\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(644\)
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.cs

\(\chi_{8033}(2,\cdot)\) \(\chi_{8033}(8,\cdot)\) \(\chi_{8033}(15,\cdot)\) \(\chi_{8033}(26,\cdot)\) \(\chi_{8033}(32,\cdot)\) \(\chi_{8033}(61,\cdot)\) \(\chi_{8033}(159,\cdot)\) \(\chi_{8033}(195,\cdot)\) \(\chi_{8033}(235,\cdot)\) \(\chi_{8033}(240,\cdot)\) \(\chi_{8033}(251,\cdot)\) \(\chi_{8033}(309,\cdot)\) \(\chi_{8033}(338,\cdot)\) \(\chi_{8033}(350,\cdot)\) \(\chi_{8033}(395,\cdot)\) \(\chi_{8033}(416,\cdot)\) \(\chi_{8033}(450,\cdot)\) \(\chi_{8033}(503,\cdot)\) \(\chi_{8033}(512,\cdot)\) \(\chi_{8033}(569,\cdot)\) \(\chi_{8033}(591,\cdot)\) \(\chi_{8033}(636,\cdot)\) \(\chi_{8033}(682,\cdot)\) \(\chi_{8033}(693,\cdot)\) \(\chi_{8033}(699,\cdot)\) \(\chi_{8033}(706,\cdot)\) \(\chi_{8033}(780,\cdot)\) \(\chi_{8033}(793,\cdot)\) \(\chi_{8033}(798,\cdot)\) \(\chi_{8033}(823,\cdot)\) ...

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

\((5541,1944)\) → \((e\left(\frac{1}{28}\right),e\left(\frac{49}{92}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{53}{161}\right)\)\(e\left(\frac{199}{644}\right)\)\(e\left(\frac{106}{161}\right)\)\(e\left(\frac{205}{644}\right)\)\(e\left(\frac{411}{644}\right)\)\(e\left(\frac{47}{322}\right)\)\(e\left(\frac{159}{161}\right)\)\(e\left(\frac{199}{322}\right)\)\(e\left(\frac{417}{644}\right)\)\(e\left(\frac{100}{161}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{644})$
Fixed field: Number field defined by a degree 644 polynomial