Properties

Label 8033.182
Modulus $8033$
Conductor $8033$
Order $84$
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([9,35]))
 
pari: [g,chi] = znchar(Mod(182,8033))
 

Basic properties

Modulus: \(8033\)
Conductor: \(8033\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(84\)
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.bs

\(\chi_{8033}(182,\cdot)\) \(\chi_{8033}(649,\cdot)\) \(\chi_{8033}(1013,\cdot)\) \(\chi_{8033}(1203,\cdot)\) \(\chi_{8033}(1627,\cdot)\) \(\chi_{8033}(1697,\cdot)\) \(\chi_{8033}(1904,\cdot)\) \(\chi_{8033}(2251,\cdot)\) \(\chi_{8033}(3082,\cdot)\) \(\chi_{8033}(3229,\cdot)\) \(\chi_{8033}(3506,\cdot)\) \(\chi_{8033}(3913,\cdot)\) \(\chi_{8033}(4120,\cdot)\) \(\chi_{8033}(4527,\cdot)\) \(\chi_{8033}(4804,\cdot)\) \(\chi_{8033}(4951,\cdot)\) \(\chi_{8033}(5782,\cdot)\) \(\chi_{8033}(6129,\cdot)\) \(\chi_{8033}(6336,\cdot)\) \(\chi_{8033}(6406,\cdot)\) \(\chi_{8033}(6830,\cdot)\) \(\chi_{8033}(7020,\cdot)\) \(\chi_{8033}(7384,\cdot)\) \(\chi_{8033}(7851,\cdot)\)

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

\((5541,1944)\) → \((e\left(\frac{3}{28}\right),e\left(\frac{5}{12}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{5}{14}\right)\)\(e\left(\frac{73}{84}\right)\)\(e\left(\frac{5}{7}\right)\)\(e\left(\frac{65}{84}\right)\)\(e\left(\frac{19}{84}\right)\)\(e\left(\frac{19}{42}\right)\)\(e\left(\frac{1}{14}\right)\)\(e\left(\frac{31}{42}\right)\)\(e\left(\frac{11}{84}\right)\)\(e\left(\frac{25}{42}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{84})$
Fixed field: Number field defined by a degree 84 polynomial