Properties

Label 8033.95
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([9,77]))
 
pari: [g,chi] = znchar(Mod(95,8033))
 

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.bn

\(\chi_{8033}(95,\cdot)\) \(\chi_{8033}(242,\cdot)\) \(\chi_{8033}(519,\cdot)\) \(\chi_{8033}(736,\cdot)\) \(\chi_{8033}(926,\cdot)\) \(\chi_{8033}(1290,\cdot)\) \(\chi_{8033}(1974,\cdot)\) \(\chi_{8033}(2805,\cdot)\) \(\chi_{8033}(3142,\cdot)\) \(\chi_{8033}(3419,\cdot)\) \(\chi_{8033}(3636,\cdot)\) \(\chi_{8033}(3843,\cdot)\) \(\chi_{8033}(4190,\cdot)\) \(\chi_{8033}(4397,\cdot)\) \(\chi_{8033}(4614,\cdot)\) \(\chi_{8033}(4891,\cdot)\) \(\chi_{8033}(5228,\cdot)\) \(\chi_{8033}(6059,\cdot)\) \(\chi_{8033}(6743,\cdot)\) \(\chi_{8033}(7107,\cdot)\) \(\chi_{8033}(7297,\cdot)\) \(\chi_{8033}(7514,\cdot)\) \(\chi_{8033}(7791,\cdot)\) \(\chi_{8033}(7938,\cdot)\)

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

\((5541,1944)\) → \((e\left(\frac{3}{28}\right),e\left(\frac{11}{12}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{6}{7}\right)\)\(e\left(\frac{73}{84}\right)\)\(e\left(\frac{5}{7}\right)\)\(e\left(\frac{23}{84}\right)\)\(e\left(\frac{61}{84}\right)\)\(e\left(\frac{19}{42}\right)\)\(e\left(\frac{4}{7}\right)\)\(e\left(\frac{31}{42}\right)\)\(e\left(\frac{11}{84}\right)\)\(e\left(\frac{2}{21}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{84})$
Fixed field: Number field defined by a degree %d polynomial (not computed)