Properties

Label 8033.104
Modulus $8033$
Conductor $8033$
Order $92$
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([69,37]))
 
pari: [g,chi] = znchar(Mod(104,8033))
 

Basic properties

Modulus: \(8033\)
Conductor: \(8033\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(92\)
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.bt

\(\chi_{8033}(104,\cdot)\) \(\chi_{8033}(128,\cdot)\) \(\chi_{8033}(244,\cdot)\) \(\chi_{8033}(539,\cdot)\) \(\chi_{8033}(713,\cdot)\) \(\chi_{8033}(940,\cdot)\) \(\chi_{8033}(1699,\cdot)\) \(\chi_{8033}(1810,\cdot)\) \(\chi_{8033}(1931,\cdot)\) \(\chi_{8033}(2071,\cdot)\) \(\chi_{8033}(2134,\cdot)\) \(\chi_{8033}(2535,\cdot)\) \(\chi_{8033}(2709,\cdot)\) \(\chi_{8033}(2738,\cdot)\) \(\chi_{8033}(2772,\cdot)\) \(\chi_{8033}(2796,\cdot)\) \(\chi_{8033}(3120,\cdot)\) \(\chi_{8033}(3463,\cdot)\) \(\chi_{8033}(3550,\cdot)\) \(\chi_{8033}(3753,\cdot)\) \(\chi_{8033}(3840,\cdot)\) \(\chi_{8033}(3932,\cdot)\) \(\chi_{8033}(4101,\cdot)\) \(\chi_{8033}(4193,\cdot)\) \(\chi_{8033}(4280,\cdot)\) \(\chi_{8033}(4483,\cdot)\) \(\chi_{8033}(4570,\cdot)\) \(\chi_{8033}(4913,\cdot)\) \(\chi_{8033}(5237,\cdot)\) \(\chi_{8033}(5261,\cdot)\) ...

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

\((5541,1944)\) → \((-i,e\left(\frac{37}{92}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{20}{23}\right)\)\(e\left(\frac{33}{92}\right)\)\(e\left(\frac{17}{23}\right)\)\(e\left(\frac{83}{92}\right)\)\(e\left(\frac{21}{92}\right)\)\(e\left(\frac{39}{46}\right)\)\(e\left(\frac{14}{23}\right)\)\(e\left(\frac{33}{46}\right)\)\(e\left(\frac{71}{92}\right)\)\(e\left(\frac{13}{23}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{92})$
Fixed field: Number field defined by a degree 92 polynomial