Properties

Label 8033.331
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([23,53]))
 
pari: [g,chi] = znchar(Mod(331,8033))
 

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.by

\(\chi_{8033}(331,\cdot)\) \(\chi_{8033}(481,\cdot)\) \(\chi_{8033}(592,\cdot)\) \(\chi_{8033}(679,\cdot)\) \(\chi_{8033}(829,\cdot)\) \(\chi_{8033}(882,\cdot)\) \(\chi_{8033}(969,\cdot)\) \(\chi_{8033}(1467,\cdot)\) \(\chi_{8033}(1636,\cdot)\) \(\chi_{8033}(1670,\cdot)\) \(\chi_{8033}(1694,\cdot)\) \(\chi_{8033}(1723,\cdot)\) \(\chi_{8033}(1897,\cdot)\) \(\chi_{8033}(1902,\cdot)\) \(\chi_{8033}(2361,\cdot)\) \(\chi_{8033}(2622,\cdot)\) \(\chi_{8033}(2888,\cdot)\) \(\chi_{8033}(3062,\cdot)\) \(\chi_{8033}(3492,\cdot)\) \(\chi_{8033}(3497,\cdot)\) \(\chi_{8033}(3729,\cdot)\) \(\chi_{8033}(3845,\cdot)\) \(\chi_{8033}(4188,\cdot)\) \(\chi_{8033}(4304,\cdot)\) \(\chi_{8033}(4536,\cdot)\) \(\chi_{8033}(4541,\cdot)\) \(\chi_{8033}(4971,\cdot)\) \(\chi_{8033}(5145,\cdot)\) \(\chi_{8033}(5411,\cdot)\) \(\chi_{8033}(5672,\cdot)\) ...

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

\((5541,1944)\) → \((i,e\left(\frac{53}{92}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{43}{46}\right)\)\(e\left(\frac{51}{92}\right)\)\(e\left(\frac{20}{23}\right)\)\(e\left(\frac{7}{92}\right)\)\(e\left(\frac{45}{92}\right)\)\(e\left(\frac{31}{46}\right)\)\(e\left(\frac{37}{46}\right)\)\(e\left(\frac{5}{46}\right)\)\(e\left(\frac{1}{92}\right)\)\(e\left(\frac{13}{46}\right)\)
value at e.g. 2

Related number fields

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