Properties

Label 8033.99
Modulus $8033$
Conductor $8033$
Order $276$
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([69,107]))
 
pari: [g,chi] = znchar(Mod(99,8033))
 

Basic properties

Modulus: \(8033\)
Conductor: \(8033\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(276\)
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.ci

\(\chi_{8033}(99,\cdot)\) \(\chi_{8033}(447,\cdot)\) \(\chi_{8033}(476,\cdot)\) \(\chi_{8033}(568,\cdot)\) \(\chi_{8033}(626,\cdot)\) \(\chi_{8033}(650,\cdot)\) \(\chi_{8033}(655,\cdot)\) \(\chi_{8033}(737,\cdot)\) \(\chi_{8033}(800,\cdot)\) \(\chi_{8033}(974,\cdot)\) \(\chi_{8033}(1003,\cdot)\) \(\chi_{8033}(1090,\cdot)\) \(\chi_{8033}(1114,\cdot)\) \(\chi_{8033}(1201,\cdot)\) \(\chi_{8033}(1259,\cdot)\) \(\chi_{8033}(1288,\cdot)\) \(\chi_{8033}(1317,\cdot)\) \(\chi_{8033}(1409,\cdot)\) \(\chi_{8033}(1525,\cdot)\) \(\chi_{8033}(1786,\cdot)\) \(\chi_{8033}(1989,\cdot)\) \(\chi_{8033}(2042,\cdot)\) \(\chi_{8033}(2105,\cdot)\) \(\chi_{8033}(2158,\cdot)\) \(\chi_{8033}(2163,\cdot)\) \(\chi_{8033}(2221,\cdot)\) \(\chi_{8033}(2366,\cdot)\) \(\chi_{8033}(2395,\cdot)\) \(\chi_{8033}(2448,\cdot)\) \(\chi_{8033}(2482,\cdot)\) ...

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

\((5541,1944)\) → \((i,e\left(\frac{107}{276}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{11}{46}\right)\)\(e\left(\frac{37}{276}\right)\)\(e\left(\frac{11}{23}\right)\)\(e\left(\frac{245}{276}\right)\)\(e\left(\frac{103}{276}\right)\)\(e\left(\frac{73}{138}\right)\)\(e\left(\frac{33}{46}\right)\)\(e\left(\frac{37}{138}\right)\)\(e\left(\frac{35}{276}\right)\)\(e\left(\frac{133}{138}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{276})$
Fixed field: Number field defined by a degree 276 polynomial