Properties

Label 8033.86
Modulus $8033$
Conductor $8033$
Order $138$
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([69,101]))
 
pari: [g,chi] = znchar(Mod(86,8033))
 

Basic properties

Modulus: \(8033\)
Conductor: \(8033\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(138\)
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.bz

\(\chi_{8033}(86,\cdot)\) \(\chi_{8033}(289,\cdot)\) \(\chi_{8033}(347,\cdot)\) \(\chi_{8033}(463,\cdot)\) \(\chi_{8033}(579,\cdot)\) \(\chi_{8033}(637,\cdot)\) \(\chi_{8033}(666,\cdot)\) \(\chi_{8033}(695,\cdot)\) \(\chi_{8033}(782,\cdot)\) \(\chi_{8033}(1130,\cdot)\) \(\chi_{8033}(1304,\cdot)\) \(\chi_{8033}(1362,\cdot)\) \(\chi_{8033}(1652,\cdot)\) \(\chi_{8033}(1768,\cdot)\) \(\chi_{8033}(1884,\cdot)\) \(\chi_{8033}(2116,\cdot)\) \(\chi_{8033}(2145,\cdot)\) \(\chi_{8033}(2522,\cdot)\) \(\chi_{8033}(2580,\cdot)\) \(\chi_{8033}(2957,\cdot)\) \(\chi_{8033}(3044,\cdot)\) \(\chi_{8033}(3276,\cdot)\) \(\chi_{8033}(3363,\cdot)\) \(\chi_{8033}(3885,\cdot)\) \(\chi_{8033}(3914,\cdot)\) \(\chi_{8033}(4001,\cdot)\) \(\chi_{8033}(4088,\cdot)\) \(\chi_{8033}(4146,\cdot)\) \(\chi_{8033}(4494,\cdot)\) \(\chi_{8033}(4784,\cdot)\) ...

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

\((5541,1944)\) → \((-1,e\left(\frac{101}{138}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{2}{23}\right)\)\(e\left(\frac{13}{138}\right)\)\(e\left(\frac{4}{23}\right)\)\(e\left(\frac{101}{138}\right)\)\(e\left(\frac{25}{138}\right)\)\(e\left(\frac{7}{69}\right)\)\(e\left(\frac{6}{23}\right)\)\(e\left(\frac{13}{69}\right)\)\(e\left(\frac{113}{138}\right)\)\(e\left(\frac{43}{69}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{69})$
Fixed field: Number field defined by a degree %d polynomial (not computed)