Properties

Label 8033.225
Modulus $8033$
Conductor $8033$
Order $322$
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([299,119]))
 
pari: [g,chi] = znchar(Mod(225,8033))
 

Basic properties

Modulus: \(8033\)
Conductor: \(8033\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(322\)
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.cl

\(\chi_{8033}(4,\cdot)\) \(\chi_{8033}(13,\cdot)\) \(\chi_{8033}(64,\cdot)\) \(\chi_{8033}(120,\cdot)\) \(\chi_{8033}(122,\cdot)\) \(\chi_{8033}(208,\cdot)\) \(\chi_{8033}(225,\cdot)\) \(\chi_{8033}(341,\cdot)\) \(\chi_{8033}(353,\cdot)\) \(\chi_{8033}(390,\cdot)\) \(\chi_{8033}(399,\cdot)\) \(\chi_{8033}(470,\cdot)\) \(\chi_{8033}(502,\cdot)\) \(\chi_{8033}(527,\cdot)\) \(\chi_{8033}(535,\cdot)\) \(\chi_{8033}(613,\cdot)\) \(\chi_{8033}(618,\cdot)\) \(\chi_{8033}(676,\cdot)\) \(\chi_{8033}(700,\cdot)\) \(\chi_{8033}(747,\cdot)\) \(\chi_{8033}(905,\cdot)\) \(\chi_{8033}(933,\cdot)\) \(\chi_{8033}(1024,\cdot)\) \(\chi_{8033}(1078,\cdot)\) \(\chi_{8033}(1182,\cdot)\) \(\chi_{8033}(1369,\cdot)\) \(\chi_{8033}(1398,\cdot)\) \(\chi_{8033}(1426,\cdot)\) \(\chi_{8033}(1459,\cdot)\) \(\chi_{8033}(1646,\cdot)\) ...

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

\((5541,1944)\) → \((e\left(\frac{13}{14}\right),e\left(\frac{17}{46}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{41}{161}\right)\)\(e\left(\frac{39}{322}\right)\)\(e\left(\frac{82}{161}\right)\)\(e\left(\frac{257}{322}\right)\)\(e\left(\frac{121}{322}\right)\)\(e\left(\frac{44}{161}\right)\)\(e\left(\frac{123}{161}\right)\)\(e\left(\frac{39}{161}\right)\)\(e\left(\frac{17}{322}\right)\)\(e\left(\frac{129}{161}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{161})$
Fixed field: Number field defined by a degree 322 polynomial