Properties

Label 8033.16
Modulus $8033$
Conductor $8033$
Order $161$
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([23,21]))
 
pari: [g,chi] = znchar(Mod(16,8033))
 

Basic properties

Modulus: \(8033\)
Conductor: \(8033\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(161\)
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.cc

\(\chi_{8033}(16,\cdot)\) \(\chi_{8033}(52,\cdot)\) \(\chi_{8033}(169,\cdot)\) \(\chi_{8033}(256,\cdot)\) \(\chi_{8033}(480,\cdot)\) \(\chi_{8033}(488,\cdot)\) \(\chi_{8033}(513,\cdot)\) \(\chi_{8033}(790,\cdot)\) \(\chi_{8033}(861,\cdot)\) \(\chi_{8033}(915,\cdot)\) \(\chi_{8033}(1006,\cdot)\) \(\chi_{8033}(1067,\cdot)\) \(\chi_{8033}(1127,\cdot)\) \(\chi_{8033}(1138,\cdot)\) \(\chi_{8033}(1263,\cdot)\) \(\chi_{8033}(1272,\cdot)\) \(\chi_{8033}(1283,\cdot)\) \(\chi_{8033}(1321,\cdot)\) \(\chi_{8033}(1412,\cdot)\) \(\chi_{8033}(1415,\cdot)\) \(\chi_{8033}(1437,\cdot)\) \(\chi_{8033}(1560,\cdot)\) \(\chi_{8033}(1586,\cdot)\) \(\chi_{8033}(1649,\cdot)\) \(\chi_{8033}(1678,\cdot)\) \(\chi_{8033}(1689,\cdot)\) \(\chi_{8033}(1731,\cdot)\) \(\chi_{8033}(1793,\cdot)\) \(\chi_{8033}(1863,\cdot)\) \(\chi_{8033}(1880,\cdot)\) ...

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

\((5541,1944)\) → \((e\left(\frac{1}{7}\right),e\left(\frac{3}{23}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{51}{161}\right)\)\(e\left(\frac{38}{161}\right)\)\(e\left(\frac{102}{161}\right)\)\(e\left(\frac{44}{161}\right)\)\(e\left(\frac{89}{161}\right)\)\(e\left(\frac{94}{161}\right)\)\(e\left(\frac{153}{161}\right)\)\(e\left(\frac{76}{161}\right)\)\(e\left(\frac{95}{161}\right)\)\(e\left(\frac{78}{161}\right)\)
value at e.g. 2

Related number fields

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