Properties

Label 8033.30
Modulus $8033$
Conductor $277$
Order $23$
Real no
Primitive no
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([0,5]))
 
pari: [g,chi] = znchar(Mod(30,8033))
 

Basic properties

Modulus: \(8033\)
Conductor: \(277\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(23\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{277}(30,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8033.z

\(\chi_{8033}(30,\cdot)\) \(\chi_{8033}(175,\cdot)\) \(\chi_{8033}(581,\cdot)\) \(\chi_{8033}(755,\cdot)\) \(\chi_{8033}(900,\cdot)\) \(\chi_{8033}(1277,\cdot)\) \(\chi_{8033}(1364,\cdot)\) \(\chi_{8033}(1596,\cdot)\) \(\chi_{8033}(2901,\cdot)\) \(\chi_{8033}(2988,\cdot)\) \(\chi_{8033}(3481,\cdot)\) \(\chi_{8033}(3597,\cdot)\) \(\chi_{8033}(4728,\cdot)\) \(\chi_{8033}(4873,\cdot)\) \(\chi_{8033}(5250,\cdot)\) \(\chi_{8033}(5279,\cdot)\) \(\chi_{8033}(5743,\cdot)\) \(\chi_{8033}(6178,\cdot)\) \(\chi_{8033}(6526,\cdot)\) \(\chi_{8033}(6584,\cdot)\) \(\chi_{8033}(6700,\cdot)\) \(\chi_{8033}(7715,\cdot)\)

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

\((5541,1944)\) → \((1,e\left(\frac{5}{23}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{22}{23}\right)\)\(e\left(\frac{20}{23}\right)\)\(e\left(\frac{21}{23}\right)\)\(e\left(\frac{5}{23}\right)\)\(e\left(\frac{19}{23}\right)\)\(e\left(\frac{18}{23}\right)\)\(e\left(\frac{20}{23}\right)\)\(e\left(\frac{17}{23}\right)\)\(e\left(\frac{4}{23}\right)\)\(e\left(\frac{12}{23}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{23})\)
Fixed field: 23.23.542693874230042671882983450092579839839306394717839529.1