Properties

Label 3024.403
Modulus $3024$
Conductor $3024$
Order $36$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(3024, base_ring=CyclotomicField(36))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([18,27,20,24]))
 
pari: [g,chi] = znchar(Mod(403,3024))
 

Basic properties

Modulus: \(3024\)
Conductor: \(3024\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(36\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3024.hj

\(\chi_{3024}(403,\cdot)\) \(\chi_{3024}(499,\cdot)\) \(\chi_{3024}(907,\cdot)\) \(\chi_{3024}(1003,\cdot)\) \(\chi_{3024}(1411,\cdot)\) \(\chi_{3024}(1507,\cdot)\) \(\chi_{3024}(1915,\cdot)\) \(\chi_{3024}(2011,\cdot)\) \(\chi_{3024}(2419,\cdot)\) \(\chi_{3024}(2515,\cdot)\) \(\chi_{3024}(2923,\cdot)\) \(\chi_{3024}(3019,\cdot)\)

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

\((1135,757,785,2593)\) → \((-1,-i,e\left(\frac{5}{9}\right),e\left(\frac{2}{3}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)
\(-1\)\(1\)\(e\left(\frac{31}{36}\right)\)\(e\left(\frac{5}{36}\right)\)\(e\left(\frac{25}{36}\right)\)\(1\)\(-i\)\(e\left(\frac{4}{9}\right)\)\(e\left(\frac{13}{18}\right)\)\(e\left(\frac{29}{36}\right)\)\(e\left(\frac{5}{18}\right)\)\(e\left(\frac{5}{12}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{36})\)
Fixed field: 36.0.117758684758985699996902956217469271672208115645173978137187292837108269299091373604332371968.1