Properties

Label 3024.149
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([0,9,34,12]))
 
pari: [g,chi] = znchar(Mod(149,3024))
 

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.gn

\(\chi_{3024}(149,\cdot)\) \(\chi_{3024}(389,\cdot)\) \(\chi_{3024}(653,\cdot)\) \(\chi_{3024}(893,\cdot)\) \(\chi_{3024}(1157,\cdot)\) \(\chi_{3024}(1397,\cdot)\) \(\chi_{3024}(1661,\cdot)\) \(\chi_{3024}(1901,\cdot)\) \(\chi_{3024}(2165,\cdot)\) \(\chi_{3024}(2405,\cdot)\) \(\chi_{3024}(2669,\cdot)\) \(\chi_{3024}(2909,\cdot)\)

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

\((1135,757,785,2593)\) → \((1,i,e\left(\frac{17}{18}\right),e\left(\frac{1}{3}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)
\(-1\)\(1\)\(e\left(\frac{23}{36}\right)\)\(e\left(\frac{31}{36}\right)\)\(e\left(\frac{11}{36}\right)\)\(-1\)\(-i\)\(e\left(\frac{5}{9}\right)\)\(e\left(\frac{5}{18}\right)\)\(e\left(\frac{25}{36}\right)\)\(e\left(\frac{2}{9}\right)\)\(e\left(\frac{7}{12}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{36})\)
Fixed field: 36.0.1059828162830871299972126605957223445049873040806565803234685635533974423691822362438991347712.2