Properties

Label 3744.173
Modulus $3744$
Conductor $3744$
Order $24$
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(3744)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,21,4,4]))
 
pari: [g,chi] = znchar(Mod(173,3744))
 

Basic properties

Modulus: \(3744\)
Conductor: \(3744\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(24\)
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 3744.jj

\(\chi_{3744}(173,\cdot)\) \(\chi_{3744}(725,\cdot)\) \(\chi_{3744}(1109,\cdot)\) \(\chi_{3744}(1661,\cdot)\) \(\chi_{3744}(2045,\cdot)\) \(\chi_{3744}(2597,\cdot)\) \(\chi_{3744}(2981,\cdot)\) \(\chi_{3744}(3533,\cdot)\)

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

\((703,2341,2081,2017)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{1}{6}\right),e\left(\frac{1}{6}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(35\)
\(-1\)\(1\)\(e\left(\frac{5}{24}\right)\)\(i\)\(e\left(\frac{17}{24}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{23}{24}\right)\)\(-i\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{11}{24}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{11}{24}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{24})\)
Fixed field: 24.0.28250218603813031599655036078609034294762679685705575368736408338432.1