Properties

Label 1148.47
Modulus $1148$
Conductor $1148$
Order $120$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1148, base_ring=CyclotomicField(120))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([60,100,3]))
 
pari: [g,chi] = znchar(Mod(47,1148))
 

Basic properties

Modulus: \(1148\)
Conductor: \(1148\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(120\)
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 1148.ck

\(\chi_{1148}(19,\cdot)\) \(\chi_{1148}(47,\cdot)\) \(\chi_{1148}(75,\cdot)\) \(\chi_{1148}(171,\cdot)\) \(\chi_{1148}(199,\cdot)\) \(\chi_{1148}(227,\cdot)\) \(\chi_{1148}(299,\cdot)\) \(\chi_{1148}(311,\cdot)\) \(\chi_{1148}(339,\cdot)\) \(\chi_{1148}(395,\cdot)\) \(\chi_{1148}(423,\cdot)\) \(\chi_{1148}(439,\cdot)\) \(\chi_{1148}(479,\cdot)\) \(\chi_{1148}(507,\cdot)\) \(\chi_{1148}(563,\cdot)\) \(\chi_{1148}(591,\cdot)\) \(\chi_{1148}(663,\cdot)\) \(\chi_{1148}(675,\cdot)\) \(\chi_{1148}(691,\cdot)\) \(\chi_{1148}(703,\cdot)\) \(\chi_{1148}(719,\cdot)\) \(\chi_{1148}(731,\cdot)\) \(\chi_{1148}(803,\cdot)\) \(\chi_{1148}(831,\cdot)\) \(\chi_{1148}(887,\cdot)\) \(\chi_{1148}(915,\cdot)\) \(\chi_{1148}(955,\cdot)\) \(\chi_{1148}(971,\cdot)\) \(\chi_{1148}(999,\cdot)\) \(\chi_{1148}(1055,\cdot)\) ...

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: $\Q(\zeta_{120})$
Fixed field: Number field defined by a degree 120 polynomial (not computed)

Values on generators

\((575,493,785)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{1}{40}\right))\)

Values

\(-1\)\(1\)\(3\)\(5\)\(9\)\(11\)\(13\)\(15\)\(17\)\(19\)\(23\)\(25\)
\(-1\)\(1\)\(e\left(\frac{17}{24}\right)\)\(e\left(\frac{43}{60}\right)\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{109}{120}\right)\)\(e\left(\frac{11}{40}\right)\)\(e\left(\frac{17}{40}\right)\)\(e\left(\frac{79}{120}\right)\)\(e\left(\frac{107}{120}\right)\)\(e\left(\frac{1}{15}\right)\)\(e\left(\frac{13}{30}\right)\)
value at e.g. 2