Properties

Label 1148.67
Modulus $1148$
Conductor $1148$
Order $120$
Real no
Primitive yes
Minimal yes
Parity even

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([60,80,51]))
 
pari: [g,chi] = znchar(Mod(67,1148))
 

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: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1148.cl

\(\chi_{1148}(11,\cdot)\) \(\chi_{1148}(67,\cdot)\) \(\chi_{1148}(95,\cdot)\) \(\chi_{1148}(135,\cdot)\) \(\chi_{1148}(151,\cdot)\) \(\chi_{1148}(179,\cdot)\) \(\chi_{1148}(235,\cdot)\) \(\chi_{1148}(263,\cdot)\) \(\chi_{1148}(275,\cdot)\) \(\chi_{1148}(347,\cdot)\) \(\chi_{1148}(375,\cdot)\) \(\chi_{1148}(403,\cdot)\) \(\chi_{1148}(499,\cdot)\) \(\chi_{1148}(527,\cdot)\) \(\chi_{1148}(555,\cdot)\) \(\chi_{1148}(627,\cdot)\) \(\chi_{1148}(639,\cdot)\) \(\chi_{1148}(667,\cdot)\) \(\chi_{1148}(723,\cdot)\) \(\chi_{1148}(751,\cdot)\) \(\chi_{1148}(767,\cdot)\) \(\chi_{1148}(807,\cdot)\) \(\chi_{1148}(835,\cdot)\) \(\chi_{1148}(891,\cdot)\) \(\chi_{1148}(919,\cdot)\) \(\chi_{1148}(991,\cdot)\) \(\chi_{1148}(1003,\cdot)\) \(\chi_{1148}(1019,\cdot)\) \(\chi_{1148}(1031,\cdot)\) \(\chi_{1148}(1047,\cdot)\) ...

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

\((575,493,785)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{17}{40}\right))\)

Values

\(-1\)\(1\)\(3\)\(5\)\(9\)\(11\)\(13\)\(15\)\(17\)\(19\)\(23\)\(25\)
\(1\)\(1\)\(e\left(\frac{13}{24}\right)\)\(e\left(\frac{41}{60}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{53}{120}\right)\)\(e\left(\frac{7}{40}\right)\)\(e\left(\frac{9}{40}\right)\)\(e\left(\frac{83}{120}\right)\)\(e\left(\frac{79}{120}\right)\)\(e\left(\frac{2}{15}\right)\)\(e\left(\frac{11}{30}\right)\)
value at e.g. 2