Properties

Label 1148.65
Modulus $1148$
Conductor $287$
Order $120$
Real no
Primitive no
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([0,40,39]))
 
pari: [g,chi] = znchar(Mod(65,1148))
 

Basic properties

Modulus: \(1148\)
Conductor: \(287\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(120\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{287}(65,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1148.ci

\(\chi_{1148}(53,\cdot)\) \(\chi_{1148}(65,\cdot)\) \(\chi_{1148}(93,\cdot)\) \(\chi_{1148}(149,\cdot)\) \(\chi_{1148}(177,\cdot)\) \(\chi_{1148}(193,\cdot)\) \(\chi_{1148}(233,\cdot)\) \(\chi_{1148}(261,\cdot)\) \(\chi_{1148}(317,\cdot)\) \(\chi_{1148}(345,\cdot)\) \(\chi_{1148}(417,\cdot)\) \(\chi_{1148}(429,\cdot)\) \(\chi_{1148}(445,\cdot)\) \(\chi_{1148}(457,\cdot)\) \(\chi_{1148}(473,\cdot)\) \(\chi_{1148}(485,\cdot)\) \(\chi_{1148}(557,\cdot)\) \(\chi_{1148}(585,\cdot)\) \(\chi_{1148}(641,\cdot)\) \(\chi_{1148}(669,\cdot)\) \(\chi_{1148}(709,\cdot)\) \(\chi_{1148}(725,\cdot)\) \(\chi_{1148}(753,\cdot)\) \(\chi_{1148}(809,\cdot)\) \(\chi_{1148}(837,\cdot)\) \(\chi_{1148}(849,\cdot)\) \(\chi_{1148}(921,\cdot)\) \(\chi_{1148}(949,\cdot)\) \(\chi_{1148}(977,\cdot)\) \(\chi_{1148}(1073,\cdot)\) ...

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

\((575,493,785)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{13}{40}\right))\)

Values

\(-1\)\(1\)\(3\)\(5\)\(9\)\(11\)\(13\)\(15\)\(17\)\(19\)\(23\)\(25\)
\(-1\)\(1\)\(e\left(\frac{5}{24}\right)\)\(e\left(\frac{49}{60}\right)\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{37}{120}\right)\)\(e\left(\frac{3}{40}\right)\)\(e\left(\frac{1}{40}\right)\)\(e\left(\frac{7}{120}\right)\)\(e\left(\frac{71}{120}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{19}{30}\right)\)
value at e.g. 2