Properties

Label 1148.17
Modulus $1148$
Conductor $287$
Order $120$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more about

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([0,20,99]))
 
pari: [g,chi] = znchar(Mod(17,1148))
 

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 \(\chi_{287}(17,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1148.cj

\(\chi_{1148}(17,\cdot)\) \(\chi_{1148}(89,\cdot)\) \(\chi_{1148}(101,\cdot)\) \(\chi_{1148}(117,\cdot)\) \(\chi_{1148}(129,\cdot)\) \(\chi_{1148}(145,\cdot)\) \(\chi_{1148}(157,\cdot)\) \(\chi_{1148}(229,\cdot)\) \(\chi_{1148}(257,\cdot)\) \(\chi_{1148}(313,\cdot)\) \(\chi_{1148}(341,\cdot)\) \(\chi_{1148}(381,\cdot)\) \(\chi_{1148}(397,\cdot)\) \(\chi_{1148}(425,\cdot)\) \(\chi_{1148}(481,\cdot)\) \(\chi_{1148}(509,\cdot)\) \(\chi_{1148}(521,\cdot)\) \(\chi_{1148}(593,\cdot)\) \(\chi_{1148}(621,\cdot)\) \(\chi_{1148}(649,\cdot)\) \(\chi_{1148}(745,\cdot)\) \(\chi_{1148}(773,\cdot)\) \(\chi_{1148}(801,\cdot)\) \(\chi_{1148}(873,\cdot)\) \(\chi_{1148}(885,\cdot)\) \(\chi_{1148}(913,\cdot)\) \(\chi_{1148}(969,\cdot)\) \(\chi_{1148}(997,\cdot)\) \(\chi_{1148}(1013,\cdot)\) \(\chi_{1148}(1053,\cdot)\) ...

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

\((575,493,785)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{33}{40}\right))\)

Values

\(-1\)\(1\)\(3\)\(5\)\(9\)\(11\)\(13\)\(15\)\(17\)\(19\)\(23\)\(25\)
\(1\)\(1\)\(e\left(\frac{13}{24}\right)\)\(e\left(\frac{59}{60}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{17}{120}\right)\)\(e\left(\frac{3}{40}\right)\)\(e\left(\frac{21}{40}\right)\)\(e\left(\frac{47}{120}\right)\)\(e\left(\frac{31}{120}\right)\)\(e\left(\frac{1}{30}\right)\)\(e\left(\frac{29}{30}\right)\)
value at e.g. 2