Properties

Label 6664.927
Modulus 66646664
Conductor 33323332
Order 168168
Real no
Primitive no
Minimal no
Parity even

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6664, base_ring=CyclotomicField(168)) M = H._module chi = DirichletCharacter(H, M([84,0,124,21]))
 
Copy content pari:[g,chi] = znchar(Mod(927,6664))
 

Basic properties

Modulus: 66646664
Conductor: 33323332
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 168168
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from χ3332(927,)\chi_{3332}(927,\cdot)
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Galois orbit 6664.fo

χ6664(87,)\chi_{6664}(87,\cdot) χ6664(383,)\chi_{6664}(383,\cdot) χ6664(495,)\chi_{6664}(495,\cdot) χ6664(535,)\chi_{6664}(535,\cdot) χ6664(831,)\chi_{6664}(831,\cdot) χ6664(927,)\chi_{6664}(927,\cdot) χ6664(943,)\chi_{6664}(943,\cdot) χ6664(1039,)\chi_{6664}(1039,\cdot) χ6664(1335,)\chi_{6664}(1335,\cdot) χ6664(1375,)\chi_{6664}(1375,\cdot) χ6664(1447,)\chi_{6664}(1447,\cdot) χ6664(1487,)\chi_{6664}(1487,\cdot) χ6664(1879,)\chi_{6664}(1879,\cdot) χ6664(1895,)\chi_{6664}(1895,\cdot) χ6664(2287,)\chi_{6664}(2287,\cdot) χ6664(2327,)\chi_{6664}(2327,\cdot) χ6664(2399,)\chi_{6664}(2399,\cdot) χ6664(2439,)\chi_{6664}(2439,\cdot) χ6664(2735,)\chi_{6664}(2735,\cdot) χ6664(2831,)\chi_{6664}(2831,\cdot) χ6664(2847,)\chi_{6664}(2847,\cdot) χ6664(2943,)\chi_{6664}(2943,\cdot) χ6664(3239,)\chi_{6664}(3239,\cdot) χ6664(3279,)\chi_{6664}(3279,\cdot) χ6664(3391,)\chi_{6664}(3391,\cdot) χ6664(3687,)\chi_{6664}(3687,\cdot) χ6664(3783,)\chi_{6664}(3783,\cdot) χ6664(3799,)\chi_{6664}(3799,\cdot) χ6664(3895,)\chi_{6664}(3895,\cdot) χ6664(4191,)\chi_{6664}(4191,\cdot) ...

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

Related number fields

Field of values: Q(ζ168)\Q(\zeta_{168})
Fixed field: Number field defined by a degree 168 polynomial (not computed)

Values on generators

(4999,3333,4217,785)(4999,3333,4217,785)(1,1,e(3142),e(18))(-1,1,e\left(\frac{31}{42}\right),e\left(\frac{1}{8}\right))

First values

aa 1-1113355991111131315151919232325252727
χ6664(927,a) \chi_{ 6664 }(927, a) 1111e(61168)e\left(\frac{61}{168}\right)e(5168)e\left(\frac{5}{168}\right)e(6184)e\left(\frac{61}{84}\right)e(151168)e\left(\frac{151}{168}\right)e(67)e\left(\frac{6}{7}\right)e(1128)e\left(\frac{11}{28}\right)e(112)e\left(\frac{1}{12}\right)e(71168)e\left(\frac{71}{168}\right)e(584)e\left(\frac{5}{84}\right)e(556)e\left(\frac{5}{56}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ6664(927,a)   \chi_{ 6664 }(927,a) \; at   a=\;a = e.g. 2