Properties

Label 4729.1079
Modulus 47294729
Conductor 47294729
Order 394394
Real no
Primitive yes
Minimal yes
Parity even

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4729, base_ring=CyclotomicField(394)) M = H._module chi = DirichletCharacter(H, M([387]))
 
Copy content pari:[g,chi] = znchar(Mod(1079,4729))
 

Basic properties

Modulus: 47294729
Conductor: 47294729
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 394394
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: yes
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Galois orbit 4729.j

χ4729(4,)\chi_{4729}(4,\cdot) χ4729(6,)\chi_{4729}(6,\cdot) χ4729(9,)\chi_{4729}(9,\cdot) χ4729(64,)\chi_{4729}(64,\cdot) χ4729(96,)\chi_{4729}(96,\cdot) χ4729(144,)\chi_{4729}(144,\cdot) χ4729(197,)\chi_{4729}(197,\cdot) χ4729(216,)\chi_{4729}(216,\cdot) χ4729(242,)\chi_{4729}(242,\cdot) χ4729(254,)\chi_{4729}(254,\cdot) χ4729(324,)\chi_{4729}(324,\cdot) χ4729(350,)\chi_{4729}(350,\cdot) χ4729(355,)\chi_{4729}(355,\cdot) χ4729(363,)\chi_{4729}(363,\cdot) χ4729(381,)\chi_{4729}(381,\cdot) χ4729(413,)\chi_{4729}(413,\cdot) χ4729(422,)\chi_{4729}(422,\cdot) χ4729(451,)\chi_{4729}(451,\cdot) χ4729(454,)\chi_{4729}(454,\cdot) χ4729(455,)\chi_{4729}(455,\cdot) χ4729(458,)\chi_{4729}(458,\cdot) χ4729(475,)\chi_{4729}(475,\cdot) χ4729(486,)\chi_{4729}(486,\cdot) χ4729(525,)\chi_{4729}(525,\cdot) χ4729(607,)\chi_{4729}(607,\cdot) χ4729(613,)\chi_{4729}(613,\cdot) χ4729(633,)\chi_{4729}(633,\cdot) χ4729(634,)\chi_{4729}(634,\cdot) χ4729(643,)\chi_{4729}(643,\cdot) χ4729(670,)\chi_{4729}(670,\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(ζ197)\Q(\zeta_{197})
Fixed field: Number field defined by a degree 394 polynomial (not computed)

Values on generators

1717e(387394)e\left(\frac{387}{394}\right)

First values

aa 1-111223344556677889910101111
χ4729(1079,a) \chi_{ 4729 }(1079, a) 1111e(69197)e\left(\frac{69}{197}\right)e(193197)e\left(\frac{193}{197}\right)e(138197)e\left(\frac{138}{197}\right)e(74197)e\left(\frac{74}{197}\right)e(65197)e\left(\frac{65}{197}\right)e(2197)e\left(\frac{2}{197}\right)e(10197)e\left(\frac{10}{197}\right)e(189197)e\left(\frac{189}{197}\right)e(143197)e\left(\frac{143}{197}\right)e(219394)e\left(\frac{219}{394}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ4729(1079,a)   \chi_{ 4729 }(1079,a) \; at   a=\;a = e.g. 2