Properties

Label 2681.412
Modulus 26812681
Conductor 26812681
Order 382382
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2681, base_ring=CyclotomicField(382)) M = H._module chi = DirichletCharacter(H, M([191,296]))
 
Copy content pari:[g,chi] = znchar(Mod(412,2681))
 

Basic properties

Modulus: 26812681
Conductor: 26812681
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 382382
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: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Galois orbit 2681.l

χ2681(6,)\chi_{2681}(6,\cdot) χ2681(27,)\chi_{2681}(27,\cdot) χ2681(34,)\chi_{2681}(34,\cdot) χ2681(48,)\chi_{2681}(48,\cdot) χ2681(55,)\chi_{2681}(55,\cdot) χ2681(62,)\chi_{2681}(62,\cdot) χ2681(69,)\chi_{2681}(69,\cdot) χ2681(76,)\chi_{2681}(76,\cdot) χ2681(139,)\chi_{2681}(139,\cdot) χ2681(146,)\chi_{2681}(146,\cdot) χ2681(153,)\chi_{2681}(153,\cdot) χ2681(174,)\chi_{2681}(174,\cdot) χ2681(195,)\chi_{2681}(195,\cdot) χ2681(202,)\chi_{2681}(202,\cdot) χ2681(216,)\chi_{2681}(216,\cdot) χ2681(223,)\chi_{2681}(223,\cdot) χ2681(251,)\chi_{2681}(251,\cdot) χ2681(258,)\chi_{2681}(258,\cdot) χ2681(265,)\chi_{2681}(265,\cdot) χ2681(272,)\chi_{2681}(272,\cdot) χ2681(279,)\chi_{2681}(279,\cdot) χ2681(286,)\chi_{2681}(286,\cdot) χ2681(293,)\chi_{2681}(293,\cdot) χ2681(300,)\chi_{2681}(300,\cdot) χ2681(342,)\chi_{2681}(342,\cdot) χ2681(363,)\chi_{2681}(363,\cdot) χ2681(370,)\chi_{2681}(370,\cdot) χ2681(391,)\chi_{2681}(391,\cdot) χ2681(412,)\chi_{2681}(412,\cdot) χ2681(419,)\chi_{2681}(419,\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(ζ191)\Q(\zeta_{191})
Fixed field: Number field defined by a degree 382 polynomial (not computed)

Values on generators

(2299,771)(2299,771)(1,e(148191))(-1,e\left(\frac{148}{191}\right))

First values

aa 1-11122334455668899101011111212
χ2681(412,a) \chi_{ 2681 }(412, a) 1-111e(159191)e\left(\frac{159}{191}\right)e(257382)e\left(\frac{257}{382}\right)e(127191)e\left(\frac{127}{191}\right)e(105382)e\left(\frac{105}{382}\right)e(193382)e\left(\frac{193}{382}\right)e(95191)e\left(\frac{95}{191}\right)e(66191)e\left(\frac{66}{191}\right)e(41382)e\left(\frac{41}{382}\right)e(121191)e\left(\frac{121}{191}\right)e(129382)e\left(\frac{129}{382}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ2681(412,a)   \chi_{ 2681 }(412,a) \; at   a=\;a = e.g. 2