Properties

Label 2058.677
Modulus 20582058
Conductor 10291029
Order 294294
Real no
Primitive no
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2058, base_ring=CyclotomicField(294)) M = H._module chi = DirichletCharacter(H, M([147,149]))
 
Copy content pari:[g,chi] = znchar(Mod(677,2058))
 

Basic properties

Modulus: 20582058
Conductor: 10291029
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 294294
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from χ1029(677,)\chi_{1029}(677,\cdot)
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 2058.x

χ2058(5,)\chi_{2058}(5,\cdot) χ2058(17,)\chi_{2058}(17,\cdot) χ2058(47,)\chi_{2058}(47,\cdot) χ2058(59,)\chi_{2058}(59,\cdot) χ2058(89,)\chi_{2058}(89,\cdot) χ2058(101,)\chi_{2058}(101,\cdot) χ2058(131,)\chi_{2058}(131,\cdot) χ2058(143,)\chi_{2058}(143,\cdot) χ2058(173,)\chi_{2058}(173,\cdot) χ2058(185,)\chi_{2058}(185,\cdot) χ2058(257,)\chi_{2058}(257,\cdot) χ2058(269,)\chi_{2058}(269,\cdot) χ2058(299,)\chi_{2058}(299,\cdot) χ2058(311,)\chi_{2058}(311,\cdot) χ2058(341,)\chi_{2058}(341,\cdot) χ2058(353,)\chi_{2058}(353,\cdot) χ2058(383,)\chi_{2058}(383,\cdot) χ2058(395,)\chi_{2058}(395,\cdot) χ2058(425,)\chi_{2058}(425,\cdot) χ2058(437,)\chi_{2058}(437,\cdot) χ2058(467,)\chi_{2058}(467,\cdot) χ2058(479,)\chi_{2058}(479,\cdot) χ2058(551,)\chi_{2058}(551,\cdot) χ2058(563,)\chi_{2058}(563,\cdot) χ2058(593,)\chi_{2058}(593,\cdot) χ2058(605,)\chi_{2058}(605,\cdot) χ2058(635,)\chi_{2058}(635,\cdot) χ2058(647,)\chi_{2058}(647,\cdot) χ2058(677,)\chi_{2058}(677,\cdot) χ2058(689,)\chi_{2058}(689,\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(ζ147)\Q(\zeta_{147})
Fixed field: Number field defined by a degree 294 polynomial (not computed)

Values on generators

(1373,1375)(1373,1375)(1,e(149294))(-1,e\left(\frac{149}{294}\right))

First values

aa 1-11155111113131717191923232525292931313737
χ2058(677,a) \chi_{ 2058 }(677, a) 1111e(29147)e\left(\frac{29}{147}\right)e(269294)e\left(\frac{269}{294}\right)e(4398)e\left(\frac{43}{98}\right)e(25147)e\left(\frac{25}{147}\right)e(16)e\left(\frac{1}{6}\right)e(181294)e\left(\frac{181}{294}\right)e(58147)e\left(\frac{58}{147}\right)e(598)e\left(\frac{5}{98}\right)e(1742)e\left(\frac{17}{42}\right)e(74147)e\left(\frac{74}{147}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ2058(677,a)   \chi_{ 2058 }(677,a) \; at   a=\;a = e.g. 2