Properties

Label 2675.593
Modulus 26752675
Conductor 535535
Order 212212
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(2675, base_ring=CyclotomicField(212)) M = H._module chi = DirichletCharacter(H, M([159,66]))
 
Copy content pari:[g,chi] = znchar(Mod(593,2675))
 

Basic properties

Modulus: 26752675
Conductor: 535535
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 212212
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from χ535(58,)\chi_{535}(58,\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 2675.r

χ2675(7,)\chi_{2675}(7,\cdot) χ2675(18,)\chi_{2675}(18,\cdot) χ2675(32,)\chi_{2675}(32,\cdot) χ2675(43,)\chi_{2675}(43,\cdot) χ2675(68,)\chi_{2675}(68,\cdot) χ2675(82,)\chi_{2675}(82,\cdot) χ2675(93,)\chi_{2675}(93,\cdot) χ2675(157,)\chi_{2675}(157,\cdot) χ2675(232,)\chi_{2675}(232,\cdot) χ2675(257,)\chi_{2675}(257,\cdot) χ2675(268,)\chi_{2675}(268,\cdot) χ2675(282,)\chi_{2675}(282,\cdot) χ2675(307,)\chi_{2675}(307,\cdot) χ2675(318,)\chi_{2675}(318,\cdot) χ2675(343,)\chi_{2675}(343,\cdot) χ2675(393,)\chi_{2675}(393,\cdot) χ2675(418,)\chi_{2675}(418,\cdot) χ2675(443,)\chi_{2675}(443,\cdot) χ2675(482,)\chi_{2675}(482,\cdot) χ2675(493,)\chi_{2675}(493,\cdot) χ2675(532,)\chi_{2675}(532,\cdot) χ2675(543,)\chi_{2675}(543,\cdot) χ2675(557,)\chi_{2675}(557,\cdot) χ2675(593,)\chi_{2675}(593,\cdot) χ2675(607,)\chi_{2675}(607,\cdot) χ2675(632,)\chi_{2675}(632,\cdot) χ2675(657,)\chi_{2675}(657,\cdot) χ2675(668,)\chi_{2675}(668,\cdot) χ2675(693,)\chi_{2675}(693,\cdot) χ2675(707,)\chi_{2675}(707,\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(ζ212)\Q(\zeta_{212})
Fixed field: Number field defined by a degree 212 polynomial (not computed)

Values on generators

(1927,751)(1927,751)(i,e(33106))(-i,e\left(\frac{33}{106}\right))

First values

aa 1-11122334466778899111112121313
χ2675(593,a) \chi_{ 2675 }(593, a) 1111e(13212)e\left(\frac{13}{212}\right)e(9212)e\left(\frac{9}{212}\right)e(13106)e\left(\frac{13}{106}\right)e(11106)e\left(\frac{11}{106}\right)e(29212)e\left(\frac{29}{212}\right)e(39212)e\left(\frac{39}{212}\right)e(9106)e\left(\frac{9}{106}\right)e(4553)e\left(\frac{45}{53}\right)e(35212)e\left(\frac{35}{212}\right)e(129212)e\left(\frac{129}{212}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ2675(593,a)   \chi_{ 2675 }(593,a) \; at   a=\;a = e.g. 2