Properties

Label 9200.8833
Modulus 92009200
Conductor 2525
Order 2020
Real no
Primitive no
Minimal no
Parity odd

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9200, base_ring=CyclotomicField(20)) M = H._module chi = DirichletCharacter(H, M([0,0,3,0]))
 
Copy content pari:[g,chi] = znchar(Mod(8833,9200))
 

Basic properties

Modulus: 92009200
Conductor: 2525
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 2020
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from χ25(8,)\chi_{25}(8,\cdot)
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Galois orbit 9200.co

χ9200(737,)\chi_{9200}(737,\cdot) χ9200(1473,)\chi_{9200}(1473,\cdot) χ9200(2577,)\chi_{9200}(2577,\cdot) χ9200(3313,)\chi_{9200}(3313,\cdot) χ9200(4417,)\chi_{9200}(4417,\cdot) χ9200(5153,)\chi_{9200}(5153,\cdot) χ9200(8097,)\chi_{9200}(8097,\cdot) χ9200(8833,)\chi_{9200}(8833,\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(ζ20)\Q(\zeta_{20})
Fixed field: Number field defined by a degree 20 polynomial

Values on generators

(1151,6901,2577,1201)(1151,6901,2577,1201)(1,1,e(320),1)(1,1,e\left(\frac{3}{20}\right),1)

First values

aa 1-1113377991111131317171919212127272929
χ9200(8833,a) \chi_{ 9200 }(8833, a) 1-111e(120)e\left(\frac{1}{20}\right)i-ie(110)e\left(\frac{1}{10}\right)e(25)e\left(\frac{2}{5}\right)e(1720)e\left(\frac{17}{20}\right)e(1920)e\left(\frac{19}{20}\right)e(710)e\left(\frac{7}{10}\right)e(45)e\left(\frac{4}{5}\right)e(320)e\left(\frac{3}{20}\right)e(310)e\left(\frac{3}{10}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ9200(8833,a)   \chi_{ 9200 }(8833,a) \; at   a=\;a = e.g. 2