Properties

Label 1920.1123
Modulus 19201920
Conductor 640640
Order 3232
Real no
Primitive no
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(1920, base_ring=CyclotomicField(32)) M = H._module chi = DirichletCharacter(H, M([16,27,0,24]))
 
Copy content pari:[g,chi] = znchar(Mod(1123,1920))
 

Basic properties

Modulus: 19201920
Conductor: 640640
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 3232
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from χ640(483,)\chi_{640}(483,\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 1920.cx

χ1920(163,)\chi_{1920}(163,\cdot) χ1920(187,)\chi_{1920}(187,\cdot) χ1920(403,)\chi_{1920}(403,\cdot) χ1920(427,)\chi_{1920}(427,\cdot) χ1920(643,)\chi_{1920}(643,\cdot) χ1920(667,)\chi_{1920}(667,\cdot) χ1920(883,)\chi_{1920}(883,\cdot) χ1920(907,)\chi_{1920}(907,\cdot) χ1920(1123,)\chi_{1920}(1123,\cdot) χ1920(1147,)\chi_{1920}(1147,\cdot) χ1920(1363,)\chi_{1920}(1363,\cdot) χ1920(1387,)\chi_{1920}(1387,\cdot) χ1920(1603,)\chi_{1920}(1603,\cdot) χ1920(1627,)\chi_{1920}(1627,\cdot) χ1920(1843,)\chi_{1920}(1843,\cdot) χ1920(1867,)\chi_{1920}(1867,\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(ζ32)\Q(\zeta_{32})
Fixed field: 32.32.187072209578355573530071658587684226515959365500928000000000000000000000000.2

Values on generators

(511,901,641,1537)(511,901,641,1537)(1,e(2732),1,i)(-1,e\left(\frac{27}{32}\right),1,-i)

First values

aa 1-11177111113131717191923232929313137374141
χ1920(1123,a) \chi_{ 1920 }(1123, a) 1111e(1116)e\left(\frac{11}{16}\right)e(732)e\left(\frac{7}{32}\right)e(2932)e\left(\frac{29}{32}\right)e(38)e\left(\frac{3}{8}\right)e(1332)e\left(\frac{13}{32}\right)e(916)e\left(\frac{9}{16}\right)e(932)e\left(\frac{9}{32}\right)iie(2732)e\left(\frac{27}{32}\right)e(516)e\left(\frac{5}{16}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ1920(1123,a)   \chi_{ 1920 }(1123,a) \; at   a=\;a = e.g. 2