Properties

Label 1920.829
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([0,19,0,16]))
 
Copy content pari:[g,chi] = znchar(Mod(829,1920))
 

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(189,)\chi_{640}(189,\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.cz

χ1920(109,)\chi_{1920}(109,\cdot) χ1920(229,)\chi_{1920}(229,\cdot) χ1920(349,)\chi_{1920}(349,\cdot) χ1920(469,)\chi_{1920}(469,\cdot) χ1920(589,)\chi_{1920}(589,\cdot) χ1920(709,)\chi_{1920}(709,\cdot) χ1920(829,)\chi_{1920}(829,\cdot) χ1920(949,)\chi_{1920}(949,\cdot) χ1920(1069,)\chi_{1920}(1069,\cdot) χ1920(1189,)\chi_{1920}(1189,\cdot) χ1920(1309,)\chi_{1920}(1309,\cdot) χ1920(1429,)\chi_{1920}(1429,\cdot) χ1920(1549,)\chi_{1920}(1549,\cdot) χ1920(1669,)\chi_{1920}(1669,\cdot) χ1920(1789,)\chi_{1920}(1789,\cdot) χ1920(1909,)\chi_{1920}(1909,\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: 32.32.478904856520590268236983445984471619880855975682375680000000000000000.1

Values on generators

(511,901,641,1537)(511,901,641,1537)(1,e(1932),1,1)(1,e\left(\frac{19}{32}\right),1,-1)

First values

aa 1-11177111113131717191923232929313137374141
χ1920(829,a) \chi_{ 1920 }(829, a) 1111e(716)e\left(\frac{7}{16}\right)e(1532)e\left(\frac{15}{32}\right)e(1332)e\left(\frac{13}{32}\right)e(18)e\left(\frac{1}{8}\right)e(2132)e\left(\frac{21}{32}\right)e(1316)e\left(\frac{13}{16}\right)e(132)e\left(\frac{1}{32}\right)i-ie(1132)e\left(\frac{11}{32}\right)e(1316)e\left(\frac{13}{16}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ1920(829,a)   \chi_{ 1920 }(829,a) \; at   a=\;a = e.g. 2