Properties

Label 1920.1883
Modulus $1920$
Conductor $1920$
Order $32$
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1920, base_ring=CyclotomicField(32))
 
M = H._module
 
chi = DirichletCharacter(H, M([16,25,16,24]))
 
pari: [g,chi] = znchar(Mod(1883,1920))
 

Basic properties

Modulus: \(1920\)
Conductor: \(1920\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(32\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1920.dg

\(\chi_{1920}(203,\cdot)\) \(\chi_{1920}(227,\cdot)\) \(\chi_{1920}(443,\cdot)\) \(\chi_{1920}(467,\cdot)\) \(\chi_{1920}(683,\cdot)\) \(\chi_{1920}(707,\cdot)\) \(\chi_{1920}(923,\cdot)\) \(\chi_{1920}(947,\cdot)\) \(\chi_{1920}(1163,\cdot)\) \(\chi_{1920}(1187,\cdot)\) \(\chi_{1920}(1403,\cdot)\) \(\chi_{1920}(1427,\cdot)\) \(\chi_{1920}(1643,\cdot)\) \(\chi_{1920}(1667,\cdot)\) \(\chi_{1920}(1883,\cdot)\) \(\chi_{1920}(1907,\cdot)\)

sage: chi.galois_orbit()
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: \(\Q(\zeta_{32})\)
Fixed field: 32.0.8052845212573000012543979797231296934933304854055472857088000000000000000000000000.2

Values on generators

\((511,901,641,1537)\) → \((-1,e\left(\frac{25}{32}\right),-1,-i)\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)
\( \chi_{ 1920 }(1883, a) \) \(-1\)\(1\)\(e\left(\frac{1}{16}\right)\)\(e\left(\frac{13}{32}\right)\)\(e\left(\frac{31}{32}\right)\)\(e\left(\frac{1}{8}\right)\)\(e\left(\frac{31}{32}\right)\)\(e\left(\frac{3}{16}\right)\)\(e\left(\frac{3}{32}\right)\)\(-i\)\(e\left(\frac{9}{32}\right)\)\(e\left(\frac{15}{16}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 1920 }(1883,a) \;\) at \(\;a = \) e.g. 2