Properties

Label 2432.1861
Modulus $2432$
Conductor $2432$
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(2432, base_ring=CyclotomicField(32))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,17,16]))
 
pari: [g,chi] = znchar(Mod(1861,2432))
 

Basic properties

Modulus: \(2432\)
Conductor: \(2432\)
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 2432.bt

\(\chi_{2432}(37,\cdot)\) \(\chi_{2432}(189,\cdot)\) \(\chi_{2432}(341,\cdot)\) \(\chi_{2432}(493,\cdot)\) \(\chi_{2432}(645,\cdot)\) \(\chi_{2432}(797,\cdot)\) \(\chi_{2432}(949,\cdot)\) \(\chi_{2432}(1101,\cdot)\) \(\chi_{2432}(1253,\cdot)\) \(\chi_{2432}(1405,\cdot)\) \(\chi_{2432}(1557,\cdot)\) \(\chi_{2432}(1709,\cdot)\) \(\chi_{2432}(1861,\cdot)\) \(\chi_{2432}(2013,\cdot)\) \(\chi_{2432}(2165,\cdot)\) \(\chi_{2432}(2317,\cdot)\)

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: 32.0.905288048831351058796666807211863041216387224344298280390835989733155786457088.1

Values on generators

\((1407,2053,1921)\) → \((1,e\left(\frac{17}{32}\right),-1)\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(7\)\(9\)\(11\)\(13\)\(15\)\(17\)\(21\)\(23\)
\( \chi_{ 2432 }(1861, a) \) \(-1\)\(1\)\(e\left(\frac{3}{32}\right)\)\(e\left(\frac{17}{32}\right)\)\(e\left(\frac{5}{16}\right)\)\(e\left(\frac{3}{16}\right)\)\(e\left(\frac{5}{32}\right)\)\(e\left(\frac{15}{32}\right)\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{7}{8}\right)\)\(e\left(\frac{13}{32}\right)\)\(e\left(\frac{7}{16}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 2432 }(1861,a) \;\) at \(\;a = \) e.g. 2