Properties

Label 1664.987
Modulus $1664$
Conductor $1664$
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(1664, base_ring=CyclotomicField(32))
 
M = H._module
 
chi = DirichletCharacter(H, M([16,25,16]))
 
pari: [g,chi] = znchar(Mod(987,1664))
 

Basic properties

Modulus: \(1664\)
Conductor: \(1664\)
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 1664.co

\(\chi_{1664}(51,\cdot)\) \(\chi_{1664}(155,\cdot)\) \(\chi_{1664}(259,\cdot)\) \(\chi_{1664}(363,\cdot)\) \(\chi_{1664}(467,\cdot)\) \(\chi_{1664}(571,\cdot)\) \(\chi_{1664}(675,\cdot)\) \(\chi_{1664}(779,\cdot)\) \(\chi_{1664}(883,\cdot)\) \(\chi_{1664}(987,\cdot)\) \(\chi_{1664}(1091,\cdot)\) \(\chi_{1664}(1195,\cdot)\) \(\chi_{1664}(1299,\cdot)\) \(\chi_{1664}(1403,\cdot)\) \(\chi_{1664}(1507,\cdot)\) \(\chi_{1664}(1611,\cdot)\)

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: 32.0.2088443876129429457733048543333054873029337200425307489036314630977400864768.1

Values on generators

\((1535,261,769)\) → \((-1,e\left(\frac{25}{32}\right),-1)\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(7\)\(9\)\(11\)\(15\)\(17\)\(19\)\(21\)\(23\)
\( \chi_{ 1664 }(987, a) \) \(-1\)\(1\)\(e\left(\frac{27}{32}\right)\)\(e\left(\frac{9}{32}\right)\)\(e\left(\frac{13}{16}\right)\)\(e\left(\frac{11}{16}\right)\)\(e\left(\frac{13}{32}\right)\)\(e\left(\frac{1}{8}\right)\)\(e\left(\frac{7}{8}\right)\)\(e\left(\frac{31}{32}\right)\)\(e\left(\frac{21}{32}\right)\)\(e\left(\frac{7}{16}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 1664 }(987,a) \;\) at \(\;a = \) e.g. 2