Properties

Label 2944.2667
Modulus $2944$
Conductor $2944$
Order $32$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2944, base_ring=CyclotomicField(32))
 
M = H._module
 
chi = DirichletCharacter(H, M([16,13,16]))
 
pari: [g,chi] = znchar(Mod(2667,2944))
 

Basic properties

Modulus: \(2944\)
Conductor: \(2944\)
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: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2944.bd

\(\chi_{2944}(91,\cdot)\) \(\chi_{2944}(275,\cdot)\) \(\chi_{2944}(459,\cdot)\) \(\chi_{2944}(643,\cdot)\) \(\chi_{2944}(827,\cdot)\) \(\chi_{2944}(1011,\cdot)\) \(\chi_{2944}(1195,\cdot)\) \(\chi_{2944}(1379,\cdot)\) \(\chi_{2944}(1563,\cdot)\) \(\chi_{2944}(1747,\cdot)\) \(\chi_{2944}(1931,\cdot)\) \(\chi_{2944}(2115,\cdot)\) \(\chi_{2944}(2299,\cdot)\) \(\chi_{2944}(2483,\cdot)\) \(\chi_{2944}(2667,\cdot)\) \(\chi_{2944}(2851,\cdot)\)

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: 32.32.19247509741360815152884297845798278938249171496527684529937635790938725865750528.1

Values on generators

\((1151,645,2305)\) → \((-1,e\left(\frac{13}{32}\right),-1)\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(7\)\(9\)\(11\)\(13\)\(15\)\(17\)\(19\)\(21\)
\( \chi_{ 2944 }(2667, a) \) \(1\)\(1\)\(e\left(\frac{23}{32}\right)\)\(e\left(\frac{29}{32}\right)\)\(e\left(\frac{1}{16}\right)\)\(e\left(\frac{7}{16}\right)\)\(e\left(\frac{17}{32}\right)\)\(e\left(\frac{3}{32}\right)\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{7}{8}\right)\)\(e\left(\frac{11}{32}\right)\)\(e\left(\frac{25}{32}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 2944 }(2667,a) \;\) at \(\;a = \) e.g. 2