Properties

Label 1344.1123
Modulus 13441344
Conductor 448448
Order 4848
Real no
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1344, base_ring=CyclotomicField(48))
 
M = H._module
 
chi = DirichletCharacter(H, M([24,33,0,8]))
 
pari: [g,chi] = znchar(Mod(1123,1344))
 

Basic properties

Modulus: 13441344
Conductor: 448448
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 4848
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from χ448(227,)\chi_{448}(227,\cdot)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1344.cy

χ1344(19,)\chi_{1344}(19,\cdot) χ1344(115,)\chi_{1344}(115,\cdot) χ1344(187,)\chi_{1344}(187,\cdot) χ1344(283,)\chi_{1344}(283,\cdot) χ1344(355,)\chi_{1344}(355,\cdot) χ1344(451,)\chi_{1344}(451,\cdot) χ1344(523,)\chi_{1344}(523,\cdot) χ1344(619,)\chi_{1344}(619,\cdot) χ1344(691,)\chi_{1344}(691,\cdot) χ1344(787,)\chi_{1344}(787,\cdot) χ1344(859,)\chi_{1344}(859,\cdot) χ1344(955,)\chi_{1344}(955,\cdot) χ1344(1027,)\chi_{1344}(1027,\cdot) χ1344(1123,)\chi_{1344}(1123,\cdot) χ1344(1195,)\chi_{1344}(1195,\cdot) χ1344(1291,)\chi_{1344}(1291,\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(ζ48)\Q(\zeta_{48})
Fixed field: Number field defined by a degree 48 polynomial

Values on generators

(127,1093,449,577)(127,1093,449,577)(1,e(1116),1,e(16))(-1,e\left(\frac{11}{16}\right),1,e\left(\frac{1}{6}\right))

First values

aa 1-11155111113131717191923232525292931313737
χ1344(1123,a) \chi_{ 1344 }(1123, a) 1111e(2548)e\left(\frac{25}{48}\right)e(2948)e\left(\frac{29}{48}\right)e(1316)e\left(\frac{13}{16}\right)e(512)e\left(\frac{5}{12}\right)e(748)e\left(\frac{7}{48}\right)e(1124)e\left(\frac{11}{24}\right)e(124)e\left(\frac{1}{24}\right)e(916)e\left(\frac{9}{16}\right)e(16)e\left(\frac{1}{6}\right)e(2548)e\left(\frac{25}{48}\right)
sage: chi.jacobi_sum(n)
 
χ1344(1123,a)   \chi_{ 1344 }(1123,a) \; at   a=\;a = e.g. 2