Properties

Label 3888.91
Modulus 38883888
Conductor 12961296
Order 108108
Real no
Primitive no
Minimal no
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3888, base_ring=CyclotomicField(108))
 
M = H._module
 
chi = DirichletCharacter(H, M([54,27,52]))
 
pari: [g,chi] = znchar(Mod(91,3888))
 

Basic properties

Modulus: 38883888
Conductor: 12961296
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 108108
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from χ1296(283,)\chi_{1296}(283,\cdot)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3888.bu

χ3888(19,)\chi_{3888}(19,\cdot) χ3888(91,)\chi_{3888}(91,\cdot) χ3888(235,)\chi_{3888}(235,\cdot) χ3888(307,)\chi_{3888}(307,\cdot) χ3888(451,)\chi_{3888}(451,\cdot) χ3888(523,)\chi_{3888}(523,\cdot) χ3888(667,)\chi_{3888}(667,\cdot) χ3888(739,)\chi_{3888}(739,\cdot) χ3888(883,)\chi_{3888}(883,\cdot) χ3888(955,)\chi_{3888}(955,\cdot) χ3888(1099,)\chi_{3888}(1099,\cdot) χ3888(1171,)\chi_{3888}(1171,\cdot) χ3888(1315,)\chi_{3888}(1315,\cdot) χ3888(1387,)\chi_{3888}(1387,\cdot) χ3888(1531,)\chi_{3888}(1531,\cdot) χ3888(1603,)\chi_{3888}(1603,\cdot) χ3888(1747,)\chi_{3888}(1747,\cdot) χ3888(1819,)\chi_{3888}(1819,\cdot) χ3888(1963,)\chi_{3888}(1963,\cdot) χ3888(2035,)\chi_{3888}(2035,\cdot) χ3888(2179,)\chi_{3888}(2179,\cdot) χ3888(2251,)\chi_{3888}(2251,\cdot) χ3888(2395,)\chi_{3888}(2395,\cdot) χ3888(2467,)\chi_{3888}(2467,\cdot) χ3888(2611,)\chi_{3888}(2611,\cdot) χ3888(2683,)\chi_{3888}(2683,\cdot) χ3888(2827,)\chi_{3888}(2827,\cdot) χ3888(2899,)\chi_{3888}(2899,\cdot) χ3888(3043,)\chi_{3888}(3043,\cdot) χ3888(3115,)\chi_{3888}(3115,\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(ζ108)\Q(\zeta_{108})
Fixed field: Number field defined by a degree 108 polynomial (not computed)

Values on generators

(2431,2917,1217)(2431,2917,1217)(1,i,e(1327))(-1,i,e\left(\frac{13}{27}\right))

First values

aa 1-111557711111313171719192323252529293131
χ3888(91,a) \chi_{ 3888 }(91, a) 1-111e(35108)e\left(\frac{35}{108}\right)e(1927)e\left(\frac{19}{27}\right)e(1108)e\left(\frac{1}{108}\right)e(65108)e\left(\frac{65}{108}\right)e(89)e\left(\frac{8}{9}\right)e(1336)e\left(\frac{13}{36}\right)e(827)e\left(\frac{8}{27}\right)e(3554)e\left(\frac{35}{54}\right)e(61108)e\left(\frac{61}{108}\right)e(754)e\left(\frac{7}{54}\right)
sage: chi.jacobi_sum(n)
 
χ3888(91,a)   \chi_{ 3888 }(91,a) \; at   a=\;a = e.g. 2