Properties

Label 2793.2144
Modulus 27932793
Conductor 27932793
Order 126126
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2793, base_ring=CyclotomicField(126))
 
M = H._module
 
chi = DirichletCharacter(H, M([63,96,28]))
 
pari: [g,chi] = znchar(Mod(2144,2793))
 

Basic properties

Modulus: 27932793
Conductor: 27932793
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 126126
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 2793.eo

χ2793(137,)\chi_{2793}(137,\cdot) χ2793(149,)\chi_{2793}(149,\cdot) χ2793(158,)\chi_{2793}(158,\cdot) χ2793(233,)\chi_{2793}(233,\cdot) χ2793(359,)\chi_{2793}(359,\cdot) χ2793(389,)\chi_{2793}(389,\cdot) χ2793(536,)\chi_{2793}(536,\cdot) χ2793(548,)\chi_{2793}(548,\cdot) χ2793(632,)\chi_{2793}(632,\cdot) χ2793(758,)\chi_{2793}(758,\cdot) χ2793(788,)\chi_{2793}(788,\cdot) χ2793(935,)\chi_{2793}(935,\cdot) χ2793(947,)\chi_{2793}(947,\cdot) χ2793(956,)\chi_{2793}(956,\cdot) χ2793(1031,)\chi_{2793}(1031,\cdot) χ2793(1187,)\chi_{2793}(1187,\cdot) χ2793(1334,)\chi_{2793}(1334,\cdot) χ2793(1346,)\chi_{2793}(1346,\cdot) χ2793(1355,)\chi_{2793}(1355,\cdot) χ2793(1430,)\chi_{2793}(1430,\cdot) χ2793(1556,)\chi_{2793}(1556,\cdot) χ2793(1754,)\chi_{2793}(1754,\cdot) χ2793(1829,)\chi_{2793}(1829,\cdot) χ2793(1955,)\chi_{2793}(1955,\cdot) χ2793(1985,)\chi_{2793}(1985,\cdot) χ2793(2132,)\chi_{2793}(2132,\cdot) χ2793(2144,)\chi_{2793}(2144,\cdot) χ2793(2153,)\chi_{2793}(2153,\cdot) χ2793(2228,)\chi_{2793}(2228,\cdot) χ2793(2354,)\chi_{2793}(2354,\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(ζ63)\Q(\zeta_{63})
Fixed field: Number field defined by a degree 126 polynomial (not computed)

Values on generators

(932,2110,2206)(932,2110,2206)(1,e(1621),e(29))(-1,e\left(\frac{16}{21}\right),e\left(\frac{2}{9}\right))

First values

aa 1-11122445588101011111313161617172020
χ2793(2144,a) \chi_{ 2793 }(2144, a) 1-111e(67126)e\left(\frac{67}{126}\right)e(463)e\left(\frac{4}{63}\right)e(19126)e\left(\frac{19}{126}\right)e(2542)e\left(\frac{25}{42}\right)e(4363)e\left(\frac{43}{63}\right)e(914)e\left(\frac{9}{14}\right)e(1663)e\left(\frac{16}{63}\right)e(863)e\left(\frac{8}{63}\right)e(97126)e\left(\frac{97}{126}\right)e(314)e\left(\frac{3}{14}\right)
sage: chi.jacobi_sum(n)
 
χ2793(2144,a)   \chi_{ 2793 }(2144,a) \; at   a=\;a = e.g. 2