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Properties

Label 2793.bu
Modulus 27932793
Conductor 27932793
Order 1414
Real no
Primitive yes
Minimal yes
Parity even

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2793, base_ring=CyclotomicField(14))
 
M = H._module
 
chi = DirichletCharacter(H, M([7,10,7]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(113,2793))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 27932793
Conductor: 27932793
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 1414
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)
 

Related number fields

Field of values: Q(ζ7)\Q(\zeta_{7})
Fixed field: Number field defined by a degree 14 polynomial

Characters in Galois orbit

Character −1-1 11 22 44 55 88 1010 1111 1313 1616 1717 2020
χ2793(113,⋅)\chi_{2793}(113,\cdot) 11 11 e(47)e\left(\frac{4}{7}\right) e(17)e\left(\frac{1}{7}\right) e(314)e\left(\frac{3}{14}\right) e(57)e\left(\frac{5}{7}\right) e(1114)e\left(\frac{11}{14}\right) e(114)e\left(\frac{1}{14}\right) e(114)e\left(\frac{1}{14}\right) e(27)e\left(\frac{2}{7}\right) e(514)e\left(\frac{5}{14}\right) e(514)e\left(\frac{5}{14}\right)
χ2793(512,⋅)\chi_{2793}(512,\cdot) 11 11 e(67)e\left(\frac{6}{7}\right) e(57)e\left(\frac{5}{7}\right) e(114)e\left(\frac{1}{14}\right) e(47)e\left(\frac{4}{7}\right) e(1314)e\left(\frac{13}{14}\right) e(514)e\left(\frac{5}{14}\right) e(514)e\left(\frac{5}{14}\right) e(37)e\left(\frac{3}{7}\right) e(1114)e\left(\frac{11}{14}\right) e(1114)e\left(\frac{11}{14}\right)
χ2793(911,⋅)\chi_{2793}(911,\cdot) 11 11 e(17)e\left(\frac{1}{7}\right) e(27)e\left(\frac{2}{7}\right) e(1314)e\left(\frac{13}{14}\right) e(37)e\left(\frac{3}{7}\right) e(114)e\left(\frac{1}{14}\right) e(914)e\left(\frac{9}{14}\right) e(914)e\left(\frac{9}{14}\right) e(47)e\left(\frac{4}{7}\right) e(314)e\left(\frac{3}{14}\right) e(314)e\left(\frac{3}{14}\right)
χ2793(1310,⋅)\chi_{2793}(1310,\cdot) 11 11 e(37)e\left(\frac{3}{7}\right) e(67)e\left(\frac{6}{7}\right) e(1114)e\left(\frac{11}{14}\right) e(27)e\left(\frac{2}{7}\right) e(314)e\left(\frac{3}{14}\right) e(1314)e\left(\frac{13}{14}\right) e(1314)e\left(\frac{13}{14}\right) e(57)e\left(\frac{5}{7}\right) e(914)e\left(\frac{9}{14}\right) e(914)e\left(\frac{9}{14}\right)
χ2793(1709,⋅)\chi_{2793}(1709,\cdot) 11 11 e(57)e\left(\frac{5}{7}\right) e(37)e\left(\frac{3}{7}\right) e(914)e\left(\frac{9}{14}\right) e(17)e\left(\frac{1}{7}\right) e(514)e\left(\frac{5}{14}\right) e(314)e\left(\frac{3}{14}\right) e(314)e\left(\frac{3}{14}\right) e(67)e\left(\frac{6}{7}\right) e(114)e\left(\frac{1}{14}\right) e(114)e\left(\frac{1}{14}\right)
χ2793(2507,⋅)\chi_{2793}(2507,\cdot) 11 11 e(27)e\left(\frac{2}{7}\right) e(47)e\left(\frac{4}{7}\right) e(514)e\left(\frac{5}{14}\right) e(67)e\left(\frac{6}{7}\right) e(914)e\left(\frac{9}{14}\right) e(1114)e\left(\frac{11}{14}\right) e(1114)e\left(\frac{11}{14}\right) e(17)e\left(\frac{1}{7}\right) e(1314)e\left(\frac{13}{14}\right) e(1314)e\left(\frac{13}{14}\right)