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Properties

Label 2303.j
Modulus 23032303
Conductor 23032303
Order 1414
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2303, base_ring=CyclotomicField(14))
 
M = H._module
 
chi = DirichletCharacter(H, M([4,7]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(281,2303))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 23032303
Conductor: 23032303
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: odd
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 33 44 55 66 88 99 1010 1111 1212
χ2303(281,⋅)\chi_{2303}(281,\cdot) −1-1 11 e(37)e\left(\frac{3}{7}\right) e(27)e\left(\frac{2}{7}\right) e(67)e\left(\frac{6}{7}\right) e(1114)e\left(\frac{11}{14}\right) e(57)e\left(\frac{5}{7}\right) e(27)e\left(\frac{2}{7}\right) e(47)e\left(\frac{4}{7}\right) e(314)e\left(\frac{3}{14}\right) e(1314)e\left(\frac{13}{14}\right) e(17)e\left(\frac{1}{7}\right)
χ2303(610,⋅)\chi_{2303}(610,\cdot) −1-1 11 e(67)e\left(\frac{6}{7}\right) e(47)e\left(\frac{4}{7}\right) e(57)e\left(\frac{5}{7}\right) e(114)e\left(\frac{1}{14}\right) e(37)e\left(\frac{3}{7}\right) e(47)e\left(\frac{4}{7}\right) e(17)e\left(\frac{1}{7}\right) e(1314)e\left(\frac{13}{14}\right) e(514)e\left(\frac{5}{14}\right) e(27)e\left(\frac{2}{7}\right)
χ2303(939,⋅)\chi_{2303}(939,\cdot) −1-1 11 e(27)e\left(\frac{2}{7}\right) e(67)e\left(\frac{6}{7}\right) e(47)e\left(\frac{4}{7}\right) e(514)e\left(\frac{5}{14}\right) e(17)e\left(\frac{1}{7}\right) e(67)e\left(\frac{6}{7}\right) e(57)e\left(\frac{5}{7}\right) e(914)e\left(\frac{9}{14}\right) e(1114)e\left(\frac{11}{14}\right) e(37)e\left(\frac{3}{7}\right)
χ2303(1268,⋅)\chi_{2303}(1268,\cdot) −1-1 11 e(57)e\left(\frac{5}{7}\right) e(17)e\left(\frac{1}{7}\right) e(37)e\left(\frac{3}{7}\right) e(914)e\left(\frac{9}{14}\right) e(67)e\left(\frac{6}{7}\right) e(17)e\left(\frac{1}{7}\right) e(27)e\left(\frac{2}{7}\right) e(514)e\left(\frac{5}{14}\right) e(314)e\left(\frac{3}{14}\right) e(47)e\left(\frac{4}{7}\right)
χ2303(1597,⋅)\chi_{2303}(1597,\cdot) −1-1 11 e(17)e\left(\frac{1}{7}\right) e(37)e\left(\frac{3}{7}\right) e(27)e\left(\frac{2}{7}\right) e(1314)e\left(\frac{13}{14}\right) e(47)e\left(\frac{4}{7}\right) e(37)e\left(\frac{3}{7}\right) e(67)e\left(\frac{6}{7}\right) e(114)e\left(\frac{1}{14}\right) e(914)e\left(\frac{9}{14}\right) e(57)e\left(\frac{5}{7}\right)
χ2303(1926,⋅)\chi_{2303}(1926,\cdot) −1-1 11 e(47)e\left(\frac{4}{7}\right) e(57)e\left(\frac{5}{7}\right) e(17)e\left(\frac{1}{7}\right) e(314)e\left(\frac{3}{14}\right) e(27)e\left(\frac{2}{7}\right) e(57)e\left(\frac{5}{7}\right) e(37)e\left(\frac{3}{7}\right) e(1114)e\left(\frac{11}{14}\right) e(114)e\left(\frac{1}{14}\right) e(67)e\left(\frac{6}{7}\right)