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Properties

Label 3380.bm
Modulus 33803380
Conductor 6565
Order 1212
Real no
Primitive no
Minimal no
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3380, base_ring=CyclotomicField(12))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,6,7]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(89,3380))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 33803380
Conductor: 6565
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 1212
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 65.s
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ12)\Q(\zeta_{12})
Fixed field: 12.0.28002506156828125.1

Characters in Galois orbit

Character −1-1 11 33 77 99 1111 1717 1919 2121 2323 2727 2929
χ3380(89,⋅)\chi_{3380}(89,\cdot) −1-1 11 e(56)e\left(\frac{5}{6}\right) e(1112)e\left(\frac{11}{12}\right) e(23)e\left(\frac{2}{3}\right) e(112)e\left(\frac{1}{12}\right) e(23)e\left(\frac{2}{3}\right) e(1112)e\left(\frac{11}{12}\right) −i-i e(13)e\left(\frac{1}{3}\right) −1-1 e(13)e\left(\frac{1}{3}\right)
χ3380(249,⋅)\chi_{3380}(249,\cdot) −1-1 11 e(56)e\left(\frac{5}{6}\right) e(512)e\left(\frac{5}{12}\right) e(23)e\left(\frac{2}{3}\right) e(712)e\left(\frac{7}{12}\right) e(23)e\left(\frac{2}{3}\right) e(512)e\left(\frac{5}{12}\right) ii e(13)e\left(\frac{1}{3}\right) −1-1 e(13)e\left(\frac{1}{3}\right)
χ3380(1709,⋅)\chi_{3380}(1709,\cdot) −1-1 11 e(16)e\left(\frac{1}{6}\right) e(112)e\left(\frac{1}{12}\right) e(13)e\left(\frac{1}{3}\right) e(1112)e\left(\frac{11}{12}\right) e(13)e\left(\frac{1}{3}\right) e(112)e\left(\frac{1}{12}\right) ii e(23)e\left(\frac{2}{3}\right) −1-1 e(23)e\left(\frac{2}{3}\right)
χ3380(2009,⋅)\chi_{3380}(2009,\cdot) −1-1 11 e(16)e\left(\frac{1}{6}\right) e(712)e\left(\frac{7}{12}\right) e(13)e\left(\frac{1}{3}\right) e(512)e\left(\frac{5}{12}\right) e(13)e\left(\frac{1}{3}\right) e(712)e\left(\frac{7}{12}\right) −i-i e(23)e\left(\frac{2}{3}\right) −1-1 e(23)e\left(\frac{2}{3}\right)