Properties

Label 8100.1549
Modulus $8100$
Conductor $135$
Order $18$
Real no
Primitive no
Minimal no
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8100, base_ring=CyclotomicField(18))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,8,9]))
 
pari: [g,chi] = znchar(Mod(1549,8100))
 

Basic properties

Modulus: \(8100\)
Conductor: \(135\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(18\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{135}(94,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8100.bm

\(\chi_{8100}(1549,\cdot)\) \(\chi_{8100}(2449,\cdot)\) \(\chi_{8100}(4249,\cdot)\) \(\chi_{8100}(5149,\cdot)\) \(\chi_{8100}(6949,\cdot)\) \(\chi_{8100}(7849,\cdot)\)

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: \(\Q(\zeta_{9})\)
Fixed field: 18.18.1923380668327365689220703125.1

Values on generators

\((4051,6401,7777)\) → \((1,e\left(\frac{4}{9}\right),-1)\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)
\( \chi_{ 8100 }(1549, a) \) \(1\)\(1\)\(e\left(\frac{11}{18}\right)\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{1}{18}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{7}{18}\right)\)\(e\left(\frac{4}{9}\right)\)\(e\left(\frac{8}{9}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{5}{9}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 8100 }(1549,a) \;\) at \(\;a = \) e.g. 2