Properties

Label 8280.121
Modulus $8280$
Conductor $207$
Order $33$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8280, base_ring=CyclotomicField(66))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,0,22,0,54]))
 
pari: [g,chi] = znchar(Mod(121,8280))
 

Basic properties

Modulus: \(8280\)
Conductor: \(207\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(33\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{207}(121,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8280.ey

\(\chi_{8280}(121,\cdot)\) \(\chi_{8280}(601,\cdot)\) \(\chi_{8280}(841,\cdot)\) \(\chi_{8280}(961,\cdot)\) \(\chi_{8280}(1681,\cdot)\) \(\chi_{8280}(1921,\cdot)\) \(\chi_{8280}(2281,\cdot)\) \(\chi_{8280}(2401,\cdot)\) \(\chi_{8280}(3121,\cdot)\) \(\chi_{8280}(3361,\cdot)\) \(\chi_{8280}(3481,\cdot)\) \(\chi_{8280}(3721,\cdot)\) \(\chi_{8280}(4441,\cdot)\) \(\chi_{8280}(5161,\cdot)\) \(\chi_{8280}(5641,\cdot)\) \(\chi_{8280}(5881,\cdot)\) \(\chi_{8280}(6241,\cdot)\) \(\chi_{8280}(6361,\cdot)\) \(\chi_{8280}(7441,\cdot)\) \(\chi_{8280}(7801,\cdot)\)

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: \(\Q(\zeta_{33})\)
Fixed field: 33.33.70011645999218458416472683122408534303895571350166174758601569.1

Values on generators

\((2071,4141,4601,1657,3961)\) → \((1,1,e\left(\frac{1}{3}\right),1,e\left(\frac{9}{11}\right))\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 8280 }(121, a) \) \(1\)\(1\)\(e\left(\frac{29}{33}\right)\)\(e\left(\frac{23}{33}\right)\)\(e\left(\frac{4}{33}\right)\)\(e\left(\frac{8}{11}\right)\)\(e\left(\frac{3}{11}\right)\)\(e\left(\frac{2}{33}\right)\)\(e\left(\frac{19}{33}\right)\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{16}{33}\right)\)\(e\left(\frac{14}{33}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 8280 }(121,a) \;\) at \(\;a = \) e.g. 2