Properties

Label 3484.11
Modulus $3484$
Conductor $3484$
Order $132$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3484, base_ring=CyclotomicField(132))
 
M = H._module
 
chi = DirichletCharacter(H, M([66,77,118]))
 
pari: [g,chi] = znchar(Mod(11,3484))
 

Basic properties

Modulus: \(3484\)
Conductor: \(3484\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(132\)
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)
 

Galois orbit 3484.ei

\(\chi_{3484}(11,\cdot)\) \(\chi_{3484}(63,\cdot)\) \(\chi_{3484}(111,\cdot)\) \(\chi_{3484}(275,\cdot)\) \(\chi_{3484}(319,\cdot)\) \(\chi_{3484}(383,\cdot)\) \(\chi_{3484}(487,\cdot)\) \(\chi_{3484}(631,\cdot)\) \(\chi_{3484}(635,\cdot)\) \(\chi_{3484}(683,\cdot)\) \(\chi_{3484}(787,\cdot)\) \(\chi_{3484}(995,\cdot)\) \(\chi_{3484}(1007,\cdot)\) \(\chi_{3484}(1051,\cdot)\) \(\chi_{3484}(1103,\cdot)\) \(\chi_{3484}(1159,\cdot)\) \(\chi_{3484}(1267,\cdot)\) \(\chi_{3484}(1419,\cdot)\) \(\chi_{3484}(1575,\cdot)\) \(\chi_{3484}(1723,\cdot)\) \(\chi_{3484}(1783,\cdot)\) \(\chi_{3484}(1827,\cdot)\) \(\chi_{3484}(1883,\cdot)\) \(\chi_{3484}(1887,\cdot)\) \(\chi_{3484}(1939,\cdot)\) \(\chi_{3484}(2255,\cdot)\) \(\chi_{3484}(2347,\cdot)\) \(\chi_{3484}(2463,\cdot)\) \(\chi_{3484}(2511,\cdot)\) \(\chi_{3484}(2607,\cdot)\) ...

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: $\Q(\zeta_{132})$
Fixed field: Number field defined by a degree 132 polynomial (not computed)

Values on generators

\((1743,1341,3017)\) → \((-1,e\left(\frac{7}{12}\right),e\left(\frac{59}{66}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(7\)\(9\)\(11\)\(15\)\(17\)\(19\)\(21\)\(23\)
\( \chi_{ 3484 }(11, a) \) \(-1\)\(1\)\(e\left(\frac{23}{33}\right)\)\(e\left(\frac{29}{44}\right)\)\(e\left(\frac{21}{44}\right)\)\(e\left(\frac{13}{33}\right)\)\(e\left(\frac{43}{132}\right)\)\(e\left(\frac{47}{132}\right)\)\(e\left(\frac{25}{66}\right)\)\(e\left(\frac{47}{132}\right)\)\(e\left(\frac{23}{132}\right)\)\(e\left(\frac{4}{11}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 3484 }(11,a) \;\) at \(\;a = \) e.g. 2