Properties

Label 3484.93
Modulus $3484$
Conductor $871$
Order $132$
Real no
Primitive no
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3484, base_ring=CyclotomicField(132))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,11,40]))
 
pari: [g,chi] = znchar(Mod(93,3484))
 

Basic properties

Modulus: \(3484\)
Conductor: \(871\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(132\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{871}(93,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3484.el

\(\chi_{3484}(93,\cdot)\) \(\chi_{3484}(301,\cdot)\) \(\chi_{3484}(345,\cdot)\) \(\chi_{3484}(457,\cdot)\) \(\chi_{3484}(505,\cdot)\) \(\chi_{3484}(553,\cdot)\) \(\chi_{3484}(557,\cdot)\) \(\chi_{3484}(657,\cdot)\) \(\chi_{3484}(709,\cdot)\) \(\chi_{3484}(717,\cdot)\) \(\chi_{3484}(877,\cdot)\) \(\chi_{3484}(973,\cdot)\) \(\chi_{3484}(1021,\cdot)\) \(\chi_{3484}(1137,\cdot)\) \(\chi_{3484}(1229,\cdot)\) \(\chi_{3484}(1545,\cdot)\) \(\chi_{3484}(1597,\cdot)\) \(\chi_{3484}(1601,\cdot)\) \(\chi_{3484}(1657,\cdot)\) \(\chi_{3484}(1701,\cdot)\) \(\chi_{3484}(1761,\cdot)\) \(\chi_{3484}(1909,\cdot)\) \(\chi_{3484}(2065,\cdot)\) \(\chi_{3484}(2217,\cdot)\) \(\chi_{3484}(2325,\cdot)\) \(\chi_{3484}(2381,\cdot)\) \(\chi_{3484}(2433,\cdot)\) \(\chi_{3484}(2477,\cdot)\) \(\chi_{3484}(2489,\cdot)\) \(\chi_{3484}(2697,\cdot)\) ...

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

\((1743,1341,3017)\) → \((1,e\left(\frac{1}{12}\right),e\left(\frac{10}{33}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(7\)\(9\)\(11\)\(15\)\(17\)\(19\)\(21\)\(23\)
\( \chi_{ 3484 }(93, a) \) \(-1\)\(1\)\(e\left(\frac{5}{33}\right)\)\(e\left(\frac{13}{44}\right)\)\(e\left(\frac{39}{44}\right)\)\(e\left(\frac{10}{33}\right)\)\(e\left(\frac{61}{132}\right)\)\(e\left(\frac{59}{132}\right)\)\(e\left(\frac{37}{66}\right)\)\(e\left(\frac{59}{132}\right)\)\(e\left(\frac{5}{132}\right)\)\(e\left(\frac{7}{22}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 3484 }(93,a) \;\) at \(\;a = \) e.g. 2