Properties

Label 5445.2
Modulus $5445$
Conductor $5445$
Order $660$
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5445, base_ring=CyclotomicField(660))
 
M = H._module
 
chi = DirichletCharacter(H, M([110,165,6]))
 
pari: [g,chi] = znchar(Mod(2,5445))
 

Basic properties

Modulus: \(5445\)
Conductor: \(5445\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(660\)
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 5445.dp

\(\chi_{5445}(2,\cdot)\) \(\chi_{5445}(68,\cdot)\) \(\chi_{5445}(83,\cdot)\) \(\chi_{5445}(128,\cdot)\) \(\chi_{5445}(167,\cdot)\) \(\chi_{5445}(173,\cdot)\) \(\chi_{5445}(182,\cdot)\) \(\chi_{5445}(227,\cdot)\) \(\chi_{5445}(248,\cdot)\) \(\chi_{5445}(272,\cdot)\) \(\chi_{5445}(293,\cdot)\) \(\chi_{5445}(338,\cdot)\) \(\chi_{5445}(347,\cdot)\) \(\chi_{5445}(392,\cdot)\) \(\chi_{5445}(398,\cdot)\) \(\chi_{5445}(437,\cdot)\) \(\chi_{5445}(497,\cdot)\) \(\chi_{5445}(563,\cdot)\) \(\chi_{5445}(623,\cdot)\) \(\chi_{5445}(662,\cdot)\) \(\chi_{5445}(668,\cdot)\) \(\chi_{5445}(677,\cdot)\) \(\chi_{5445}(722,\cdot)\) \(\chi_{5445}(743,\cdot)\) \(\chi_{5445}(767,\cdot)\) \(\chi_{5445}(788,\cdot)\) \(\chi_{5445}(833,\cdot)\) \(\chi_{5445}(842,\cdot)\) \(\chi_{5445}(893,\cdot)\) \(\chi_{5445}(932,\cdot)\) ...

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: $\Q(\zeta_{660})$
Fixed field: Number field defined by a degree 660 polynomial (not computed)

Values on generators

\((3026,4357,3511)\) → \((e\left(\frac{1}{6}\right),i,e\left(\frac{1}{110}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(4\)\(7\)\(8\)\(13\)\(14\)\(16\)\(17\)\(19\)\(23\)
\( \chi_{ 5445 }(2, a) \) \(-1\)\(1\)\(e\left(\frac{281}{660}\right)\)\(e\left(\frac{281}{330}\right)\)\(e\left(\frac{647}{660}\right)\)\(e\left(\frac{61}{220}\right)\)\(e\left(\frac{1}{660}\right)\)\(e\left(\frac{67}{165}\right)\)\(e\left(\frac{116}{165}\right)\)\(e\left(\frac{43}{220}\right)\)\(e\left(\frac{14}{55}\right)\)\(e\left(\frac{29}{132}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 5445 }(2,a) \;\) at \(\;a = \) e.g. 2