Properties

Label 6030.433
Modulus $6030$
Conductor $335$
Order $132$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6030, base_ring=CyclotomicField(132))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,99,94]))
 
pari: [g,chi] = znchar(Mod(433,6030))
 

Basic properties

Modulus: \(6030\)
Conductor: \(335\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(132\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{335}(98,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6030.ee

\(\chi_{6030}(433,\cdot)\) \(\chi_{6030}(487,\cdot)\) \(\chi_{6030}(577,\cdot)\) \(\chi_{6030}(757,\cdot)\) \(\chi_{6030}(883,\cdot)\) \(\chi_{6030}(1693,\cdot)\) \(\chi_{6030}(1783,\cdot)\) \(\chi_{6030}(1837,\cdot)\) \(\chi_{6030}(1927,\cdot)\) \(\chi_{6030}(1963,\cdot)\) \(\chi_{6030}(2017,\cdot)\) \(\chi_{6030}(2377,\cdot)\) \(\chi_{6030}(2557,\cdot)\) \(\chi_{6030}(2647,\cdot)\) \(\chi_{6030}(2737,\cdot)\) \(\chi_{6030}(2827,\cdot)\) \(\chi_{6030}(3043,\cdot)\) \(\chi_{6030}(3133,\cdot)\) \(\chi_{6030}(3223,\cdot)\) \(\chi_{6030}(3277,\cdot)\) \(\chi_{6030}(3547,\cdot)\) \(\chi_{6030}(3583,\cdot)\) \(\chi_{6030}(3763,\cdot)\) \(\chi_{6030}(3853,\cdot)\) \(\chi_{6030}(3943,\cdot)\) \(\chi_{6030}(3997,\cdot)\) \(\chi_{6030}(4033,\cdot)\) \(\chi_{6030}(4267,\cdot)\) \(\chi_{6030}(4357,\cdot)\) \(\chi_{6030}(4483,\cdot)\) ...

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

\((4691,1207,3151)\) → \((1,-i,e\left(\frac{47}{66}\right))\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)
\( \chi_{ 6030 }(433, a) \) \(1\)\(1\)\(e\left(\frac{17}{132}\right)\)\(e\left(\frac{1}{66}\right)\)\(e\left(\frac{103}{132}\right)\)\(e\left(\frac{43}{132}\right)\)\(e\left(\frac{41}{66}\right)\)\(e\left(\frac{25}{132}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{31}{66}\right)\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{49}{66}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6030 }(433,a) \;\) at \(\;a = \) e.g. 2