Properties

Label 6030.263
Modulus $6030$
Conductor $3015$
Order $132$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6030, base_ring=CyclotomicField(132))
 
M = H._module
 
chi = DirichletCharacter(H, M([22,99,96]))
 
pari: [g,chi] = znchar(Mod(263,6030))
 

Basic properties

Modulus: \(6030\)
Conductor: \(3015\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(132\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{3015}(263,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6030.eg

\(\chi_{6030}(263,\cdot)\) \(\chi_{6030}(293,\cdot)\) \(\chi_{6030}(533,\cdot)\) \(\chi_{6030}(617,\cdot)\) \(\chi_{6030}(893,\cdot)\) \(\chi_{6030}(947,\cdot)\) \(\chi_{6030}(1067,\cdot)\) \(\chi_{6030}(1163,\cdot)\) \(\chi_{6030}(1337,\cdot)\) \(\chi_{6030}(1667,\cdot)\) \(\chi_{6030}(1697,\cdot)\) \(\chi_{6030}(1757,\cdot)\) \(\chi_{6030}(1823,\cdot)\) \(\chi_{6030}(1967,\cdot)\) \(\chi_{6030}(2117,\cdot)\) \(\chi_{6030}(2153,\cdot)\) \(\chi_{6030}(2273,\cdot)\) \(\chi_{6030}(2543,\cdot)\) \(\chi_{6030}(2873,\cdot)\) \(\chi_{6030}(2903,\cdot)\) \(\chi_{6030}(2957,\cdot)\) \(\chi_{6030}(2963,\cdot)\) \(\chi_{6030}(3107,\cdot)\) \(\chi_{6030}(3173,\cdot)\) \(\chi_{6030}(3323,\cdot)\) \(\chi_{6030}(3677,\cdot)\) \(\chi_{6030}(3767,\cdot)\) \(\chi_{6030}(4127,\cdot)\) \(\chi_{6030}(4163,\cdot)\) \(\chi_{6030}(4313,\cdot)\) ...

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

\((4691,1207,3151)\) → \((e\left(\frac{1}{6}\right),-i,e\left(\frac{8}{11}\right))\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)
\( \chi_{ 6030 }(263, a) \) \(1\)\(1\)\(e\left(\frac{19}{132}\right)\)\(e\left(\frac{5}{66}\right)\)\(e\left(\frac{53}{132}\right)\)\(e\left(\frac{35}{44}\right)\)\(e\left(\frac{17}{22}\right)\)\(e\left(\frac{59}{132}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{17}{33}\right)\)\(-i\)\(e\left(\frac{25}{66}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6030 }(263,a) \;\) at \(\;a = \) e.g. 2