Properties

Label 4020.2473
Modulus $4020$
Conductor $335$
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(4020, base_ring=CyclotomicField(132))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,0,99,14]))
 
pari: [g,chi] = znchar(Mod(2473,4020))
 

Basic properties

Modulus: \(4020\)
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 \(\chi_{335}(128,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4020.dl

\(\chi_{4020}(13,\cdot)\) \(\chi_{4020}(337,\cdot)\) \(\chi_{4020}(433,\cdot)\) \(\chi_{4020}(517,\cdot)\) \(\chi_{4020}(577,\cdot)\) \(\chi_{4020}(637,\cdot)\) \(\chi_{4020}(733,\cdot)\) \(\chi_{4020}(757,\cdot)\) \(\chi_{4020}(817,\cdot)\) \(\chi_{4020}(1033,\cdot)\) \(\chi_{4020}(1213,\cdot)\) \(\chi_{4020}(1237,\cdot)\) \(\chi_{4020}(1453,\cdot)\) \(\chi_{4020}(1537,\cdot)\) \(\chi_{4020}(1573,\cdot)\) \(\chi_{4020}(1693,\cdot)\) \(\chi_{4020}(1753,\cdot)\) \(\chi_{4020}(1837,\cdot)\) \(\chi_{4020}(1933,\cdot)\) \(\chi_{4020}(1993,\cdot)\) \(\chi_{4020}(2017,\cdot)\) \(\chi_{4020}(2257,\cdot)\) \(\chi_{4020}(2377,\cdot)\) \(\chi_{4020}(2473,\cdot)\) \(\chi_{4020}(2497,\cdot)\) \(\chi_{4020}(2557,\cdot)\) \(\chi_{4020}(2737,\cdot)\) \(\chi_{4020}(2797,\cdot)\) \(\chi_{4020}(2893,\cdot)\) \(\chi_{4020}(3133,\cdot)\) ...

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

\((2011,2681,3217,1141)\) → \((1,1,-i,e\left(\frac{7}{66}\right))\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)
\( \chi_{ 4020 }(2473, a) \) \(1\)\(1\)\(e\left(\frac{25}{132}\right)\)\(e\left(\frac{17}{66}\right)\)\(e\left(\frac{35}{132}\right)\)\(e\left(\frac{71}{132}\right)\)\(e\left(\frac{37}{66}\right)\)\(e\left(\frac{29}{132}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{65}{66}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{41}{66}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4020 }(2473,a) \;\) at \(\;a = \) e.g. 2