Properties

Label 4020.2023
Modulus $4020$
Conductor $1340$
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(4020, base_ring=CyclotomicField(132))
 
M = H._module
 
chi = DirichletCharacter(H, M([66,0,99,38]))
 
pari: [g,chi] = znchar(Mod(2023,4020))
 

Basic properties

Modulus: \(4020\)
Conductor: \(1340\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(132\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1340}(683,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4020.dr

\(\chi_{4020}(7,\cdot)\) \(\chi_{4020}(247,\cdot)\) \(\chi_{4020}(367,\cdot)\) \(\chi_{4020}(463,\cdot)\) \(\chi_{4020}(487,\cdot)\) \(\chi_{4020}(547,\cdot)\) \(\chi_{4020}(727,\cdot)\) \(\chi_{4020}(787,\cdot)\) \(\chi_{4020}(883,\cdot)\) \(\chi_{4020}(1123,\cdot)\) \(\chi_{4020}(1183,\cdot)\) \(\chi_{4020}(1267,\cdot)\) \(\chi_{4020}(1543,\cdot)\) \(\chi_{4020}(1687,\cdot)\) \(\chi_{4020}(1723,\cdot)\) \(\chi_{4020}(1783,\cdot)\) \(\chi_{4020}(1843,\cdot)\) \(\chi_{4020}(1927,\cdot)\) \(\chi_{4020}(1963,\cdot)\) \(\chi_{4020}(1987,\cdot)\) \(\chi_{4020}(2023,\cdot)\) \(\chi_{4020}(2347,\cdot)\) \(\chi_{4020}(2443,\cdot)\) \(\chi_{4020}(2527,\cdot)\) \(\chi_{4020}(2587,\cdot)\) \(\chi_{4020}(2647,\cdot)\) \(\chi_{4020}(2743,\cdot)\) \(\chi_{4020}(2767,\cdot)\) \(\chi_{4020}(2827,\cdot)\) \(\chi_{4020}(3043,\cdot)\) ...

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

\((2011,2681,3217,1141)\) → \((-1,1,-i,e\left(\frac{19}{66}\right))\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)
\( \chi_{ 4020 }(2023, a) \) \(-1\)\(1\)\(e\left(\frac{115}{132}\right)\)\(e\left(\frac{16}{33}\right)\)\(e\left(\frac{95}{132}\right)\)\(e\left(\frac{23}{132}\right)\)\(e\left(\frac{29}{33}\right)\)\(e\left(\frac{107}{132}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{1}{33}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{17}{66}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4020 }(2023,a) \;\) at \(\;a = \) e.g. 2