Properties

Label 4020.2483
Modulus $4020$
Conductor $4020$
Order $132$
Real no
Primitive yes
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([66,66,99,4]))
 
pari: [g,chi] = znchar(Mod(2483,4020))
 

Basic properties

Modulus: \(4020\)
Conductor: \(4020\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(132\)
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 4020.dq

\(\chi_{4020}(23,\cdot)\) \(\chi_{4020}(47,\cdot)\) \(\chi_{4020}(83,\cdot)\) \(\chi_{4020}(167,\cdot)\) \(\chi_{4020}(227,\cdot)\) \(\chi_{4020}(287,\cdot)\) \(\chi_{4020}(323,\cdot)\) \(\chi_{4020}(467,\cdot)\) \(\chi_{4020}(743,\cdot)\) \(\chi_{4020}(827,\cdot)\) \(\chi_{4020}(887,\cdot)\) \(\chi_{4020}(1127,\cdot)\) \(\chi_{4020}(1223,\cdot)\) \(\chi_{4020}(1283,\cdot)\) \(\chi_{4020}(1463,\cdot)\) \(\chi_{4020}(1523,\cdot)\) \(\chi_{4020}(1547,\cdot)\) \(\chi_{4020}(1643,\cdot)\) \(\chi_{4020}(1763,\cdot)\) \(\chi_{4020}(2003,\cdot)\) \(\chi_{4020}(2027,\cdot)\) \(\chi_{4020}(2087,\cdot)\) \(\chi_{4020}(2183,\cdot)\) \(\chi_{4020}(2267,\cdot)\) \(\chi_{4020}(2327,\cdot)\) \(\chi_{4020}(2447,\cdot)\) \(\chi_{4020}(2483,\cdot)\) \(\chi_{4020}(2567,\cdot)\) \(\chi_{4020}(2783,\cdot)\) \(\chi_{4020}(2807,\cdot)\) ...

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

\((2011,2681,3217,1141)\) → \((-1,-1,-i,e\left(\frac{1}{33}\right))\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)
\( \chi_{ 4020 }(2483, a) \) \(-1\)\(1\)\(e\left(\frac{125}{132}\right)\)\(e\left(\frac{26}{33}\right)\)\(e\left(\frac{109}{132}\right)\)\(e\left(\frac{25}{132}\right)\)\(e\left(\frac{10}{33}\right)\)\(e\left(\frac{13}{132}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{61}{66}\right)\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{7}{66}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4020 }(2483,a) \;\) at \(\;a = \) e.g. 2