Properties

Label 4020.1141
Modulus $4020$
Conductor $67$
Order $66$
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(66))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,0,0,1]))
 
pari: [g,chi] = znchar(Mod(1141,4020))
 

Basic properties

Modulus: \(4020\)
Conductor: \(67\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(66\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{67}(2,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4020.cv

\(\chi_{4020}(61,\cdot)\) \(\chi_{4020}(481,\cdot)\) \(\chi_{4020}(721,\cdot)\) \(\chi_{4020}(781,\cdot)\) \(\chi_{4020}(1141,\cdot)\) \(\chi_{4020}(1321,\cdot)\) \(\chi_{4020}(1381,\cdot)\) \(\chi_{4020}(1441,\cdot)\) \(\chi_{4020}(1561,\cdot)\) \(\chi_{4020}(1621,\cdot)\) \(\chi_{4020}(2041,\cdot)\) \(\chi_{4020}(2341,\cdot)\) \(\chi_{4020}(2641,\cdot)\) \(\chi_{4020}(2821,\cdot)\) \(\chi_{4020}(3061,\cdot)\) \(\chi_{4020}(3181,\cdot)\) \(\chi_{4020}(3301,\cdot)\) \(\chi_{4020}(3361,\cdot)\) \(\chi_{4020}(3541,\cdot)\) \(\chi_{4020}(3601,\cdot)\)

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: \(\Q(\zeta_{33})\)
Fixed field: Number field defined by a degree 66 polynomial

Values on generators

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

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)
\( \chi_{ 4020 }(1141, a) \) \(-1\)\(1\)\(e\left(\frac{23}{66}\right)\)\(e\left(\frac{59}{66}\right)\)\(e\left(\frac{19}{66}\right)\)\(e\left(\frac{32}{33}\right)\)\(e\left(\frac{5}{33}\right)\)\(e\left(\frac{14}{33}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{47}{66}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{53}{66}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4020 }(1141,a) \;\) at \(\;a = \) e.g. 2