Properties

Label 4020.281
Modulus $4020$
Conductor $201$
Order $66$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4020, base_ring=CyclotomicField(66))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,33,0,19]))
 
pari: [g,chi] = znchar(Mod(281,4020))
 

Basic properties

Modulus: \(4020\)
Conductor: \(201\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(66\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{201}(80,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4020.da

\(\chi_{4020}(41,\cdot)\) \(\chi_{4020}(101,\cdot)\) \(\chi_{4020}(221,\cdot)\) \(\chi_{4020}(281,\cdot)\) \(\chi_{4020}(701,\cdot)\) \(\chi_{4020}(1001,\cdot)\) \(\chi_{4020}(1301,\cdot)\) \(\chi_{4020}(1481,\cdot)\) \(\chi_{4020}(1721,\cdot)\) \(\chi_{4020}(1841,\cdot)\) \(\chi_{4020}(1961,\cdot)\) \(\chi_{4020}(2021,\cdot)\) \(\chi_{4020}(2201,\cdot)\) \(\chi_{4020}(2261,\cdot)\) \(\chi_{4020}(2741,\cdot)\) \(\chi_{4020}(3161,\cdot)\) \(\chi_{4020}(3401,\cdot)\) \(\chi_{4020}(3461,\cdot)\) \(\chi_{4020}(3821,\cdot)\) \(\chi_{4020}(4001,\cdot)\)

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

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

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)
\( \chi_{ 4020 }(281, a) \) \(1\)\(1\)\(e\left(\frac{41}{66}\right)\)\(e\left(\frac{16}{33}\right)\)\(e\left(\frac{31}{66}\right)\)\(e\left(\frac{61}{66}\right)\)\(e\left(\frac{29}{33}\right)\)\(e\left(\frac{37}{66}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{35}{66}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{25}{33}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4020 }(281,a) \;\) at \(\;a = \) e.g. 2