Properties

Label 4650.523
Modulus $4650$
Conductor $775$
Order $20$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4650, base_ring=CyclotomicField(20))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,11,2]))
 
pari: [g,chi] = znchar(Mod(523,4650))
 

Basic properties

Modulus: \(4650\)
Conductor: \(775\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(20\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{775}(523,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4650.du

\(\chi_{4650}(523,\cdot)\) \(\chi_{4650}(697,\cdot)\) \(\chi_{4650}(1387,\cdot)\) \(\chi_{4650}(3067,\cdot)\) \(\chi_{4650}(3127,\cdot)\) \(\chi_{4650}(4183,\cdot)\) \(\chi_{4650}(4363,\cdot)\) \(\chi_{4650}(4603,\cdot)\)

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: \(\Q(\zeta_{20})\)
Fixed field: Number field defined by a degree 20 polynomial

Values on generators

\((3101,2977,1801)\) → \((1,e\left(\frac{11}{20}\right),e\left(\frac{1}{10}\right))\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(37\)\(41\)\(43\)
\( \chi_{ 4650 }(523, a) \) \(1\)\(1\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{17}{20}\right)\)\(e\left(\frac{3}{10}\right)\)\(-i\)\(1\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{3}{20}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4650 }(523,a) \;\) at \(\;a = \) e.g. 2