Properties

Label 2888.2467
Modulus $2888$
Conductor $2888$
Order $342$
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2888, base_ring=CyclotomicField(342))
 
M = H._module
 
chi = DirichletCharacter(H, M([171,171,202]))
 
pari: [g,chi] = znchar(Mod(2467,2888))
 

Basic properties

Modulus: \(2888\)
Conductor: \(2888\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(342\)
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 2888.bs

\(\chi_{2888}(35,\cdot)\) \(\chi_{2888}(43,\cdot)\) \(\chi_{2888}(123,\cdot)\) \(\chi_{2888}(131,\cdot)\) \(\chi_{2888}(139,\cdot)\) \(\chi_{2888}(187,\cdot)\) \(\chi_{2888}(195,\cdot)\) \(\chi_{2888}(251,\cdot)\) \(\chi_{2888}(275,\cdot)\) \(\chi_{2888}(283,\cdot)\) \(\chi_{2888}(291,\cdot)\) \(\chi_{2888}(339,\cdot)\) \(\chi_{2888}(347,\cdot)\) \(\chi_{2888}(403,\cdot)\) \(\chi_{2888}(427,\cdot)\) \(\chi_{2888}(435,\cdot)\) \(\chi_{2888}(443,\cdot)\) \(\chi_{2888}(491,\cdot)\) \(\chi_{2888}(499,\cdot)\) \(\chi_{2888}(555,\cdot)\) \(\chi_{2888}(579,\cdot)\) \(\chi_{2888}(587,\cdot)\) \(\chi_{2888}(643,\cdot)\) \(\chi_{2888}(651,\cdot)\) \(\chi_{2888}(707,\cdot)\) \(\chi_{2888}(731,\cdot)\) \(\chi_{2888}(739,\cdot)\) \(\chi_{2888}(747,\cdot)\) \(\chi_{2888}(795,\cdot)\) \(\chi_{2888}(803,\cdot)\) ...

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: $\Q(\zeta_{171})$
Fixed field: Number field defined by a degree 342 polynomial (not computed)

Values on generators

\((2167,1445,2529)\) → \((-1,-1,e\left(\frac{101}{171}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(7\)\(9\)\(11\)\(13\)\(15\)\(17\)\(21\)\(23\)
\( \chi_{ 2888 }(2467, a) \) \(-1\)\(1\)\(e\left(\frac{17}{171}\right)\)\(e\left(\frac{181}{342}\right)\)\(e\left(\frac{11}{114}\right)\)\(e\left(\frac{34}{171}\right)\)\(e\left(\frac{14}{57}\right)\)\(e\left(\frac{281}{342}\right)\)\(e\left(\frac{215}{342}\right)\)\(e\left(\frac{83}{171}\right)\)\(e\left(\frac{67}{342}\right)\)\(e\left(\frac{251}{342}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 2888 }(2467,a) \;\) at \(\;a = \) e.g. 2