Properties

Label 2888.25
Modulus $2888$
Conductor $361$
Order $171$
Real no
Primitive no
Minimal yes
Parity even

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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([0,0,122]))
 
pari: [g,chi] = znchar(Mod(25,2888))
 

Basic properties

Modulus: \(2888\)
Conductor: \(361\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(171\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{361}(25,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2888.bo

\(\chi_{2888}(9,\cdot)\) \(\chi_{2888}(17,\cdot)\) \(\chi_{2888}(25,\cdot)\) \(\chi_{2888}(73,\cdot)\) \(\chi_{2888}(81,\cdot)\) \(\chi_{2888}(137,\cdot)\) \(\chi_{2888}(161,\cdot)\) \(\chi_{2888}(169,\cdot)\) \(\chi_{2888}(177,\cdot)\) \(\chi_{2888}(225,\cdot)\) \(\chi_{2888}(233,\cdot)\) \(\chi_{2888}(289,\cdot)\) \(\chi_{2888}(313,\cdot)\) \(\chi_{2888}(321,\cdot)\) \(\chi_{2888}(329,\cdot)\) \(\chi_{2888}(377,\cdot)\) \(\chi_{2888}(385,\cdot)\) \(\chi_{2888}(441,\cdot)\) \(\chi_{2888}(465,\cdot)\) \(\chi_{2888}(473,\cdot)\) \(\chi_{2888}(481,\cdot)\) \(\chi_{2888}(529,\cdot)\) \(\chi_{2888}(537,\cdot)\) \(\chi_{2888}(593,\cdot)\) \(\chi_{2888}(617,\cdot)\) \(\chi_{2888}(625,\cdot)\) \(\chi_{2888}(633,\cdot)\) \(\chi_{2888}(681,\cdot)\) \(\chi_{2888}(689,\cdot)\) \(\chi_{2888}(745,\cdot)\) ...

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 171 polynomial (not computed)

Values on generators

\((2167,1445,2529)\) → \((1,1,e\left(\frac{61}{171}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(7\)\(9\)\(11\)\(13\)\(15\)\(17\)\(21\)\(23\)
\( \chi_{ 2888 }(25, a) \) \(1\)\(1\)\(e\left(\frac{100}{171}\right)\)\(e\left(\frac{130}{171}\right)\)\(e\left(\frac{29}{57}\right)\)\(e\left(\frac{29}{171}\right)\)\(e\left(\frac{22}{57}\right)\)\(e\left(\frac{62}{171}\right)\)\(e\left(\frac{59}{171}\right)\)\(e\left(\frac{106}{171}\right)\)\(e\left(\frac{16}{171}\right)\)\(e\left(\frac{14}{171}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 2888 }(25,a) \;\) at \(\;a = \) e.g. 2