Properties

Label 2888.875
Modulus $2888$
Conductor $2888$
Order $38$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

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Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(2888, base_ring=CyclotomicField(38))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([19,19,18]))
 
pari: [g,chi] = znchar(Mod(875,2888))
 

Basic properties

Modulus: \(2888\)
Conductor: \(2888\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(38\)
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.bb

\(\chi_{2888}(115,\cdot)\) \(\chi_{2888}(267,\cdot)\) \(\chi_{2888}(419,\cdot)\) \(\chi_{2888}(571,\cdot)\) \(\chi_{2888}(875,\cdot)\) \(\chi_{2888}(1027,\cdot)\) \(\chi_{2888}(1179,\cdot)\) \(\chi_{2888}(1331,\cdot)\) \(\chi_{2888}(1483,\cdot)\) \(\chi_{2888}(1635,\cdot)\) \(\chi_{2888}(1787,\cdot)\) \(\chi_{2888}(1939,\cdot)\) \(\chi_{2888}(2091,\cdot)\) \(\chi_{2888}(2243,\cdot)\) \(\chi_{2888}(2395,\cdot)\) \(\chi_{2888}(2547,\cdot)\) \(\chi_{2888}(2699,\cdot)\) \(\chi_{2888}(2851,\cdot)\)

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: \(\Q(\zeta_{19})\)
Fixed field: 38.0.16942169463783688515274712980459055357466629107345696737681001440761438215014074919167299388239251805665492992.1

Values on generators

\((2167,1445,2529)\) → \((-1,-1,e\left(\frac{9}{19}\right))\)

Values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(7\)\(9\)\(11\)\(13\)\(15\)\(17\)\(21\)\(23\)
\( \chi_{ 2888 }(875, a) \) \(-1\)\(1\)\(e\left(\frac{16}{19}\right)\)\(e\left(\frac{15}{38}\right)\)\(e\left(\frac{21}{38}\right)\)\(e\left(\frac{13}{19}\right)\)\(e\left(\frac{6}{19}\right)\)\(e\left(\frac{13}{38}\right)\)\(e\left(\frac{9}{38}\right)\)\(e\left(\frac{1}{19}\right)\)\(e\left(\frac{15}{38}\right)\)\(e\left(\frac{25}{38}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 2888 }(875,a) \;\) at \(\;a = \) e.g. 2