Properties

Label 7942.151
Modulus $7942$
Conductor $3971$
Order $190$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7942, base_ring=CyclotomicField(190))
 
M = H._module
 
chi = DirichletCharacter(H, M([57,5]))
 
pari: [g,chi] = znchar(Mod(151,7942))
 

Basic properties

Modulus: \(7942\)
Conductor: \(3971\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(190\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{3971}(151,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 7942.bi

\(\chi_{7942}(151,\cdot)\) \(\chi_{7942}(189,\cdot)\) \(\chi_{7942}(227,\cdot)\) \(\chi_{7942}(303,\cdot)\) \(\chi_{7942}(569,\cdot)\) \(\chi_{7942}(607,\cdot)\) \(\chi_{7942}(645,\cdot)\) \(\chi_{7942}(987,\cdot)\) \(\chi_{7942}(1025,\cdot)\) \(\chi_{7942}(1063,\cdot)\) \(\chi_{7942}(1139,\cdot)\) \(\chi_{7942}(1405,\cdot)\) \(\chi_{7942}(1481,\cdot)\) \(\chi_{7942}(1557,\cdot)\) \(\chi_{7942}(1823,\cdot)\) \(\chi_{7942}(1861,\cdot)\) \(\chi_{7942}(1899,\cdot)\) \(\chi_{7942}(1975,\cdot)\) \(\chi_{7942}(2241,\cdot)\) \(\chi_{7942}(2279,\cdot)\) \(\chi_{7942}(2317,\cdot)\) \(\chi_{7942}(2393,\cdot)\) \(\chi_{7942}(2659,\cdot)\) \(\chi_{7942}(2697,\cdot)\) \(\chi_{7942}(2735,\cdot)\) \(\chi_{7942}(2811,\cdot)\) \(\chi_{7942}(3077,\cdot)\) \(\chi_{7942}(3115,\cdot)\) \(\chi_{7942}(3153,\cdot)\) \(\chi_{7942}(3229,\cdot)\) ...

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: $\Q(\zeta_{95})$
Fixed field: Number field defined by a degree 190 polynomial (not computed)

Values on generators

\((5777,6139)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{1}{38}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(7\)\(9\)\(13\)\(15\)\(17\)\(21\)\(23\)\(25\)
\( \chi_{ 7942 }(151, a) \) \(1\)\(1\)\(e\left(\frac{11}{190}\right)\)\(e\left(\frac{29}{95}\right)\)\(e\left(\frac{9}{190}\right)\)\(e\left(\frac{11}{95}\right)\)\(e\left(\frac{91}{95}\right)\)\(e\left(\frac{69}{190}\right)\)\(e\left(\frac{123}{190}\right)\)\(e\left(\frac{2}{19}\right)\)\(e\left(\frac{16}{19}\right)\)\(e\left(\frac{58}{95}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 7942 }(151,a) \;\) at \(\;a = \) e.g. 2