Properties

Label 8033.1699
Modulus $8033$
Conductor $8033$
Order $92$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8033, base_ring=CyclotomicField(92))
 
M = H._module
 
chi = DirichletCharacter(H, M([69,29]))
 
pari: [g,chi] = znchar(Mod(1699,8033))
 

Basic properties

Modulus: \(8033\)
Conductor: \(8033\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(92\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8033.bt

\(\chi_{8033}(104,\cdot)\) \(\chi_{8033}(128,\cdot)\) \(\chi_{8033}(244,\cdot)\) \(\chi_{8033}(539,\cdot)\) \(\chi_{8033}(713,\cdot)\) \(\chi_{8033}(940,\cdot)\) \(\chi_{8033}(1699,\cdot)\) \(\chi_{8033}(1810,\cdot)\) \(\chi_{8033}(1931,\cdot)\) \(\chi_{8033}(2071,\cdot)\) \(\chi_{8033}(2134,\cdot)\) \(\chi_{8033}(2535,\cdot)\) \(\chi_{8033}(2709,\cdot)\) \(\chi_{8033}(2738,\cdot)\) \(\chi_{8033}(2772,\cdot)\) \(\chi_{8033}(2796,\cdot)\) \(\chi_{8033}(3120,\cdot)\) \(\chi_{8033}(3463,\cdot)\) \(\chi_{8033}(3550,\cdot)\) \(\chi_{8033}(3753,\cdot)\) \(\chi_{8033}(3840,\cdot)\) \(\chi_{8033}(3932,\cdot)\) \(\chi_{8033}(4101,\cdot)\) \(\chi_{8033}(4193,\cdot)\) \(\chi_{8033}(4280,\cdot)\) \(\chi_{8033}(4483,\cdot)\) \(\chi_{8033}(4570,\cdot)\) \(\chi_{8033}(4913,\cdot)\) \(\chi_{8033}(5237,\cdot)\) \(\chi_{8033}(5261,\cdot)\) ...

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: $\Q(\zeta_{92})$
Fixed field: Number field defined by a degree 92 polynomial

Values on generators

\((5541,1944)\) → \((-i,e\left(\frac{29}{92}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\( \chi_{ 8033 }(1699, a) \) \(1\)\(1\)\(e\left(\frac{2}{23}\right)\)\(e\left(\frac{1}{92}\right)\)\(e\left(\frac{4}{23}\right)\)\(e\left(\frac{75}{92}\right)\)\(e\left(\frac{9}{92}\right)\)\(e\left(\frac{43}{46}\right)\)\(e\left(\frac{6}{23}\right)\)\(e\left(\frac{1}{46}\right)\)\(e\left(\frac{83}{92}\right)\)\(e\left(\frac{22}{23}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 8033 }(1699,a) \;\) at \(\;a = \) e.g. 2