Properties

Label 8280.233
Modulus $8280$
Conductor $345$
Order $44$
Real no
Primitive no
Minimal no
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8280, base_ring=CyclotomicField(44))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,0,22,33,32]))
 
pari: [g,chi] = znchar(Mod(233,8280))
 

Basic properties

Modulus: \(8280\)
Conductor: \(345\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{345}(233,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8280.fl

\(\chi_{8280}(233,\cdot)\) \(\chi_{8280}(377,\cdot)\) \(\chi_{8280}(593,\cdot)\) \(\chi_{8280}(1097,\cdot)\) \(\chi_{8280}(1313,\cdot)\) \(\chi_{8280}(1457,\cdot)\) \(\chi_{8280}(2033,\cdot)\) \(\chi_{8280}(2753,\cdot)\) \(\chi_{8280}(3113,\cdot)\) \(\chi_{8280}(3617,\cdot)\) \(\chi_{8280}(4337,\cdot)\) \(\chi_{8280}(5273,\cdot)\) \(\chi_{8280}(5417,\cdot)\) \(\chi_{8280}(5777,\cdot)\) \(\chi_{8280}(5993,\cdot)\) \(\chi_{8280}(6857,\cdot)\) \(\chi_{8280}(7073,\cdot)\) \(\chi_{8280}(7217,\cdot)\) \(\chi_{8280}(7433,\cdot)\) \(\chi_{8280}(7937,\cdot)\)

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: \(\Q(\zeta_{44})\)
Fixed field: Number field defined by a degree 44 polynomial

Values on generators

\((2071,4141,4601,1657,3961)\) → \((1,1,-1,-i,e\left(\frac{8}{11}\right))\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 8280 }(233, a) \) \(1\)\(1\)\(e\left(\frac{25}{44}\right)\)\(e\left(\frac{1}{22}\right)\)\(e\left(\frac{19}{44}\right)\)\(e\left(\frac{15}{44}\right)\)\(e\left(\frac{9}{22}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{4}{11}\right)\)\(e\left(\frac{1}{44}\right)\)\(e\left(\frac{5}{22}\right)\)\(e\left(\frac{39}{44}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 8280 }(233,a) \;\) at \(\;a = \) e.g. 2