Properties

Label 6017.2465
Modulus $6017$
Conductor $547$
Order $91$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6017, base_ring=CyclotomicField(182))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,34]))
 
pari: [g,chi] = znchar(Mod(2465,6017))
 

Basic properties

Modulus: \(6017\)
Conductor: \(547\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(91\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{547}(277,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6017.bl

\(\chi_{6017}(100,\cdot)\) \(\chi_{6017}(309,\cdot)\) \(\chi_{6017}(661,\cdot)\) \(\chi_{6017}(771,\cdot)\) \(\chi_{6017}(815,\cdot)\) \(\chi_{6017}(837,\cdot)\) \(\chi_{6017}(969,\cdot)\) \(\chi_{6017}(991,\cdot)\) \(\chi_{6017}(1123,\cdot)\) \(\chi_{6017}(1178,\cdot)\) \(\chi_{6017}(1255,\cdot)\) \(\chi_{6017}(1299,\cdot)\) \(\chi_{6017}(1310,\cdot)\) \(\chi_{6017}(1376,\cdot)\) \(\chi_{6017}(1409,\cdot)\) \(\chi_{6017}(1508,\cdot)\) \(\chi_{6017}(1552,\cdot)\) \(\chi_{6017}(1651,\cdot)\) \(\chi_{6017}(1772,\cdot)\) \(\chi_{6017}(1904,\cdot)\) \(\chi_{6017}(2157,\cdot)\) \(\chi_{6017}(2212,\cdot)\) \(\chi_{6017}(2223,\cdot)\) \(\chi_{6017}(2278,\cdot)\) \(\chi_{6017}(2355,\cdot)\) \(\chi_{6017}(2465,\cdot)\) \(\chi_{6017}(2509,\cdot)\) \(\chi_{6017}(2597,\cdot)\) \(\chi_{6017}(2630,\cdot)\) \(\chi_{6017}(2641,\cdot)\) ...

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: $\Q(\zeta_{91})$
Fixed field: Number field defined by a degree 91 polynomial

Values on generators

\((3830,2190)\) → \((1,e\left(\frac{17}{91}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(12\)
\( \chi_{ 6017 }(2465, a) \) \(1\)\(1\)\(e\left(\frac{17}{91}\right)\)\(e\left(\frac{1}{7}\right)\)\(e\left(\frac{34}{91}\right)\)\(e\left(\frac{40}{91}\right)\)\(e\left(\frac{30}{91}\right)\)\(e\left(\frac{22}{91}\right)\)\(e\left(\frac{51}{91}\right)\)\(e\left(\frac{2}{7}\right)\)\(e\left(\frac{57}{91}\right)\)\(e\left(\frac{47}{91}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6017 }(2465,a) \;\) at \(\;a = \) e.g. 2