Properties

Label 7440.607
Modulus $7440$
Conductor $620$
Order $60$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7440, base_ring=CyclotomicField(60))
 
M = H._module
 
chi = DirichletCharacter(H, M([30,0,0,15,52]))
 
pari: [g,chi] = znchar(Mod(607,7440))
 

Basic properties

Modulus: \(7440\)
Conductor: \(620\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(60\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{620}(607,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 7440.lb

\(\chi_{7440}(607,\cdot)\) \(\chi_{7440}(847,\cdot)\) \(\chi_{7440}(1423,\cdot)\) \(\chi_{7440}(1663,\cdot)\) \(\chi_{7440}(1807,\cdot)\) \(\chi_{7440}(2623,\cdot)\) \(\chi_{7440}(3583,\cdot)\) \(\chi_{7440}(3727,\cdot)\) \(\chi_{7440}(3823,\cdot)\) \(\chi_{7440}(4447,\cdot)\) \(\chi_{7440}(4783,\cdot)\) \(\chi_{7440}(5887,\cdot)\) \(\chi_{7440}(6127,\cdot)\) \(\chi_{7440}(6703,\cdot)\) \(\chi_{7440}(7087,\cdot)\) \(\chi_{7440}(7423,\cdot)\)

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: \(\Q(\zeta_{60})\)
Fixed field: Number field defined by a degree 60 polynomial

Values on generators

\((6511,1861,4961,2977,5521)\) → \((-1,1,1,i,e\left(\frac{13}{15}\right))\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(37\)\(41\)\(43\)
\( \chi_{ 7440 }(607, a) \) \(1\)\(1\)\(e\left(\frac{1}{60}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{17}{60}\right)\)\(e\left(\frac{19}{60}\right)\)\(e\left(\frac{7}{15}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{2}{15}\right)\)\(e\left(\frac{43}{60}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 7440 }(607,a) \;\) at \(\;a = \) e.g. 2