Properties

Label 2960.69
Modulus $2960$
Conductor $2960$
Order $36$
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2960, base_ring=CyclotomicField(36))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,9,18,5]))
 
pari: [g,chi] = znchar(Mod(69,2960))
 

Basic properties

Modulus: \(2960\)
Conductor: \(2960\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(36\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2960.hc

\(\chi_{2960}(69,\cdot)\) \(\chi_{2960}(109,\cdot)\) \(\chi_{2960}(429,\cdot)\) \(\chi_{2960}(869,\cdot)\) \(\chi_{2960}(949,\cdot)\) \(\chi_{2960}(1789,\cdot)\) \(\chi_{2960}(1869,\cdot)\) \(\chi_{2960}(2309,\cdot)\) \(\chi_{2960}(2629,\cdot)\) \(\chi_{2960}(2669,\cdot)\) \(\chi_{2960}(2829,\cdot)\) \(\chi_{2960}(2869,\cdot)\)

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: \(\Q(\zeta_{36})\)
Fixed field: Number field defined by a degree 36 polynomial

Values on generators

\((2591,741,1777,2481)\) → \((1,i,-1,e\left(\frac{5}{36}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(17\)\(19\)\(21\)\(23\)\(27\)
\( \chi_{ 2960 }(69, a) \) \(-1\)\(1\)\(e\left(\frac{31}{36}\right)\)\(e\left(\frac{4}{9}\right)\)\(e\left(\frac{13}{18}\right)\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{17}{36}\right)\)\(e\left(\frac{11}{18}\right)\)\(e\left(\frac{11}{36}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{7}{12}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 2960 }(69,a) \;\) at \(\;a = \) e.g. 2