Properties

Label 2960.gq
Modulus $2960$
Conductor $2960$
Order $36$
Real no
Primitive yes
Minimal yes
Parity even

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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([0,27,27,11]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(13,2960))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

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: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

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

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(13\) \(17\) \(19\) \(21\) \(23\) \(27\)
\(\chi_{2960}(13,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{2960}(93,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{2960}(277,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{2960}(357,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{2960}(893,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{2960}(1053,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{2960}(1293,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{2960}(1613,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{2960}(1717,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{2960}(2037,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{2960}(2277,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{2960}(2437,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)