Properties

Label 7056.ij
Modulus $7056$
Conductor $2352$
Order $84$
Real no
Primitive no
Minimal no
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7056, base_ring=CyclotomicField(84))
 
M = H._module
 
chi = DirichletCharacter(H, M([42,21,42,4]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(107,7056))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(7056\)
Conductor: \(2352\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(84\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 2352.dl
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: $\Q(\zeta_{84})$
Fixed field: Number field defined by a degree 84 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\) \(37\)
\(\chi_{7056}(107,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{65}{84}\right)\)
\(\chi_{7056}(179,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{67}{84}\right)\)
\(\chi_{7056}(611,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{59}{84}\right)\)
\(\chi_{7056}(683,\cdot)\) \(1\) \(1\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{84}\right)\)
\(\chi_{7056}(1115,\cdot)\) \(1\) \(1\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{53}{84}\right)\)
\(\chi_{7056}(1187,\cdot)\) \(1\) \(1\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{19}{84}\right)\)
\(\chi_{7056}(1619,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{47}{84}\right)\)
\(\chi_{7056}(1691,\cdot)\) \(1\) \(1\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{37}{84}\right)\)
\(\chi_{7056}(2123,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{41}{84}\right)\)
\(\chi_{7056}(2195,\cdot)\) \(1\) \(1\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{55}{84}\right)\)
\(\chi_{7056}(2699,\cdot)\) \(1\) \(1\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{73}{84}\right)\)
\(\chi_{7056}(3131,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{29}{84}\right)\)
\(\chi_{7056}(3635,\cdot)\) \(1\) \(1\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{23}{84}\right)\)
\(\chi_{7056}(3707,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{25}{84}\right)\)
\(\chi_{7056}(4139,\cdot)\) \(1\) \(1\) \(e\left(\frac{83}{84}\right)\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{84}\right)\)
\(\chi_{7056}(4211,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{43}{84}\right)\)
\(\chi_{7056}(4643,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{84}\right)\)
\(\chi_{7056}(4715,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{61}{84}\right)\)
\(\chi_{7056}(5147,\cdot)\) \(1\) \(1\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{84}\right)\)
\(\chi_{7056}(5219,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{83}{84}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{79}{84}\right)\)
\(\chi_{7056}(5651,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{83}{84}\right)\)
\(\chi_{7056}(5723,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{84}\right)\)
\(\chi_{7056}(6227,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{31}{84}\right)\)
\(\chi_{7056}(6659,\cdot)\) \(1\) \(1\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{71}{84}\right)\)