Properties

Label 7056.ig
Modulus $7056$
Conductor $7056$
Order $84$
Real no
Primitive yes
Minimal yes
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([42,21,14,80]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(11,7056))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(7056\)
Conductor: \(7056\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(84\)
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: $\Q(\zeta_{84})$
Fixed field: Number field defined by a degree 84 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\) \(37\)
\(\chi_{7056}(11,\cdot)\) \(1\) \(1\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{5}{84}\right)\) \(-1\) \(e\left(\frac{61}{84}\right)\)
\(\chi_{7056}(515,\cdot)\) \(1\) \(1\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{23}{84}\right)\) \(-1\) \(e\left(\frac{79}{84}\right)\)
\(\chi_{7056}(779,\cdot)\) \(1\) \(1\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{1}{84}\right)\) \(-1\) \(e\left(\frac{29}{84}\right)\)
\(\chi_{7056}(1019,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{41}{84}\right)\) \(-1\) \(e\left(\frac{13}{84}\right)\)
\(\chi_{7056}(1283,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{83}{84}\right)\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{79}{84}\right)\) \(-1\) \(e\left(\frac{23}{84}\right)\)
\(\chi_{7056}(1523,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{59}{84}\right)\) \(-1\) \(e\left(\frac{31}{84}\right)\)
\(\chi_{7056}(1787,\cdot)\) \(1\) \(1\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{73}{84}\right)\) \(-1\) \(e\left(\frac{17}{84}\right)\)
\(\chi_{7056}(2291,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{67}{84}\right)\) \(-1\) \(e\left(\frac{11}{84}\right)\)
\(\chi_{7056}(2531,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{11}{84}\right)\) \(-1\) \(e\left(\frac{67}{84}\right)\)
\(\chi_{7056}(2795,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{61}{84}\right)\) \(-1\) \(e\left(\frac{5}{84}\right)\)
\(\chi_{7056}(3035,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{29}{84}\right)\) \(-1\) \(e\left(\frac{1}{84}\right)\)
\(\chi_{7056}(3299,\cdot)\) \(1\) \(1\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{55}{84}\right)\) \(-1\) \(e\left(\frac{83}{84}\right)\)
\(\chi_{7056}(3539,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{47}{84}\right)\) \(-1\) \(e\left(\frac{19}{84}\right)\)
\(\chi_{7056}(4043,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{65}{84}\right)\) \(-1\) \(e\left(\frac{37}{84}\right)\)
\(\chi_{7056}(4307,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{43}{84}\right)\) \(-1\) \(e\left(\frac{71}{84}\right)\)
\(\chi_{7056}(4547,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{83}{84}\right)\) \(-1\) \(e\left(\frac{55}{84}\right)\)
\(\chi_{7056}(4811,\cdot)\) \(1\) \(1\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{83}{84}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{37}{84}\right)\) \(-1\) \(e\left(\frac{65}{84}\right)\)
\(\chi_{7056}(5051,\cdot)\) \(1\) \(1\) \(e\left(\frac{83}{84}\right)\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{17}{84}\right)\) \(-1\) \(e\left(\frac{73}{84}\right)\)
\(\chi_{7056}(5315,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{31}{84}\right)\) \(-1\) \(e\left(\frac{59}{84}\right)\)
\(\chi_{7056}(5819,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{25}{84}\right)\) \(-1\) \(e\left(\frac{53}{84}\right)\)
\(\chi_{7056}(6059,\cdot)\) \(1\) \(1\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{53}{84}\right)\) \(-1\) \(e\left(\frac{25}{84}\right)\)
\(\chi_{7056}(6323,\cdot)\) \(1\) \(1\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{19}{84}\right)\) \(-1\) \(e\left(\frac{47}{84}\right)\)
\(\chi_{7056}(6563,\cdot)\) \(1\) \(1\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{71}{84}\right)\) \(-1\) \(e\left(\frac{43}{84}\right)\)
\(\chi_{7056}(6827,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{13}{84}\right)\) \(-1\) \(e\left(\frac{41}{84}\right)\)