Properties

Label 7056.je
Modulus $7056$
Conductor $7056$
Order $84$
Real no
Primitive yes
Minimal yes
Parity odd

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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([0,63,14,36]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(29,7056))
 
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: odd
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 \(-1\) \(1\) \(5\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\) \(37\)
\(\chi_{7056}(29,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{3}{14}\right)\) \(i\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{28}\right)\)
\(\chi_{7056}(365,\cdot)\) \(-1\) \(1\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{11}{14}\right)\) \(i\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{28}\right)\)
\(\chi_{7056}(533,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{1}{14}\right)\) \(-i\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{23}{28}\right)\)
\(\chi_{7056}(869,\cdot)\) \(-1\) \(1\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{9}{14}\right)\) \(-i\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{28}\right)\)
\(\chi_{7056}(1037,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{13}{14}\right)\) \(i\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{28}\right)\)
\(\chi_{7056}(1541,\cdot)\) \(-1\) \(1\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{11}{14}\right)\) \(-i\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{15}{28}\right)\)
\(\chi_{7056}(1877,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{83}{84}\right)\) \(e\left(\frac{5}{14}\right)\) \(-i\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{28}\right)\)
\(\chi_{7056}(2045,\cdot)\) \(-1\) \(1\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{9}{14}\right)\) \(i\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{25}{28}\right)\)
\(\chi_{7056}(2381,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{3}{14}\right)\) \(i\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{28}\right)\)
\(\chi_{7056}(2885,\cdot)\) \(-1\) \(1\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{1}{14}\right)\) \(-i\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{23}{28}\right)\)
\(\chi_{7056}(3053,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{5}{14}\right)\) \(i\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{17}{28}\right)\)
\(\chi_{7056}(3389,\cdot)\) \(-1\) \(1\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{13}{14}\right)\) \(i\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{28}\right)\)
\(\chi_{7056}(3557,\cdot)\) \(-1\) \(1\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{3}{14}\right)\) \(-i\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{27}{28}\right)\)
\(\chi_{7056}(3893,\cdot)\) \(-1\) \(1\) \(e\left(\frac{83}{84}\right)\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{11}{14}\right)\) \(-i\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{15}{28}\right)\)
\(\chi_{7056}(4061,\cdot)\) \(-1\) \(1\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{1}{14}\right)\) \(i\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{83}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{9}{28}\right)\)
\(\chi_{7056}(4397,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{9}{14}\right)\) \(i\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{25}{28}\right)\)
\(\chi_{7056}(4565,\cdot)\) \(-1\) \(1\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{13}{14}\right)\) \(-i\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{19}{28}\right)\)
\(\chi_{7056}(5069,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{11}{14}\right)\) \(i\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{28}\right)\)
\(\chi_{7056}(5405,\cdot)\) \(-1\) \(1\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{5}{14}\right)\) \(i\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{28}\right)\)
\(\chi_{7056}(5573,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{9}{14}\right)\) \(-i\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{28}\right)\)
\(\chi_{7056}(5909,\cdot)\) \(-1\) \(1\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{3}{14}\right)\) \(-i\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{27}{28}\right)\)
\(\chi_{7056}(6413,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{1}{14}\right)\) \(i\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{9}{28}\right)\)
\(\chi_{7056}(6581,\cdot)\) \(-1\) \(1\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{83}{84}\right)\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{5}{14}\right)\) \(-i\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{28}\right)\)
\(\chi_{7056}(6917,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{13}{14}\right)\) \(-i\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{19}{28}\right)\)