Properties

Label 7728.gx
Modulus $7728$
Conductor $2576$
Order $132$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7728, base_ring=CyclotomicField(132))
 
M = H._module
 
chi = DirichletCharacter(H, M([66,99,0,88,78]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(67,7728))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(7728\)
Conductor: \(2576\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(132\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 2576.dl
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: $\Q(\zeta_{132})$
Fixed field: Number field defined by a degree 132 polynomial (not computed)

First 31 of 40 characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(11\) \(13\) \(17\) \(19\) \(25\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{7728}(67,\cdot)\) \(1\) \(1\) \(e\left(\frac{89}{132}\right)\) \(e\left(\frac{31}{132}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{125}{132}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{65}{132}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{7728}(235,\cdot)\) \(1\) \(1\) \(e\left(\frac{83}{132}\right)\) \(e\left(\frac{109}{132}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{35}{132}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{71}{132}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{7728}(571,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{132}\right)\) \(e\left(\frac{73}{132}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{107}{132}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{119}{132}\right)\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{7728}(835,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{132}\right)\) \(e\left(\frac{47}{132}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{49}{132}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{73}{132}\right)\) \(e\left(\frac{19}{22}\right)\)
\(\chi_{7728}(907,\cdot)\) \(1\) \(1\) \(e\left(\frac{95}{132}\right)\) \(e\left(\frac{85}{132}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{83}{132}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{59}{132}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{7728}(1003,\cdot)\) \(1\) \(1\) \(e\left(\frac{115}{132}\right)\) \(e\left(\frac{89}{132}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{31}{132}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{127}{132}\right)\) \(e\left(\frac{21}{22}\right)\)
\(\chi_{7728}(1075,\cdot)\) \(1\) \(1\) \(e\left(\frac{53}{132}\right)\) \(e\left(\frac{103}{132}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{113}{132}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{101}{132}\right)\) \(e\left(\frac{7}{22}\right)\)
\(\chi_{7728}(1171,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{132}\right)\) \(e\left(\frac{119}{132}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{37}{132}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{109}{132}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{7728}(1339,\cdot)\) \(1\) \(1\) \(e\left(\frac{127}{132}\right)\) \(e\left(\frac{65}{132}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{79}{132}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{115}{132}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{7728}(1579,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{132}\right)\) \(e\left(\frac{49}{132}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{23}{132}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{107}{132}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{7728}(1675,\cdot)\) \(1\) \(1\) \(e\left(\frac{79}{132}\right)\) \(e\left(\frac{29}{132}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{19}{132}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{31}{132}\right)\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{7728}(2011,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{132}\right)\) \(e\left(\frac{41}{132}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{127}{132}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{103}{132}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{7728}(2179,\cdot)\) \(1\) \(1\) \(e\left(\frac{97}{132}\right)\) \(e\left(\frac{59}{132}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{25}{132}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{13}{132}\right)\) \(e\left(\frac{7}{22}\right)\)
\(\chi_{7728}(2251,\cdot)\) \(1\) \(1\) \(e\left(\frac{107}{132}\right)\) \(e\left(\frac{61}{132}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{131}{132}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{47}{132}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{7728}(2587,\cdot)\) \(1\) \(1\) \(e\left(\frac{131}{132}\right)\) \(e\left(\frac{13}{132}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{95}{132}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{23}{132}\right)\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{7728}(2683,\cdot)\) \(1\) \(1\) \(e\left(\frac{91}{132}\right)\) \(e\left(\frac{5}{132}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{67}{132}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{19}{132}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{7728}(3355,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{132}\right)\) \(e\left(\frac{17}{132}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{43}{132}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{91}{132}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{7728}(3595,\cdot)\) \(1\) \(1\) \(e\left(\frac{59}{132}\right)\) \(e\left(\frac{25}{132}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{71}{132}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{95}{132}\right)\) \(e\left(\frac{19}{22}\right)\)
\(\chi_{7728}(3691,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{132}\right)\) \(e\left(\frac{101}{132}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{7}{132}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{67}{132}\right)\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{7728}(3763,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{132}\right)\) \(e\left(\frac{67}{132}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{53}{132}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{17}{132}\right)\) \(e\left(\frac{21}{22}\right)\)
\(\chi_{7728}(3931,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{132}\right)\) \(e\left(\frac{97}{132}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{59}{132}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{131}{132}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{7728}(4099,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{132}\right)\) \(e\left(\frac{43}{132}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{101}{132}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{5}{132}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{7728}(4435,\cdot)\) \(1\) \(1\) \(e\left(\frac{101}{132}\right)\) \(e\left(\frac{7}{132}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{41}{132}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{53}{132}\right)\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{7728}(4699,\cdot)\) \(1\) \(1\) \(e\left(\frac{103}{132}\right)\) \(e\left(\frac{113}{132}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{115}{132}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{7}{132}\right)\) \(e\left(\frac{19}{22}\right)\)
\(\chi_{7728}(4771,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{132}\right)\) \(e\left(\frac{19}{132}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{17}{132}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{125}{132}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{7728}(4867,\cdot)\) \(1\) \(1\) \(e\left(\frac{49}{132}\right)\) \(e\left(\frac{23}{132}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{97}{132}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{61}{132}\right)\) \(e\left(\frac{21}{22}\right)\)
\(\chi_{7728}(4939,\cdot)\) \(1\) \(1\) \(e\left(\frac{119}{132}\right)\) \(e\left(\frac{37}{132}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{47}{132}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{35}{132}\right)\) \(e\left(\frac{7}{22}\right)\)
\(\chi_{7728}(5035,\cdot)\) \(1\) \(1\) \(e\left(\frac{67}{132}\right)\) \(e\left(\frac{53}{132}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{103}{132}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{43}{132}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{7728}(5203,\cdot)\) \(1\) \(1\) \(e\left(\frac{61}{132}\right)\) \(e\left(\frac{131}{132}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{13}{132}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{49}{132}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{7728}(5443,\cdot)\) \(1\) \(1\) \(e\left(\frac{113}{132}\right)\) \(e\left(\frac{115}{132}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{89}{132}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{41}{132}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{7728}(5539,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{132}\right)\) \(e\left(\frac{95}{132}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{85}{132}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{97}{132}\right)\) \(e\left(\frac{15}{22}\right)\)